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@article{fds362956,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {Extending a Van Der Pol-Based Reduced-Order Model for
Fluid-Structure Interaction Applied to Non-Synchronous
Vibrations in Turbomachinery},
Journal = {Journal of Turbomachinery},
Volume = {144},
Number = {3},
Year = {2022},
Month = {March},
url = {http://dx.doi.org/10.1115/1.4052405},
Abstract = {This paper expands upon a multi-degree-of-freedom, Van der
Pol oscillator used to model buffet and nonsynchronous
vibrations (NSV) in turbines. Two degrees-of-freedom are
used, a fluid tracking variable incorporating a Van der Pol
oscillator and a classic spring, mass, damper mounted
cylinder variable; thus, this model is one of
fluid-structure interaction. This model has been previously
shown to exhibit the two main aspects of NSV. The first is
the lock-in or entrainment phenomenon of the fluid shedding
frequency jumping onto the natural frequency of the
oscillator, while the second is a stable limit cycle
oscillation (LCO) once the transient solution disappears.
Improvements are made to the previous model to better
understand this aeroelastic phenomenon. First, an error
minimizing technique through a system identification method
is used to tune the coefficients in the reduced-order model
(ROM) to improve the accuracy in comparison to experimental
data. Second, a cubic stiffness term is added to the fluid
equation; this term is often seen in the Duffing Oscillator
equation, which allows this ROM to capture the experimental
behavior more accurately, seen in previous literature. The
finalized model captures the experimental cylinder data
found in literature much better than the previous model.
These improvements also open the door for future models,
such as that of a pitching airfoil or a turbomachinery
blade, to create a preliminary design tool for studying NSV
in turbomachinery.},
Doi = {10.1115/1.4052405},
Key = {fds362956}
}
@article{fds361785,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {Unsteady Pressure Analysis of an Oscillating Cylinder
Exhibiting Non-Synchronous Vibrations},
Journal = {Aiaa Science and Technology Forum and Exposition, Aiaa
Scitech Forum 2022},
Year = {2022},
Month = {January},
ISBN = {9781624106316},
url = {http://dx.doi.org/10.2514/6.2022-0561},
Abstract = {When an unsteady aerodynamic instability interacts with the
natural modes of vibration of a rigid body, lies a
phenomenon known as Non-Synchronous Vibrations (NSV), often
referred to as Vortex-Induced Vibrations (VIV). These
vibrations cause blade failure in jet engines; however, the
underlying flow physics are much less understood than other
aeroelastic phenomenon such as flutter or forced response.
When the buffeting frequency of the flow around a body nears
a natural frequency of said body, the former frequency
“locks in” to the latter. Within this “lock in”
region there is only one main frequency, while outside of it
there are two. Although this phenomenon has been documented
both experimentally and computationally, the unsteady
pressures associated with this phenomenon have not been
accurately measured. First, we collected the spectra of
pressure frequencies around a circular cylinder exhibiting
NSV using computational fluid dynamics. Then, time domain
pressure data is Fast Fourier Transformed to provide
frequency domain data. Finally, the data analyzed as well as
validated against experimental results as well as other
numerical models, providing good agreement. Understanding
the unsteady pressures and how they affect the flow physics
of NSV allows for further studies into this phenomenon,
paving the way for the design of more efficient and powerful
engines.},
Doi = {10.2514/6.2022-0561},
Key = {fds361785}
}
@article{fds361786,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {Unsteady Pressures Analysis of an Oscillating Airfoil
Exhibiting Nonsynchronous Vibrations as Applied to
Turbomachinery},
Journal = {Aiaa Science and Technology Forum and Exposition, Aiaa
Scitech Forum 2022},
Year = {2022},
Month = {January},
ISBN = {9781624106316},
url = {http://dx.doi.org/10.2514/6.2022-0562},
Abstract = {When an unsteady aerodynamic instability interacts with the
natural modes of vibration of a rigid body, lies a
phenomenon known as Non-Synchronous Vibrations (NSV), also
known as Vortex-Induced Vibrations (VIV). These vibrations
cause blade failure in jet engines and turbomachinery;
however, the underlying flow physics are much less
understood compared to other aeroelastic phenomenon such as
flutter or forced response. When the buffeting frequency of
the flow around a body nears a natural frequency of said
body, the former locks on to the latter in a process known
as “lock on”. Within this “lock on” region there is
only one main frequency, while outside of it there are two.
Although this phenomenon has been documented experimentally
and computationally, the unsteady pressures associated with
this phenomenon have not measured. First, we collected the
spectra of pressure frequencies around a NACA 0012 airfoil
exhibiting NSV in a low-speed wind tunnel. Then the time
domain pressure data is Fast Fourier Transformed into
frequency domain results. Finally, the unsteady pressure
content from the aerodynamics is separated from the content
from the motion of the airfoil, allowing for greater
understanding of the unsteady aeroelastic behavior. The
results are compared to previous experiments as well as
Computational Fluid Dynamics (CFD) simulations.
Understanding the pressures and how they affect the flow
physics of NSV allows for further studies into this
phenomenon, paving the way for the design of more efficient
and safer jet engines.},
Doi = {10.2514/6.2022-0562},
Key = {fds361786}
}
@article{fds362126,
Author = {Tedesco, MB and Hall, KC},
Title = {Blade Vibration and Its Effect on the Optimal Performance of
Helicopter Rotors},
Journal = {Journal of Aircraft},
Volume = {59},
Number = {1},
Pages = {184-195},
Year = {2022},
Month = {January},
url = {http://dx.doi.org/10.2514/1.C036336},
Abstract = {In this paper, we develop a computationally efficient
frequency-domain model that can be used to compute the
required shaft power and vibratory loads for a trimmed
helicopter rotor with flexible blades in forward flight. The
aerodynamic forces and power are modeled using a
vortex-lattice method. A finite element model based on the
linearized form of the Hodges–Dowell rotating beam
equations is used to model the vibrating blades. Guyan
reduction and harmonic balance are used to reduce the number
of degrees of freedom. The model is validated against
several previous computational and experimental models, with
generally good agreement. For rotors that use higher
harmonic control, the problem of minimizing the required
power and/or vibratory loads is cast as a quadratic
programming problem requiring a single linear matrix solve
to find the optimum. We show that for moderate and high
advance ratios, higher harmonic control can substantially
reduce vertical hub forces, but only with an increase in
required cruise power. For example, using
four-per-revolution higher harmonic control, the vertical
vibratory loads on the four-bladed HART II rotor can be
decreased by about 30% for a 3.0% increase in induced power
for at a forward flight advance ratio of
0.45.},
Doi = {10.2514/1.C036336},
Key = {fds362126}
}
@article{fds367795,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {AN IMPROVED PRELIMINARY DESIGN TOOL FOR TURBOMACHINERY
BLADES USING VAN DER POL BASED REDUCED-ORDER MODEL FOR
NON-SYNCHRONOUS VIBRATIONS},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {10-D},
Year = {2022},
Month = {January},
ISBN = {9780791886120},
url = {http://dx.doi.org/10.1115/GT2022-83391},
Abstract = {Starting from an oscillating cylinder, this paper navigates
the shift of a Van der Pol based Reduced-Order Model from
that simple case to airfoil and turbomachinery blade. The
structure will be free to vibrate under the influence of a
von Karman vortex street. The first degree of freedom tracks
the oscillatory motion of the vortex shedding utilizing a
combined Van der Pol and a Duffing equation, previously
shown to better match the flow physics. The other degree of
freedom is a cylinder or pitching blade with stiffness,
mass, and damping, making the coupled system one of
fluid-structure interaction. A third degree of freedom is
added in a separate configuration to provide the airfoil
with both pitching and plunging motion. Using this model to
study the time-history of the fluid and the structure
oscillation, additional parameters are extracted to
understand the underlying mechanisms of frequency lock-in
and limit cycle oscillation. The coefficients in the model
are tuned to match limit cycle oscillation data captured in
experiments. Then, the phase shift between the vortex
shedding and the structural motion is calculated when the
former locks-on to the latter, and then unlocks. Also, the
work done per cycle of vibration is analyzed from the
contributions of the mass, spring, and damping forces to
determine the dominant contributor when locking-in versus
unlocking. This model is a more accurate case for
turbomachinery applications compared to the previous models.
This model, especially with the third degree of freedom,
will serve as the preliminary design tool for engine
manufacturers to use for preventing Non-Synchronous
Vibrations in turbomachinery.},
Doi = {10.1115/GT2022-83391},
Key = {fds367795}
}
@article{fds367796,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {A FLUID-STRUCTURE INTERACTION TOOL USING A VAN DER POL BASED
REDUCED-ORDER MODEL FOR BUFFET AND NON-SYNCHRONOUS
VIBRATIONS},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {10-D},
Number = {1},
Year = {2022},
Month = {January},
ISBN = {9780791886120},
url = {http://dx.doi.org/10.1115/GT2022-80277},
Abstract = {This paper builds upon a two-degree-of-freedom Van der Pol
oscillator based Reduced-Order Model for studying the
mechanisms around Non-Synchronous Vibrations (NSV) in
turbomachinery. One degree tracks the fluid motion utilizing
a combination of a traditional Van der Pol Oscillator and a
Duffing Oscillator; the other degree of freedom is a mass on
a spring and a damper, in this case a cylinder. Thus, this
model can be considered one of fluid-structure interaction.
The cubic stiffening from the Duffing Oscillator proved to
improve the match to experimental data. Using this model to
study the timehistory of the fluid and the structure
oscillation, additional parameters are extracted to
understand the underlying mechanisms of frequency lock-in
and limit cycle oscillation. First, the phase shift between
the vortex shedding and the structural motion is calculated
when it locks-in then unlocks. Second, the work done per
cycle is analyzed from the contributions of the mass,
spring, and damping forces to determine the dominant
contributor when locking-in versus unlocking. Third, the
phase portrait is plotted on a Poincare Map to further study
the locked-in versus unlocked responses. This model is then
validated against not only experimental data, but also
computational simulation results and previous reduced-order
models. The finalized model can now serve as a preliminary
design tool for turbomachinery applications. For more
realistic and accurate modeling, a third degree-of-freedom
in the form of an airfoil pitching motion will be added in a
separate paper as well.},
Doi = {10.1115/GT2022-80277},
Key = {fds367796}
}
@article{fds359499,
Author = {Hollenbach, R and Kielb, R and Hall, K},
Title = {Extending a van der pol based reduced-order model for
fluid-structure interaction applied to non-synchronous
vibrations in turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {2C-2021},
Year = {2021},
Month = {January},
ISBN = {9780791884928},
url = {http://dx.doi.org/10.1115/GT2021-58965},
Abstract = {This paper expands upon a multi-degree-of-freedom, Van der
Pol oscillator used to model buffet and Nonsynchronous
Vibrations (NSV) in turbines. Two degreesof-freedom are
used, a fluid tracking variable incorporating a Van der Pol
oscillator and a classic spring, mass, damper mounted
cylinder variable; thus, this model is one of fluidstructure
interaction. This model has been previously shown to exhibit
the two main aspects of NSV. The first is the lock-in or
entrainment phenomenon of the fluid shedding frequency
jumping onto the natural frequency of the oscillator, while
the second is a stable limit cycle oscillation (LCO) once
the transient solution disappears. Improvements are made to
the previous model to better understand this aeroelastic
phenomenon. First, an error minimizing technique through a
system identification method is used to tune the
coefficients in the Reduced Order Model (ROM) to improve the
accuracy in comparison to experimental data. Secondly, a
cubic stiffness term is added to the fluid equation; this
term is often seen in the Duffing Oscillator equation, which
allows this ROM to capture the experimental behavior more
accurately, seen in previous literature. The finalized model
captures the experimental cylinder data found in literature
much better than the previous model. These improvements also
open the door for future models, such as that of a pitching
airfoil or a turbomachinery blade, to create a preliminary
design tool for studying NSV in turbomachinery.},
Doi = {10.1115/GT2021-58965},
Key = {fds359499}
}
@article{fds362063,
Author = {He, L and Hall, KC},
Title = {ISUAAAT15 Special Issue},
Journal = {Journal of Turbomachinery},
Volume = {141},
Number = {10},
Publisher = {ASME International},
Year = {2019},
Month = {October},
url = {http://dx.doi.org/10.1115/1.4044448},
Doi = {10.1115/1.4044448},
Key = {fds362063}
}
@article{fds350637,
Author = {Hall, KC and Coutier-Delgosha, O},
Title = {Special issue on the 17th ISROMAC conference},
Journal = {Journal of Turbomachinery},
Volume = {141},
Number = {2},
Year = {2019},
Month = {February},
url = {http://dx.doi.org/10.1115/1.4042566},
Doi = {10.1115/1.4042566},
Key = {fds350637}
}
@article{fds331496,
Author = {Giovanetti, EB and Hall, KC},
Title = {Minimum loss load, twist, and chord distributions for
coaxial helicopters in hover},
Journal = {Journal of the American Helicopter Society},
Volume = {62},
Number = {1},
Pages = {1-9},
Publisher = {American Helicopter Society},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.4050/JAHS.62.012001},
Abstract = {This paper presents an approach for determining the optimal
(minimum power) geometry of a hovering coaxial rotor using
blade element momentum theory, including swirl. The analysis
accounts for the presence of a finite number of blades using
the Prandtl tip loss factor, the effect of profile drag
using experimentally or computationally determined drag
polars, and the mutual interference between the two rotors
using an empirically determined influence coefficient
method. Numerical results show that including the induced
swirl in the model decreases the optimal figure of merit and
that swirl has a larger impact at higher disk loadings. At
the disk loadings typically found on helicopters, the effect
of swirl is relatively small, particularly compared to
mutual rotor interference or tip losses. Additionally,
accounting for swirl affects the optimal rotor design near
the blade root, at locations that would often be part of the
root cutout of a realistic rotor.},
Doi = {10.4050/JAHS.62.012001},
Key = {fds331496}
}
@article{fds331497,
Author = {Giovanetti, EB and Hall, KC},
Title = {Axisymmetric potential flow model of single or coaxial
actuator disks},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {1},
Pages = {747-757},
Year = {2016},
Month = {January},
ISBN = {9781510825062},
Abstract = {This papcr prcscnts a computationally cfficicnt method for
computing the axisymmetric three-dimensional flow field
induced by the trailing vortex system of either a single
actuator disk or a pair of closely spaced coaxial actuator
disks. A rotor in axial flight or hover (or a pair of
coaxial rotors) is modeled as an actuator disk (or disks);
the associated wake is modeled using contracting cylindrical
sheets of vorticity approximated by discrete vortex rings.
The resulting system of vortex sheets is axisymrnetric and
aligned with flow streamlines. The location of the sheets of
vorticity is found using Newton iteration. A singularity
occurs where the outer vortex sheet vortex sheet terminates
at the edge of the actuator disk. This singularity is
resolved through the formation of a 45° logarithmic spiral
in hover, which produces a non-uniform inflow at the face of
the disk, particularly near the edge of the disk where the
flow field is entirely reversed. Finally, the model is
applied to coaxial actuator disks to quantify the mutual
interference of coaxial rotors at various axial spacings,
and when operating in either a torque-balanced or and equal
circulation state.},
Key = {fds331497}
}
@article{fds300330,
Author = {Hall, KC and Marpu, RP and Custer, CH and Venkataramanan, S and Weiss,
JM},
Title = {Comparison of Numerical Methods for the Prediction of
Time-Averaged Flow Quantities in a Cooled Multistage
Turbine},
Journal = {Asme Turbo Expo 2015: Turbine Technical Conference and
Exposition},
Volume = {2C},
Pages = {V02CT44A028-V02CT44A028},
Publisher = {ASME},
Year = {2015},
Month = {June},
ISBN = {978-0-7918-5665-9},
url = {http://dx.doi.org/10.1115/GT2015-43717},
Abstract = {An unsteady simulation of a two-stage, cooled, high pressure
turbine cascade is achieved by applying the harmonic balance
method, a mixed time domain and frequency domain
computational fluid dynamic technique for efficiently
solving periodic unsteady flows. A comparison of computed
temperature and pressure profile predictions generated using
the harmonic balance method and a conventional steady mixing
plane analysis is presented. The predicted temperature and
pressure profiles are also compared to experimental data at
the stage exit plane. The harmonic balance solver is able to
efficiently model unsteady flows caused by wake interaction
and secondary flow effects due to cooling flows. It is
demonstrated that modeling the unsteady effects is critical
to the accurate prediction of time-averaged flow field
quantities, particularly for cooled machines.},
Doi = {10.1115/GT2015-43717},
Key = {fds300330}
}
@article{fds281214,
Author = {Giovanetti, EB and Hall, KC},
Title = {A variational approach to multipoint aerodynamic
optimization of conventional and coaxial helicopter
rotors},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {2},
Number = {May},
Pages = {752-764},
Year = {2015},
Month = {May},
ISSN = {1552-2938},
Abstract = {© 2015 by the American Helicopter Society International,
Inc. We present a variational approach to the multipoint
aerodynamic design optimization of conventional and coaxial
helicopter rotors. The optimal design problem is cast as a
variational statement that minimizes the weighted sum of
induced and viscous power losses between two flight
conditions for prescribed vehicle trim constraints at each
flight condition. The resulting nonlinear constrained
optimization problem is solved via Newton iteration and may
be used to map the Pareto frontier, i.e., the set of rotor
designs (radial twist and chord distributions and harmonic
blade pilch inputs) for which it is not possible to improve
upon the performance in one flight conditions without
degrading performance in the other. The two flight
conditions can represent different advance ratios (including
hover), disk loadings, altitude, or other conditions of
interest. For forward flight computations, the rotor control
inputs arc related to the circulation on the blades (and in
the wake) through a lifting-line/vortex-lattice method that
accounts for nonlinear sectional lift and drag polars. For
hovering flight, the rotor performance is analyzed using
Blade Element Momentum Theory. We map the Pareto frontier
for both a cruise/cruise and hover/cruise multipoint
optimization, and show that significant tradeoffs must be
made in designing a rotor to balance performance between two
flight conditions, particularly hover and high speed forward
flight. We also show that higher harmonic control is capable
of reducing rotor power and improving the Pareto frontier,
particularly for coaxial rotors. Finally, we present a
number of rotor designs that best balance performance
between two flight conditions.},
Key = {fds281214}
}
@article{fds281211,
Author = {Giovanetti, EB and Hall, KC},
Title = {Minimum loss load, twist and chord distributions for coaxial
helicopters in Hover},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {1},
Number = {January},
Pages = {648-657},
Year = {2015},
Month = {January},
ISSN = {1552-2938},
Abstract = {We present an approach for determining the optimal (minimum
power) torque-balanced coaxial hovering rotor using Blade
Element Momentum Theory including swirl. We quantify the
effects of the swirl component of induced velocity on
performance, optimal induced wash distribution, and optimal
blade twist and chord. The optimization accounts for the
presence of a finite number of blades using the Prandtl tip
loss factor, the effect of profile drag using experimentally
or computationally determined drag polars, and the mutual
interference between the two rotors using an empirically
determined influence coefficient method. We show that
including the swirl component of induced wash decreases the
optimal figure of merit and has a larger impact at higher
disk loadings, as expected. However, at the disk loadings
typically found on helicopters, the effect of swirl is
relatively small, particularly compared to other physical
effects such as mutual interference or tip losses.
Additionally, accounting for swirl affects the optimal rotor
design near the root of the blade, at locations that would
often be part of the root cutout of a realistic
rotor.},
Key = {fds281211}
}
@article{fds281212,
Author = {Giovanetti, EB and Hall, KC},
Title = {Optimum design of compound helicopters that use higher
harmonic control},
Journal = {Journal of Aircraft},
Volume = {52},
Number = {5},
Pages = {1444-1453},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2015},
Month = {January},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.C032941},
Abstract = {The optimal design of a compound helicopter comprised of
counterrotating coaxial rotors, a propeller, and optionally
a fixed wing is investigated. The blade geometry, azimuthal
blade pitch inputs, optimal shaft angle (rotor angle of
attack), and division of propulsive and lifting forces among
the components that minimize the total power for a given
flight condition are determined. The optimal design problem
is cast as a variational statement that minimizes the sum of
induced and viscous power losses for a prescribed lift,
propulsive force, and vehicle trim condition. The rotor,
propeller, and wing geometry and control inputs are related
to the far-field circulation through a lifting-line model
that accounts for experimentally or computationally
determined nonlinear lift and drag polars. The variational
statement is discretized using a vortex lattice wake, and
the resulting nonlinear constrained optimization problem is
solved via Newton iteration. Results show that varying the
prescribed propulsive force of the system affects the
optimal shaft angle and rotor design, that higher harmonic
control reduces the total vehicle power loss (inefficiency)
in high-speed flight by as much as 15%, and that imposing a
maximum allowable lateral lift offset can greatly increase
the power loss of the coaxial rotors.},
Doi = {10.2514/1.C032941},
Key = {fds281212}
}
@article{fds281216,
Author = {Giovanetti, EB and Hall, KC},
Title = {Optimum design of compound helicopters using higher harmonic
control},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {4},
Pages = {2607-2618},
Year = {2014},
Month = {January},
ISBN = {9781632666918},
ISSN = {1552-2938},
Abstract = {We investigate the optimal design of a compound helicopter
comprised of counter-rotating coaxial rotors, a propeller,
and optionally a fixed wing. We determine the blade
geometry, azimuthal blade pitch inputs, optimal shaft angle
(rotor angle of attack), and division of propulsive and
lifting forces among the components that minimize the total
power for a given flight condition. The optimal design
problem is cast as a variational statement that minimizes
the sum of induced and viscous power losses for a prescribed
lift, propulsive force, and vehicle trim condition. The
rotor, propeller, and wing geometry and control inputs are
related to the far-field circulation through a lifting line
model that accounts for experimentally or computationally
determined nonlinear lift and drag polars. The variational
statement is discretized using a vortex lattice wake, and
the resulting nonlinear constrained optimization problem is
solved via Newton iteration. We show that varying the
prescribed propulsive force of the system affects the
optimal shaft angle and rotor design, and that higher
harmonic control reduces total vehicle power loss
(inefficiency) in high speed flight by as much as 15
percent. We also show that imposing a maximum allowable
lateral lift offset can greatly increase the power loss of
the coaxial rotors. © 2014 by the American Helicopter
Society International, Inc. All rights reserved.},
Key = {fds281216}
}
@article{fds281228,
Author = {Clark, ST and Kielb, RE and Hall, KC},
Title = {A van der pol based reduced-order model for non-synchronous
vibration (NSV) in turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {7 B},
Publisher = {ASME},
Year = {2013},
Month = {December},
ISBN = {9780791855270},
url = {http://dx.doi.org/10.1115/GT2013-95741},
Abstract = {This paper demonstrates the potential of using a
multidegree- of-freedom, traditional van der Pol oscillator
to model non-synchronous vibration (NSV) in turbomachinery.
It is shown that the two main characteristics of NSV are
captured by the reduced-order, van der Pol model. First, a
stable limit cycle oscillation (LCO) is maintained for
various conditions. Second, the lock-in phenomenon typical
of NSV is captured for various fluid-structure frequency
ratios. This research identifies values and significance of
the coupling parameters used in the van der Pol model. These
coefficients are chosen to model confirmed instances of
experimental NSV, and to develop a preliminary design tool
that engineers can use to better design turbo machinery for
NSV. Specifically, coefficient tuning from experimental
instances of NSV are considered to identify the unknown
coupling coefficients in the van der Pol model. The goal of
future research will be to identify values and significance
of the coupling parameters used in the van der Pol model, to
match these coefficients with confirmed instances of
experimental NSV, and to develop a preliminary design tool
that engineers can use to better design turbo machinery for
NSV. Proper orthogonal decomposition (POD) CFD techniques
and coefficient tuning from experimental instances of NSV
have been considered to identify the unknown coupling
coefficients in the van der Pol model. The finalization of
this preliminary design research will be completed in future
research. Copyright © 2013 by ASME.},
Doi = {10.1115/GT2013-95741},
Key = {fds281228}
}
@article{fds281229,
Author = {Subramanian, V and Custer, CH and Weiss, JM and Hall,
KC},
Title = {Unsteady simulation of a two-stage cooled high pressure
turbine using an efficient non-linear harmonic balance
method},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {6 C},
Publisher = {ASME},
Year = {2013},
Month = {December},
ISBN = {9780791855249},
url = {http://dx.doi.org/10.1115/GT2013-94574},
Abstract = {The harmonic balance method is a mixed time domain and
frequency domain approach for efficiently solving periodic
unsteady flows. The implementation described in this paper
is designed to efficiently handle the multiple frequencies
that arise within a multistage turbomachine due to differing
blade counts in each blade row. We present two alternative
algorithms that can be used to determine which unique set of
frequencies to consider in each blade row. The first, an all
blade row algorithm, retains the complete set of frequencies
produced by a given blade row's interaction with all other
blade rows. The second, a nearest neighbor algorithm,
retains only the dominant frequencies in a given blade row
that arise from direct interaction with the adjacent rows. A
comparison of results from a multiple blade row simulation
based on these two approaches is presented. We will
demonstrate that unsteady blade row interactions are
accurately captured with the reduced frequency set of the
nearest neighbor algorithm, and at a lower computational
cost compared to the all blade row algorithm. An unsteady
simulation of a two-stage, cooled, high pressure turbine
cascade is achieved using the present harmonic balance
method and the nearest neighbor algorithm. The unsteady
results obtained are compared to steady simulation results
to demonstrate the value of performing an unsteady analysis.
Considering an unsteady flow through a single blade row
turbine blade passage, it is further shown that unsteady
effects are important even if the objective is to obtain
accurate time-averaged integrated values, such as
efficiency. Copyright © 2013 by ASME.},
Doi = {10.1115/GT2013-94574},
Key = {fds281229}
}
@article{fds281232,
Author = {Hall, KC and Giovanetti, EB},
Title = {Minimum power requirements and optimal rotor design for
conventional and compound helicopters using higher harmonic
control},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {3},
Pages = {1867-1883},
Year = {2013},
Month = {September},
ISSN = {1552-2938},
Abstract = {We present a method for computing the optimal aerodynamic
performance of conventional and compound helicopters in
trimmed forward flight with a limited set of design
variables and control inputs, including conventional and
higher harmonic blade control, and radial twist and chord
distributions. The optimal design problem, which is cast as
a variational statement, minimizes the sum of the induced
and viscous power required to develop a prescribed lift
and/or thrust. The variational statement is discretized and
solved efficiently using a vortex-lattice technique. We
present two variants of the analysis. In the first, the
sectional blade aerodynamics are modeled using a linear lift
curve and a quadratic drag polar, and flow angles are
assumed to be small. The result is a quadratic programming
problem that yields a linear set of equations to solve for
the unknown optimal design variables and control inputs. In
the second approach, the problem is cast as a constrained
nonlinear optimization problem, which is solved using
mathematical programming via augmented Lagrangians. This
approach, which accounts for realistic lift and drag
coefficients including the effects of stall and the
attendant increase in drag at high angles of attack, is
capable of optimizing the blade planform in addition to the
radial twist distribution and conventional and higher
harmonic blade control. We show that for conventional and
coaxial counterrotating rotors, using radially varying twist
and chord distributions and higher harmonic blade pitch
control can produce significant reductions in required
power, especially at high advance ratios. © 2013 by the
American Helicopter Society International, Inc. All rights
reserved.},
Key = {fds281232}
}
@article{fds281237,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Discrete adjoint method for nonlinear aeroelastic
sensitivities for compressible and viscous
flows},
Journal = {54th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics,
and Materials Conference},
Publisher = {American Institute of Aeronautics and Astronautics},
Year = {2013},
Month = {August},
ISBN = {9781624102233},
url = {http://dx.doi.org/10.2514/6.2013-1860},
Abstract = {Presented is a discrete adjoint approach for computing
nonlinear aeroelastic design sensitivities for transonic and
viscous flows based on Reynolds Averaged Navier-Stokes
computational fluid dynamic models. The method is based on a
harmonic balance nonlinear frequency domain technique for
modeling nonlinear aerodynamics in the frequency domain.
Automatic differentiation is used to derive the computer
code representing the adjoint gradient of the harmonic
balance computational fluid dynamic solver. Discrete adjoint
method airfoil geometric design sensitivities are
demonstrated for a benchmark transonic airfoil aeroelastic
configuration. Results are compared with finite-difference
computations to demonstrate the accuracy of the methodology.
© 2013 by Jeffrey P. Thomas, Earl H. Dowell, and Kenneth C.
Hall.},
Doi = {10.2514/6.2013-1860},
Key = {fds281237}
}
@article{fds281240,
Author = {Thomas, JP and Custer, CH and Dowell, EH and Hall, KC and Corre,
C},
Title = {Compact implementation strategy for a harmonic balance
method within implicit flow solvers},
Journal = {Aiaa Journal},
Volume = {51},
Number = {6},
Pages = {1374-1381},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2013},
Month = {June},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.J051823},
Abstract = {A two-step approximate factorization technique for
implementing a computationally stable nonlinear unsteady
frequency-domain harmonic balance solution method within
existing implicit computational fluid dynamic flow solver
codes is presented. The approach uses an explicit
discretization of the harmonic balance source term, and no
new implicit code development is required. Both of these
features enable the harmonic balance method to be
implemented within existing implicit flow solver codes with
minimal modification necessary to the underlying flow solver
code. The resulting harmonic balance solver can then be used
for modeling nonlinear periodic unsteady flows. The
methodology is applied to the NASA OVERFLOW flow solver
code, and results are presented for transonic viscous flow
past an unsteady pitching airfoil section.},
Doi = {10.2514/1.J051823},
Key = {fds281240}
}
@article{fds281242,
Author = {Ekici, K and Hall, KC and Huang, H and Thomas, JP},
Title = {Stabilization of explicit flow solvers using a
proper-orthogonal- decomposition technique},
Journal = {Aiaa Journal},
Volume = {51},
Number = {5},
Pages = {1095-1104},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2013},
Month = {May},
url = {http://dx.doi.org/10.2514/1.J051945},
Abstract = {A new numerical technique for the stabilization of explicit
computational-fluid-dynamic solvers is presented. When using
computational-fluid-dynamic codes to solve practical
problems one sometimes finds the solution fails to converge
due to the presence of a small number of eigenvalues of the
flow solver outside the unit circle. In this paper we use
the proper orthogonal decomposition technique to estimate
the unstable eigenvalues and eigenmodes of the flow solver
as the solution diverges for linear problems or exhibits
limit-cycle oscillations for nonlinear problems. We use the
resulting eigeninformation to construct a preconditioner
that repositions the unstable eigenvalues from outside the
unit circle to a point inside the unit circle close to the
origin resulting in a stable flow solver. In this work the
proposed method is applied to a nonlinear steady cascade
solver. However, the technique can be easily applied to
external flow solvers and to unsteady frequency-domain
(time-linearized and harmonic-balance) flow solvers.
Copyright © 2012 by Kivanc Ekici, Kenneth C. Hall, Huang
Huang and Jeffrey P. Thomas. Published by the American
Institute of Aeronautics and Astronautics,
Inc.},
Doi = {10.2514/1.J051945},
Key = {fds281242}
}
@article{fds281245,
Author = {Hall, KC and Ekici, K and Thomas, JP and Dowell, EH},
Title = {Harmonic balance methods applied to computational fluid
dynamics problems},
Journal = {International Journal of Computational Fluid
Dynamics},
Volume = {27},
Number = {2},
Pages = {52-67},
Year = {2013},
Month = {February},
ISSN = {1061-8562},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000316655100002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {In this paper, we briefly review the classical harmonic
balance method, and describe the adaptation of the method
required for its application to computational fluid dynamics
models of unsteady time periodic flows. We describe several
variations of the method including a classical balancing
method with pseudo time relaxation, the nonlinear frequency
domain form and the time spectral form. We show that the
maximum stable Courant-Friedrichs-Lewy (CFL) number for
explicit schemes is dependent on the grid reduced frequency,
a non-dimensional parameter that depends on the cell size,
characteristic wave speed, and the highest frequency
retained in the harmonic balance analysis. We apply the
harmonic balance methods to several nonlinear unsteady flow
problems and show that even strongly nonlinear flows can be
modelled accurately with a small number of harmonics
retained in the model. © 2013 Copyright Taylor and Francis
Group, LLC.},
Doi = {10.1080/10618562.2012.742512},
Key = {fds281245}
}
@article{fds281218,
Author = {Lipp, GM and Hall, KC and Mann, BP},
Title = {Effect of rider position on bicycle stability},
Journal = {Asme International Mechanical Engineering Congress and
Exposition, Proceedings (Imece)},
Volume = {4 A},
Publisher = {ASME},
Year = {2013},
Month = {January},
ISBN = {9780791856246},
url = {http://dx.doi.org/10.1115/IMECE2013-63809},
Abstract = {Bicycle stability has been of interest to dynamicists and
athletes since before J. W. Whipple described the canonical
model for bicycle motion in 1899. Since then, the subject
has fascinated many who sought to find a simple way to
describe the essence of stability for a hands free bicycle
at a prescribed forward speed. Caster and gyroscopic effects
have been shown to be helpful, but not necessary for there
to exist a stable range of forward speeds. This work focuses
on showing how using the eigenvalues of the linearized
equations for roll and steer (with and without a steering
torque) can illuminate the stabilizing and destabilizing
effects of changing bicycle geometry and rider position. Of
particular interest is the mathematical demonstration of the
decreased stability a cyclist on a time trial bike
experiences when in the aerodynamic position, as opposed to
riding with hands on the brake hoods or bull horns.
Copyright © 2013 by ASME.},
Doi = {10.1115/IMECE2013-63809},
Key = {fds281218}
}
@article{fds281283,
Author = {Ekici, K and Kielb, RE and Hall, KC},
Title = {The effect of aerodynamic asymmetries on turbomachinery
flutter},
Journal = {Journal of Fluids and Structures},
Volume = {36},
Pages = {1-17},
Publisher = {Elsevier BV},
Year = {2013},
Month = {January},
ISSN = {0889-9746},
url = {http://dx.doi.org/10.1016/j.jfluidstructs.2012.08.009},
Abstract = {In this paper, the effect of aerodynamic asymmetries on the
flutter characteristics of turbomachinery blades is
investigated. Specifically, the present method is used to
study the effect of leading edge blending in loaded and
unloaded rotors. The unsteady aerodynamic response of the
blades to self-excited vibrations is modeled using a
harmonic balance method, which allows one to model the
entire wheel using complex periodic boundary conditions and
a computational grid spanning a single sector (symmetry
group). This reduces the computational and memory
requirements dramatically compared to similar time-accurate
analyses. It is shown that alternate blending degrades the
stability of a loaded rotor whereas it improves the
stability of an unloaded rotor. On the other hand, when
blends are spaced five blades apart their effect is less
pronounced. © 2012 Elsevier Ltd.},
Doi = {10.1016/j.jfluidstructs.2012.08.009},
Key = {fds281283}
}
@article{fds281235,
Author = {Custer, CH and Weiss, JM and Subramanian, V and Clark, WS and Hall,
KC},
Title = {Unsteady simulation of a 1.5 stage turbine using an
implicitly coupled nonlinear harmonic balance
method},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {8},
Number = {PARTS A, B, AND C},
Pages = {2303-2317},
Publisher = {ASME},
Year = {2012},
Month = {December},
ISBN = {9780791844748},
url = {http://dx.doi.org/10.1115/GT2012-69690},
Abstract = {The harmonic balance method implemented within STARCCM+ is a
mixed frequency/time domain computational fluid dynamic
technique, which enables the efficient calculation of
timeperiodic flows. The unsteady solution is stored at a
small number of fixed time levels over one temporal period
of the unsteady flow in a single blade passage in each blade
row; thus the solution is periodic by construction. The
individual time levels are coupled to one another through a
spectral operator representing the time derivative term in
the Navier-Stokes equation, and at the boundaries of the
computational domain through the application of periodic and
nonreflecting boundary conditions. The blade rows are
connected to one another via a small number of fluid dynamic
spinning modes characterized by nodal diameter and
frequency. This periodic solution is driven to the correct
solution using conventional (steady) CFD acceleration
techniques, and thus is computationally efficient. Upon
convergence, the time level solutions are Fourier
transformed to obtain spatially varying Fourier coefficients
of the flow variables. We find that a small number of time
levels (or, equivalently, Fourier coefficients) are adequate
to model even strongly nonlinear flows. Consequently, the
method provides an unsteady solution at a computational cost
significantly lower than traditional unsteady time marching
methods. The implementation of this nonlinear harmonic
balance method within STAR-CCM+ allows for the simulation of
multiple blade rows. This capability is demonstrated and
validated using a 1.5 stage cold flow axial turbine
developed by the University of Aachen. Results produced
using the harmonic balance method are compared to
conventional time domain simulations using STAR-CCM+, and
are also compared to published experimental data. It is
shown that the harmonic balance method is able to accurately
model the unsteady flow structures at a computational cost
significantly lower than unsteady time domain simulation.
Copyright © 2012 by ASME.},
Doi = {10.1115/GT2012-69690},
Key = {fds281235}
}
@article{fds281236,
Author = {Clark, ST and Kielb, RE and Hall, KC},
Title = {Developing a reduced-order model to understand
nonsynchronous vibration (NSV) in turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {7},
Number = {PARTS A AND B},
Pages = {1373-1382},
Publisher = {ASME},
Year = {2012},
Month = {December},
ISBN = {9780791844731},
url = {http://dx.doi.org/10.1115/GT2012-68145},
Abstract = {This paper demonstrates the potential of using a
multidegree- of-freedom, traditional van der Pol oscillator
to model Non-Synchronous Vibration (NSV) in turbomachinery.
It is shown that the two main characteristics of NSV are
captured by the reduced-order, van der Pol model. First, a
stable limit cycle oscillation (LCO) is maintained for
various conditions. Second, the lock-in phenomenon typical
of NSV is captured for various fluid-structure frequency
ratios. The results also show the maximum amplitude of the
LCO occurs at an off-resonant condition, i.e., when the
natural shedding frequency of the aerodynamic instability is
not coincident with the natural modal frequency of the
structure. This conclusion is especially relevant in
preliminary design in industry because it suggests that
design engineers cannot treat NSV as a normal
Campbell-diagram crossing as they would for preliminary
design for forced response; it is possible that by
redesigning the blade, the response amplitude of the blade
may actually be higher. The goal of future research will be
to identify values and significance of the coupling
parameters used in the van der Pol model, to match these
coefficients with confirmed instances of experimental NSV,
and to develop a preliminary design tool that engineers can
use to better design turbomachinery for NSV. Proper
Orthogonal Decomposition (POD) CFD techniques and
coefficient tuning from experimental instances of NSV have
been considered to identify the unknown coupling
coefficients in the van der Pol model. Both the modeling of
experimental NSV and preliminary design development will
occur in future research. Copyright © 2012 by
ASME.},
Doi = {10.1115/GT2012-68145},
Key = {fds281236}
}
@article{fds281241,
Author = {Ekici, K and Hall, KC and Huang, H},
Title = {Stabilization of explicit flow solvers using a proper
orthogonal decomposition technique},
Journal = {50th Aiaa Aerospace Sciences Meeting Including the New
Horizons Forum and Aerospace Exposition},
Volume = {51},
Number = {5},
Pages = {1095-1104},
Year = {2012},
Month = {December},
ISSN = {0001-1452},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318260700007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {A new numerical technique for the stabilization of explicit
computational fluid dynamic (CFD) solvers is presented. When
using CFD codes to solve practical problems, one sometimes
finds the solution fails to converge due to the presence of
a small number of eigenvalues of the flow solver outside the
unit circle. In this paper, we use the proper orthogonal
decomposition technique to estimate the unstable eigenvalues
and eigenmodes of the flow solver as the solution diverges
for linear problems, or exhibits limit cycle oscillations
for nonlinear problems. We use the resulting
eigen-information to construct a preconditioner that
repositions the unstable eigenvalues from outside the unit
circle to a point inside the unit close to the origin,
resulting in a stable flow solver. In this work, the
proposed method is applied to a nonlinear steady cascade
solver. However, the technique can be easily applied to
external flow solvers, and to unsteady frequency-domain
(time-linearized and harmonic balance) flow solvers.
Copyright © 2012 by Kivanc Ekici, Kenneth C. Hall and Huang
Huang.},
Doi = {10.2514/6.2012-1096},
Key = {fds281241}
}
@article{fds281244,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {An automatic differentiation based nonlinear reduced order
modeling technique for unsteady separated
flows},
Journal = {50th Aiaa Aerospace Sciences Meeting Including the New
Horizons Forum and Aerospace Exposition},
Publisher = {American Institute of Aeronautics and Astronautics},
Year = {2012},
Month = {December},
url = {http://dx.doi.org/10.2514/6.2012-1098},
Abstract = {This paper discusses the development and implementation of
an automatic differentiation based nonlinear reduced order
model for unsteady separated flows. The objective of the
research presented herein has been to test the capability
and limits of the methodology for highly nonlinear unsteady
separated flows. In the following, we demonstrate the
methodology as applied to unsteady laminar vortex flow
shedding aft of a cylinder in crossflow as well as airfoil
unsteady transonic flow buffeting. Once constructed, the
nonlinear reduced order model provides approximate solutions
at a substantial computational cost savings as compared to
directly computed flow solutions. However, the limits of the
methodology have been found to be rather restrictive for
highly nonlinear separated flows, in particular for the
airfoil unsteady transonic flow buffet case. For cases where
the methodology does work, it is demonstrated that in
general the results are more accurate for the nonlinear
reduced order model as compared to results for a linear
reduced order model. Copyright © 2012 by Jeffrey P. Thomas,
Earl H. Dowell, and Kenneth C. Hall.},
Doi = {10.2514/6.2012-1098},
Key = {fds281244}
}
@article{fds281282,
Author = {Weiss, JM and Subramanian, V and Hall, KC},
Title = {Simulation of unsteady turbomachinery flows using an
implicitly coupled nonlinear harmonic balance
method},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {7},
Number = {PARTS A, B, AND C},
Pages = {1405-1412},
Publisher = {ASME},
Year = {2011},
Month = {December},
ISBN = {9780791854679},
url = {http://dx.doi.org/10.1115/GT2011-46367},
Abstract = {A nonlinear harmonic balance method for the simulation of
turbomachinery flows is presented. The method is based on
representing an unsteady, time periodic flow by a Fourier
series in time and then solving a set of mathematically
steady-state equations to obtain the Fourier coefficients.
The steady-state solutions are stored at discrete time
levels distributed throughout one period of unsteadiness and
are coupled via the physical time derivative and at periodic
boundaries. Implicit coupling between time levels is
achieved in a computationally efficient manner through
approximate factorization of the linear system that results
from the discretized equations. Unsteady, rotor-stator
interactions are performed to validate the implementation.
Results based on the harmonic balance method are compared
against those obtained using a full unsteady, time-accurate
calculation using moving meshes. The implicitly coupled
nonlinear harmonic balance method is shown to produce a
solution of reasonable accuracy compared to the full
unsteady approach but with significantly less computational
cost. Copyright © 2011 by ASME.},
Doi = {10.1115/GT2011-46367},
Key = {fds281282}
}
@article{fds281281,
Author = {Ekici, K and Hall, KC},
Title = {Harmonic balance analysis of limit cycle oscillations in
turbomachinery},
Journal = {Aiaa Journal},
Volume = {49},
Number = {7},
Pages = {1478-1487},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2011},
Month = {July},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.J050858},
Abstract = {A harmonic balance technique for the analysis of limit cycle
oscillations of turbomachinery blades is presented. This
method couples a computational fluid dynamics model to a
single-degree-of-freedom structural dynamic model of the
turbomachinery blades. The computational fluid dynamics
solver uses a nonlinear frequency-domain (harmonic balance)
approach that allows one to model the blade row of a
turbomachine on a computational grid spanning a single blade
passage. Using the harmonic balance approach, several
solutions, each one corresponding to a different subtime
level of the periodic unsteady flow, are computed
simultaneously. These subtime-level solutions are coupled to
each other in the computational field by a spectral
approximation of the time-derivative term in the
Navier-Stokes equation and also by application of far-field
and periodic boundary conditions. The structural dynamic
model is based on a similar approach in which a single
vibratory mode of interest is modeled using the harmonic
balance technique. The two solvers are coupled together
through the upwash condition on the surface of the blade and
the resulting generalized aerodynamic forces. In the
proposed approach, the limit cycle oscillation frequency is
treated as another unknown, which is solved iteratively,
together with the governing equations of fluid flow and
structural dynamics, thereby driving the residual of the
aeroelastic problem to convergence in a single computational
fluid dynamics run. The accuracy of the new method is
compared with two other techniques and it is shown to offer
significant computational savings. Copyright © 2011 by
Kivanc Ekici and Kenneth C. Hall. Published by the American
Institute of Aeronautics and Astronautics,
Inc.},
Doi = {10.2514/1.J050858},
Key = {fds281281}
}
@article{fds281310,
Author = {Thomas, JP and Custer, CH and Dowell, EH and Hall,
KC},
Title = {F-16 fighter aeroelastic computations using a harmonic
balance implementation of the OVERFLOW 2 flow
solver},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Year = {2010},
Month = {December},
ISBN = {9781600867422},
ISSN = {0273-4508},
Abstract = {Presented are flutter-onset trends of the F-16 fighter
computed using a harmonic balance version of the NASA
OVERFLOW 2 flow solver code. The harmonic technique enables
one to model unsteady aerodynamics and aeroelastic response
in the frequency domain with reduced computational cost
compared to time marching solutions. Computed results
compare well to flutter results computed using a separate
harmonic balance computational flow solver code developed at
Duke University. Select aeroelastic limit cycle oscillation
results are also presented. © 2010 by Jeffrey P. Thomas,
Chad H. Custer, Earl H. Dowell, and Kenneth C.
Hall.},
Key = {fds281310}
}
@article{fds281279,
Author = {Hall, KC and Hall, SR},
Title = {A variational method for computing the optimal aerodynamic
performance of conventional and compound
helicopters},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {3},
Number = {4},
Pages = {2767-2784},
Publisher = {American Helicopter Society},
Year = {2010},
Month = {December},
ISSN = {0002-8711},
url = {http://dx.doi.org/10.4050/jahs.55.042006},
Abstract = {Abstract We present a variational method for computing the
optimal aerodynamic performance of conventional and compound
helicopters in trimmed flight. The optimal circulation
distribution minimizes the sum of the induced and viscous
power required to develop a prescribed lift and/or thrust,
including any constraints that the helicopter be trimmed in
pitch and roll. The minimum total power circulation
distribution problem is cast as a variational problem, which
in turn is solved efficiently using a vortex-lattice
technique. Included in the analysis is the viscous profile
power, which is estimated at each airfoil section using an
experimental or numerically computed drag polar. The
resulting analysis - which is the viscous helicopter
analogue of Goldstein's inviscid propeller theory - gives
rigorous upper bounds on the performance of conventional and
compound helicopters, and may be used to predict the
rotor/wing loadings that produce optimal performance. We
show that helicopters with either coaxial rotor systems or
wing/rotor combinations substantially reduce power loss by
dramatically reducing the induced power associated with roll
trim and by producing a more efficient wake structure. ©
2010 by the American Helicopter Society International,
Inc.},
Doi = {10.4050/jahs.55.042006},
Key = {fds281279}
}
@article{fds281280,
Author = {Ekici, K and Hall, KC},
Title = {Harmonic balance analysis of limit cycle oscillations in
turbomachinery},
Journal = {46th Aiaa/Asme/Sae/Asee Joint Propulsion Conference and
Exhibit},
Year = {2010},
Month = {December},
Abstract = {A harmonic balance technique for the analysis of limit cycle
oscillations (LCO) of turbomachinery blades is presented.
This method couples a computational fluid dynamics (CFD)
model to a single-degree of freedom structural dynamic model
of the turbomachinery blades. The CFD solver uses a
nonlinear frequency-domain (harmonic balance) approach that
allows one to model the blade row of a turbomachine on a
computational grid spanning a single blade passage. Using
the harmonic balance approach, several solutions, each one
corresponding to a different subtime level of the periodic
unsteady flow, are computed simultaneously. These subtime
level solutions are coupled to each other in the
computational field by a spectral approximation of the time
derivative term in the Navier-Stokes equation, and also by
application of far-field and periodic boundary conditions.
The structural dynamic model is based on a similar approach
where a single vibratory mode of interest is modeled using
the harmonic balance technique. The two solvers are coupled
together through the upwash condition on the surface of the
blade and the resulting generalized aerodynamic forces. In
the proposed approach, the limit cycle oscillation frequency
is treated as another unknown, which is solved iteratively
together with the governing equations of fluid flow and
structural dynamics, thereby driving the residual of the
aeroelastic problem to zero in a single CFD run. The
accuracy of the new method is compared to two other
techniques and it is shown to offer significant
computational savings. Copyright © 2010 by Kivanc Ekici and
Kenneth C. Hall.},
Key = {fds281280}
}
@article{fds281276,
Author = {Hall, KC and Hall, SR},
Title = {A variational method for computing the optimal aerodynamic
performance of conventional and compound
helicopters},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {1},
Pages = {577-594},
Year = {2010},
Month = {November},
ISSN = {1552-2938},
Abstract = {We present a variational method for computing the optimal
aerodynamic performance of conventional and compound
helicopters in trimmed flight. The optimal circulation
distribution minimizes the sum of the induced and viscous
power required to develop a prescribed lift and/or thrust,
including any constraints that the helicopter be trimmed in
pitch and roll. The minimum total power circulation
distribution problem is cast as a variational problem, which
in turn is solved efficiently using a vortex-lattice
technique. Included in the analysis is the viscous profile
power, which is estimated at each airfoil section using an
experimental or numerically computed drag polar. The
resulting analysis - which is the viscous helicopter
analogue of Goldstein's inviscid propeller theory - gives
rigorous upper bounds on the performance of conventional and
compound helicopters, and may be used to predict the
rotor/wing loadings that produce optimal performance. We
show that helicopters with either coaxial rotor systems or
wing/rotor combinations substantially reduce power loss by
dramatically reducing the induced power associated with roll
trim and by producing a more efficient wake structure.
Copyright © 2010 by the American Helicopter Society
International, Inc. All rights reserved.},
Key = {fds281276}
}
@article{fds281230,
Author = {Hall, KC and Hall, SR},
Title = {A variational method for computing the optimal aerodynamic
performance of conventional and compound
helicopters},
Journal = {Journal of the American Helicopter Society},
Volume = {55},
Number = {4},
Pages = {0420061-04200616},
Year = {2010},
Month = {October},
ISSN = {0002-8711},
url = {http://dx.doi.org/10.4050/JAHS.55.042006},
Abstract = {We present a variational method for computing the optimal
aerodynamic performance of conventional and compound
helicopters in trimmed flight. The optimal circulation
distribution minimizes the sum of the induced and viscous
power required to develop a prescribed lift and/or thrust,
subject to any constraints that the helicopter be trimmed in
pitch and roll. The minimum total power circulation
distribution problem is cast as a variational problem, which
in turn is solved efficiently using a vortex-lattice
technique. Included in the analysis is the viscous profile
power, which is estimated at each airfoil section using an
experimental or numerically computed drag polar. The
resulting analysis-which is the viscous helicopter analogue
of Goldstein's inviscid propeller theory-gives rigorous
upper bounds on the performance of conventional and compound
helicopters and may be used to predict the rotor/wing
loadings that produce optimal performance. We show that
helicopters with either coaxial rotors or a wing and rotor
in combination can substantially reduce power loss by
producing a more efficient wake structure and by reducing
the induced power associated with roll trim. © 2010 The
American Helicopter Society.},
Doi = {10.4050/JAHS.55.042006},
Key = {fds281230}
}
@article{fds281277,
Author = {Ekici, K and Kielb, RE and Hall, KC},
Title = {Forced response analysis of aerodynamically asymmetric
cascades},
Journal = {46th Aiaa/Asme/Sae/Asee Joint Propulsion Conference and
Exhibit},
Year = {2010},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2010-6535},
Abstract = {The effect of aerodynamic asymmetries on forced response
characteristics of cascades is investigated. Specifically,
the present method is used to study the effect of leading
edge blending in loaded rotors. The unsteady aerodynamic
response of the blades to self-excited vibrations and gust
response is modeled using a harmonic balance method, which
allows one to model the entire wheel using complex periodic
boundary conditions and a computational grid spanning a
single sector (symmetry group). This reduces the
computational and memory requirements dramatically compared
to similar time-accurate analyses. The results show that
compared to symmetric cascades, the amplitude of the forcing
functions due to wake passing see an increase for blended
rotors. The maximum amplification factors for forced
response calculations are found to be around 1.3, which are
significantly lower than the case of typical frequency
mistuning. This indicates that there is no mode localization
effect due to aerodynamic asymmetries. Copyright © 2010 by
Kivanc Ekici, Robert E. Kielb and Kenneth C.
Hall.},
Doi = {10.2514/6.2010-6535},
Key = {fds281277}
}
@article{fds281278,
Author = {Ekici, K and Hall, KC and Kielb, RE},
Title = {Harmonic balance analysis of blade row interactions in a
transonic compressor},
Journal = {Journal of Propulsion and Power},
Volume = {26},
Number = {2},
Pages = {335-343},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2010},
Month = {January},
ISSN = {0748-4658},
url = {http://dx.doi.org/10.2514/1.43879},
Abstract = {In this paper we apply the harmonic balance technique to
analyze an inlet guide vane and rotor interaction problem,
and compare the computed flow solutions to existing
experimental data. The computed results, which compare well
with the experimental data, demonstrate that the technique
can accurately and efficiently model strongly nonlinear
periodic flows, including shock/vane interaction and
unsteady shock motion. Using the harmonic balance approach,
each blade row is modeled using a computational grid
spanning just a single blade passage regardless of the
actual blade counts. For each blade row, several subtime
level solutions that span a single time period are stored.
These subtime level solutions are related to each other
through the time derivative term in the Euler (or
Navier.Stokes) equations, which is approximated by a
pseudo-spectral operator, by complex periodicity conditions
along the periodic boundary of each blade row's
computational domain, and by the interface boundary
conditions between the vane and rotor. Casting the governing
equations in harmonic balance form removes the explicit
dependence on time. Mathematically, the equations to be
solved are similar in form to the steady Euler (or
Navier.Stokes) equations with an additional source term
proportional to the fundamental frequency of the
unsteadiness. Thus, conventional steady-state computational
fluid dynamics techniques, including local time stepping and
multigrid acceleration, are used to accelerate convergence,
resulting in a very efficient unsteady flow solver.
Copyright © 2009 by Kivanc Ekici, Kenneth C. Hall and
Robert E. Kielb.},
Doi = {10.2514/1.43879},
Key = {fds281278}
}
@article{fds281309,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Using automatic differentiation to create a nonlinear
reduced-order-model aerodynamic solver},
Journal = {Aiaa Journal},
Volume = {48},
Number = {1},
Pages = {19-24},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2010},
Month = {January},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.36414},
Abstract = {A novel nonlinear reduced-order-modeling technique for
computational aerodynamics and aeroelasticity is presented.
The method is based on a Taylor series expansion of a
frequency-domain harmonic balance computational fluid
dynamic solver residual. The first- and second-order
gradient matrices and tensors of the Taylor series expansion
are computed using automatic differentiation via FORTRAN
90=95 operator overloading. A Ritz-type expansion using
proper orthogonal decomposition shapes is then used in the
Taylor series expansion to create the nonlinear
reduced-order model. The nonlinear reduced-order-modeling
technique is applied to a viscous flow about an aeroelastic
NLR 7301 airfoil model to determine limit cycle
oscillations. Computational times are decreased from hours
to seconds using the nonlinear reduced-order model.
Copyright © 2009 by Jeffrey P. Thomas, Earl H. Dowell, and
Kenneth C. Hall.},
Doi = {10.2514/1.36414},
Key = {fds281309}
}
@article{fds281231,
Author = {Hall, KC and Hall, SR},
Title = {A variational method for computing the optimal aerodynamic
performance of conventional and compound
helicopters},
Journal = {Annual Forum Proceedings Ahs International},
Volume = {3},
Pages = {2767-2784},
Year = {2010},
ISSN = {1552-2938},
Abstract = {Abstract We present a variational method for computing the
optimal aerodynamic performance of conventional and compound
helicopters in trimmed flight. The optimal circulation
distribution minimizes the sum of the induced and viscous
power required to develop a prescribed lift and/or thrust,
including any constraints that the helicopter be trimmed in
pitch and roll. The minimum total power circulation
distribution problem is cast as a variational problem, which
in turn is solved efficiently using a vortex-lattice
technique. Included in the analysis is the viscous profile
power, which is estimated at each airfoil section using an
experimental or numerically computed drag polar. The
resulting analysis - which is the viscous helicopter
analogue of Goldstein's inviscid propeller theory - gives
rigorous upper bounds on the performance of conventional and
compound helicopters, and may be used to predict the
rotor/wing loadings that produce optimal performance. We
show that helicopters with either coaxial rotor systems or
wing/rotor combinations substantially reduce power loss by
dramatically reducing the induced power associated with roll
trim and by producing a more efficient wake structure. ©
2010 by the American Helicopter Society International,
Inc.},
Key = {fds281231}
}
@article{fds281274,
Author = {Miyakozawa, T and Kielb, RE and Hall, KC},
Title = {The Effects of aerodynamic asymmetric perturbations on
forced response of bladed disks},
Journal = {Journal of Turbomachinery},
Volume = {131},
Number = {4},
Pages = {1-8},
Publisher = {ASME International},
Year = {2009},
Month = {October},
ISSN = {0889-504X},
url = {http://dx.doi.org/10.1115/1.3068319},
Abstract = {Most of the existing mistuning research assumes that the
aerodynamic forces on each of the blades are identical
except for an interblade phase angle shift. In reality,
blades also undergo asymmetric steady and unsteady
aerodynamic forces due to manufacturing variations,
blending, mis-staggered, or in-service wear or damage, which
cause aerodynamically asymmetric systems. This paper
presents the results of sensitivity studies on forced
response due to aerodynamic asymmetry perturbations. The
focus is only on the asymmetries due to blade motions.
Hence, no asymmetric forcing functions are considered.
Aerodynamic coupling due to blade motions in the equation of
motion is represented using the single family of modes
approach. The unsteady aerodynamic forces are computed using
computational fluid dynamics (CFD) methods assuming
aerodynamic symmetry. Then, the aerodynamic asymmetry is
applied by perturbing the influence coefficient matrix in
the physical coordinates such that the matrix is no longer
circulant. Therefore, the resulting aerodynamic modal forces
in the traveling wave coordinates become a full matrix.
These aerodynamic perturbations influence both stiffness and
damping while traditional frequency mistuning analysis only
perturbs the stiffness. It was found that maximum blade
amplitudes are significantly influenced by the perturbation
of the imaginary part (damping) of unsteady aerodynamic
modal forces. This is contrary to blade frequency mistuning
where the stiffness perturbation dominates. © 2009 by
ASME.},
Doi = {10.1115/1.3068319},
Key = {fds281274}
}
@article{fds281271,
Author = {Ekici, K and Kielb, RE and Hall, KC},
Title = {The effect of aerodynamic asymmetries on turbomachinery
flutter},
Journal = {47th Aiaa Aerospace Sciences Meeting Including the New
Horizons Forum and Aerospace Exposition},
Year = {2009},
Month = {January},
ISBN = {9781563479694},
url = {http://dx.doi.org/10.2514/6.2009-893},
Abstract = {In this paper, the effect of aerodynamic asymmetries on the
flutter characteristics of turbomachinery blades is
investigated. Specifically, the present method is used to
study the effect of leading edge blending in loaded and
unloaded rotors. The unsteady aerodynamic response of the
blades to self-excited vibrations is modeled using a
harmonic balance method, which allows one to model the
entire wheel using complex periodic boundary conditions and
a computational grid spanning a single sector (symmetry
group). This reduces the computational and memory
requirements dramatically compared to similar time-accurate
analyses. It is shown that alternate blending degrades the
stability of a loaded rotor whereas it improves the
stability of an unloaded rotor. On the other hand, when
blends are spaced five blades apart their effect is less
pronounced. Copyright © 2009 by Kivanc Ekici, Robert E.
Kielb, and Kenneth C. Hall.},
Doi = {10.2514/6.2009-893},
Key = {fds281271}
}
@article{fds281272,
Author = {Ekici, K and Hall, KC and Kielb, RE},
Title = {Harmonic balance analysis of forced response in a transonic
compressor},
Journal = {47th Aiaa Aerospace Sciences Meeting Including the New
Horizons Forum and Aerospace Exposition},
Year = {2009},
Month = {January},
ISBN = {9781563479694},
url = {http://dx.doi.org/10.2514/6.2009-1240},
Abstract = {A harmonic balance technique for the analysis of nonlinear
forced response phenomenon in a two-row transonic compressor
is presented. Using the present approach, each blade row is
modeled using a computational grid spanning a single blade
passage regardless of the the actual blade counts. In the
harmonic balance analysis several sub-time level solutions
that span a single time-period are stored. These sub-time
level solutions are related to each other through the time
derivative term, which is approximated by a pseudo-spectral
operator in the governing equations, and through boundary
conditions. The complex periodicity conditions connect the
sub-time levels within a blade passage, and inter-row
boundary conditions connect the solutions among blade rows.
Because of the fact that the resulting discretized equations
are mathematically steady, the flowfield can be solved very
efficiently using multi-grid acceleration and local
time-stepping techniques. In this paper, we apply the
harmonic balance technique to an inlet guide vane (IGV) and
rotor interaction problem and illustrate that quite accurate
solutions can be obtained very efficiently. Copyright ©
2009 by Kivanc Ekici, Kenneth C. Hall, Robert E.
Kielb.},
Doi = {10.2514/6.2009-1240},
Key = {fds281272}
}
@article{fds281273,
Author = {Spiker, MA and Kielb, RE and Thomas, JP and Hall,
KC},
Title = {Application of enforced motion to study 2-D cascade lock-in
effect},
Journal = {47th Aiaa Aerospace Sciences Meeting Including the New
Horizons Forum and Aerospace Exposition},
Year = {2009},
Month = {January},
ISBN = {9781563479694},
url = {http://dx.doi.org/10.2514/6.2009-892},
Abstract = {The vortex lock-in effect has been well-studied for an
oscillating cylinder and numerous experimental and
computational data are available. However, only recently has
this phenomenon been observed for two-dimensional isolated
airfoils as well as turbine cascades. This paper
investigates a flow instability about a two-dimensional
airfoil tip section of a modern front stage compressor blade
operated at an off-design condition. The governing
nonlinear, unsteady Navier-Stokes equations are solved using
a novel harmonic balance (HB) method. For periodic unsteady
flows, such as the transonic flow through a turbomachinery
cascade, this method requires one to two orders of magnitude
less computational time than conventional time-accurate
solvers. The vortex shedding frequency is obtained using a
unique phase error method. Enforced motion is then used to
encourage lock-on of the frequency of the blades' motion to
the natural shedding frequency. In particular, it is assumed
that the airfoils vibrate harmonically in pitch about their
elastic axis at a given frequency and amplitude. Analogous
to the circular cylinder, a V-shaped lock-in region is
observed. The aeroelastic stability of the rotor is
determined and the results indicate that the largest limit
cycle oscillation (LCO) amplitude is not at the natural
shedding frequency. Furthermore, the system is always stable
at the natural shedding frequency. This is contrary to
conventional thought in which the most significant response
is assumed to be when the blade frequency and the frequency
of the fluid instability are coincident. Therefore, the
results indicate how both the natural shedding frequency and
blade frequency should be considered in design analysis.
Copyright © 2009 by the American Institute of Aeronautics
and Astronautics, Inc.},
Doi = {10.2514/6.2009-892},
Key = {fds281273}
}
@article{fds281306,
Author = {Thomas, JP and Custer, CH and Dowell, EH and Hall,
KC},
Title = {Unsteady flow computation using a harmonic balance approach
implemented about the OVERFLOW 2 flow solver},
Journal = {19th Aiaa Computational Fluid Dynamics Conference},
Year = {2009},
Month = {January},
ISBN = {9781563479755},
url = {http://dx.doi.org/10.2514/6.2009-4270},
Abstract = {A novel approach for implementing a nonlinear unsteady
frequency domain harmonic balance solution technique about
existing implicit computational fluid dynamic flow solvers
is presented. This approach uses an explicit discretization
of the harmonic balance source term, which enables the
harmonic balance method to be applied to existing implicit
flow solvers with minimal need for modification to the
underlying implicit flow solver code. The resulting harmonic
balance solver can then be used for modeling nonlinear
periodic unsteady flows. The methodology is applied to the
OVERFLOW 2 flow solver code, and results are presented for
transonic viscous flow past an unsteady pitching airfoil
section. Unsteady aerodynamic and aeroelastic results for
the F-16 fighter wing are also presented. Copyright © 2009
by Jeffrey P. Thomas, Chad H. Custer, Earl H. Dowell, and
Kenneth C. Hall.},
Doi = {10.2514/6.2009-4270},
Key = {fds281306}
}
@article{fds281307,
Author = {Dowell, EH and Thomas, JP and Hall, KC and Denegri,
CM},
Title = {Theoretical predictions of F-16 fighter limit cycle
oscillations for flight flutter testing},
Journal = {Journal of Aircraft},
Volume = {46},
Number = {5},
Pages = {1667-1672},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2009},
Month = {January},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.42352},
Abstract = {A computational investigation of the flutter onset and limit
cycle oscillation behavior of various F-16 fighter weapons
and stores configurations is presented. A nonlinear harmonic
balance compressible Reynolds-averaged Navier-Stokes
computational fluid dynamic flow solver is used to model the
unsteady aerodynamics of the F-16 wing. Slender body/wing
theory is used as an approximate method for accounting for
the unsteady aerodynamic effects of wing-tip launchers and
missiles. Details of the computational model are presented
along with an examination of the sensitivity of computed
aeroelastic behavior to characteristics and parameters of
the structural and fluid dynamic model. Comparisons with
flight-test data are also shown. Copyright © 2009 by the
American Institute of Aeronautics and Astronautics,
Inc.},
Doi = {10.2514/1.42352},
Key = {fds281307}
}
@article{fds281308,
Author = {Schwarz, JB and Dowell, EH and Thomas, JP and Hall, KC and Rausch, RD and Bartels, RE},
Title = {Improved flutter boundary prediction for an isolated
two-degree-of-freedom airfoil},
Journal = {Journal of Aircraft},
Volume = {46},
Number = {6},
Pages = {2069-2076},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2009},
Month = {January},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.30703},
Abstract = {A novel method of computing the flutter boundary for an
isolated airfoil based on a high-fidelity computational
fluid dynamics model reveals unusual behavior in a critical
transonic range. Inviscid and viscous predictions of the
flutter boundary for the two airfoils examined differ
substantially in this critical region and become sensitive
to Mach number and grid topology due to complicated
shock/boundary-layer interactions. Computational fluid
dynamics predictions of the flutter boundary for a NACA 0012
section airfoil are also compared with previous experimental
results.},
Doi = {10.2514/1.30703},
Key = {fds281308}
}
@article{fds281239,
Author = {Dowell, EH and Hall, KC and Thomas, JP and Kielb, RE and Spiker, MA and Li,
A and Denegri, CM},
Title = {Reduced order models in unsteady aerodynamic models,
aeroelasticity and molecular dynamics},
Journal = {Icas Secretariat 26th Congress of International Council of
the Aeronautical Sciences 2008, Icas 2008},
Volume = {1},
Pages = {4002-4014},
Year = {2008},
Month = {December},
ISBN = {9781605607153},
Abstract = {The state of reduced order modeling of unsteady aerodynamic
flows for the efficient calculation of fluid-structure
interaction (aeroelasticity) is discussed as well as very
recent work on olecular dynamics simulations. Starting with
either a time domain or frequency domain computational fluid
dynamics (CFD) analysis of unsteady aerodynamic flows, a
large, sparse eigenvalue problem is solved. Then, using just
a few of the resulting aerodynamic eigenmodes, a Reduced
Order Model (ROM) of the unsteady flow is constructed. The
aerodynamic ROM can then be combined with a similar ROM for
the structure to provide a Reduced Order Aeroelastic Model
that reduces computational model sized and cost by several
orders of magnitude. Moreover, the aerodynamic and
aeroelastic eigenvalue and eigenmode information provides
important insights into the physics of unsteady flows and
fluid-structure interaction. As an alternative to the use of
aerodynamic eigenmodes, Proper Orthogonal Decomposition
(POD) has also been explored. POD is an attractive
alternative because of the greater simplicity of calculating
POD modes rather than fluid eigenmodes per se. Moreover once
the POD modes have been used to construct a Reduced Order
Model, this ROM may be used to find a good approximation to
the dominant aerodynamic eigenmodes. After the Hopf
Bifurcation (flutter) condition is determined for the
fluid-structural system, a novel High Dimensional Harmonic
Balance (HDHB) solution method for the fluid (and
structural) model(s) proves to be a very efficient technique
for determining limit cycle oscillations in fluid-structural
systems. Examples will be discussed including the limit
cycle oscillations (LCO) of the F-16 aircraft and the limit
cycle oscillations (LCO) of the Von Karman vortex street
behind a cylinder in a cross-flow. The latter is a
prototypical example of self-excited fluid oscillations that
occur for bluff bodies including wings at high angles of
attack. Correlation of theoretical calculations with
experiment will also be shown. Finally a discussion of how
similar methods may be used for molecular dynamics
simulations concludes the paper.},
Key = {fds281239}
}
@article{fds281267,
Author = {Ekici, K and Kielb, RE and Hall, KC},
Title = {Aerodynamic asymmetry analysis of unsteady flows in
turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Number = {PART B},
Pages = {821-834},
Publisher = {ASME},
Year = {2008},
Month = {December},
ISBN = {9780791843154},
url = {http://dx.doi.org/10.1115/GT2008-51176},
Abstract = {A nonlinear harmonic balance technique for the analysis of
aerodynamic asymmetry of unsteady flows in turboma-chinery
is presented. The present method uses a mixed
time-domain/frequency-domain approach that allows one to
compute the unsteady aerodynamic response of turbomachinery
blades to self-excited vibrations. Traditionally,
researchers have investigated the unsteady response of a
blade row with the assumption that all the blades in the row
are identical. With this assumption the entire wheel can be
modeled using complex periodic boundary conditions and a
computational grid spanning a single blade passage. In this
study, the steady/unsteady aerodynamic asymmetry is modeled
using multiple passages. Specifically, the method has been
applied to aerodynamic ally asymmetric flutter problems for
a rotor with a symmetry group of two. The effect of
geometric asymmetries on the unsteady aerodynamic response
of a blade row is illustrated. For the cases investigated in
this paper, the change in the diagonal terms (blade on
itself) dominated the change in stability. Very little mode
coupling effect caused by the off-diagonal terms was found.
Copyright © 2008 by ASME.},
Doi = {10.1115/GT2008-51176},
Key = {fds281267}
}
@article{fds281268,
Author = {Miyakozawa, T and Kielb, RE and Hall, KC},
Title = {The effects of aerodynamic asymmetric perturbations on
forced response of bladed disks},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Number = {PART B},
Pages = {779-790},
Publisher = {ASME},
Year = {2008},
Month = {December},
ISBN = {9780791843154},
url = {http://dx.doi.org/10.1115/GT2008-50719},
Abstract = {Most of the existing mistuning research assumes that the
aerodynamic forces on each of the blades are identical
except for an interblade phase angle shift. In reality,
blades also undergo asymmetric steady and unsteady
aerodynamic forces due to manufacturing variations,
blending, mis-staggered blades or in-service wear or damage,
which cause aerodynamically asymmetric systems. This paper
presents the results of sensitivity studies on forced
response due to aerodynamic asymmetry perturbations. The
focus is only on the asymmetries due to blade motions.
Hence, no asymmetric forcing functions are considered.
Aerodynamic coupling due to blade motions in the equation of
motion is represented using the single family of modes
approach. The unsteady aerodynamic forces are computed using
CFD methods assuming aerodynamic symmetry. Then, the
aerodynamic asymmetry is applied by perturbing the influence
coefficient matrix in the physical coordinates such that the
matrix is no longer circulant. Therefore, the resulting
aerodynamic modal forces in the traveling wave coordinates
become a full matrix. These aerodynamic perturbations
influence both stiffness and damping while traditional
frequency mistuning analysis only perturbs the stiffness. It
was found that maximum blade amplitudes are significantly
influenced by the perturbation of the imaginary part
(damping) of unsteady aerodynamic modal forces. This is
contrary to blade frequency mistuning where the stiffness
perturbation dominates. Copyright © 2008 by
ASME.},
Doi = {10.1115/GT2008-50719},
Key = {fds281268}
}
@article{fds281269,
Author = {Spiker, MA and Kielb, RE and Hall, KC and Thomas,
JP},
Title = {Efficient design method for non-synchronous vibrations using
enforced motion},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Number = {PART B},
Pages = {735-747},
Publisher = {ASME},
Year = {2008},
Month = {December},
ISBN = {9780791843154},
url = {http://dx.doi.org/10.1115/GT2008-50599},
Abstract = {This paper presents the results of a new enforced motion
method using harmonic balance computational fluid dynamics
(CFD) analysis to design for NSV. Currently, most
researchers employ a time domain CFD technique to directly
find the frequency of the underlying flow instability which
can take significant computational time. NSV is said to
occur when the frequency of the instability coincides with a
blade mode frequency. The enforced motion design method uses
blade motion to attempt to force the fluid frequency to
lock-on to the blade vibration frequency at a specified
amplitude. For a fixed critical amplitude and blade mode
frequency, a range of interblade phase angles (IBPAs) is
investigated to determine the aerodynamic damping. A
negative value of damping at any IBPA deems the design
unacceptable. Furthermore, a procedure for blade re-design
(frequency changing) is presented. At the least stable IBPA,
the damping is determined for a range of blade frequencies
and amplitudes to determine the Limit Cycle Oscillation
(LCO) amplitude. A better design is then at the blade
frequency that minimizes the blade vibration amplitude.
Therefore, these preliminary results indicate that it is
advantageous to include blade motion in NSV design
approaches. Most significantly, it gives designers a quick
and efficient method to assess a design for NSV. Copyright
© 2008 by ASME.},
Doi = {10.1115/GT2008-50599},
Key = {fds281269}
}
@article{fds281270,
Author = {Ekici, K and Hall, KC},
Title = {Nonlinear Frequency-Domain Analysis of Unsteady Flows in
Turbomachinery with Multiple Excitation Frequencies},
Journal = {Aiaa Journal},
Volume = {46},
Number = {8},
Pages = {1912-1920},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2008},
Month = {August},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.26006},
Abstract = {A harmonic balance technique for the analysis of nonlinear
unsteady flows in turbomachinery arising from several
excitation sources, possibly with frequencies with
irrational ratios, is presented in this paper. This method
uses a mixed time-domain/frequency-domain approach that
allows one to model the blade row on a computational grid
spanning just a single blade passage, no matter the
interblade phase angles of the original disturbances. Using
this approach, we compute several solutions, each one
corresponding to one of several times spanning one period
for periodic flows or over a representative time interval
for aperiodic flows. These time levels are coupled through a
spectral time-derivative operator in the interior of the
computational domain and through the far-field and periodic
boundary conditions around the boundary of the domain. In
this paper, we apply the method to the two-dimensional Euler
equations (although the method can be applied to
three-dimensional and viscous flows) and examine the
nonlinear interaction of wake passing with blade vibration.
Copyright © 2008 by Kivanc Ekici and Kenneth C. Hall.
Published by the American Institute of Aeronautics and
Astronautics, Inc.},
Doi = {10.2514/1.26006},
Key = {fds281270}
}
@article{fds281303,
Author = {Ekici, K and Hall, KC and Dowell, EH},
Title = {Computationally fast harmonic balance methods for unsteady
aerodynamic predictions of helicopter rotors},
Journal = {Journal of Computational Physics},
Volume = {227},
Number = {12},
Pages = {6206-6225},
Publisher = {Elsevier BV},
Year = {2008},
Month = {June},
url = {http://dx.doi.org/10.1016/j.jcp.2008.02.028},
Abstract = {A harmonic balance technique for the analysis of unsteady
flows about helicopter rotors in forward flight and hover is
presented in this paper. The aerodynamics of forward flight
are highly nonlinear, with transonic flow on the advancing
blade, subsonic flow on the retreating blade, and stalled
flow over the inner portion of the rotor. Nevertheless, the
unsteady flow is essentially periodic in time making it well
suited for frequency domain analysis. The present method
uses periodic boundary conditions that allows one to model
the flow field on a computational grid around a single
helicopter blade, no matter the actual blade count. Using
this approach, we compute several solutions, each one
corresponding to one of several instants in time over one
period. These time levels are coupled to each other through
a spectral time derivative operator in the interior of the
computational domain and through the far-field and periodic
boundary conditions around the boundary of the domain. In
this paper, we apply the method to the three-dimensional
Euler equations (although the method can also be applied to
three-dimensional viscous flows), and examine the steady and
unsteady aerodynamics about wings and rotors. © 2008
Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.jcp.2008.02.028},
Key = {fds281303}
}
@article{fds281305,
Author = {Ekici, K and Hall, KC and Dowell, EH},
Title = {Computationally Fast Harmonic Balance Methods for Unsteady
Aerodynamic Predictions of Helicopter Rotors},
Journal = {Journal of Computational Physics},
Volume = {227},
Number = {12},
Pages = {6206-6225},
Publisher = {Elsevier},
Year = {2008},
Month = {June},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.2514/6.2008-1439},
Abstract = {A harmonic balance technique for the analysis of unsteady
flows about helicopter rotors in forward flight and hover is
presented in this paper. The aerodynamics of forward flight
are highly nonlinear, with transonic flow on the advancing
blade, subsonic flow on the retreating blade, and stalled
flow over the inner portion of the rotor. Nevertheless, the
unsteady flow is essentially periodic in time making it well
suited for frequency domain analysis. The present method
uses periodic boundary conditions that allows one to model
the flow-field on a computational grid around a single
helicopter blade, no matter the actual blade count. Using
this approach, we compute several solutions, each one
corresponding to one of several instants in time over one
period. These time levels are coupled to each other through
a spectral time derivative operator in the interior of the
computational domain, and through the far-field and periodic
boundary conditions around the boundary of the domain. In
this paper, we apply the method to the three-dimensional
Euler equations (although the method can also be applied to
three-dimensional viscous flows), and examine the steady and
unsteady aerodynamics about wings and rotors. Copyright ©
2008 by Kivanc Ekici, Kenneth C. Hall and Earl H.
Dowell.},
Doi = {10.2514/6.2008-1439},
Key = {fds281305}
}
@article{fds281304,
Author = {Dowell, EH and Hall, KC and Thomas, JP and Kielb, RE and Spiker, MA and Denegri, CM},
Title = {A new solution method for unsteady flows around oscillating
bluff bodies},
Journal = {IUTAM Bookseries},
Volume = {8},
Pages = {37-44},
Publisher = {Springer Netherlands},
Year = {2008},
Month = {January},
ISSN = {1875-3507},
url = {http://dx.doi.org/10.1007/978-1-4020-8630-4_4},
Doi = {10.1007/978-1-4020-8630-4_4},
Key = {fds281304}
}
@article{fds281275,
Author = {Ekici, K and Kielb, RE and Hall, KC},
Title = {Aerodynamic Asymmetry Analysis of Unsteady Flows in
Turbomachinery},
Journal = {Journal of Turbomachinery},
Volume = {132},
Number = {1},
Pages = {011006-011006},
Publisher = {ASME International},
Year = {2008},
ISSN = {0889-504X},
url = {http://dx.doi.org/10.1115/1.3103922},
Abstract = {A nonlinear harmonic balance technique for the analysis of
aerodynamic asymmetry of unsteady flows in turbomachinery is
presented. The present method uses a mixed
timedomain/frequency-domain approach that allows one to
compute the unsteady aerodynamic response of turbomachinery
blades to self-excited vibrations. Traditionally,
researchers have investigated the unsteady response of a
blade row with the assumption that all the blades in the row
are identical. With this assumption the entire wheel can be
modeled using complex periodic boundary conditions and a
computational grid spanning a single blade passage. In this
study, the steady/unsteady aerodynamic asymmetry is modeled
using multiple passages. Specifically, the method has been
applied to aerodynamically asymmetric flutter problems for a
rotor with a symmetry group of 2. The effect of geometric
asymmetries on the unsteady aerodynamic response of a blade
row is illustrated. For the cases investigated in this
paper, the change in the diagonal terms (blade on itself)
dominated the change in stability. Very little mode coupling
effect caused by the off-diagonal terms was found. © 2010
by ASME.},
Doi = {10.1115/1.3103922},
Key = {fds281275}
}
@article{fds281266,
Author = {Thomas, JP and Dowels, EH and Hall, KC and Denegri,
CM},
Title = {Virtual aeroelastic flight testing for the F-16 fighter with
stores},
Journal = {Collection of Technical Papers U.S. Air Force T and E Days,
2007(Test and Evaluation},
Pages = {339-346},
Year = {2007},
Month = {November},
ISBN = {1563478919},
Abstract = {In the following, we present computational aeroelastic
flutter onset and limit cycle oscillation response trends
for various stores and weapons configurations of the F-16
fighter. A nonlinear harmonic balance compressible Reynolds
averaged Navier-Stokes computational fluid dynamic flow
solver is used to model the unsteady aerodynamics of the
F-16 wing. However, slender body/wing theory is used as an
approximate method in accounting for the unsteady
aerodynamic effects of wingtip launchers and
missiles.},
Key = {fds281266}
}
@article{fds281264,
Author = {Kielb, RE and Hall, KC and Miyakozawa, T},
Title = {The effect of unsteady aerodynamic asymmetric perturbations
on flutter},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Pages = {649-654},
Publisher = {ASME},
Year = {2007},
Month = {September},
ISBN = {079184790X},
url = {http://dx.doi.org/10.1115/GT2007-27503},
Abstract = {Nearly all turbomachinery aeroelastic analyses assume that
the blades are "tuned" aerodynamically. That is, all blades
experience identical steady and unsteady loads (except for
an interblade phase shift). This paper presents the results
of a perturbations sensitivity study of the effects of
aerodynamic asymmetries on flutter of bladed disks. A high
fidelity model including both structural and aerodynamic
coupling is used. The types of asymmetry considered are
single blade, symmetric group, and random. For the case of
one blade perturbation, and symmetry group of 2
perturbations, the effect is to suppress flutter. This is
similar to the effect of frequency mistuning. However, the
results from random perturbations of all blades suggest that
manufacturing variations or field damage may cause an engine
to flutter. This provides a strong motivation to conduct
additional research in this area. Copyright © 2007 by
ASME.},
Doi = {10.1115/GT2007-27503},
Key = {fds281264}
}
@article{fds281265,
Author = {Ekici, K and Hall, KC},
Title = {Nonlinear analysis of unsteady flows in multistage
turbomachines using harmonic balance},
Journal = {Aiaa Journal},
Volume = {45},
Number = {5},
Pages = {1047-1057},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2007},
Month = {May},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.22888},
Abstract = {A harmonic balance technique for the analysis of
two-dimensional linear (small-disturbance) and nonlinear
unsteady flows in multistage turbomachines is presented. The
present method uses a mixed time-domain/frequency-domain
approach that allows one to compute the unsteady aerodynamic
response of multistage machines to both blade vibration (the
flutter problem) and wake interaction (the forced response
problem). In general, the flowfield may have multiple
excitation frequencies that are not integer multiples of
each other, so that the unsteady flow is (sometimes)
aperiodic in time. Using our approach, we model each blade
row using a computational grid spanning a single blade
passage. In each blade row, we store several sublime level
solutions. For flows that are periodic in tune, these
subtime levels span a single time period. For aperiodic
flows, the temporal period spanned by these subtime level
solutions is sufficiently long to sample the relevant
discrete frequencies contained in the aperiodic flow. In
both cases, these subtime level solutions are related to
each other through the time-derivative terms in the Euler or
Navier-Stokes equations and boundary conditions; complex
periodicity conditions connect the subtime levels within a
blade passage, and interrow boundary conditions connect the
solutions among blade rows. The resulting discretized
equations, which are mathematically steady because time
derivatives have been replaced by a pseudospectral operator
in which the excitation frequencies appear as parameters,
can be solved very efficiently using multigrid acceleration
techniques. In this paper, we apply the technique to both
flutter and wake-interaction problems and illustrate the
influence of neighboring blade rows on the unsteady
aerodynamic response of a blade row.},
Doi = {10.2514/1.22888},
Key = {fds281265}
}
@article{fds281263,
Author = {Gopinath, AK and Van Der Weide and E and Alonso, JJ and Jameson, A and Ekici, K and Hall, KC},
Title = {Three-dimensional unsteady multi-stage turbomachinery
simulations using the harmonic balance technique},
Journal = {Collection of Technical Papers 45th Aiaa Aerospace Sciences
Meeting},
Volume = {16},
Pages = {10753-10772},
Year = {2007},
Month = {January},
ISBN = {1563478900},
url = {http://dx.doi.org/10.2514/6.2007-892},
Abstract = {In this paper, we propose an extension of the Harmonic
Balance method for three-dimensional, unsteady, multi-stage
turbomachinery problems modeled by the Unsteady
Reynolds-Averaged Navier-Stokes (URANS) equations. This
time-domain algorithm simulates the true geometry of the
turbomachine (with the exact blade counts) using only one
blade passage per blade row, thus leading to drastic savings
in both CPU and memory requirements. Modified periodic
boundary conditions are applied on the upper and lower
boundaries of the single passage in order to account for the
lack of a common periodic interval for each blade row. The
solution algorithm allows each blade row to resolve a
specified set of frequencies in order to obtain the desired
computation accuracy; typically, a blade row resolves only
the blade passing frequencies of its neighbors. Since every
blade row is setup to resolve different frequencies the
actual Harmonic Balance solution in each of these blade rows
is obtained at different instances in time or time levels.
The interaction between blade rows occurs through sliding
mesh interfaces in physical time. Space and time
interpolation are carried out at these interfaces and can,
if not properly treated, introduce aliasing errors that can
lead to instabilities. With appropriate resolution of the
time interpolation, all instabilities are eliminated. This
new procedure is demonstrated using both two-and three
dimensional test cases and can be shown to significantly
reduce the cost of multi-stage simulations while capturing
the dominant unsteadiness in the problem.},
Doi = {10.2514/6.2007-892},
Key = {fds281263}
}
@article{fds281302,
Author = {Liu, LP and Dowell, EH and Hall, KC},
Title = {A novel harmonic balance analysis for the Van Der Pol
oscillator},
Journal = {International Journal of Non Linear Mechanics},
Volume = {42},
Number = {1},
Pages = {2-12},
Publisher = {Elsevier BV},
Year = {2007},
Month = {January},
ISSN = {0020-7462},
url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2006.09.004},
Abstract = {This study focuses on a novel harmonic balance formulation,
the high-dimensional harmonic balance method. To investigate
a non-linearity in the damping term, the system chosen for
study is the Van der Pol's oscillator. Both unforced and
forced oscillators are analyzed. The results from the
analysis are compared with those obtained from the classical
harmonic balance and the time marching (Runge-Kutta)
methods. (C) 2007 Elsevier Ltd. All rights
reserved.},
Doi = {10.1016/j.ijnonlinmec.2006.09.004},
Key = {fds281302}
}
@article{fds281299,
Author = {Thomas, JP and Dowell, EH and Hall, KC and Denegri,
CM},
Title = {An investigation of the sensitivity of F-16 fighter flutter
onset and limit cycle oscillations to uncertainties},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {5},
Pages = {3137-3144},
Year = {2006},
Month = {December},
ISBN = {1563478080},
ISSN = {0273-4508},
Abstract = {A computational investigation of flutter onset and limit
cycle oscillations of the F-16 fighter using a nonlinear
frequency-domain harmonic-balance approach is presented. In
this latest study, we examine the sensitivity of computed
aeroelastic behavior to characteristics and parameters of
the structural and fluid dynamic model. Three different F-16
weapons and stores configurations are considered. Results
indicate that the flutter onset Mach number is very
sensitive to the structural natural frequencies, and, more
specifically, the difference between the natural
frequencies, of the first two antisymmetric structural mode
shapes. Wing mean angle-of-attack is also shown to be very
important. The results presented herein may prove useful and
provide insight to other researchers modeling F-16 fighter
aeroelastic behavior, and who also may be observing large
sensitivities in their computational solutions.},
Key = {fds281299}
}
@article{fds281260,
Author = {Hall, KC},
Title = {Message from the conference chair},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {1},
Pages = {iii},
Year = {2006},
Month = {November},
ISBN = {0791842363},
Key = {fds281260}
}
@article{9298052,
Author = {Ekici, K and Hall, KC},
Title = {Fast estimation of unsteady flows in turbomachinery at
multiple interblade phase angles},
Journal = {Aiaa J. (Usa)},
Volume = {44},
Number = {9},
Pages = {2136-2142},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2006},
Month = {September},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.23288},
Keywords = {aerodynamics;blades;computational fluid dynamics;damping;flow
instability;rotors;turbomachinery;},
Abstract = {Time-linearized computational fluid dynamic (CFD) models for
the computation of unsteady flows in turbomachinery are now
used routinely in the design and analysis of turbomachinery
blade rows, particularly to predict the onset of flutter. A
typical flutter analysis of a rotor requires one to compute
unsteady flow solutions over the full range of interblade
phase angles, and hence requires significant computational
time even for relatively efficient time-linearized flow
solvers. Typically, one might compute the unsteady
aerodynamic damping at several dozen interblade phase angles
to ensure that no single interblade phase angle will
flutter. In this note, we describe a fast technique that
significantly reduces the computational time required to
perform such a flutter clearance analysis},
Doi = {10.2514/1.23288},
Key = {9298052}
}
@article{065110313119,
Author = {Ekici, K and Hall, KC},
Title = {Nonlinear frequency-domain analysis of unsteady flows in
turbomachinery with multiple excitation frequencies},
Journal = {Collection of Technical Papers Aiaa Applied Aerodynamics
Conference},
Volume = {1},
Pages = {623-636},
Address = {San Francisco, CA, United States},
Year = {2006},
Month = {January},
ISBN = {1563478129},
ISSN = {1048-5953},
url = {http://dx.doi.org/10.2514/6.2006-2995},
Keywords = {Unsteady flow;Frequency domain analysis;Natural
frequencies;Harmonic analysis;Time domain
analysis;Computational fluid dynamics;},
Abstract = {A harmonic balance technique for the analysis of nonlinear
unsteady flows in turbomachiney arising from several
excitation sources, possibly with frequencies with
irrational ratios, is presented in this paper. This method
uses a mixed time-domain/frequency-domain approach that
allows one to model the blade row on a computational grid
spanning just a single blade passage, no matter the
interblade phase angles of the original disturbances. Using
this approach, we compute several solutions, each one
corresponding to one of several times over one period for
periodic flows, or over a representative time interval for
aperiodic flows. These time levels are coupled to each other
through a spectral time derivative operator in the interior
of the computational domain, and through the far-field and
periodic boundary conditions around the boundary of the
domain. In this paper, we apply the method to the
two-dimensional Euler equations (although the method can be
applied to three-dimensional and viscous flows), and examine
the nonlinear interaction of wake passing with blade
vibration.},
Doi = {10.2514/6.2006-2995},
Key = {065110313119}
}
@article{fds281262,
Author = {Ekici, K and Hall, KC},
Title = {Nonlinear analysis of unsteady flows in multistage
turbomachines using the harmonic balance
technique},
Journal = {Collection of Technical Papers 44th Aiaa Aerospace Sciences
Meeting},
Volume = {7},
Pages = {4920-4933},
Year = {2006},
Month = {January},
ISBN = {1563478072},
url = {http://dx.doi.org/10.2514/6.2006-422},
Abstract = {harmonic balance technique for the analysis of two and
three-dimensional linear (small-disturbance) and nonlinear
unsteady flows in multistage turbomachines is presented. The
present method uses a mixed time-domain/ frequency-domain
approach that allows one to compute the unsteady aerodynamic
response of multistage machines to both blade vibration (the
flutter problem) and wake interaction (the forced response
problem). In general, the flow field may have multiple
excitation frequencies that are not integer multiples of
each other, so that the unsteady flow is (sometimes)
aperiodic in time. Using our approach, we model each blade
row using a computational grid spanning a single blade
passage. In each blade row, we store several sub-time level
solutions. For flows that are periodic in time, these
sub-time levels span a single time period. For aperiodic
flows, the temporal "period" spanned by these sub-time level
solutions is sufficiently long to sample the relevant
discrete frequencies contained in the aperiodic flow. In
both cases, these sub-time level solutions are related to
each other through the time derivative terms in the Euler or
Navier-Stokes equations, and boundary conditions - complex
periodicity conditions connect the sub-time levels within a
blade passage, and inter-row boundary conditions connect the
solutions among blade rows. The resulting discretized
equations - which are mathematically "steady" because
time-derivatives have been replaced by a pseudo-spectral
operator in which the excitation frequencies appear as
parameters - can be solved very efficiently using multi-grid
acceleration techniques. In this paper, we apply the
technique to both flutter and wake interaction problems and
illustrate the influence of neighboring blade rows on the
unsteady aerodynamic response of a blade
row.},
Doi = {10.2514/6.2006-422},
Key = {fds281262}
}
@article{070510403031,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Using automatic differentiation to create a nonlinear
reduced order model of a computational fluid dynamic
solver},
Journal = {Collection of Technical Papers 11th Aiaa/Issmo
Multidisciplinary Analysis and Optimization
Conference},
Volume = {4},
Pages = {2437-2449},
Address = {Portsmouth, VA, United States},
Year = {2006},
Month = {January},
ISBN = {1563478234},
url = {http://dx.doi.org/10.2514/6.2006-7115},
Keywords = {Airfoils;Frequency domain analysis;Nonlinear systems;Problem
solving;Transonic aerodynamics;},
Abstract = {Presented is a technique for developing a nonlinear reduced
order model of a computational fluid dynamic solver. The
method is based on a Taylor series expansion of a frequency
domain harmonic balance computational fluid dynamic solver
residual. The computational routines used to compute the
matrices and tensors of the Taylor series expansion are
created using automatic differentiation. A Ritz type
expansion using proper orthogonal decomposition shapes is
then used in the Taylor series expansion to create the
nonlinear reduced order model. Results are presented and
compared to a linear reduced order model for an inviscid
transonic airfoil configuration.},
Doi = {10.2514/6.2006-7115},
Key = {070510403031}
}
@article{fds281301,
Author = {Spiker, MA and Thomas, JP and Hall, KC and Kielb, RE and Dowell,
EH},
Title = {Modeling cylinder flow vortex shedding with enforced motion
using a harmonic balance approach},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {7},
Pages = {4549-4558},
Year = {2006},
Month = {January},
ISBN = {1563478080},
ISSN = {0273-4508},
url = {http://dx.doi.org/10.2514/6.2006-1965},
Abstract = {In recent years, new aeromechanical problems have been
encountered in turbomachinery. In particular,
non-synchronous vibrations (NSV) in blades have been
observed by engine companies and occur as a result of flow
instabilities. As a first step towards better understanding
the NSV in turbine engine configurations, the
two-dimensional shedding flow about a circular cylinder is
investigated in this study. The governing nonlinear,
unsteady Navier-Stokes equations are solved using a novel
harmonic balance method. This method requires one to two
orders of magnitude less computational time than
conventional time-marching computational fluid dynamic (CFD)
techniques. In this paper, results are presented for a
stationary cylinder in cross flow and a cylinder with
enforced motion in the low Reynolds number regime (47 < Re <
180). A unique phase error method is used to determine the
shedding frequency and oscillatory lift for the stationary
cylinder case. A relationship between Reynolds number and
Strouhal number is determined and compared with existing
computational and experimental data. The lock-in effect for
the prescribed motion case is observed, and results show
that cylinder motion does not significantly affect the
unsteady lift for cylinder oscillation amplitudes of 10% or
less of the cylinder's diameter and the lift actually
decreases for higher oscillatory amplitudes. This is
significant because it implies that it may not be necessary
to couple the NSV aerodynamic solution with blade motion for
some applications, which would require much less computation
time than a fully coupled aerodynamic/structural solution.
In all cases, the results agreed well with existing
experimental and computational data.},
Doi = {10.2514/6.2006-1965},
Key = {fds281301}
}
@article{fds281251,
Author = {Dowell, EH and Hall, KC and Thomas, JP and Kielb, RE and Spiker, MA and Denegri, CM},
Title = {Reduced Order Models in Unsteady Aerodynamic Models,
Aeroelasticity and Molecular Dynamics},
Volume = {6},
Pages = {247-267},
Publisher = {Springer Netherlands},
Year = {2006},
ISBN = {9781402049781},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000239535900014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Doi = {10.1007/978-1-4020-4979-8_14},
Key = {fds281251}
}
@article{9050667,
Author = {Liu, L and Thomas, JP and Dowell, EH and Attar, P and Hall,
KC},
Title = {A comparison of classical and high dimensional harmonic
balance approaches for a Duffing oscillator},
Journal = {J. Comput. Phys. (Usa)},
Volume = {215},
Number = {1},
Pages = {298-320},
Publisher = {Elsevier BV},
Year = {2006},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.1016/j.jcp.2005.10.026},
Keywords = {bifurcation;nonlinear dynamical systems;numerical
analysis;oscillations;},
Abstract = {The present study focuses on a novel harmonic balance
formulation, which is much easier to implement than the
standard/classical harmonic balance method for complex
nonlinear mathematical models and algorithms. Both harmonic
balance approaches are applied to Duffing's oscillator to
demonstrate the advantages and disadvantages of the two
approaches. A fundamental understanding of the difference
between these two methods is achieved, and the properties of
each method are analyzed in detail. [All rights reserved
Elsevier]},
Doi = {10.1016/j.jcp.2005.10.026},
Key = {9050667}
}
@article{064610237524,
Author = {Kielb, RE and Hall, KC and Hong, E and Pai, SS},
Title = {Probabilistic flutter analysis of a mistuned bladed
disk},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5 PART B},
Pages = {1145-1150},
Address = {Barcelona, Spain},
Year = {2006},
ISBN = {0791842401},
Keywords = {Flutter (aerodynamics);Probabilistic logics;Information
analysis;Natural frequencies;},
Abstract = {This paper presents the results of a probabilistic flutter
study of a mistuned bladed disk using a high fidelity model
including both structural and aerodynamic coupling. The
approach used in this paper is relatively fast because it
does not require any additional information than that
required of a tuned flutter analysis, with the exception of
the mistuned blade frequencies. The case study shows that
the stability of the fleet can be significantly affected by
the standard deviation of blade frequencies and the pattern
in which they are arranged in the wheel. A method for
understanding and identifying the beneficial patterns is
presented. Copyright © 2006 by ASME.},
Key = {064610237524}
}
@article{9215082,
Author = {Thomas Jeffrey and P and Dowell Earl and H and Hall Kenneth,
C},
Title = {Static/dynamic correction approach for reduced-order
modeling of unsteady aerodynamics},
Journal = {Journal of Aircraft},
Volume = {43},
Number = {4},
Pages = {865-878},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2006},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.12349},
Keywords = {aerodynamics;aerospace components;computational fluid
dynamics;eigenvalues and eigenfunctions;elasticity;frequency-domain
analysis;Mach number;transonic flow;},
Abstract = {Presented is a newly devised static/dynamic correction
approach for eigenvector expansion based reduced-order
modeling (ROM). When compared to the fundamental Ritz ROM
formulation, along with the static and multiple static
correction ROM approaches, the technique is demonstrated to
have much better performance in modeling unsteady linearized
frequency-domain aerodynamics in region of the complex
frequency plane near the imaginary axis, and up to a
prescribed frequency of interest. As with the static and
multiple static correction approaches, the method requires a
directly computed solution at zero frequency. The method
then requires one additional direct solution to be computed
at some nonzero frequency, which typically is the maximum
frequency of interest. When compared to the multiple static
corrections method, the method circumvents the necessity of
having to determine each of the multiple static corrections,
which require a solution to an alternate set of equations
that must be formulated and which can be costly to solve for
large systems. We also consider the feasibility of using a
proper orthogonal decomposition (POD) to determine
approximations for the least damped fluid-dynamic
eigenvectors. We demonstrate that in certain situations
these approximate eigenvectors can be used in conjuction
with the static/dynamic correction ROM approach to achieve
an improvement in performance over the recently devised
POD/ROM method where the POD shapes alone are used as ROM
shape vectors. Finally, we illustrate how the method can be
coupled with a structural model to compute the Mach-number
flutter speed trend for a large computational-fluid-dynamics
model of a three-dimensional transonic wing
configuration.},
Doi = {10.2514/1.12349},
Key = {9215082}
}
@article{05519593279,
Author = {Thomas, JP and Dowell, EH and Hall, KC and Denegri,
CM},
Title = {Further investigation of modeling limit cycle oscillation
behavior of the F-16 fighter using a harmonic balance
approach},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {3},
Pages = {1457-1466},
Address = {Austin, TX, United States},
Year = {2005},
Month = {December},
ISSN = {0273-4508},
Keywords = {Fighter aircraft;Frequency domain analysis;Harmonic
analysis;Wings;Flutter (aerodynamics);Aerodynamics;Computer
simulation;},
Abstract = {A computational investigation of limit cycle oscillation
behavior of the F-16 fighter configuration using a nonlinear
frequency-domain harmonic-balance approach is presented. The
research discussed in this latest paper is a follow-on to
our work presented at the 2004 SDM conference. Our latest
efforts have been directed toward assessing the effects of
mean angle-of-attack, wingtip geometry, wing twist, and
static aeroelastic deformation on flutter onset and LCO
response.},
Key = {05519593279}
}
@article{fds281233,
Author = {Dowell, EH and Clark, R and Cox, D and Curtiss, HC and Edwards, JW and Hall, KC and Peters, DA and Scanlan, R and Simiu, E and Sisto, F and Strganac, TW},
Title = {A modern course in aeroelasticity},
Volume = {116},
Pages = {1-766},
Year = {2005},
Month = {December},
ISBN = {9781402020391},
ISSN = {0925-0042},
Key = {fds281233}
}
@article{fds281234,
Author = {Dowell, EH and Hall, KC and Thomas, JP and Kielb, RE and Spiker, MA and Denegri, CM},
Title = {Reduced order unsteady aerodynamic models and
aeroelasticity},
Journal = {12th International Congress on Sound and Vibration 2005,
Icsv 2005},
Volume = {1},
Pages = {47-64},
Year = {2005},
Month = {December},
ISBN = {9781627481496},
Abstract = {The state of reduced order modeling of unsteady aerodynamic
flows for the efficient calculation of fluid-structure
interaction (aeroelasticity) is discussed. Reduced order
modeling is a set of conceptually novel and computationally
efficient techniques for computing unsteady flow about
airfoils, wings, and turbomachinery cascades. Starting with
either a time domain or frequency domain computational fluid
dynamics (CFD) analysis of unsteady aerodynamic flows, a
large, sparse eigenvalue problem is solved. Then, using just
a few of the resulting aerodynamic eigenmodes, a Reduced
Order Model (ROM) of the unsteady flow is constructed. The
aerodynamic ROM can then be combined with a similar ROM for
the structure to provide a Reduced Order Aeroelastic Model
that reduces computational model sized and cost by several
orders of magnitude. Moreover, the aerodynamic and
aeroelastic eigenvalue and eigenmode information provides
important insights into the physics of unsteady flows and
fluid-structure interaction. The method is particularly well
suited for use in the active control of aeroelastic
(fluid-structural) and unsteady aerodynamic phenomena as
well as in standard aeroelastic analysis. As an alternative
to the use of aerodynamic eigenmodes, Proper Orthogonal
Decomposition (POD) has also been explored. POD is an
attractive alternative because of the greater simplicity of
calculating POD modes rather than fluid eigenmodes per se.
Moreover once the POD modes have been used to construct a
Reduced Order Model, this ROM may be used to find a good
approximation to the dominant aerodynamic eigenmodes. After
the Hopf Bifurcation (flutter) condition is determined for
the fluid-structural system, a novel High Dimensional
Harmonic Balance (HDHB) solution method for the fluid (and
structural) model(s) proves to be a very efficient technique
for determining limit cycle oscillations in fluid-structural
systems. In this approach one exploits the knowledge of the
aeroelastic eigenmode determined from the aeroelastic ROM.
Several examples will be discussed including the limit cycle
oscillations (LCO) of the F-16 aircraft and the limit cycle
oscillations (LCO) of the Von Karman vortex street behind a
cylinder in a cross-flow. The latter is a prototypical
example of self-excited fluid oscillations that occur for
bluff bodies including wings at high angles of attack.
Correlation of theoretical calculations with experiment will
also be shown.},
Key = {fds281234}
}
@article{06049656684,
Author = {Hall, KC and Kielb, RE and Ekici, K and Thomas, JP and Clark,
WS},
Title = {Recent advancements in turbomachinery aeroelastic design
analysis},
Journal = {43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting
Papers},
Pages = {11253-11274},
Address = {Reno, NV, United States},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2005-14},
Keywords = {Turbomachinery;Machine design;Frequency domain
analysis;Stability;Aerodynamic loads;},
Abstract = {In this paper, we review some recent developments for
computing unsteady aerodynamic loads associated with
turbomachinery aeromechanics. In particular, we example the
use of frequency domain techniques for computing unsteady
flows in turbomachinery. The frequency domain approaches,
which can be used to model both small-disturbance and
nonlinear time periodic flows, are computationally very
efficient, typically at least one order of magnitude more
efficient than time domain techniques. Furthermore, they can
be used to analyze a wide variety of aeromechanic,
performance, unsteady heat transfer, and flow stability
problems in turbomachinery, including the important problem
of unsteady flows in multistage machines. We show a number
of novel uses of frequency domain techniques including their
use to model nonlinear flows, multistage flows, and
self-excited non-synchronous fluid instabilities.},
Doi = {10.2514/6.2005-14},
Key = {06049656684}
}
@article{06049656915,
Author = {Ekici, K and Voytovycht, DM and Hall, KC},
Title = {Time-linearized Navier-Stokes analysis of flutter in
multistage turbomachines},
Journal = {43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting
Papers},
Pages = {14259-14277},
Address = {Reno, NV, United States},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2005-836},
Keywords = {Navier Stokes equations;Turbomachine blades;Problem
solving;Entropy;Mathematical models;Computer
simulation;},
Abstract = {We present an efficient and accurate computational method
for predicting three dimensional unsteady flows in
multistage turbomachinery. Specifically, a time-linearized
unsteady Navier-Stokes method is developed to solve the
turbomachinery flutter problem, including unsteady blade row
interaction. A time-linearized approach allows us to model
each blade row with a computational grid spanning only a
single blade passage. The aerodynamic interaction of blade
rows is caused by propagation of acoustic, vortical and
entropic waves in the working fluid. Each wave has a
particular frequency and interblade phase angle related to
the circumferential wavelength of the scattered wave and the
frequency and the wavelength of the original wave that
produced it. The waves propagating between the rows are
modeled by exchanging information among various unsteady
solutions at the interrow computational boundaries.
Fortunately, a small number of unsteady waves and
corresponding unsteady flow solutions must be retained in
the model to compute accurately the unsteady aerodynamic
response. This is important for the computational time,
which is proportional to the number of unsteady solutions
and the number of blade rows. In this paper, computational
results are compared to those of a previously developed
two-dimensional solver for an inviscid, compressible
multistage compressor comprised of three blade rows. We also
present the steady-state viscous solution and linearized
unsteady solution for one and one half stages of a modern
front stage compressor. Finally, we investigate the steady
and multistage unsteady flow in the NASA Rotor 67
fan.},
Doi = {10.2514/6.2005-836},
Key = {06049656915}
}
@article{06049656142,
Author = {Carlson, HA and Feng, JQ and Thomas, JP and Kielb, RE and Hall, KC and Dowell, EH},
Title = {Computational models for nonlinear aeroelasticity},
Journal = {43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting
Papers},
Pages = {4143-4152},
Address = {Reno, NV, United States},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2005-1085},
Keywords = {Aerodynamics;Computational fluid dynamics;Harmonic
generation;},
Abstract = {Two distinctly different reduced-order models are formulated
for fully nonlinear aeroelastic systems. The first is based
on Proper Orthogonal Decomposition (POD). The velocity field
is decomposed into a finite number of orthonormal modes,
effecting order reduction by transforming from physical
space to a low-dimensional eigenspace. The second model is
based on the method of Harmonic Balancing (HB). It retains
the same physical dimensions of a high-order CFD model but
transforms from the time domain to the frequency domain,
requiring a single solution for each harmonic frequency
included in the model. The number of harmonic frequencies is
much smaller than the number of time steps required in a
time-accurate simulation. Comparisons are made between POD
and HB model output and experimental data for a set of
canonical problems involving viscous effects, now
separation, and fully nonlinear aeroelastic behavior: now
past a stationary cylinder, a cylinder with forced
oscillations, and a self-excited, plunging cylinder.
Copyright © 2005 by the American Institute of Aeronautics
and Astronautics, Inc. All rights reserved.},
Doi = {10.2514/6.2005-1085},
Key = {06049656142}
}
@article{8706842,
Author = {Thomas Jeffrey and P and Hall Kenneth and C and Dowell Earl,
H},
Title = {Discrete adjoint approach for modeling unsteady aerodynamic
design sensitivities},
Journal = {Aiaa Journal},
Volume = {43},
Number = {9},
Pages = {1931-1936},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2005},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/1.731},
Keywords = {aerodynamics;compressible flow;design engineering;flow
instability;flow simulation;mechanical engineering
computing;},
Abstract = {A discrete adjoint approach is presented for computing
steady and unsteady aerodynamic design sensitivities for
compressible viscous flows about airfoil configurations. The
nominal flow solver method is based on a harmonic balance
solution technique, which is capable of modeling both steady
and nonlinear periodic unsteady flows. The computer code for
the discrete adjoint solver, which is derived from the
nominal harmonic balance solver, has been generated with the
aid of the advanced automatic differentiation software tool
known as TAF (Transformation of Algorithms in
FORTRAN).},
Doi = {10.2514/1.731},
Key = {8706842}
}
@article{8589431,
Author = {Hall, KC and Ekici, K},
Title = {Multistage coupling for unsteady flows in
turbomachinery},
Journal = {Aiaa J. (Usa)},
Volume = {43},
Number = {3},
Pages = {624-632},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2005},
ISBN = {1-4020-4267-1},
ISSN = {0001-1452},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000237275800017&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {aerodynamics;blades;entropy;flow instability;turbomachinery;vortices;waves;},
Abstract = {We present a three-dimensional time-linearized unsteady
Euler solver for computing unsteady flows in multistage
turbomachines. Using this approach, each blade row is
modeled on a computational grid spanning a single blade
passage. Within each blade passage, several time-linearized
unsteady solutions, each of which have different frequencies
and interblade phase angles, are computed. These various
solutions are coupled together at the interrow boundaries
between the blade rows. The coupling allows one to pass the
pressure, entropy, and vorticity waves traveling between
neighboring blade rows resulting in an efficient multistage
analysis of unsteady flows in turbomachinery. Results that
demonstrate the accuracy and efficiency of the method, as
well as the importance of multistage effects, are presented
for several geometries. In particular, we show that
multistage effects can be significant for the aerodynamic
loads acting on a given blade row. Furthermore, the method
presented is highly efficient. For example, a flutter
calculation requires only about three times the CPU time of
one steady flow computation for each interblade phase angle
and frequency considered},
Doi = {10.2514/1.8520},
Key = {8589431}
}
@article{05169046041,
Author = {Thomas, JP and Dowell, EH and Hall, KC and Denegri,
CM},
Title = {Modeling limit cycle oscillation behavior of the F-16
fighter using a harmonic balance approach},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {3},
Pages = {2044-2050},
Address = {Palm Springs, CA, United States},
Year = {2004},
Month = {December},
ISSN = {0273-4508},
Keywords = {Fighter aircraft;Oscillators (mechanical);Wings;Reynolds
number;Iterative methods;Computer simulation;Frequency
domain analysis;},
Abstract = {A computational investigation of limit cycle oscillation
behavior of the F-16 fighter configuration using a nonlinear
frequency-domain harmonic-balance approach is presented.
Computed limit cycle response results correlate well with
experiment. Details of the computational model and
methodology are presented. Copyright © 2004 by Jeffrey P.
Thomas, Earl H. Dowell, Kenneth C. Hall and Charles M.
Denegri Jr.},
Key = {05169046041}
}
@article{04098039426,
Author = {Dowell, E.H. and Thomas, J.P. and Hall, K.C.},
Title = {Transonic limit cycle oscillation analysis using reduced
order aerodynamic models},
Journal = {Journal of Fluids and Structures},
Volume = {19},
Number = {1},
Pages = {17 - 27},
Year = {2004},
url = {http://dx.doi.org/10.1016/j.jfluidstructs.2003.07.018},
Keywords = {Oscillations;Aircraft;Wind tunnels;Transonic
flow;Mathematical models;},
Abstract = {Limit cycle oscillations have been observed in flight
operations of modern aircraft, wind tunnel experiments and
mathematical models. Both fluid and structural
nonlinearities are thought to contribute to these phenomena.
With recent advances in reduced order aerodynamic modeling,
it is now feasible to analyze limit cycle oscillations that
may occur in transonic flow including the effects of
structural and fluid nonlinearities. In this paper an
airfoil with control surface freeplay (a common structural
nonlinearity) is used to investigate transonic flutter and
limit cycle oscillations. The reduced order aerodynamic
model used in this paper assumes the shock motion is small
and in proportion to the structural motions. © 2003
Elsevier Ltd. All rights reserved.},
Key = {04098039426}
}
@article{fds281296,
Author = {Thomas Jeffrey and P and Dowell Earl and H and Hall Kenneth,
C},
Title = {Modeling viscous transonic limit-cycle oscillation behavior
using a harmonic balance approach},
Journal = {Journal of Aircraft},
Volume = {41},
Number = {6},
Pages = {1266-1274},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2004},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.9839},
Abstract = {Presented is a harmonic-balance computational fluid dynamic
approach for modeling limit-cycle oscillation behavior of
aeroelastic airfoil configurations in a viscous transonic
flow. For the NLR 7301 airfoil configuration studied,
accounting for viscous effects is shown to significantly
influence computed limit-cycle oscillation trends when
compared to an inviscid analysis. A methodology for
accounting for changes in mean angle of attack during
limit-cycle oscillation is also developed.},
Doi = {10.2514/1.9839},
Key = {fds281296}
}
@article{04378349850,
Author = {Kholodar Denis and B and Dowell Earl and H and Thomas Jeffrey and P and Hall
Kenneth, C},
Title = {Improved understanding of transonic flutter: A
three-parameter flutter surface},
Journal = {Journal of Aircraft},
Volume = {41},
Number = {4},
Pages = {911-917},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2004},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.467},
Keywords = {Transonic aerodynamics;Airfoils;Velocity control;Thickness
measurement;Degrees of freedom (mechanics);Frequencies;Pressure
effects;Trajectories;Calculations;},
Abstract = {An understanding of transonic flutter is often critical for
high-speed aircraft development. A presentation of the
transonic flutter velocity as a function of the Mach number
and mass ratio is shown here to provide many advantages.
Such a presentation offers new insights when comparing
computational and wind-tunnel flutter results. The benefits
of such a presentation are also evident in parameter
studies. Finally, the subject of flutter similarity rules
for airfoils of different thicknesses is also
addressed.},
Doi = {10.2514/1.467},
Key = {04378349850}
}
@article{04478465713,
Author = {Kholodar Denis and B and Dowell Earl and H and Thomas Jeffrey and P and Hall
Kenneth, C},
Title = {Limit-cycle oscillations of a typical airfoil in transonic
flow},
Journal = {Journal of Aircraft},
Volume = {41},
Number = {5},
Pages = {1067-1072},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2004},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/1.618},
Keywords = {Oscillations;Transonic flow;Computational fluid
dynamics;Mathematical models;Harmonic analysis;Degrees of
freedom (mechanics);Stiffness;Elasticity;Natural
frequencies;},
Abstract = {Using an inviscid flow computational-fluid-dynamic model and
a harmonic balance flow solver, a parametric investigation
of how structural-inertial parameters and freestream Mach
number of a transonic flow affect the limit-cycle
oscillation characteristics of a typical
two-degree-of-freedom transonic airfoil configuration is
presented. The computational efficiency of the harmonic
balance aerodynamic model allows a much more thorough
exploration of the parameter range than has been possible
previously.},
Doi = {10.2514/1.618},
Key = {04478465713}
}
@article{04288255944,
Author = {Dowell, EH and Thomas, JP and Hall, KC},
Title = {Transonic limit cycle oscillation analysis using reduced
order aerodynamic models},
Journal = {Journal of Fluids and Structures},
Volume = {18},
Number = {SUPPL},
Pages = {17-27},
Publisher = {Elsevier BV},
Year = {2004},
url = {http://dx.doi.org/10.1016/j.jfluidstructs.2003.07.018},
Keywords = {Oscillations;Aircraft;Wind tunnels;Nonlinear
systems;Transonic flow;Mathematical models;},
Abstract = {Limit cycle oscillations have been observed in flight
operations of modern aircraft, wind tunnel experiments and
mathematical models. Both fluid and structural
nonlinearities are thought to contribute to these phenomena.
With recent advances in reduced order aerodynamic modeling,
it is now feasible to analyze limit cycle oscillations that
may occur in transonic flow including the effects of
structural and fluid nonlinearities. In this paper an
airfoil with control surface freeplay (a common structural
nonlinearity) is used to investigate transonic flutter and
limit cycle oscillations. The reduced order aerodynamic
model used in this paper assumes the shock motion is small
and in proportion to the structural motions. © 2003
Elsevier Ltd. All rights reserved.},
Doi = {10.1016/j.jfluidstructs.2003.07.018},
Key = {04288255944}
}
@article{fds281223,
Author = {Thomas, JP and Hall, KC and Dowell, EH},
Title = {A discrete adjoint approach for modeling unsteady
aerodynamic design sensitivities},
Journal = {41st Aerospace Sciences Meeting and Exhibit},
Year = {2003},
Month = {December},
ISBN = {9781624100994},
Abstract = {Presented is a discrete adjoint approach for computing
steady and unsteady aerodynamic design sensitivities for
compressible viscous flows about airfoil configurations. The
nominal flow solver method is based on a harmonic balance
solution technique, which is capable of modeling both steady
and nonlinear periodic unsteady flows. The computer code for
the discrete adjoint solver, which is derived from the
nominal harmonic balance solver, has been generated with the
aid of the advanced automatic differentiation software tool
known as TAF (Transformation of Algorithms in Fortran). ©
2003 by Jeffrey P. Thomas, Kenneth C. Hall, and Earl H.
Dowell.},
Key = {fds281223}
}
@article{fds281224,
Author = {Hall, KC and Thomas, JP and Ekici, K and Voytovych,
DM},
Title = {Frequency domain techniques for complex and nonlinear flows
in turbomachinery},
Journal = {33rd Aiaa Fluid Dynamics Conference and Exhibit},
Year = {2003},
Month = {December},
ISBN = {9781624100956},
Abstract = {In this paper, we review frequency domain techniques for
computing unsteady flows in turbomachinery. The frequency
domain approaches, which can be used to model both
small-disturbance and nonlinear time periodic flows, are
computationally very efficient, typically one to two orders
of magnitude more efficient than time domain techniques.
Furthermore, they can be used to analyze a wide variety of
aeromechanic, performance, unsteady heat transfer, and flow
stability problems in turbomachinery, including the
important problem of unsteady flows in multistage machines.
© 2003 by Kenneth C. Hall, Jeffrey P. Thomas, Kivanc Ekici,
Dmytro Voytovych. Published by the American Institute of
Aeronautics and Astronautics, Inc.},
Key = {fds281224}
}
@article{fds340709,
Author = {Thomas, JP and Hall, KC and Dowell, EH},
Title = {A harmonic balance approach for modeling nonlinear
aeroelastic behavior of wings in transonic viscous
flow},
Journal = {44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics,
and Materials Conference},
Year = {2003},
Month = {December},
ISBN = {9781624101007},
Abstract = {Presented is a frequency-domain harmonic-balance (HB)
computational fluid dynamic (CFD) approach for modeling
flutter onset and limit cycle oscillation (LCO) behavior of
viscous transonic aeroelastic wing configurations. The AGARD
445.6 transonic wing configuration is studied and results
are compared to a recent inviscid analysis for a supersonic
Mach number flow condition. © 2003 by Jeffrey P. Thomas,
Kenneth C. Hall, and Earl H. Dowell. Published by the
American Institute of Aeronautics and Astronautics,
Inc.},
Key = {fds340709}
}
@article{fds340717,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Modeling limit cycle oscillations for an NLR 7301 airfoil
aeroelastic configuration including correlation with
experiment},
Journal = {44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics,
and Materials Conference},
Year = {2003},
Month = {December},
ISBN = {9781624101007},
Abstract = {Presented is an investigation into the modeling of limit
cycle oscillation (LCO) behavior of an experimental
transonic airfoil aeroelastic configuration using a
frequency-domain harmonic-balance (HB) computational fluid
dynamic (CFD) approach. The aeroelastic model has a single
structural degree-of-freedom in pitch. Wind-tunnel wall
interference effects are included in the CFD model. A
wind-tunnel resonance is observed near the flutter onset and
LCO conditions. © 2003 by Jeffrey P. Thomas, Earl H.
Dowell, and Kenneth C. Hall. Published by the American
Institute of Aeronautics and Astronautics,
Inc.},
Key = {fds340717}
}
@article{03357614260,
Author = {Thomas, JP and Hall, KC and Dowell, EH},
Title = {A harmonic balance approach for modeling nonlinear
aeroelastic behavior of wings in transonic viscous
flow},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {7},
Pages = {4779-4784},
Address = {Norfolk, VA, United States},
Year = {2003},
Month = {August},
ISBN = {9781624101007},
Keywords = {Wings;Flutter (aerodynamics);Transonic flow;Viscous
flow;Computational fluid dynamics;Mathematical
models;Frequency domain analysis;Oscillations;Supersonic
flow;},
Abstract = {Presented is a frequency-domain harmonic-balance (HB)
computational fluid dynamic (CFD) approach for modeling
flutter onset and limit cycle oscillation (LCO) behavior of
viscous transonic aeroelastic wing configurations. The AGARD
445.6 transonic wing configuration is studied and results
are compared to a recent inviscid analysis for a supersonic
Mach number flow condition.},
Key = {03357614260}
}
@article{03357613841,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Modeling limit cycle oscillations for an NLR 7301 airfoil
aeroelastic configuration including correlation with
experiment},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {1},
Pages = {289-297},
Address = {Norfolk, VA, United States},
Year = {2003},
Month = {January},
ISBN = {9781624101007},
url = {http://dx.doi.org/10.2514/6.2003-1429},
Keywords = {Aerodynamics;Oscillations;Mathematical models;Frequency
domain analysis;Degrees of freedom (mechanics);Wind
tunnels;Computational fluid dynamics;Natural
frequencies;Flutter (aerodynamics);},
Abstract = {Presented is an investigation into the modeling of limit
cycle oscillation (LCO) behavior of an experimental
transonic airfoil aeroelastic configuration using a
frequency-domain harmonic-balance (HB) computational fluid
dynamic (CFD) approach. The aeroelastic model has a single
structural degree-of-freedom in pitch. Wind-tunnel wall
interference effects are included in the CFD model. A
wind-tunnel resonance is observed near the flutter onset and
LCO conditions.},
Doi = {10.2514/6.2003-1429},
Key = {03357613841}
}
@article{fds350825,
Author = {Thomas, JP and Hall, KC and Dowell, EH},
Title = {A harmonic balance approach for modeling nonlinear
aeroelastic behavior of wings in transonic viscous
flow},
Journal = {44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics,
and Materials Conference},
Year = {2003},
Month = {January},
ISBN = {9781624101007},
url = {http://dx.doi.org/10.2514/6.2003-1924},
Abstract = {Presented is a frequency-domain harmonic-balance (HB)
computational fluid dynamic (CFD) approach for modeling
flutter onset and limit cycle oscillation (LCO) behavior of
viscous transonic aeroelastic wing configurations. The AGARD
445.6 transonic wing configuration is studied and results
are compared to a recent inviscid analysis for a supersonic
Mach number flow condition. © 2003 by Jeffrey P. Thomas,
Kenneth C. Hall, and Earl H. Dowell. Published by the
American Institute of Aeronautics and Astronautics,
Inc.},
Doi = {10.2514/6.2003-1924},
Key = {fds350825}
}
@article{fds349955,
Author = {Thomas, JP and Hall, KC and Dowell, EH},
Title = {A discrete adjoint approach for modeling unsteady
aerodynamic design sensitivities},
Journal = {41st Aerospace Sciences Meeting and Exhibit},
Year = {2003},
Month = {January},
ISBN = {9781624100994},
url = {http://dx.doi.org/10.2514/6.2003-41},
Abstract = {Presented is a discrete adjoint approach for computing
steady and unsteady aerodynamic design sensitivities for
compressible viscous flows about airfoil configurations. The
nominal flow solver method is based on a harmonic balance
solution technique, which is capable of modeling both steady
and nonlinear periodic unsteady flows. The computer code for
the discrete adjoint solver, which is derived from the
nominal harmonic balance solver, has been generated with the
aid of the advanced automatic differentiation software tool
known as TAF (Transformation of Algorithms in Fortran). ©
2003 by Jeffrey P. Thomas, Kenneth C. Hall, and Earl H.
Dowell.},
Doi = {10.2514/6.2003-41},
Key = {fds349955}
}
@article{04027807172,
Author = {Kielb Robert and E and Thomas Jeffrey and P and Barter John and W and Hall
Kenneth, C},
Title = {Blade excitation by aerodynamic instabilities - A compressor
blade study},
Journal = {American Society of Mechanical Engineers, International Gas
Turbine Institute, Turbo Expo (Publication)
Igti},
Volume = {4},
Pages = {399-406},
Publisher = {ASME},
Address = {Atlanta, GA, United States},
Year = {2003},
ISBN = {0791836878},
url = {http://dx.doi.org/10.1115/GT2003-38634},
Keywords = {Turbomachine blades;Vibrations (mechanical);Computational
fluid dynamics;Unsteady flow;Rotors;Reynolds
number;Entropy;Navier Stokes equations;Computational
methods;},
Abstract = {In this paper, we investigate non-synchronous vibrations
(NSV) in turbomachinery, an aeromechanic phenomenon in which
rotor blades are driven by a fluid dynamic instability.
Unlike flutter, a self-excited vibration in which vibrating
rotor blades and the resulting unsteady aerodynamic forces
are mutually reinforcing, NSV is primarily a fluid dynamic
instability that can cause large amplitude vibrations if the
natural frequency of the instability is near the natural
frequency of the rotor blade. In this paper, we present both
experimental and computational data. Experimental data was
obtained from a full size compressor rig where the
instrumentation consisted of blade-mounted strain gages and
case-mounted unsteady pressure transducers. The
computational simulation used a three-dimensional Reynolds
averaged Navier-Stokes (RANS) time accurate flow solver. The
computational results suggest that the primary flow features
of NSV are a coupled suction side vortex shedding and a tip
flow instability. The simulation predicts a fluid dynamic
instability frequency that is in reasonable agreement with
the experimentally measured value.},
Doi = {10.1115/GT2003-38634},
Key = {04027807172}
}
@article{03187459095,
Author = {Kholodar Denis and B and Thomas Jeffrey and P and Dowell Earl and H and Hall
Kenneth, C},
Title = {Parametric study of flutter for an airfoil in inviscid
transonic flow},
Journal = {Journal of Aircraft},
Volume = {40},
Number = {2},
Pages = {303-313},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2003},
url = {http://dx.doi.org/10.2514/2.3094},
Keywords = {Transonic aerodynamics;Airfoils;Computational fluid
dynamics;Harmonic analysis;Degrees of freedom
(mechanics);},
Abstract = {A parametric study of flutter was conducted for an airfoil
in inviscid transonic flow. An inviscid computational flow
dynamic harmonic balance aerodynamic-Euler-based code was
used for the investigation. The computational efficiency of
the time-linearized option of the harmonic balance
aerodynamic model allows a much more thorough exploration of
the parameter range than was previously achieved.},
Doi = {10.2514/2.3094},
Key = {03187459095}
}
@article{03287539711,
Author = {Thomas Jeffrey and P and Dowell Earl and H and Hall Kenneth,
C},
Title = {Three-dimensional transonic aeroelasticity using proper
orthogonal decomposition-based reduced-order
models},
Journal = {Journal of Aircraft},
Volume = {40},
Number = {3},
Pages = {544-551},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2003},
url = {http://dx.doi.org/10.2514/2.3128},
Keywords = {Mathematical models;Three dimensional;Unsteady
flow;Frequency domain analysis;Vectors;Calculations;Matrix
algebra;Computational fluid dynamics;Laplace
transforms;Natural frequencies;},
Abstract = {The proper orthogonal decomposition (POD-) based
reduced-order modeling technique for modeling unsteady
frequency-domain aerodynamics is developed for a large-scale
computational model of an inviscid flow transonic wing
configuration. When the methodology is used, it is shown
that a computational fluid dynamic model with over
three-quarters of a million degrees of freedom can be
reduced to a system with just a few dozen degrees of
freedom, while still retaining the accuracy of the unsteady
aerodynamics of the full system representation. Furthermore,
POD vectors generated from unsteady flow solution snapshots
based on one set of structural mode shapes can be used for
different structural mode shapes so long as solution
snapshots at the endpoints of the frequency range of
interest are included in the overall snapshot ensemble.
Thus, the snapshot computation aspect of the method, which
is the most computationally expensive part of the procedure,
does not have to be fully repeated as different structural
configurations are considered.},
Doi = {10.2514/2.3128},
Key = {03287539711}
}
@article{fds281250,
Author = {Hall, KC and Hall, SR},
Title = {A rational engineering analysis of the efficiency of
flapping flight},
Journal = {Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle
Applications},
Volume = {195},
Pages = {249-274},
Publisher = {AMER INST AERONAUTICS & ASTRONAUTICS},
Editor = {Mueller, TJ},
Year = {2002},
Month = {January},
ISBN = {1-56347-517-0},
ISSN = {0079-6050},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000173139900013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Key = {fds281250}
}
@article{02277001459,
Author = {Kholodar, DB and Thomas, JP and Dowell, EH and Hall,
KC},
Title = {A parameter study of transonic airfoil flutter and limit
cycle oscillation behavior},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {1},
Pages = {64-79},
Address = {Denver, CO},
Year = {2002},
Month = {January},
Keywords = {Transonic flow;Flutter (aerodynamics);Oscillations;Computational
fluid dynamics;Degrees of freedom (mechanics);},
Abstract = {A parameter study of transonic airfoil flutter and limit
cycle oscillation (LCO) behavior was presented. The effect
of structural parameters and freestream Mach number of a
transonic flow on the flutter and LCO was found out using
inviscid computational fluid dynamics (CFD) harmonic balance
(HB) flow solver. The analysis showed that the computational
efficiency of the harmonic balance aerodynamic model allows
a thorough exploration of the parameter range.},
Key = {02277001459}
}
@article{02277001608,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Modeling viscous transonic limit cycle oscillation behavior
using a harmonic balance approach},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {3},
Pages = {1658-1666},
Address = {Denver, CO},
Year = {2002},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2002-1414},
Keywords = {Oscillations;Airfoils;Viscous flow;Computational fluid
dynamics;Harmonic analysis;Computer simulation;},
Abstract = {Presented is a harmonic-balance (HB) computational fluid
dynamic (CFD) approach for modeling limit cycle oscillation
(LCO) behavior of aeroelastic airfoil configurations in a
viscous transonic flow. For the NLM 7301 airfoil
configuration studied, accounting for viscous effects is
shown to significantly influence computed LCO trends when
compared to an inviscid analysis. Methodology for accounting
for changes in mean angle-of-attack during LCO is also
developed.},
Doi = {10.2514/6.2002-1414},
Key = {02277001608}
}
@article{fds319909,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {A harmonic balance approach for modeling three-dimensional
nonlinear unsteady aerodynamics and aeroelasticity},
Journal = {Asme International Mechanical Engineering Congress and
Exposition, Proceedings},
Volume = {253},
Number = {2},
Pages = {1323-1334},
Year = {2002},
Month = {January},
ISBN = {0791836592},
url = {http://dx.doi.org/10.1115/IMECE2002-32532},
Abstract = {Presented is a frequency domain harmonic balance (HB)
technique for modeling nonlinear unsteady aerodynamics of
three-dimensional transonic inviscid flows about wing
configurations. The method can be used to model efficiently
nonlinear unsteady aerodynamic forces due to finite
amplitude motions of a prescribed unsteady oscillation
frequency. When combined with a suitable structural model,
aeroelastic (fluid-structure), analyses may be performed at
a greatly reduced cost relative to time marching methods to
determine the limit cycle oscillations (LCO) that may arise.
As a demonstration of the method, nonlinear unsteady
aerodynamic response and limit cycle oscillation trends are
presented for the AGARD 445.6 wing configuration.
Computational results based on the inviscid flow model
indicate that the AGARD 445.6 wing configuration exhibits
only mildly nonlinear unsteady aerodynamic effects for
relatively large amplitude motions. Furthermore, and most
likely a consequence of the observed mild nonlinear
aerodynamic behavior, the aeroelastic limit cycle
oscillation amplitude is predicted to increase rapidly for
reduced velocities beyond the flutter boundary. This is
consistent with results from other time-domain calculations.
Although not a configuration that exhibits strong LCO
characteristics, the AGARD 445.6 wing nonetheless serves as
an excellent example for demonstrating the HB/LCO solution
procedure. Copyright © 2002 by ASME.},
Doi = {10.1115/IMECE2002-32532},
Key = {fds319909}
}
@article{7315206,
Author = {Hall Kenneth and C and Thomas Jeffrey and P and Clark,
WS},
Title = {Computation of unsteady nonlinear flows in cascades using a
harmonic balance technique},
Journal = {Aiaa Journal},
Volume = {40},
Number = {5},
Pages = {879-886},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2002},
url = {http://dx.doi.org/10.2514/2.1754},
Keywords = {computational fluid dynamics;flow instability;Fourier
series;Navier-Stokes equations;transonic
flow;},
Abstract = {A harmonic balance technique for modeling unsteady nonlinear
flows in turbomachinery is presented. The analysis exploits
the fact that many unsteady flows of interest in
turbomachinery are periodic in time. Thus, the unsteady flow
conservation variables may be represented by a Fourier
series in time with spatially varying coefficients. This
assumption leads to a harmonic balance form of the Euler or
Navier-Stokes equations, which, in turn, can be solved
efficiently as a steady problem using conventional
computational fluid dynamic (CFD) methods, including
pseudotime time marching with local time stepping and
multigrid acceleration. Thus, the method is computationally
efficient, at least one to two orders of magnitude faster
than conventional nonlinear time-domain CFD simulations.
Computational results for unsteady, transonic, viscous flow
in the front stage rotor of a high-pressure compressor
demonstrate that even strongly nonlinear flows can be
modeled to engineering accuracy with a small number of terms
retained in the Fourier series representation of the flow.
Furthermore, in some cases, fluid nonlinearities are found
to be important for surprisingly small blade
vibrations.},
Doi = {10.2514/2.1754},
Key = {7315206}
}
@article{7275569,
Author = {Thomas Jeffrey and P and Dowell Earl and H and Hall Kenneth,
C},
Title = {Nonlinear inviscid aerodynamic effects on transonic
divergence, flutter, and limit-cycle oscillations},
Journal = {Aiaa Journal},
Volume = {40},
Number = {4},
Pages = {638-646},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2002},
url = {http://dx.doi.org/10.2514/2.1720},
Keywords = {aerodynamics;computational fluid dynamics;fluid
oscillations;transonic flow;},
Abstract = {By the use of a state-of-the-art computational fluid dynamic
(CFD) method to model nonlinear steady and unsteady
transonic flows in conjunction with a linear structural
model, an investigation is made into how nonlinear
aerodynamics can effect the divergence, flutter, and
limit-cycle oscillation (LCO) characteristics of a transonic
airfoil configuration. A single-degree-of-freedom (DOF)
model is studied for divergence, and one- and two-DOF models
are studied for flutter and LCO. A harmonic balance method
in conjunction with the CFD solver is used to determine the
aerodynamics for finite amplitude unsteady excitations of a
prescribed frequency. A procedure for determining the LCO
solution is also presented. For the configuration
investigated, nonlinear aerodynamic effects are found to
produce a favorable transonic divergence trend and unstable
and stable LCO solutions, respectively, for the one- and
two-DOF flutter models.},
Doi = {10.2514/2.1720},
Key = {7275569}
}
@article{7580700,
Author = {Epureanu, BI and Dowell, EH and Hall, KC},
Title = {Mach number influence on reduced-order models of inviscid
potential flows in turbomachinery},
Journal = {Trans. Asme, J. Fluids Eng. (Usa)},
Volume = {124},
Number = {4},
Pages = {977-987},
Publisher = {ASME International},
Year = {2002},
ISSN = {0098-2202},
url = {http://dx.doi.org/10.1115/1.1511165},
Keywords = {aerodynamics;flow instability;fluid oscillations;subsonic
flow;transonic flow;},
Abstract = {An unsteady inviscid flow through a cascade of oscillating
airfoils is investigated. An inviscid nonlinear subsonic and
transonic model is used to compute the steady flow solution.
Then a small amplitude motion of the airfoils about their
steady flow configuration is considered. The unsteady flow
is linearized about the nonlinear steady response based on
the observation that in many practical cases the
unsteadiness in the flow has a substantially smaller
magnitude than the steady component. Several reduced-order
modal models are constructed in the frequency domain using
the proper orthogonal decomposition technique. The
dependency of the required number of aerodynamic modes in a
reduced-order model on the far-field upstream Mach number is
investigated. It is shown that the transonic reduced-order
models require a larger number of modes than the subsonic
models for a similar geometry, range of reduced frequencies
and interblade phase angles. The increased number of modes
may be due to the increased Mach number per se, or the
presence of the strong spatial gradients in the region of
the shock. These two possible causes are investigated. Also,
the geometry of the cascade is shown to influence strongly
the shape of the aerodynamic modes, but only weakly the
required dimension of the reduced-order models},
Doi = {10.1115/1.1511165},
Key = {7580700}
}
@article{fds281220,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {A static/dynamic correction approach for reduced-order
modeling of unsteady aerodynamics},
Journal = {39th Aerospace Sciences Meeting and Exhibit},
Year = {2001},
Month = {December},
Abstract = {Presented is a newly devised static/dynamic correction
approach for eigenvector expansion based reduced-order
modeling (ROM). When compared to the fundamental Ritz ROM
formulation, along with the static and multiple static
correction ROM approaches, the technique is demonstrated to
have much better performance in modeling unsteady linearized
frequency domain aerodynamics in regions of complex
frequency plane near the imaginary axis and up to a
prescribed frequency of interest. As with the static and
multiple static correction approaches, the method requires a
directly computed solution at zero frequency. The method
then requires one additional direct solution to be computed
at some non-zero frequency, which typically is the maximum
frequency of interest. When compared to the multiple static
corrections method, the method circumvents the necessity of
having to determine each of the multiple static corrections,
which require a solution to an alternate set equations that
must be formulated and which may be costly to solve for
large systems. We also consider the feasibility of using a
proper orthogonal decomposition (POD) to determine
approximations for the least damped fluid dynamic
eigenvectors. We demonstrate that in certain situations,
these approximate eigenvectors can be used in conjunction
with the static/dynamic correction ROM approach to achieve
an improvement in performance over the recently devised
POD/ROM method where the POD shapes alone are used as ROM
shape vectors. Finally, we illustrate how the method can be
coupled with a structural model, and compute the Mach number
flutter speed trend for a large CFD model of a
three-dimensional transonic wing configuration. © 2001 by
Jeffrey P. Thomas, Earl H. Dowell, and Kenneth C. Hall.
Published by the American Institute of Aeronautics and
Astronautics, Inc.},
Key = {fds281220}
}
@article{fds340718,
Author = {Dowell, EH and Thomas, JP and Hall, KC},
Title = {Transonic limit cycle oscillation analysis using reduced
order aerodynamic models},
Journal = {19th Aiaa Applied Aerodynamics Conference},
Year = {2001},
Month = {December},
Abstract = {Limit cycle oscillations have been observed in flight
operations of modern aircraft, wind tunnel experiments and
mathematical models. Both fluid and structural
nonlinearities are thought to contribute to these phenomena.
With recent advances in reduced order aerodynamic modeling,
it is now feasible to analyze limit cycle oscillations that
may occur in transonic flow including the effects of
structural and fluid nonlinearities. In this paper an
airfoil with control surface freeplay (a common structural
nonlinearity) is used to investigate transonic flutter and
limit cycle oscillations. The reduced order aerodynamic
model used in this paper assumes the shock motion is small
and in proportion to the structural motions. © 2001 by Earl
H. Dowell, Jeffrey P. Thomas, and Kenneth C.
Hall.},
Key = {fds340718}
}
@article{fds340719,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Three-Dimensional transonic Aeroelasticity using proper
orthogonal decomposition based reduced order
models},
Journal = {19th Aiaa Applied Aerodynamics Conference},
Year = {2001},
Month = {December},
Abstract = {The proper orthogonal decomposition (POD) based reduced
order modeling (ROM) technique for modeling unsteady
frequency domain aerodynamics is developed for a large scale
computational model of an inviscid flow transonic wing
configuration. Using the methodology, it is shown that a
computational fluid dynamic (CFD) model with over a three
quarters of a million degrees of freedom can be reduced to a
system with just a few dozen degrees of freedom, while still
retaining the accuracy of the unsteady aerodynamics of the
full system representation. Furthermore, POD vectors
generated from unsteady flow solution snapshots based on one
set of structural mode shapes can be used for different
structural mode shapes so long as solution snapshots at the
endpoints of the frequency range of interest are included in
the overall snapshot ensemble. Thus, the snapshot
computation aspect of the method, which is the most
computationally expensive part of the procedure, does not
have to be fully repeated as different structural
configurations are considered. © 2001 by Jeffrey P. Thomas,
Earl H. Dowell, and Kenneth C. Hall.},
Key = {fds340719}
}
@article{fds340720,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Nonlinear inviscid aerodynamic effects on transonic
divergence, flutter and limit cycle oscillations},
Journal = {19th Aiaa Applied Aerodynamics Conference},
Year = {2001},
Month = {December},
Abstract = {Using a state of the art computational fluid dynamic (CFD)
method to model nonlinear steady and unsteady transonic
flows in conjunction with a linear structural model, an
investigation is made into how nonlinear aerodynamics can
effect the divergence, flutter, and limit cycle oscillation
(LCO) characteristics of a transonic airfoil configuration.
A single degree of freedom (DOF) model is studied for
divergence, and one and two DOF models are studied for
flutter and LCO. A harmonic balance method in conjunction
with the CFD solver is used to determine the aerodynamics
for finite amplitude unsteady excitations of a prescribed
frequency. A procedure for determining the LCO solution is
also presented. For the configuration investigated,
nonlinear aerodynamic effects are found to produce a
favorable transonic divergence trend, and unstable and
stable LCO solutions respectively for the one and two DOF
flutter models. © 2001 by Jeffrey.},
Key = {fds340720}
}
@article{fds281217,
Author = {Epureanu, BI and Dowell, EH and Hall, KC},
Title = {A parametric analysis of reduced order models of potential
flows in turbomachinery using proper orthogonal
decomposition},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {1},
Publisher = {ASME},
Year = {2001},
Month = {January},
ISBN = {9780791878507},
url = {http://dx.doi.org/10.1115/2001-GT-0434},
Abstract = {An unsteady inviscid flow through a cascade of oscillating
airfoils is investigated. An inviscid nonlinear subsonic and
transonic model is used to compute the steady flow solution.
Then a small amplitude motion of the airfoils about their
steady flow configuration is considered. The unsteady flow
is linearized about the nonlinear steady response based on
the observation that in many practical cases the
unsteadiness in the flow has a substantially smaller
magnitude than the steady component. Several reduced order
modal models are constructed in the frequency domain using
the proper orthogonal decomposition technique. The
dependency of the required number of aerodynamic modes in a
reduced order model on the far-field upstream Mach number is
investigated. It is shown that the transonic reduced order
models require a larger number of modes than the subsonic
models for a similar geometry, range of reduced frequencies
and interblade phase angles. The increased number of modes
may be due to the increased Mach number per se, or the
presence of the strong spatial gradients in the region of
the shock. These two possible causes are investigated. Also,
the geometry of the cascade is shown to influence strongly
the shape of the aerodynamic modes, but only weakly the
required dimension of the reduced order models. Copyright ©
2001 by ASME.},
Doi = {10.1115/2001-GT-0434},
Key = {fds281217}
}
@article{01276568013,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Nonlinear inviscid aerodynamic effects on transonic
divergence, flutter and limit cycle oscillations},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {1},
Pages = {230-241},
Address = {Seattle, WA},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2001-1209},
Keywords = {Aerodynamics;Transonic flow;Flutter (aerodynamics);Oscillations;Computational
fluid dynamics;Mathematical models;Degrees of freedom
(mechanics);},
Abstract = {Using a state of the art computational fluid dynamic (CFD)
method to model nonlinear steady and unsteady transonic
flows in conjunction with a linear structural model, an
investigation is made into how nonlinear aerodynamics can
effect the divergence, flutter, and limit cycle oscillation
(LCO) characteristics of a transonic airfoil configuration.
A single degree of freedom (DOF) model is studied for
divergence, and one and two DOF models are studied for
flutter and LCO. A harmonic balance method in conjunction
with the CFD solver is used to determine the aerodynamics
for finite amplitude unsteady excitations of a prescribed
frequency. A procedure for determining the LCO solution is
also presented. For the configuration investigated,
nonlinear aerodynamic effects are found to produce a
favorable transonic divergence trend, and unstable and
stable LCO solutions respectively for the one and two DOF
flutter models.},
Doi = {10.2514/6.2001-1209},
Key = {01276568013}
}
@article{fds350826,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {A static/dynamic correction approach for reduced-order
modeling of unsteady aerodynamics},
Journal = {39th Aerospace Sciences Meeting and Exhibit},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2001-855},
Abstract = {Presented is a newly devised static/dynamic correction
approach for eigenvector expansion based reduced-order
modeling (ROM). When compared to the fundamental Ritz ROM
formulation, along with the static and multiple static
correction ROM approaches, the technique is demonstrated to
have much better performance in modeling unsteady linearized
frequency domain aerodynamics in regions of complex
frequency plane near the imaginary axis and up to a
prescribed frequency of interest. As with the static and
multiple static correction approaches, the method requires a
directly computed solution at zero frequency. The method
then requires one additional direct solution to be computed
at some non-zero frequency, which typically is the maximum
frequency of interest. When compared to the multiple static
corrections method, the method circumvents the necessity of
having to determine each of the multiple static corrections,
which require a solution to an alternate set equations that
must be formulated and which may be costly to solve for
large systems. We also consider the feasibility of using a
proper orthogonal decomposition (POD) to determine
approximations for the least damped fluid dynamic
eigenvectors. We demonstrate that in certain situations,
these approximate eigenvectors can be used in conjunction
with the static/dynamic correction ROM approach to achieve
an improvement in performance over the recently devised
POD/ROM method where the POD shapes alone are used as ROM
shape vectors. Finally, we illustrate how the method can be
coupled with a structural model, and compute the Mach number
flutter speed trend for a large CFD model of a
three-dimensional transonic wing configuration. © 2001 by
Jeffrey P. Thomas, Earl H. Dowell, and Kenneth C. Hall.
Published by the American Institute of Aeronautics and
Astronautics, Inc.},
Doi = {10.2514/6.2001-855},
Key = {fds350826}
}
@article{fds281287,
Author = {Epureanu, BI and Hall, KC and Dowell, EH},
Title = {Reduced-order models of unsteady viscous flows in
turbomachinery using viscous-inviscid coupling},
Journal = {Journal of Fluids and Structures},
Volume = {15},
Number = {2},
Pages = {255-273},
Publisher = {Elsevier BV},
Year = {2001},
Month = {January},
ISSN = {0889-9746},
url = {http://dx.doi.org/10.1006/jfls.2000.0334},
Abstract = {The proper orthogonal decomposition technique is applied in
the frequency domain to obtain a reduced-order model of the
flow in a turbomachinery cascade. The flow is described by
an inviscid-viscous interaction model where the inviscid
part is described by the full potential equation and the
viscous part is described by an integral boundary layer
model. The fully nonlinear steady flow is computed and the
unsteady flow is linearized about the steady solution. A
frequency-domain model is constructed and validated, showing
to provide similar results when compared with previous
computational and experimental data presented in the
literature. The full model is used to obtain a reduced-order
model in the frequency domain. A cascade of airfoils forming
a slightly modified Tenth Standard Configuration is
investigated to show that the reduced-order model with only
25 degrees of freedom accurately predicts the unsteady
response of the full system with approximately 10 000
degrees of freedom. © 2001 Academic Press.},
Doi = {10.1006/jfls.2000.0334},
Key = {fds281287}
}
@article{01276568015,
Author = {Dowell, EH and Thomas, JP and Hall, KC},
Title = {Transonic limit cycle oscillation analysis using reduced
order aerodynamic models},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {1},
Pages = {255-263},
Address = {Seattle, WA},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2001-1212},
Keywords = {Aerodynamics;Transonic flow;Oscillations;Flutter
(aerodynamics);Mathematical models;Computational fluid
dynamics;},
Abstract = {Limit cycle oscillations have been observed in flight
operations of modern aircraft, wind tunnel experiments and
mathematical models. Both fluid and structural
nonlinearities are thought to contribute to these phenomena.
With recent advances in reduced order aerodynamic modeling,
it is now feasible to analyze limit cycle oscillations that
may occur in transonic flow including the effects of
structural and fluid nonlinearities. In this paper an
airfoil with control surface freeplay (a common structural
nonlinearity) is used to investigate transonic flutter and
limit cycle oscillations. The reduced order aerodynamic
model used in this paper assumes the shock motion is small
and in proportion to the structural motions.},
Doi = {10.2514/6.2001-1212},
Key = {01276568015}
}
@article{01276563617,
Author = {Thomas, JP and Dowell, EH and Hall, KC},
Title = {Three-dimensional transonic aeroelasticity using proper
orthogonal decomposition based reduced order
models},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {4},
Pages = {2555-2564},
Address = {Seattle, WA},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2001-1526},
Keywords = {Mathematical models;Frequency domain analysis;Wings;Transonic
flow;Computational fluid dynamics;Degrees of freedom
(mechanics);Vectors;Structural analysis;Three
dimensional;},
Abstract = {The proper orthogonal decomposition (POD) based reduced
order modeling (ROM) technique for modeling unsteady
frequency domain aerodynamics is developed for a large scale
computational model of an inviscid flow transonic wing
configuration. Using the methodology, it is shown that a
computational fluid dynamic (CFD) model with over a three
quarters of a million degrees of freedom can be reduced to a
system with just a few dozen degrees of freedom, while still
retaining the accuracy of the unsteady aerodynamics of the
full system representation. Furthermore, POD vectors
generated from unsteady flow solution snapshots based on one
set of structural mode shapes can be used for different
structural mode shapes so long as solution snapshots at the
endpoints of the frequency range of interest are included in
the overall snapshot ensemble. Thus, the snapshot
computation aspect of the method, which is the most
computationally expensive part of the procedure, does not
have to be fully repeated as different structural
configurations are considered.},
Doi = {10.2514/6.2001-1526},
Key = {01276563617}
}
@article{fds341419,
Author = {Florea, R and Hall, KC},
Title = {Sensitivity analysis of unsteady inviscid flow through
turbomachinery cascades},
Journal = {Aiaa Journal},
Volume = {39},
Number = {6},
Pages = {1047-1056},
Year = {2001},
Month = {January},
url = {http://dx.doi.org/10.2514/2.1445},
Abstract = {We present a novel sensitivity analysis for predicting the
effect of airfoil shape on the unsteady aerodynamic and
aeroacoustic response of turbomachinery blading. The nominal
steady and unsteady flow in a cascade of turbomachinery
blades is modeled using the steady Euler equations and the
time-linearized Euler equations, respectively. Both the
steady and unsteady Euler equations are solved using a
two-step finite-volume Lax-Wendroff discretization with
multigrid acceleration. We compute the unsteady aerodynamic
loads due to both incoming gusts and plunging motion of the
cascade airfoils. Once the nominal steady and unsteady flows
have been computed, a sensitivity analysis is performed
using the discrete adjoint equations of the computational
fluid dynamics scheme used to discretize the Euler
equations. For each objective function (e.g., the amplitude
peak of the aeroelastic blade motion), the resulting adjoint
equations are solved using the adjoint Lax-Wendroff scheme,
which is also accelerated using a multigrid technique. Once
the adjoint equations have been solved, the computed adjoint
variables may be used to compute rapidly the sensitivities
of the aeroelastic and aeroacoustic objective functions due
to arbitrary changes in geometry. The method is
computationally efficient, with similar convergence rate
histories for both the nominal and the adjoint solutions. To
demonstrate the utility of the present method, we use the
sensitivity analysis to redesign the shape of the airfoils
of a cascade for increased aeroelastic stability. We also
redesign the shape of the airfoils of an exit guide vane for
reduced downstream radiated noise.},
Doi = {10.2514/2.1445},
Key = {fds341419}
}
@article{01316601502,
Author = {Dowell, EH and Hall, KC},
Title = {Modeling of fluid-structure interaction},
Journal = {Annual Review of Fluid Mechanics},
Volume = {33},
Number = {1},
Pages = {445-490},
Publisher = {ANNUAL REVIEWS},
Year = {2001},
ISSN = {0066-4189},
url = {http://dx.doi.org/10.1146/annurev.fluid.33.1.445},
Keywords = {Time domain analysis;Frequency domain analysis;Aerodynamics;},
Abstract = {The interaction of a flexible structure with a flowing fluid
in which it is submersed or by which it is surrounded gives
rise to a rich variety of physical phenomena with
applications in many fields of engineering, for example, the
stability and response of aircraft wings, the flow of blood
through arteries, the response of bridges and tall buildings
to winds, the vibration of turbine and compressor blades,
and the oscillation of heat exchangers. To understand these
phenomena we need to model both the structure and the fluid.
However, in keeping with the overall theme of this volume,
the emphasis here is on the fluid models. Also, the
applications are largely drawn from aerospace engineering
although the methods and fundamental physical phenomena have
much wider applications. In the present article, we
emphasize recent developments and future challenges. To
provide a context for these, the article begins with a
description of the various physical models for a fluid
undergoing time-dependent motion, then moves to a discussion
of the distinction between linear and nonlinear models,
time-linearized models and their solution in either the time
or frequency domains, and various methods for treating
nonlinear models, including time marching, harmonic balance,
and systems identification. We conclude with an extended
treatment of the modal character of time-dependent flows and
the construction of reduced-order models based on an
expansion in terms of fluid modes. The emphasis is on the
enhanced physical understanding and dramatic reductions in
computational cost made possible by reduced-order models,
time linearization, and methodologies drawn from dynamical
system theory.},
Doi = {10.1146/annurev.fluid.33.1.445},
Key = {01316601502}
}
@article{01316602622,
Author = {Florea, R and Hall, KC},
Title = {Sensitivity analysis of unsteady inviscid flow through
turbomachinery cascades},
Journal = {38th Aerospace Sciences Meeting and Exhibit},
Volume = {39},
Number = {6},
Pages = {1047-1056},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2000},
Month = {December},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/2.1445},
Keywords = {Aerodynamics;Airfoils;Sensitivity analysis;Unsteady
flow;Steady flow;Cascades (fluid mechanics);Mathematical
models;Differential equations;Acceleration;Aerodynamic
loads;Computational fluid dynamics;},
Abstract = {In this paper, we present a novel sensitivity analysis for
predicting the effect of airfoil shape on the unsteady
aerodynamic and aeroacoustic response of turbomachinery
blading. The nominal steady and unsteady flow in a cascade
of turbomachinery blades is modeled using the steady Euler
cquations and the time-linearized Euler equations,
respectively. Both the steady and unsteady Euler equations
are solved using a two-step finite-volume Lax-Wendroff
discretization with multigrid acceleration. We compute the
unsteady aerodynamic loads due to both incoming gusts and
plunging motion of the cascade airfoils. Once the nominal
steady and unsteady flows have been computed, a sensitivity
analysis is performed using the discrete adjoint equations
of the computational fluid dynamics scheme used to
discretize the Euler equations. For each objective function
(e.g. the amplitude peak of the aeroelastic blade motion),
the resulting adjoint equations arc solved using the adjoint
Lax-Wendroff scheme, which is also accelcrated using a
multigrid technique. Once the adjoint equations have been
solved, the computed adjoint variables may bc used to
compute rapidly the sensitivities of the aeroelastic and
acroacoustic objective functions to arbitrary changes in
geometry. The method is computationally efficient, with
similar convergence rate histories for both the nominal and
the adjoint solutions. To demonstrate the utility of the
present method, we use the sensitivity analysis to redesign
the shape of the airfoils of a cascade for increased
acroelastic stability. We also redesign the shape of the
airfoils of an exit guide vane for reduced downstream
radiated noise. © 1999 by Rnzvan Florca and Kenneth C.
Hall.},
Doi = {10.2514/2.1445},
Key = {01316602622}
}
@article{fds350827,
Author = {Florea, R and Hall, KC},
Title = {Sensitivity analysis of unsteady inviscid flow through
turbomachinery cascades},
Journal = {38th Aerospace Sciences Meeting and Exhibit},
Year = {2000},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2000-130},
Abstract = {In this paper, we present a novel sensitivity analysis for
predicting the effect of airfoil shape on the unsteady
aerodynamic and aeroacoustic response of turbomachinery
blading. The nominal steady and unsteady flow in a cascade
of turbomachinery blades is modeled using the steady Euler
cquations and the time-linearized Euler equations,
respectively. Both the steady and unsteady Euler equations
are solved using a two-step finite-volume Lax-Wendroff
discretization with multigrid acceleration. We compute the
unsteady aerodynamic loads due to both incoming gusts and
plunging motion of the cascade airfoils. Once the nominal
steady and unsteady flows have been computed, a sensitivity
analysis is performed using the discrete adjoint equations
of the computational fluid dynamics scheme used to
discretize the Euler equations. For each objective function
(e.g. the amplitude peak of the aeroelastic blade motion),
the resulting adjoint equations arc solved using the adjoint
Lax-Wendroff scheme, which is also accelcrated using a
multigrid technique. Once the adjoint equations have been
solved, the computed adjoint variables may bc used to
compute rapidly the sensitivities of the aeroelastic and
acroacoustic objective functions to arbitrary changes in
geometry. The method is computationally efficient, with
similar convergence rate histories for both the nominal and
the adjoint solutions. To demonstrate the utility of the
present method, we use the sensitivity analysis to redesign
the shape of the airfoils of a cascade for increased
acroelastic stability. We also redesign the shape of the
airfoils of an exit guide vane for reduced downstream
radiated noise. © 1999 by Rnzvan Florca and Kenneth C.
Hall.},
Doi = {10.2514/6.2000-130},
Key = {fds350827}
}
@article{04057930207,
Author = {Epureanu, BI and Dowell, EH and Hall, KC},
Title = {Reduced-order models of unsteady transonic viscous flows in
turbomachinery},
Journal = {Journal of Fluids and Structures},
Volume = {14},
Number = {8},
Pages = {1215-1234},
Publisher = {Elsevier BV},
Year = {2000},
url = {http://dx.doi.org/10.1006/jfls.2000.0320},
Abstract = {The proper orthogonal decomposition (POD) technique is
applied in the frequency domain to obtain a reduced-order
model of the unsteady flow in a transonic turbomachinery
cascade of oscillating blades. The flow is described by a
inviscid - viscous model, i.e. a full potential equation
outer flow model and an integral equation boundary layer
model. The nonlinear transonic steady flow is computed first
and then the unsteady flow is determined by a small
perturbation linearization about the nonlinear steady
solution. Solutions are determined for a full range of
frequencies and validated. The full model results and the
POD method are used to construct a reduced-order model in
the frequency domain. A cascade of airfoils forming the
Tenth Standard Configuration is investigated to show that
the reduced-order model with only 15-75 degrees of freedom
accurately predicts the unsteady response of the full system
with approximately 15 000 degrees of freedom. © 2000
Academic Press.},
Doi = {10.1006/jfls.2000.0320},
Key = {04057930207}
}
@article{6772001,
Author = {Hall Kenneth and C and Thomas Jeffrey and P and Dowell Earl,
H},
Title = {Proper orthogonal decomposition technique for transonic
unsteady aerodynamic flows},
Journal = {Aiaa Journal},
Volume = {38},
Number = {10},
Pages = {1853-1862},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2000},
url = {http://dx.doi.org/10.2514/2.867},
Keywords = {aerodynamics;transonic flow;},
Abstract = {A new method for constructing reduced-order models (ROM) of
unsteady small-disturbance flows is presented. The
reduced-order models are constructed using basis vectors
determined from the proper orthogonal decomposition (POD) of
an ensemble of small-disturbance frequency-domain solutions.
Each of the individual frequency-domain solutions is
computed using an efficient time-linearized flow solver. We
show that reduced-order models can be constructed using just
a handful of POD basis vectors, producing low-order but
highly accurate models of the unsteady flow over a wide
range of frequencies. We apply the POD/ROM technique to
compute the unsteady aerodynamic and aeroelastic behavior of
an isolated transonic airfoil and to a two-dimensional
cascade of airfoils.},
Doi = {10.2514/2.867},
Key = {6772001}
}
@article{00105354798,
Author = {Clark William and S and Hall Kenneth and C},
Title = {Time-linearized Navier-Stokes analysis of stall
flutter},
Journal = {Journal of Turbomachinery, Transactions of the
Asme},
Volume = {122},
Number = {3},
Pages = {467-476},
Publisher = {ASME International},
Year = {2000},
url = {http://dx.doi.org/10.1115/1.1303073},
Keywords = {Navier Stokes equations;Turbomachine blades;Vibrations
(mechanical);Cascades (fluid mechanics);Viscous
flow;Unsteady flow;Mathematical models;Partial differential
equations;Linearization;Finite volume method;Time domain
analysis;},
Abstract = {A computational method for predicting unsteady viscous flow
through two-dimensional cascades accurately and efficiently
is presented. The method is intended to predict the onset of
the aeroelastic phenomenon of stall flutter. In stall
flutter, viscous effects significantly impact the
aeroelastic stability of a cascade. In the present effort,
the unsteady flow is modeled using a time-linearized
Navier-Stokes analysis. Thus, the unsteady flow field is
decomposed into a nonlinear spatially varying mean flow plus
a small-perturbation harmonically varying unsteady flow. The
resulting equations that govern the perturbation flow are
linear, variable coefficient partial differential equations.
These equations are discretized on a deforming, multiblock,
computational mesh and solved using a finite-volume
Lax-Wendroff integration scheme. Numerical modeling issues
relevant to the development of the unsteady aerodynamic
analysis, including turbulence modeling, are discussed.
Results from the present method are compared to experimental
stall flutter data, and to a nonlinear time-domain
Navier-Stokes analysis. The results presented demonstrate
the ability of the present time-linearized analysis to model
accurately the unsteady aerodynamics associated with
turbomachinery stall flutter.},
Doi = {10.1115/1.1303073},
Key = {00105354798}
}
@article{00075231071,
Author = {Florea, R and Hall, KC and Dowell, EH},
Title = {Eigenmode analysis and reduced-order modeling of unsteady
transonic potential flow around airfoils},
Journal = {Journal of Aircraft},
Volume = {37},
Number = {3},
Pages = {454-462},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {2000},
url = {http://dx.doi.org/10.2514/2.2619},
Keywords = {Transonic flow;Unsteady flow;Mathematical models;Eigenvalues
and eigenfunctions;Frequency domain analysis;Modal
analysis;Degrees of freedom (mechanics);Vectors;Flutter
(aerodynamics);Potential flow;Finite element
method;},
Abstract = {An eigenmode analysis and reduced-order models of the
unsteady transonic aerodynamic flow around isolated airfoils
are presented. The unsteady flow is modeled using the
time-linearized frequency-domain unsteady transonic full
potential equation. The full potential was discretized in
space using a finite element method. The resulting equations
are linear in the unknown velocity potential and quadratic
in the reduced frequency of excitation. The dominant
eigenfrequencies and corresponding mode shapes of the
discretized potential model are computed, and the effect of
different parameters that determine the steady and unsteady
flowfield (e.g., the far-field Mach number, the angle of
attack, and the airfoil shape) are investigated. A normal
mode analysis and a static correction technique are then
used to construct a low degree-of-freedom, reduced-order
model of the unsteady flowfield. Depending on the range of
frequencies of interest, a relatively small number of
eigenmodes are required. An alternative reduced-order
modeling technique based on Arnoldi-Ritz vectors is also
presented. For the case where the structural excitations are
known a priori, the latter method is more efficient. Using
the aerodynamic reduced-order models, we construct
aeroelastic reduced-order models and compute flutter
boundaries for different airfoils at several different Mach
numbers.},
Doi = {10.2514/2.2619},
Key = {00075231071}
}
@article{fds281213,
Author = {Clark, WS and Hall, KC},
Title = {A time-linearized Navier-Stokes analysis of stall
flutter},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {4},
Publisher = {ASME},
Year = {1999},
Month = {January},
ISBN = {9780791878613},
url = {http://dx.doi.org/10.1115/99-GT-383},
Abstract = {A computational method for accurately and efficiently
predicting unsteady viscous flow through two-dimensional
cascades is presented. The method is intended to predict the
onset of the aeroelastic phenomenon of stall flutter. In
stall flutter, viscous effects significantly impact the
aeroelastic stability of a cascade. In the present effort,
the unsteady flow is modeled using a time-linearized
Navier-Stokes analysis. Thus, the unsteady flow field is
decomposed into a nonlinear spatially varying mean flow plus
a small-perturbation harmonically varying unsteady flow. The
resulting equations that govern the perturbation flow are
linear, variable coefficient partial differential equations.
These equations are discretized on a deforming, multiblock,
computational mesh and solved using a finite-volume
Lax-Wendroff integration scheme. Numerical modelling issues
relevant to the development of the unsteady aerodynamic
analysis, including turbulence modelling, are discussed.
Results from the present method are compared to experimental
stall flutter data, and to a nonlinear time-domain
Navier-Stoke analysis. The results presented demonstrate the
ability of the present time-linearized analysis to model
accurately the unsteady aerodynamics associated with
turbomachinery stall flutter.},
Doi = {10.1115/99-GT-383},
Key = {fds281213}
}
@article{99094774137,
Author = {Dowell, EH and Hall, KC and Thomas, JP and Florea, R and Epureanu, BI and Heeg, J},
Title = {Reduced order models in unsteady aerodynamics},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {1},
Pages = {622-637},
Address = {St. Louis, MO, USA},
Year = {1999},
Month = {January},
Keywords = {Aerodynamics;Unsteady flow;Eigenvalues and
eigenfunctions;Computational fluid dynamics;Viscosity;Transonic
flow;Shock waves;},
Abstract = {A review is given on the status of reduced order modeling of
unsteady aerodynamic systems. Starting with either a time
domain or frequency domain computational fluid dynamics
(CFD) analysis of unsteady aerodynamic flows, a large,
sparse eigenvalue is solved using the Lanczos algorithm.
Following this, a Reduced Order Model of the unsteady flow
is constructed. As an alternative to the use of eigenmodes,
Proper Orthogonal Decomposition (POD) is also
considered.},
Key = {99094774137}
}
@article{99034611754,
Author = {Tang, D and Dowell, EH and Hall, KC},
Title = {Limit Cycle Oscillations of a Cantilevered Wing in Low
Subsonic Flow},
Journal = {Aiaa Journal},
Volume = {37},
Number = {2-3},
Pages = {364-371},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1999},
Month = {January},
ISSN = {0001-1452},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000078841800010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {Subsonic aerodynamics;Oscillations;Mathematical
models;Plates (structural components);Vortex flow;Aspect
ratio;},
Abstract = {A nonlinear, aeroelaslic analysis of a low-aspect,
rectangular wing modeled as a plate of constant thickness
demonstrates that limit cycle oscillations of the order of
the plate thickness are possible. The structural
nonlinearity arises from double bending in both the
chordwise and spanwise directions. The present results using
a vortex lattice aerodynamic model for low-Mach-number flows
complement earlier studies for high supersonic speed that
showed similar qualitative results. Also, the theoretical
results are consistent with experimental data reported by
other investigators for low-aspect-ratio delta
wings.},
Doi = {10.2514/2.717},
Key = {99034611754}
}
@article{fds319910,
Author = {Hall, KC and Thomas, JP and Dowell, EH},
Title = {Reduced-order modelling of unsteady small-disturbance flows
using a frequency-domain proper orthogonal decomposition
technique},
Journal = {37th Aerospace Sciences Meeting and Exhibit},
Year = {1999},
Month = {January},
url = {http://dx.doi.org/10.2514/6.1999-655},
Abstract = {A new method for constructing reduced-order models (ROM) of
unsteady small-disturbance flows is presented. The
reduced-order models are constructed using basis vectors
determined from the proper orthogonal decomposition (POD) of
an ensemble of small-disturbance frequency-domain solutions.
Each of the individual frequency-domain solutions is
computed using an efficient time-linearized flow solver. We
show that reduced-order models can be constructed using just
a handful of POD basis vectors, producing low-order but
highly accurate models of the unsteady flow over a wide
range of frequencies. In this paper, we apply the POD/ROM
technique to compute the unsteady aerodynamic and
aeroelastic behavior of an isolated transonic airfoil, and
to a two-dimensional cascade of airfoils.},
Doi = {10.2514/6.1999-655},
Key = {fds319910}
}
@article{fds315333,
Author = {Hall, KC and Thomas, JP and Dowell, EH},
Title = {Reduced-order modelling of unsteady small-disturbance flows
using a frequency-domain proper orthogonal decomposition
technique},
Journal = {37th Aerospace Sciences Meeting and Exhibit},
Year = {1999},
Month = {January},
ISBN = {9780000000002},
Abstract = {© 1999 by Kenneth C. Hall, Jeffrey P. Thomas, and Earl H.
Dowell.A new method for constructing reduced-order models
(ROM) of unsteady small-disturbance flows is presented. The
reduced-order models are constructed using basis vectors
determined from the proper orthogonal decomposition (POD) of
an ensemble of small-disturbance frequency-domain solutions.
Each of the individual frequency-domain solutions is
computed using an efficient time-linearized flow solver. We
show that reduced-order models can be constructed using just
a handful of POD basis vectors, producing low-order but
highly accurate models of the unsteady flow over a wide
range of frequencies. In this paper, we apply the POD/ROM
technique to compute the unsteady aerodynamic and
aeroelastic behavior of an isolated transonic airfoil, and
to a two-dimensional cascade of airfoils.},
Key = {fds315333}
}
@article{fds361787,
Author = {Epureanu, BI and Dowell, EH and Hall, KC},
Title = {REDUCED ORDER MODELS OF VISCOUS FLOWS IN TURBOMACHINERY
USING PROPER ORTHOGONAL DECOMPOSITION},
Journal = {Asme International Mechanical Engineering Congress and
Exposition, Proceedings (Imece)},
Volume = {1999-N},
Pages = {205-215},
Year = {1999},
Month = {January},
ISBN = {9780791816615},
url = {http://dx.doi.org/10.1115/imece1999-1232},
Abstract = {The proper orthogonal decomposition technique is applied in
the frequency domain to obtain reduced order models (ROM) of
the flow in a cascade of airfoils. The flow is described by
a inviscid-viscous interaction model where the inviscid part
is described by the full potential equation and the viscous
part is described by an integral boundary layer model. The
fully nonlinear steady flow is computed and the unsteady
flow is linearized about the steady solution. A frequency
domain model is constructed and validated showing to provide
similar results when compared with previous computational
and experimental data presented in the literature. A cascade
of airfoils forming a slightly modified Tenth Standard
Configuration is numerically investigated. We show that the
ROMs with only 10 to 40 degrees of freedom predict
accurately the unsteady response of the full system with
approximately 10,000 degrees of freedom for the subsonic
case. We also show that the ROMs with 15 to 75 degrees of
freedom predict accurately the unsteady response of the full
system with approximately 17, 500 degrees of freedom for the
transonic case. The ROMs are shown to be accurate both for a
broad range of reduced frequencies and a full spectrum of
interblade phase angles.},
Doi = {10.1115/imece1999-1232},
Key = {fds361787}
}
@article{00275178918,
Author = {Epureanu Bogdan and I and Dowell Earl and H and Hall Kenneth,
C},
Title = {Reduced order models of viscous flows in turbomachinery
using proper orthogonal decomposition},
Journal = {American Society of Mechanical Engineers, Fluids Engineering
Division (Publication) Fed},
Volume = {250},
Pages = {205-215},
Address = {Nashville, TN, USA},
Year = {1999},
ISBN = {0791816613},
Keywords = {Turbomachine blades;Computational fluid dynamics;Mathematical
models;Cascades (fluid mechanics);Airfoils;Frequency domain
analysis;Boundary layer flow;Steady flow;Unsteady
flow;Subsonic flow;Transonic flow;Degrees of freedom
(mechanics);},
Abstract = {The proper orthogonal decomposition technique is applied in
the frequency domain to obtain reduced order models (ROM) of
the flow in a cascade of airfoils. The flow is described by
a inviscid-viscous interaction model where the inviscid part
is described by the full potential equation and the viscous
part is described by an integral boundary layer model. The
fully nonlinear steady flow is computed and the unsteady
flow is linearized about the steady solution. A frequency
domain model is constructed and validated showing to provide
similar results when compared with previous computational
and experimental data presented in the literature. A cascade
of airfoils forming a slightly modified Tenth Standard
Configuration is numerically investigated. We show that the
ROMs with only 10 to 40 degrees of freedom predict
accurately the unsteady response of the full system with
approximately 10,000 degrees of freedom for the subsonic
case. We also show that the ROMs with 15 to 75 degrees of
freedom predict accurately the unsteady response of the full
system with approximately 17,500 degrees of freedom for the
transonic case. The ROMs are shown to be accurate both for a
broad range of reduced frequencies and a full spectrum of
interblade phase angles.},
Key = {00275178918}
}
@article{fds281257,
Author = {Florea, R and Hall, KC},
Title = {Eigenmode analysis of unsteady flows about
airfoils},
Journal = {Journal of Computational Physics},
Volume = {147},
Number = {2},
Pages = {568-593},
Publisher = {Elsevier BV},
Year = {1998},
Month = {December},
url = {http://dx.doi.org/10.1006/jcph.1998.6102},
Abstract = {We present a reduced-order modelling technique for analyzing
the unsteady subsonic aerodynamic flow about isolated
airfoils. To start, we model the flow using the
time-linearized full potential equation. The linearized
potential equation is discretized on a computational mesh
composed of quadrilateral elements using a variational
finite element technique. The resulting discretized
equations are linear in the unknown potential, but quadratic
in the reduced frequency of vibration. We compute the
dominant (low frequency) eigenfrequencies and mode shapes of
the unsteady fluid motion using a nonsymmetric Lanczos
algorithm, and then we use these eigenmodes to construct a
low degree-of-freedom reduced-order model of the unsteady
flow field. A static correction technique is used to account
for the high-frequency eigenmodes not retained in the model.
We show that the unsteady flow can be modelled accurately
using a relatively small number of eigenmodes. © 1998
Academic Press.},
Doi = {10.1006/jcph.1998.6102},
Key = {fds281257}
}
@article{fds281248,
Author = {Florea, R and Hall, KC and Cizmas, PGA},
Title = {Eigenmode analysis of unsteady viscous flows in
turbomachinery cascades},
Journal = {Unsteady Aerodynamics and Aeroelasticity of
Turbomachines},
Pages = {767-782},
Publisher = {SPRINGER},
Editor = {Fransson, TH},
Year = {1998},
Month = {January},
ISBN = {0-7923-5040-5},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000080066600050&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Key = {fds281248}
}
@article{fds281256,
Author = {Florea, R and Hall, KC and Cizmas, PGA},
Title = {Reduced-order modeling of unsteady viscous flow in a
compressor cascade},
Journal = {Aiaa Journal},
Volume = {36},
Number = {6},
Pages = {1039-1048},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1998},
Month = {January},
ISSN = {0001-1452},
url = {http://dx.doi.org/10.2514/2.477},
Abstract = {A simultaneously coupled viscous-inviseid interaction (VII)
analysis is used to model the unsteady viscous separated
flow through a subsonic compressor. The inner viscous flow
around the airfoil and in the wake is modeled using a finite
difference discretization of the boundary-layer equations
and a one-equation turbulence transport model. The outer
inviscid flow is modeled using a variational finite element
discretization of the compressible full potential equation.
The viscous and inviscid regions are simultaneously coupled
using a injection type boundary candition along the airfoil
and wake. The resulting nonlinear unsteady equations are
linearized about the noolinear steady flow to obtain a set
of linear equations that discribe the unsteady
small-disturbance behavior of the viscous flow through the
caseade. The discretized small-disturbance VII equations are
used to form a generalized, quadratic, non-Hermitian
eigenvalue problem that describes the eigenmodes (natural
modes) and eigenvalues (natural frequencies) of fluid motion
about the cascade. Using a Lanczos algorithm, the
eigeninformation is computed efficiently for various steady
inflow angles and unsteady interblade phase angles. The
eigenvalues and eigenmodes are then used in conjunction with
a classical mode summation technique to construct
computationally efficient reduced-order models of the
unsteady flow through the cascade. Using just a few
eigenmodes, less than 0.01% of the total number, the
unsteady aerodynamic loads acting on vibrating airfoils (the
aeroelastic stability problem) can be efficiently and
accurately computed over a relatively wide range of reduced
frequencies provided that one or more static corrections are
performed. Finally, eigenvalues the eigenvectors and provide
physical insight into the unsteady aerodynamic behavior of
the cascade. For example, we show the ability of the present
eigenanalysis to predict purely fluid mechanic instabilities
such as rotating stall.},
Doi = {10.2514/2.477},
Key = {fds281256}
}
@article{98064257200,
Author = {Hall Kenneth and C and Pigott Steven and A and Hall Steven,
R},
Title = {Power requirements for large-amplitude flapping
flight},
Journal = {Journal of Aircraft},
Volume = {35},
Number = {3},
Pages = {352-361},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1998},
ISBN = {9780000000002},
ISSN = {0021-8669},
url = {http://dx.doi.org/10.2514/2.2324},
Keywords = {Lift;Flight dynamics;Mathematical models;Approximation
theory;Vortex flow;Variational techniques;Wakes;},
Abstract = {In this paper, a method is presented for computing the
circulation distribution along the span of a flapping wing
that minimizes the power required to generate a prescribed
lift and thrust. The power is composed of three parts:
useful thrust power, induced power, and profile power. Here,
the thrust and induced power are expressed in terms of the
Kelvin impulse and kinetic energy associated with the sheet
of trailing and shed vorticity left behind the flapping
wing. The profile power is computed using a quasisteady
approximation of the two-dimensional viscous drag polar at
each spanwise station of the wing. A variational principle
is then formed to determine the necessary conditions for the
circulation distribution to be optimal. Included in the
variational principle is a constraint that the wing not
stall. This variational principle, which is essentially the
viscous extension of the well-known Betz criterion for
optimal propellers, is discretized using a vortex-lattice
model of the wake, and the optimum solution is computed
numerically. The present method is used to analyze a
conventional propeller as well as a rigid wing in
forward-flight flapping about a hinge point on the
longitudinal axis.},
Doi = {10.2514/2.2324},
Key = {98064257200}
}
@article{98084337056,
Author = {Silkowski, PD and Hall, KC},
Title = {Coupled mode analysis of unsteady multistage flows in
turbomachinery},
Journal = {Journal of Turbomachinery, Transactions of the
Asme},
Volume = {120},
Number = {3},
Pages = {410-421},
Publisher = {ASME International},
Year = {1998},
url = {http://dx.doi.org/10.1115/1.2841732},
Keywords = {Rotors;Turbomachine blades;Machine vibrations;Unsteady
flow;Aerodynamics;Mathematical models;Modal
analysis;Boundary conditions;Equations of
motion;Linearization;},
Abstract = {A computational method is presented for predicting the
unsteady aerodynamic response of a vibrating blade row that
is part of a multistage turbomachine. Most current unsteady
aerodynamic theories model a single blade row isolated in an
infinitely long duct. This assumption neglects the
potentially important influence of neighboring blade rows.
The present `coupled mode' analysis is an elegant and
computationally efficient method for modeling neighboring
blade row effects. Using this approach, the coupling between
blade rows is modeled using a subset of the so-called
spinning modes, i.e., pressure, vorticity, and entropy
waves, which propagate between the blade rows. The blade
rows themselves are represented by reflection and
transmission coefficients. These coefficients describe how
spinning modes interact with, and are scattered by, a given
blade row. The coefficients can be calculated using any
standard isolated blade row model; here we use a linearized
full potential flow model together with rapid distortion
theory to account for incident vortical gusts. The isolated
blade row reflection and transmission coefficients, interrow
coupling relationships, and appropriate boundary conditions
are all assembled into a small sparse linear system of
equations that describes the unsteady multistage flow. A
number of numerical examples are presented to validate the
method and to demonstrate the profound influence of
neighboring blade rows on the aerodynamic damping of a
cascade of vibrating airfoils.},
Doi = {10.1115/1.2841732},
Key = {98084337056}
}
@article{97113935816,
Author = {Silkowski, PD and Hall, KC},
Title = {Coupled mode analysis of unsteady multistage flows in
turbomachinery},
Journal = {American Society of Mechanical Engineers
(Paper)},
Pages = {15 -},
Address = {Orlando, FL, USA},
Year = {1997},
Month = {December},
Keywords = {Computational methods;Modal analysis;Machine
vibrations;Aerodynamics;Mathematical models;Boundary
conditions;Unsteady flow;Damping;Linearization;Airfoils;Ducts;},
Abstract = {A `coupled mode' analysis is useful in predicting the
unsteady aerodynamic response of vibrating multistage
turbomachine blades. Using this approach, the coupling
between the blade rows is modeled using a subset of spinning
modes. The blade rows are represented by reflection and
transmission coefficients which describe how spinning modes
interact with and are scattered by, a given blade row. These
coefficients are calculated using a linearized full
potential flow model together with rapid distortion theory
to account for incident vortical gusts.},
Key = {97113935816}
}
@article{98054181242,
Author = {Dowell, EH and Hall, KC and Romanowski, MC},
Title = {Reduced order aerodynamic modeling of how to make CFD useful
to an aeroelastician},
Journal = {American Society of Mechanical Engineers, Aerospace Division
(Publication) Ad},
Volume = {53-3},
Pages = {149-163},
Address = {Dallas, TX, USA},
Year = {1997},
Month = {December},
Keywords = {Computational fluid dynamics;Mathematical models;Unsteady
flow;Wings;Cascades (fluid mechanics);Turbomachinery;Eigenvalues
and eigenfunctions;Algorithms;},
Abstract = {In this article, we review the status of reduced order
modeling of unsteady aerodynamic systems. Reduced order
modeling is a conceptually novel and computationally
efficient technique for computing unsteady flow about
isolated airfoils, wings, and turbomachinery cascades.
Starting with either a time domain or frequency domain
computational fluid dynamics (CFD) analysis of unsteady
aerodynamic or aeroacoustic flows, a large, sparse
eigenvalue problem is solved using the Lanczos algorithm.
Then, using just a few of the resulting eigenmodes, a
Reduced Order Model of the unsteady flow is constructed.
With this model, one can rapidly and accurately predict the
unsteady aerodynamic response of the system over a wide
range of reduced frequencies. Moreover, the eigenmode
information provides important insights into the physics of
unsteady flows. Finally, the method is particularly well
suited for use in the active control of aeroelastic and
aeroacoustic phenomena as well as in standard aeroelastic
analysis for flutter or gust response. Numerical results
presented include: 1) comparison of the reduced order model
to classical unsteady incompressible aerodynamic theory, 2)
reduced order calculations of compressible unsteady
aerodynamics based on the full potential equation, 3)
reduced order calculations of unsteady flow about an
isolated airfoil based on the Euler equations, and 4)
reduced order calculations of unsteady viscous flows
associated with cascade stall flutter, 5) flutter analysis
using the Reduced Order Model. The presentation will include
our most recent results including the use of A-one
Orthogonal Decomposition as an alternative or complement to
eigenmodes.},
Key = {98054181242}
}
@article{fds319911,
Author = {Hall, KC and Pigott, SA and Hall, SR},
Title = {Power requirements for large-amplitude flapping
flight},
Journal = {35th Aerospace Sciences Meeting and Exhibit},
Pages = {1-11},
Year = {1997},
Month = {January},
ISBN = {9780000000002},
Abstract = {© 1997 by Kenneth C. Hall, Steven A. Pigott, and Steven R.
Hall.In this paper, a method is presented for computing the
circulation distribution along the span of a flapping wing
that minimizes the power required to generate a prescribed
lift and thrust. The power is composed of three parts: The
useful thrust power, and the wasted induced power and
profile power. Here, the thrust and induced power are
expressed in terms of the Kelvin impulse and kinetic energy
associated with the sheet of trailing and shed vorticity
left behind the flapping wing. The profile power is computed
using a quasi-steady approximation of the twodimensional
viscous drag polar at each spanwise station of the wing. A
variational principle is then formed to determine the
necessary conditions for the circulation distribution to be
optimal. Included in the variational principle is a
constraint that the wing not stall. This variational
principle, which is essentially the viscous extension of the
well-known Betz criterion for optimal propellers, is
discretized using a vortex-lattice model of the wake, and
the optimum solution is computed numerically. The present
method is used to analyze a conventional propeller as well
as a rigid wing in forward flight flapping about a hinge
point on the longitudinal axis.},
Key = {fds319911}
}
@article{fds319912,
Author = {Silkowski, PD and Hall, KC},
Title = {A coupled mode analysis of unsteady multistage flows in
turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {4},
Publisher = {ASME},
Year = {1997},
Month = {January},
ISBN = {9780791878712},
url = {http://dx.doi.org/10.1115/97-GT-186},
Abstract = {A computational method is presented for predicting the
unsteady aerodynamic response of a vibrating blade row which
is part of a multistage turbomachine. Most current unsteady
aerodynamic theories model a single blade row isolated in an
infinitely long duct This assumption neglects the
potentially important influence of neighboring blade rows.
The present 'coupled mode' analysis is an elegant and
computationally efficient method for modelling neighboring
blade row effects. Using this approach, the coupling between
blade rows is modelled using a subset of the so-called
spinning modes, i.e. pressure, vorticity, and entropy waves
which propagate between the blade rows. The blade rows
themselves are represented by reflection and transmission
coefficients. These coefficients describe how spinning modes
interact with, and are scattered by, a given blade row. The
coefficients can be calculated using any standard isolated
blade row model; here we use a linearized full potential
flow model together with rapid distortion theory to account
for incident vortical gusts. The isolated blade row
reflection and transmission coefficients, inter-row coupling
relationships, and appropriate boundary conditions are all
assembled into a small sparse linear system of equations
which describes the unsteady multistage flow. A number of
numerical examples are presented to validate the method and
to demonstrate the profound influence of neighboring blade
rows on the aerodynamic damping of a cascade of vibrating
airfoils.},
Doi = {10.1115/97-GT-186},
Key = {fds319912}
}
@article{fds319913,
Author = {Hall, KC and Pigott, SA and Hall, SR},
Title = {Power requirements for large-amplitude flapping
flight},
Journal = {35th Aerospace Sciences Meeting and Exhibit},
Pages = {1-11},
Year = {1997},
Month = {January},
Abstract = {In this paper, a method is presented for computing the
circulation distribution along the span of a flapping wing
that minimizes the power required to generate a prescribed
lift and thrust. The power is composed of three parts: The
useful thrust power, and the wasted induced power and
profile power. Here, the thrust and induced power are
expressed in terms of the Kelvin impulse and kinetic energy
associated with the sheet of trailing and shed vorticity
left behind the flapping wing. The profile power is computed
using a quasi-steady approximation of the twodimensional
viscous drag polar at each spanwise station of the wing. A
variational principle is then formed to determine the
necessary conditions for the circulation distribution to be
optimal. Included in the variational principle is a
constraint that the wing not stall. This variational
principle, which is essentially the viscous extension of the
well-known Betz criterion for optimal propellers, is
discretized using a vortex-lattice model of the wake, and
the optimum solution is computed numerically. The present
method is used to analyze a conventional propeller as well
as a rigid wing in forward flight flapping about a hinge
point on the longitudinal axis.},
Key = {fds319913}
}
@article{fds362836,
Author = {Dowell, EH and Hall, KC and Romanowski, MC},
Title = {Reduced Order Aerodynamic Modeling of How to Make CFD Useful
to An Aeroelastician},
Journal = {Asme International Mechanical Engineering Congress and
Exposition, Proceedings (Imece)},
Volume = {1997-C},
Pages = {149-163},
Year = {1997},
Month = {January},
ISBN = {9780791826775},
url = {http://dx.doi.org/10.1115/IMECE1997-0166},
Abstract = {In this article, we review the status of reduced order
modeling of unsteady aerodynamic systems. Reduced order
modeling is a conceptually novel and computationally
efficient technique for computing unsteady flow about
isolated airfoils, wings, and turbomachinery cascades.
Starting with either a time domain or frequency domain
computational fluid dynamics (CFD) analysis of unsteady
aerodynamic or aeroacoustic flows, a large, sparse
eigenvalue problem is solved using the Lanczos algorithm.
Then, using just a few of the resulting eigenmodes, a
Reduced Order Model of the unsteady flow is constructed.
With this model, one can rapidly and accurately predict the
unsteady aerodynamic response of the system over a wide
range of reduced frequencies. Moreover, the eigenmode
information provides important insights into the physics of
unsteady flows. Finally, the method is particularly well
suited for use in the active control of aeroelastic and
aeroacoustic phenomena as well as in standard aeroelastic
analysis for flutter or gust response. Numerical results
presented include: 1) comparison of the reduced order model
to classical unsteady incompressible aerodynamic theory, 2)
reduced order calculations of compressible unsteady
aerodynamics based on the full potential equation, 3)
reduced order calculations of unsteady flow about an
isolated airfoil based on the Euler equations, and 4)
reduced order calculations of unsteady viscous flows
associated with cascade stall flutter, 5) flutter analysis
using the Reduced Order Model. The presentation will include
our most recent results including the use of A-one
Orthogonal Decomposition as an alternative or complement to
eigenmodes.},
Doi = {10.1115/IMECE1997-0166},
Key = {fds362836}
}
@article{97063692003,
Author = {Dowell Earl and H and Hall Kenneth and C and Romanowski Michael,
C},
Title = {Eigenmode analysis in unsteady aerodynamics: reduced order
models},
Journal = {Applied Mechanics Reviews},
Volume = {50},
Number = {6},
Pages = {371-385},
Publisher = {ASME International},
Year = {1997},
url = {http://dx.doi.org/10.1115/1.3101718},
Keywords = {Eigenvalues and eigenfunctions;Unsteady flow;Airfoils;Wings;Computational
fluid dynamics;Algorithms;},
Abstract = {In this article, we review the status of reduced order
modeling of unsteady aerodynamic systems. Reduced order
modeling is a conceptually novel and computationally
efficient technique for computing unsteady flow about
isolated airfoils, wings, and turbomachinery cascades.
Starting with either a time domain or frequency domain
computational fluid dynamics (CFD) analysis of unsteady
aerodynamic or aeroacoustic flows, a large, sparse
eigenvalue problem is solved using the Lanczos algorithm.
Then, using just a few of the resulting eigenmodes, a
Reduced Order Model of the unsteady flow is constructed.
With this model, one can rapidly and accurately predict the
unsteady aerodynamic response of the system over a wide
range of reduced frequencies. Moreover, the eigenmode
information provides important insights into the physics of
unsteady flows. Finally, the method is particularly well
suited for use in the active control of aeroelastic and
aeroacoustic phenomena as well as in standard aeroelastic
analysis for flutter or gust response. Numerical results
presented include: 1) comparison of the reduced order model
to classical unsteady incompressible aerodynamic theory, 2)
reduced order calculations of compressible unsteady
aerodynamics based on the full potential equation, 3)
reduced order calculations of unsteady flow about an
isolated airfoil based on the Euler equations, and 4)
reduced order calculations of unsteady viscous flows
associated with cascade stall flutter, 5) flutter analysis
using the Reduced Order Model.},
Doi = {10.1115/1.3101718},
Key = {97063692003}
}
@article{97023536979,
Author = {Hall, KC and Silkowski, PD},
Title = {Influence of neighboring blade rows on the unsteady
aerodynamic response of cascades},
Journal = {Journal of Turbomachinery, Transactions of the
Asme},
Volume = {119},
Number = {1},
Pages = {85-93},
Publisher = {ASME International},
Year = {1997},
url = {http://dx.doi.org/10.1115/1.2841014},
Keywords = {Aerodynamics;Turbomachine blades;Machine
vibrations;Mathematical models;Computational fluid
dynamics;Equations of motion;Reflection;Wave
transmission;},
Abstract = {In this paper, we present an analysis of the unsteady
aerodynamic response of cascades due to incident gusts (the
forced response problem) or blade vibration (the flutter
problem) when the cascade is part of a multistage fan,
compressor, or turbine. Most current unsteady aerodynamic
models assume the cascade to be isolated in an infinitely
long duct. This assumption, however, neglects the
potentially important influence of neighboring blade rows.
We present an elegant and computationally efficient method
to model these neighboring blade row effects. In the present
method, we model the unsteady aerodynamic response due to
so-called spinning modes (pressure and vorticity waves),
with each mode corresponding to a different circumferential
wave number and frequency. Then, for each mode, we compute
the reflection and transmission coefficients for each blade
row. These coefficients can be obtained from any of the
currently available unsteady linearized aerodynamic models
of isolated cascades. A set of linear equations is then
constructed that couples together the various spinning
modes, and the linear equations are solved via LU
decomposition. Numerical results are presented for both the
gust response and blade vibration problems. To validate our
model, we compare our results to other analytical models,
and to a multistage vortex lattice model. We show that the
effect of neighboring blade rows on the aerodynamic damping
of vibrating cascades is significant, but nevertheless can
be modeled with a small number of modes.},
Doi = {10.1115/1.2841014},
Key = {97023536979}
}
@article{fds281255,
Author = {Lorence, CB and Hall, KC},
Title = {Sensitivity analysis of the aeroacoustic response of
turbomachinery blade rows},
Journal = {Aiaa Journal},
Volume = {34},
Number = {8},
Pages = {1545-1554},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1996},
Month = {January},
ISBN = {9780000000002},
url = {http://dx.doi.org/10.2514/3.13270},
Abstract = {A method for computing the change or sensitivity of the
aeroacoustic response of a cascade to small changes in
airfoil and cascade geometry is presented. The steady flow
is modeled by the full potential equation, which is
discretized using a variational finite element technique. A
streamline computational grid is generated as part of the
steady solution. Newton iteration is used to solve for the
nonlinear steady flow and grid equations with lower-upper
(LU) matrix decomposition plus one forward and one back
substitution used to solve the resulting matrix equations.
Similarly, the unsteady small disturbance flow about the
nonlinear mean flow is modeled by the linearized potential
equation together with rapid distortion theory to account
for vortical gusts. These linearized equations are
discretized using finite elements and solved with a single
LU decomposition. The sensitivities of the steady and
unsteady flowfields to small changes in geometry are
computed by perturbing the discretized equations about the
nominal solutions. The resulting linear system of equations
can be solved very efficiently because the LU factors of the
resulting matrix equations are computed as part of the
nominal steady and unsteady solution. Results are presented
in this paper to show the accuracy and efficiency of the
method, and the implications for aeroacoustic design of
turbomachinery blades are discussed.},
Doi = {10.2514/3.13270},
Key = {fds281255}
}
@article{fds314756,
Author = {Florea, R and Hall, KC and Cizmas, PGA},
Title = {Reduced order modelling of unsteady viscous flow in a
compressor cascade},
Journal = {32nd Joint Propulsion Conference and Exhibit},
Year = {1996},
Month = {January},
ISBN = {9780000000002},
Abstract = {© 1996, American Institute of Aeronautics and Astronautics,
Inc. A simultaneously coupled inviscid-viscous interaction
(IVI) analysis is used to model the unsteady viscous
separated flow through a subsonic compressor. The inner
viscous flow around the airfoil and in the wake is modelled
using a finite difference discretization of the boundary
layer equations and a one-equation turbulence transport
model. The outer inviscid flow is modelled using a
variational finite element discretization of the
compressible full potential equation. The viscous and
inviscid regions are simultaneously coupled using a
transpiration type boundary condition along the airfoil and
wake. The resulting nonlinear unsteady equations are
linearized about the nonlinear steady flow to obtain a set
of linear equations which describe the unsteady
small-disturbance behavior of the viscous flow through the
cascade. The discretized small disturbance IVI equations are
used to form a generalized, quadratic, non-Hermitian
eigenvalue problem which describes the eigenmodes (natural
modes) and eigenvalues (natural frequencies) of fluid motion
about the cascade. Using a Lanczos algorithm, the
eigen-information is computed efficiently for various steady
flow inflow angles and unsteady interblade phase angles. The
eigenvalues and eigenmodes are then used in conjunction with
a classical mode summation technique to construct
computationally efficient reduced order models of the
unsteady flow through the cascade. Using just a few
eigenmodes, less than 0.06% of the total number, the
unsteady aerodynamic loads acting on vibrating airfoils (the
aeroelastic stability problem) can be efficiently and
accurately computed over a relatively wide range of reduced
frequencies - provided that one or more static corrections
are performed. Finally, the eigenvalues and eigenvalues
provide physical insight into the unsteady aerodynamic
behavior of the cascade. For example, we show the ability of
the present eigenanalysis to predict purely fluid mechanic
instabilities such as rotating stall.},
Key = {fds314756}
}
@article{fds351229,
Author = {Florea, R and Hall, KC and Cizmas, PGA},
Title = {Reduced order modelling of unsteady viscous flow in a
compressor cascade},
Journal = {32nd Joint Propulsion Conference and Exhibit},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.2514/6.1996-2572},
Abstract = {A simultaneously coupled inviscid-viscous interaction (IVI)
analysis is used to model the unsteady viscous separated
flow through a subsonic compressor. The inner viscous flow
around the airfoil and in the wake is modelled using a
finite difference discretization of the boundary layer
equations and a one-equation turbulence transport model. The
outer inviscid flow is modelled using a variational finite
element discretization of the compressible full potential
equation. The viscous and inviscid regions are
simultaneously coupled using a transpiration type boundary
condition along the airfoil and wake. The resulting
nonlinear unsteady equations are linearized about the
nonlinear steady flow to obtain a set of linear equations
which describe the unsteady small-disturbance behavior of
the viscous flow through the cascade. The discretized small
disturbance IVI equations are used to form a generalized,
quadratic, non-Hermitian eigenvalue problem which describes
the eigenmodes (natural modes) and eigenvalues (natural
frequencies) of fluid motion about the cascade. Using a
Lanczos algorithm, the eigen-information is computed
efficiently for various steady flow inflow angles and
unsteady interblade phase angles. The eigenvalues and
eigenmodes are then used in conjunction with a classical
mode summation technique to construct computationally
efficient reduced order models of the unsteady flow through
the cascade. Using just a few eigenmodes, less than 0.06% of
the total number, the unsteady aerodynamic loads acting on
vibrating airfoils (the aeroelastic stability problem) can
be efficiently and accurately computed over a relatively
wide range of reduced frequencies - provided that one or
more static corrections are performed. Finally, the
eigenvalues and eigenvalues provide physical insight into
the unsteady aerodynamic behavior of the cascade. For
example, we show the ability of the present eigenanalysis to
predict purely fluid mechanic instabilities such as rotating
stall.},
Doi = {10.2514/6.1996-2572},
Key = {fds351229}
}
@article{96100382057,
Author = {Hall Kenneth and C and Hall Steven and R},
Title = {Minimum induced power requirements for flapping
flight},
Journal = {Journal of Fluid Mechanics},
Volume = {323},
Number = {-1},
Pages = {285-315},
Publisher = {Cambridge University Press (CUP)},
Year = {1996},
url = {http://dx.doi.org/10.1017/S0022112096000924},
Keywords = {Wings;Mathematical models;Propulsive wing aircraft;Vortex
flow;Lift;},
Abstract = {The Betz criterion for minimum induced loss is used to
compute the optimal circulation distribution along the span
of flapping wings in fast forward flight. In particular, we
consider the case where flapping motion is used to generate
both lift (weight support) and thrust. The Betz criterion is
used to develop two different numerical models of flapping.
In the first model, which applies to small-amplitude
harmonic flapping motions, the optimality condition is
reduced to a one-dimensional integral equation which we
solve numerically. In the second model, which applies to
large-amplitude periodic flapping motions, the optimal
circulation problem is reduced to solving for the flow over
an infinitely long wavy sheet translating through an
inviscid fluid at rest at infinity. This three-dimensional
flow problem is solved using a vortex-lattice technique.
Both methods predict that the induced power required to
produce thrust decreases with increasing flapping amplitude
and frequency. Using the large-amplitude theory, we find
that the induced power required to produce lift increases
with flapping amplitude and frequency. Therefore, an optimum
flapping amplitude exists when the flapping motion of wings
must simultaneously produce lift and thrust.},
Doi = {10.1017/S0022112096000924},
Key = {96100382057}
}
@article{fds281253,
Author = {Hall, KC and Florea, R},
Title = {A reduced order model of unsteady flows in
turbomachinery},
Journal = {Journal of Turbomachinery},
Volume = {117},
Number = {3},
Pages = {375-383},
Publisher = {ASME International},
Year = {1995},
Month = {January},
url = {http://dx.doi.org/10.1115/1.2835672},
Abstract = {A novel technique for computing unsteady flows about
turbomachinery cascades is presented. Starting with a
frequency domain CFD description of unsteady aerodynamic
flows, we form a large, sparse, generalized, non-Hermitian
eigenvalue problem that describes the natural modes and
frequencies of fluid motion about the cascade. We compute
the dominant left and right eigenmodes and corresponding
eigenfrequencies using a Lanczos algorithm. Then, using just
a few of the resulting eigenmodes, we construct a reduced
order model of the unsteady flow field. With this model, one
can rapidly and accurately predict the unsteady aerodynamic
loads acting on the cascade over a wide range of reduced
frequencies and arbitrary modes of vibration. Moreover, the
eigenmode information provides insights into the physics of
unsteady flows. Finally we note that the form of the reduced
order model is well suited for use in active control of
aeroelastic and aeroacoustic phenomena. © 1995
ASME.},
Doi = {10.1115/1.2835672},
Key = {fds281253}
}
@article{fds281254,
Author = {Cizmas, PGA and Hall, KC},
Title = {Computation of steady and unsteady viscous flows using a
simultaneously coupled inviscid-viscous interaction
technique},
Journal = {Journal of Fluids and Structures},
Volume = {9},
Number = {6},
Pages = {639-657},
Publisher = {Elsevier BV},
Year = {1995},
Month = {January},
ISSN = {0889-9746},
url = {http://dx.doi.org/10.1006/jfls.1995.1035},
Abstract = {An interacting viscous-inviscid method for efficiently
computing steady and unsteady low Mach number viscous flows
with separation is presented. The inviscid region is modeled
using a finite element discretization of the full potential
equation. The viscous region is modeled using a finite
difference boundary layer technique. The two regions are
simultaneously coupled through the requirement that the edge
velocities of the two regions be equal, and through an
injection velocity arising the displacement thickness. For
unsteady flows, the fluid is assumed to be composed of two
parts: a mean or steady flow plus a harmonically varying
small unsteady disturbance. This assumption results in a
nonlinear description for the mean flow, and a linear
description for the small disturbance unsteady flow. For the
solution of the mean flow, the nonlinear governing equations
are reduced to a series of linear matrix equations using
Newton iteration. The resulting mean flow solution is then
used to form the variable coefficients of the linearized
unsteady equations, which are solved directly. The present
method is able to compute flows with separation, and in the
case of unsteady flows, flows with moving separation and
reattachment points. © 1995 by Academic Press,
Inc.},
Doi = {10.1006/jfls.1995.1035},
Key = {fds281254}
}
@article{95082814130,
Author = {Hall, KC and Silkowski, PD},
Title = {Influence of neighboring blade rows on the unsteady
aerodynamic response of cascades},
Journal = {American Society of Mechanical Engineers
(Paper)},
Pages = {11pp},
Address = {Houston, TX, USA},
Year = {1995},
Month = {January},
Keywords = {Aerodynamics;Vibrations (mechanical);Turbomachine
blades;Mathematical models;Damping;Numerical methods;Wind
effects;Reflection;},
Abstract = {An analysis of the unsteady aerodynamic response of cascade
due to incident gusts or blade vibration when the cascade is
part of a multistage fan, compressor, or turbine is
presented. Since most of the current unsteady aerodynamic
models assume the cascade to be isolated thereby neglecting
the important influence of neighboring blade rows, an
elegant and computationally efficient method to model the
neighboring blade row effects is also presented. Numerical
results are shown for both the gust response and blade
vibration problems. To validate the model, the results are
compared to other analytical models, and to a multistage
vortex lattice model. It is shown that the effect of
neighboring blade rows on the aerodynamic damping of
vibrating cascades is significant, but can be modeled with a
small number of modes.},
Key = {95082814130}
}
@article{95082814470,
Author = {Clark, WS and Hall, KC},
Title = {Numerical model of the onset of stall flutter in
cascades},
Journal = {American Society of Mechanical Engineers
(Paper)},
Pages = {11pp},
Address = {Houston, TX, USA},
Year = {1995},
Month = {January},
Keywords = {Mathematical models;Computational fluid dynamics;Unsteady
flow;Turbomachinery;Laminar flow;Navier Stokes
equations;Viscosity;Airfoils;Turbomachine blades;Vibrations
(mechanical);},
Abstract = {In this paper, we present a computational fluid dynamic
model of the unsteady flow associated with the onset of
stall flutter in turbomachinery cascades. The unsteady flow
is modeled using the laminar Navier-Stokes equations. We
assume that the unsteadiness in the flow is a small harmonic
disturbance about the mean or steady flow. Therefore, the
unsteady flow is governed by a small-disturbance form of the
Navier-Stokes equations. These linear variable coefficient
equations are discretized on a deforming computational grid
and solved efficiently using a multiple-grid Lax-Wendroff
scheme. A number of numerical examples are presented which
demonstrate the destabilizing influence of viscosity on the
aeroelastic stability of airfoils in cascade, especially for
torsional modes of blade vibration.},
Key = {95082814470}
}
@article{95092877597,
Author = {Lorence, CB and Hall, KC},
Title = {Sensitivity analysis of unsteady aerodynamic loads in
cascades},
Journal = {Aiaa Journal},
Volume = {33},
Number = {9},
Pages = {1604-1610},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1995},
Month = {January},
url = {http://dx.doi.org/10.2514/3.12798},
Keywords = {Unsteady flow;Cascades (fluid mechanics);Perturbation
techniques;Finite element method;Sensitivity
analysis;Mathematical models;Iterative methods;},
Abstract = {A method for computing the effect perturbations in the shape
of airfoils in a cascade have on the steady and unsteady
flow through the cascade is presented. First, the full
potential equation is used to describe the behavior of the
nonlinear steady flow and the small disturbance unsteady
flow through the cascade. The steady flow and small
disturbance unsteady flow versions of the full potential
equation are then discretized on a computational grid of
quadrilateral cells using a variational finite element
technique. The resulting discretized equations describing
the nonlinear steady flow are solved using Newton iteration
with lower-upper decomposition at each iteration. Similarly,
the discretized unsteady small disturbance equations, which
are linear, are solved using a single lowerupper
decomposition. Next, a sensitivity analysis is performed to
determine the effect small changes in cascade and airfoil
geometry have on the steady and unsteady flowfields. The
sensitivity analysis makes use of the nominal steady and
unsteady flow lower-upper decompositions so that no
additional matrices need to be factored. Hence, the present
method is computationally very efficient. A number of cases
are presented in the paper to show the accuracy of the
present method. We also demonstrate how the sensitivity
analysis may be used to redesign a representative compressor
cascade for improved aeroelastic stability. © 1995,
American Institute of Aeronautics and Astronautics, Inc.,
All rights reserved.},
Doi = {10.2514/3.12798},
Key = {95092877597}
}
@article{fds315332,
Author = {Cizmas, PGA and Hall, KC},
Title = {A viscous-inviscid model of unsteady small-disturbance flows
in cascades},
Journal = {31st Joint Propulsion Conference and Exhibit},
Year = {1995},
Month = {January},
ISBN = {9780000000002},
Abstract = {A simultaneously coupled viscous-inviscid (IVI) procedure
for computing the unsteady flow associated with the onset of
stall flutter in turbomachinery cascades is presented. Using
this method, the flow is divided into two parts: a viscous
flow near the airfoil and in the wake, and an inviscid flow
in the rest of the flow field. The viscous flow is modeled
using a finite difference discretization of the boundary
layer equations. The inviscid flow is modeled using a
variational finite element discretization of the full
potential equation. The viscous and inviscid flow regions
are then simultaneously coupled using a transpiration type
boundary condition along the airfoil and wake. At the onset
of stall flutter, the unsteadiness in the flow is small
compared to the mean flow. Therefore, in the present
analysis, the governing unsteady flow equations are
linearized about the mean flow to obtain a set of unsteady
small disturbance equations. The solution procedure is
carried out in two steps. First, the nonlinear steady flow
is computed using Newton iteration. Next, the resulting mean
flow solution is used to form the coefficients of the small
disturbance unsteady flow equations, and the resulting
system of linear equations is solved using LU decomposition.
The small-disturbance IVI method is used to compute the
unsteady aerodynamic response of a typical compressor blade
vibrating in pitch and plunge. The computed results
demonstrate the destabilizing influence of the viscosity on
the aeroelastic stability of airfoils in
cascade.},
Key = {fds315332}
}
@article{fds319914,
Author = {Lorence, CB and Hall, KC},
Title = {Sensitivity analysis of the aeroacoustic response of
turbomachinery blade rows},
Journal = {33rd Aerospace Sciences Meeting and Exhibit},
Year = {1995},
Month = {January},
ISBN = {9780000000002},
url = {http://dx.doi.org/10.2514/6.1995-166},
Abstract = {A method for computing the sensitivity of the aeroacoustic
response of a cascade to small changes in airfoil and
cascade geometry is presented. The steady flow is modeled by
the full potential equation, which is discretized using a
variational finite element technique. A streamline
computational grid is generated as part of the steady
solution. Newton iteration is used to solve the nonlinear
steady flow and grid equations with LU decomposition used at
each iteration to factor the resulting matrix equations. The
unsteady small disturbance flow is modeled by the linearized
potential equation together with rapid distortion theory to
account for vortical gusts. These equations are discretized
using finite elements and solved with a single LU
decomposition. The sensitivities of the steady and unsteady
flow fields to small changes in geometry are computed by
perturbing the discretized equations about the nominal
solution. The resulting linear system of equations can be
solved very efficiently since the LU factors of the matrices
have already been computed as part of the nominal steady and
unsteady solution. Results are presented to show the
accuracy and efficiency of the method, and the implications
for aeroacoustic design of turbomachinery blades are
discussed.},
Doi = {10.2514/6.1995-166},
Key = {fds319914}
}
@article{fds319915,
Author = {Clark, WS and Hall, KC},
Title = {A numerical model of the onset of stall flutter in
cascades},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Publisher = {ASME},
Year = {1995},
Month = {January},
ISBN = {9780791878828},
url = {http://dx.doi.org/10.1115/95-GT-377},
Abstract = {In this paper, we present a computational fluid dynamic
model of the unsteady flow associated with the onset of
stall flutter in turbomachinery cascades. The unsteady flow
is modeled using the laminar Navier-Stokes equations. We
assume that the unsteadiness in the flow is a small harmonic
disturbance about the mean or steady flow. Therefore, the
unsteady flow is governed by a small-disturbance form of the
Navier-Stokes equations. These linear variable coefficient
equations are discretized on a deforming computational grid
and solved efficiently using a multiple-grid Lax-Wendroff
scheme. A number of numerical examples are presented which
demonstrate the destabilizing influence of viscosity on the
aeroelastic stability of airfoils in cascade, especially for
torsional modes of blade vibration.},
Doi = {10.1115/95-GT-377},
Key = {fds319915}
}
@article{fds319916,
Author = {Hall, KC and Silkowski, PD},
Title = {The influence of neighboring blade rows on the unsteady
aerodynamic response of cascades},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {1},
Publisher = {ASME},
Year = {1995},
Month = {January},
ISBN = {9780791878781},
url = {http://dx.doi.org/10.1115/95-GT-035},
Abstract = {In this paper, we present an analysis of the unsteady
aerodynamic response of cascades due to incident gusts (the
forced response problem) or blade vibration (the flutter
problem) when the cascade is part of a multistage fan,
compressor, or turbine. Most current unsteady aerodynamic
models assume the cascade to be isolated in an infinitely
long duct. This assumption, however, neglects the
potentially important influence of neighboring blade rows.
We present an elegant and computationally efficient method
to model these neighboring blade row effects. In the present
method, we model the unsteady aerodynamic response due to
so-called spinning modes (pressure and vorticity waves),
with each mode corresponding to a different circumferential
wave number and frequency. Then, for each mode, we compute
the reflection and transmission coefficients for each blade
row. These coefficients can be obtained from any of the
currently available unsteady linearized aerodynamic models
of isolated cascades. A set of linear equations is then
constructed that couples together the various spinning
modes, and the linear equations are solved via LU
decomposition. Numerical results are presented for both the
gust response and blade vibration problems. To validate our
model, we compare our results to other analytical models,
and to a multistage vortex lattice model. We show that the
effect of neighboring blade rows on the aerodynamic damping
of vibrating cascades is significant, but nevertheless can
be modeled with a small number of modes.},
Doi = {10.1115/95-GT-035},
Key = {fds319916}
}
@article{97023513794,
Author = {Lorence, C.B. and Hall, K.C.},
Title = {Sensitivity analysis of unsteady aerodynamic loads in
cascades},
Journal = {AIAA Journal},
Volume = {33},
Number = {9},
Pages = {1604 - 1610},
Year = {1995},
Keywords = {Turbomachine blades;Aerodynamic loads;Cascades (fluid
mechanics);Sensitivity analysis;},
Abstract = {A method for computing the effect perturbations in the shape
of airfoils in a cascade have on the steady and unsteady
flow through the cascade is presented. First, the full
potential equation is used to describe the behavior of the
nonlinear steady flow and the small disturbance unsteady
flow through the cascade. The steady flow and small
disturbance unsteady flow versions of the full potential
equation are then discretized on a computational grid of
quadrilateral cells using a variational finite element
technique. The resulting discretized equations describing
the nonlinear steady flow are solved using Newton iteration
with lower-upper decomposition at each iteration. Similarly,
the discretized unsteady small disturbance equations, which
are linear, are solved using a single lower-upper
decomposition. Next, a sensitivity analysis is performed to
determine the effect small changes in cascade and airfoil
geometry have on the steady and unsteady flow fields. The
sensitivity analysis makes use of the nominal steady and
unsteady flow lower-upper decompositions so that no
additional matrices need to be factored. Hence, the present
method is computationally very efficient.},
Key = {97023513794}
}
@article{95042665556,
Author = {Hall, KC},
Title = {Eigenanalysis of unsteady flows about airfoils, cascades,
and wings},
Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
Structures, Structural Dynamics and Materials
Conference},
Volume = {2},
Number = {2},
Pages = {967-976},
Address = {Hilton Head, SC, USA},
Year = {1994},
Month = {December},
Keywords = {Mathematical models;Airfoils;Wings;Cascades (fluid
mechanics);Three dimensional;Time domain
analysis;Eigenvalues and eigenfunctions;Approximation
theory;Frequency domain analysis;Aerodynamic loads;Laplace
transforms;},
Abstract = {A general technique for constructing reduced order models of
unsteady aerodynamic flows about two-dimensional isolated
airfoils, cascades of airfoils, and three-dimensional wings
was developed. The technique was applied to an unsteady
incompressible vortex lattice model. The eigenmodes of the
system, which may be thought of as aerodynamic states, were
computed and subsequently used to construct computationally
efficient, reduced order models of the unsteady flow field.
It was also shown how the reduced order model may be
incorporated into an aeroelastic flutter
model.},
Key = {95042665556}
}
@article{95012531466,
Author = {Florea, R and Hall, KC},
Title = {Reduced order modeling of unsteady flows about
airfoils},
Journal = {American Society of Mechanical Engineers, Aerospace Division
(Publication) Ad},
Volume = {44},
Pages = {49-68},
Address = {Chicago, IL, USA},
Year = {1994},
Month = {December},
Keywords = {Airfoils;Mathematical models;Finite element
method;Variational techniques;Vibrations
(mechanical);Eigenvalues and eigenfunctions;Algorithms;Degrees
of freedom (mechanics);},
Abstract = {We present a reduced order modeling technique for analyzing
the unsteady aerodynamic flow about isolated airfoils. To
start, we model the flow using the time-linearized full
potential equation. The linearized potential equation is
discretized on a computational mesh composed of
quadrilateral elements using a variational finite element
technique. The resulting discretized equations are linear in
the unknown potential, but quadratic in the reduced
frequency of vibration. We compute the dominant (low
frequency) eigenfrequencies and mode shapes of the unsteady
fluid motion using a nonsymmetric Lanczos algorithm, and
then use these eigenmodes to construct a low
degree-of-freedom reduced order model of the unsteady flow
field. A static correction technique is used to account for
the high-frequency eigenmodes not retained in the model. We
show that the unsteady flow can be modeled accurately using
a relatively small number of eigenmodes.},
Key = {95012531466}
}
@article{fds281210,
Author = {Hall, KC and Florea, R and Lanzkron, PJ},
Title = {Reduced order model of unsteady flows in
turbomachinery},
Journal = {American Society of Mechanical Engineers
(Paper)},
Volume = {5},
Pages = {1-11},
Year = {1994},
Month = {January},
ISSN = {0402-1215},
url = {http://dx.doi.org/10.1115/94-GT-291},
Abstract = {A novel technique for computing unsteady flows about
turbomachinery cascades is presented. Starting with a
frequency domain CFD description of unsteady aerodynamic
flows, we form a large, sparse, generalized, non-Hermitian
eigenvalue problem which describes the natural modes and
frequencies of fluid motion about the cascade. We compute
the dominant left and right eigenmodes and corresponding
eigenfrequencies using a Lanczos algorithm. Then, using just
a few of the resulting eigenmodes, we construct a reduced
order model of the unsteady flow field. With this model, one
can rapidly and accurately predict the unsteady aerodynamic
loads acting on the cascade over a wide range of reduced
frequencies and arbitrary modes of vibration. Moreover, the
eigenmode information provides insights into the physics of
unsteady flows. Finally we note that the form of the reduced
order model is well suited for use in active control of
aeroelastic and aeroacoustic phenomena.},
Doi = {10.1115/94-GT-291},
Key = {fds281210}
}
@article{94111438878,
Author = {Hall, KC and Florea, R and Lanzkron, PJ},
Title = {A reduced order model of unsteady flows in
turbomachinery},
Journal = {Proceedings of the Asme Turbo Expo},
Volume = {5},
Pages = {1-11},
Publisher = {ASME},
Address = {Hague, Neth},
Year = {1994},
Month = {January},
ISBN = {9780791878873},
url = {http://dx.doi.org/10.1115/94-GT-291},
Keywords = {Turbomachinery;Mathematical models;Cascades (fluid
mechanics);Frequency domain analysis;Aerodynamics;Eigenvalues
and eigenfunctions;Algorithms;Aerodynamic loads;Vibrations
(mechanical);Forecasting;Spectrum analysis;},
Abstract = {A novel technique for computing unsteady flows about
turbomachinery cascades is presented. Starting with a
frequency domain CFD description of unsteady aerodynamic
flows, we form a large, sparse, generalized, non-Hermitian
eigenvalue problem which describes the natural modes and
frequencies of fluid motion about the cascade. We compute
the dominant left and right eigenmodes and corresponding
eigenfrequencies using a Lanczos algorithm. Then, using just
a few of the resulting eigenmodes, we construct a reduced
order model of the unsteady flow field. With this model, one
can rapidly and accurately predict the unsteady aerodynamic
loads acting on the cascade over a wide range of reduced
frequencies and arbitrary modes of vibration. Moreover, the
eigenmode information provides insights into the physics of
unsteady flows. Finally we note that the form of the reduced
order model is well suited for use in active control of
aeroelastic and aeroacoustic phenomena.},
Doi = {10.1115/94-GT-291},
Key = {94111438878}
}
@article{95022577597,
Author = {Hall, KC},
Title = {Eigenanalysis of unsteady flows about airfoils, cascades,
and wings},
Journal = {Aiaa Journal},
Volume = {32},
Number = {12},
Pages = {2426-2432},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1994},
Month = {January},
url = {http://dx.doi.org/10.2514/3.12309},
Keywords = {Airfoils;Cascades (fluid mechanics);Wings;Mathematical
models;Eigenvalues and eigenfunctions;Three dimensional;Time
domain analysis;Aerodynamics;Frequency domain
analysis;Laplace transforms;},
Abstract = {A general technique for constructing reduced order models of
unsteady aerodynamic flows about twodimensional isolated
airfoils, cascades of airfoils, and three-dimensional wings
is developed. The starting point is a time domain
computational model of the unsteady small disturbance flow.
For illustration purposes, we apply the technique to an
unsteady incompressible vortex lattice model. The eigenmodes
of the system, which may be thought of as aerodynamic
states, are computed and subsequently used to construct
computationally efficient, reduced order models of the
unsteady flowfield. Only a handful of the most dominant
eigenmodes are retained in the reduced order model. The
effect of the remaining eigenmodes is included approximately
using a static correction technique. An important advantage
of the present method is that once the eigenmode information
has been computed, reduced order models can be constructed
for any number of arbitrary modes of airfoil motion very
inexpensively. Numerical examples are presented that
demonstrate the accuracy and computational efficiency of the
present method. Finally, we show how the reduced order model
may be incorporated into an aeroelastic flutter model. ©
1994 American Institute of Aeronautics and Astronautics,
Inc., All rights reserved.},
Doi = {10.2514/3.12309},
Key = {95022577597}
}
@article{94112406695,
Author = {Hall, SR and Yang, KY and Hall, KC},
Title = {Helicopter rotor lift distributions for minimum-induced
power loss},
Journal = {Journal of Aircraft},
Volume = {31},
Number = {4},
Pages = {837-845},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1994},
Month = {January},
url = {http://dx.doi.org/10.2514/3.46569},
Keywords = {Lift;Constraint theory;Finite element method;Compressibility;Energy
dissipation;Vectors;Matrix algebra;Torque;Velocity;Density
(specific gravity);Flight dynamics;},
Abstract = {A method is described for solving the minimum-induced loss
(MIL) rotor design problem. First, the generalized Betz
condition for MIL rotors is developed. Because the resulting
lift distributions would generally exceed the maximum blade
lift coefficient on the retreating side of the rotor, the
necessary conditions are extended to include constraints on
the lift. A method for solving for the optimum lift
distribution using finite elements is described. Numerical
results are presented for a typical rotor in forward flight.
The MIL rotor may have on the order of 10% less induced
power loss than a typical unoptimized rotor. © 1994
American Institute of Aeronautics and Astronautics, Inc.,
All rights reserved.},
Doi = {10.2514/3.46569},
Key = {94112406695}
}
@article{94101421472,
Author = {Hall, KC and Clark, WS and Lorence, CB},
Title = {Linearized euler analysis of unsteady transonic flows in
turbomachinery},
Journal = {Journal of Turbomachinery, Transactions of the
Asme},
Volume = {116},
Number = {3},
Pages = {477-488},
Publisher = {ASME International},
Year = {1994},
url = {http://dx.doi.org/10.1115/1.2929437},
Keywords = {Cascades (fluid mechanics);Differential equations;Transonic
flow;Linearization;Mathematical models;Three
dimensional;Fluid dynamics;Harmonic analysis;Computational
methods;Loads (forces);Flutter (aerodynamics);Stability;},
Abstract = {A computational method for efficiently predicting unsteady
transonic flows in two-and three-dimensional cascades is
presented. The unsteady flow is modeled using a linearized
Euler analysis whereby the unsteady flow field is decomposed
into a nonlinear mean flow plus a linear harmonically
varying unsteady flow. The equations that govern the
perturbation flow, the linearized Euler equations, are
linear variable coefficient equations. For transonic flows
containing shocks, shock capturing is used to model the
shock impulse (the unsteady load due to the harmonic motion
of the shock). A conservative Lax-Wendroff scheme is used to
obtain a set of linearized finite volume equations that
describe the harmonic small disturbance behavior of the
flow. Conditions under which such a discretization will
correctly predict the shock impulse are investigated.
Computational results are presented that demonstrate the
accuracy and efficiency of the present method as well as the
essential role of unsteady shock impulse loads on the
flutter stability of fans.},
Doi = {10.1115/1.2929437},
Key = {94101421472}
}
@article{fds281247,
Author = {Hall, KC and Clark, WS},
Title = {Errata: Linearized Euler Predictions of Unsteady Aerodynamic
Loads in Cascades},
Journal = {Aiaa Journal},
Volume = {31},
Number = {5},
Pages = {970-970},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1993},
Month = {May},
ISSN = {0001-1452},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993LC44400033&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Doi = {10.2514/3.49039},
Key = {fds281247}
}
@article{fds281209,
Author = {Hall, KC and Clark, WS and Lorence, CB},
Title = {Linearized Euler analysis of unsteady transonic flows in
turbomachinery},
Journal = {American Society of Mechanical Engineers
(Paper)},
Volume = {1},
Year = {1993},
Month = {January},
ISSN = {0402-1215},
url = {http://dx.doi.org/10.1115/93GT094},
Abstract = {A computational method for efficiently predicting unsteady
transonic flows in two - and three-dimensional cascades is
presented. The unsteady flow is modelled using a linearized
Euler analysis whereby the unsteady flow field is decomposed
into a nonlinear mean flow plus a linear harmonically
varying unsteady flow.},
Doi = {10.1115/93GT094},
Key = {fds281209}
}
@article{93050991543,
Author = {Hall, KC and Clark, WS},
Title = {Linearized euler predictions of unsteady aerodynamic loads
in cascades},
Journal = {Aiaa Journal},
Volume = {31},
Number = {3},
Pages = {540-550},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.2514/3.11363},
Keywords = {Aerodynamic loads;Loads (forces);Eigenvalues and
eigenfunctions;},
Abstract = {A linearized Euler solver for calculating unsteady flows in
turbomachinery blade rows due to both incident gusts and
vibratory blade motion is presented. Using the linearized
Euler technique, one decomposes the flow into a mean (or
steady) flow plus an unsteady, harmonically varying,
small-disturbance flow. Linear variable coefficient
equations describe the small-disturbance behavior of the
flow and are solved using a pseudotime time-marching
Lax-Wendroff scheme. For the blade-motion problem, a
harmonically deforming computational grid that conforms to
the motion of vibrating blades eliminates large error
producing mean flow gradient terms that would otherwise
appear in the unsteady flow tangency boundary condition.
Also presented is a new, numerically exact, nonreflecting
far-field boundary condition based on an eigenanalysis of
the discretized equations. Computed flow solutions
demonstrate the computational accuracy and efficiency of the
present method. The solution of the linearized Euler
equations requires one to two orders of magnitude less
computer time than solution of the nonlinear Euler equations
using traditional time-accurate time-marching techniques.
Furthermore, it is shown that the deformable grid technique
significantly improves the accuracy of the solution. © 1993
American Institute of Aeronautics and Astronautics, Inc.,
All rights reserved.},
Doi = {10.2514/3.11363},
Key = {93050991543}
}
@article{93061013818,
Author = {Hall, KC},
Title = {Deforming grid variational principle for unsteady small
disturbance flows in cascades},
Journal = {Aiaa Journal},
Volume = {31},
Number = {5},
Pages = {891-900},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.2514/3.11701},
Keywords = {Unsteady flow;Finite element method;Variational
techniques;Turbomachine blades;},
Abstract = {A variational method for computing unsteady subsonic flows
in turbomachinery blade rows is presented. A variational
principle that describes the harmonic small disturbance
behavior of the full potential equations about a nonlinear
mean flow is developed. Included in this variational
principle is the effect of a deforming computational grid
that conforms to the motion of vibrating airfoils. Bilinear
isoparametric finite elements are used to discretize the
variational principle, and the resulting discretized
equations are solved efficiently using lower-upper
decomposition. The use of a deforming computational grid
dramatically improves the accuracy of the method since no
error-producing extrapolation is required to apply the
upwash boundary conditions or to evaluate the unsteady
pressure on the airfoil surfaces. Results computed using
this technique are compared with experimental data and other
analytical and computational methods. © 1993 American
Institute of Aeronautics and Astronautics, Inc., All rights
reserved.},
Doi = {10.2514/3.11701},
Key = {93061013818}
}
@article{93081061934,
Author = {Hall, KC and Clark, WS and Lorence, CB},
Title = {A linearized euler analysis of unsteady transonic flows in
turbomachinery},
Journal = {Asme 1993 International Gas Turbine and Aeroengine Congress
and Exposition, Gt 1993},
Volume = {1},
Pages = {13 -},
Address = {Cincinnati, OH, USA},
Year = {1993},
Month = {January},
ISBN = {9780791878880},
url = {http://dx.doi.org/10.1115/93GT094},
Keywords = {Unsteady flow;Transonic flow;Cascades (fluid
mechanics);Mathematical models;Linearization;},
Abstract = {A computational method for efficiently predicting unsteady
transonic flows in two- and three-dimensional cascades is
presented. The unsteady flow is modelled using a linearized
Euler analysis whereby the unsteady flow field is decomposed
into a nonlinear mean flow plus a linear harmonically
varying unsteady flow. The equations that govern the
perturbation flow, the linearized Euler equations, are
linear variable coefficient equations. For transonic flows
containing shocks, shock capturing is used to model the
shock impulse (the unsteady load due to the harmonic motion
of the shock). A conservative Lax-Wendroff scheme is used to
obtain a set of linearized finite volume equations that
describe the harmonic small disturbance behavior of the
flow. Conditions under which such a discretization will
correctly predict the shock impulse are investigated.
Computational results are presented that demonstrate the
accuracy and efficiency of the present method as well as the
essential role of unsteady shock impulse loads on the
flutter stability of fans.},
Doi = {10.1115/93GT094},
Key = {93081061934}
}
@article{94011165613,
Author = {Hall, KC and Lorence, CB},
Title = {Calculation of three-dimensional unsteady flows in
turbomachinery using the linearized harmonic Euler
equations},
Journal = {Journal of Turbomachinery, Transactions of the
Asme},
Volume = {115},
Number = {4},
Pages = {800-809},
Publisher = {ASME International},
Year = {1993},
ISBN = {9780791878972},
url = {http://dx.doi.org/10.1115/1.2929318},
Keywords = {Turbomachinery;Numerical analysis;Differential
equations;Aerodynamics;},
Abstract = {An efficient three-dimensional Euler analysis of unsteady
flows in turbomachinery is presented. The unsteady flow is
modeled as the sum of a steady or mean flow field plus a
harmonically varying small perturbation flow. The linearized
Euler equations, which describe the small perturbation
unsteady flow, are found to be linear, variable coefficient
differential equations whose coefficients depend on the mean
flow. A pseudo-time time-marching finite-volume Lax-Wendroff
scheme is used to discretize and solve the linearized
equations for the unknown perturbation flow quantities.
Local time stepping and multiple-grid acceleration
techniques are used to speed convergence. For unsteady flow
problems involving blade motion, a harmonically deforming
computational grid, which conforms to the motion of the
vibrating blades, is used to eliminate large error-producing
extrapolation terms that would otherwise approach in the
airfoil surface boundary conditions and in the evaluation of
the unsteady surface pressure. Results are presented for
both linear and annular cascade geometries, and for the
latter, both rotating and nonrotating blade
rows.},
Doi = {10.1115/1.2929318},
Key = {94011165613}
}
@article{fds319917,
Author = {Hall, KC and Lorence, CB},
Title = {Calculation of Three-Dimensional Unsteady Flows in
Turbomachinery Using the Linearized Harmonic Euler
Equations},
Journal = {Asme 1992 International Gas Turbine and Aeroengine Congress
and Exposition, Gt 1992},
Volume = {5},
Year = {1992},
Month = {January},
ISBN = {9780791878972},
url = {http://dx.doi.org/10.1115/92-GT-136},
Abstract = {An efficient three-dimensional Euler analysis of unsteady
flows in turbomachinery is presented. The unsteady flow is
modelled as the sum of a steady or mean flow field plus a
harmonically varying small perturbation flow. The linearized
Euler equations, which describe the small perturbation
unsteady flow, are found to be linear, variable coefficient
differential equations whose coefficients depend on the mean
flow. A pseudo-time time-marching finite-volume Lax-Wendroff
scheme is used to discretize and solve the linearized
equations for the unknown perturbation flow quantities.
Local time stepping and multiple-grid acceleration
techniques are used to speed convergence. For unsteady flow
problems involving blade motion, a harmonically deforming
computational grid which conforms to the motion of the
vibrating blades is used to eliminate large error-producing
extrapolation terms that would otherwise appear in the
airfoil surface boundary conditions and in the evaluation of
the unsteady surface pressure. Results are presented for
both linear and annular cascade geometries, and for the
latter, both rotating and nonrotating blade
rows.},
Doi = {10.1115/92-GT-136},
Key = {fds319917}
}
@article{92010390385,
Author = {Hall, KC and Verdon, JM},
Title = {Gust response analysis for cascades operating in nonuniform
mean flows},
Journal = {Aiaa Journal},
Volume = {29},
Number = {9},
Pages = {1463-1471},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1991},
Month = {January},
url = {http://dx.doi.org/10.2514/3.10761},
Keywords = {Aerodynamics;Mathematical Techniques - Finite Difference
Method;Turbomachinery - Blades;Mathematical Techniques -
Perturbation Techniques;},
Abstract = {The unsteady aerodynamic response of a subsonic cascade
subjected to entropic, vortical, and acoustic gusts is
analyzed. Field equations for the first-order unsteady
perturbation are obtained by linearizing the time-dependent
mass, momentum, and energy conservation equations about a
nonlinear, isentropic, and irrotational mean or steady flow.
A splitting technique is then used to decompose the unsteady
velocity into irrotational and rotational parts leading to
field equations for the unsteady entropy, rotational
velocity, and irrotational velocity fluctuations that are
coupled only sequentially. The entropic and rotational
velocity fluctuations can be described in closed form in
terms of the mean-flow drift and stream functions that can
be computed numerically. The irrotational unsteady velocity
is described by an inhomogeneous linearized potential
equation that contains a source term that depends on the
rotational velocity field. This equation is solved via a
finite-difference technique. Results are presented to
indicate the status of the numerical solution procedure and
to demonstrate the impact of blade geometry and mean blade
loading on the aerodynamic response of cascades to vortical
gust excitations. The analysis described herein leads to
very efficient predictions of cascade unsteady aerodynamic
phenomena, making it useful for turbomachinery aeroelastic
and aeroacoustic design applications. © 1991 American
Institute of Aeronautics and Astronautics, Inc., All rights
reserved.},
Doi = {10.2514/3.10761},
Key = {92010390385}
}
@article{92081333000,
Author = {Verdon, JM and Barnett, M and Hall, KC and Ayer, TC},
Title = {Development of unsteady aerodynamic analyses for
turbomachinery aeroelastic and aeroacoustic
applications},
Number = {4405},
Pages = {112},
Year = {1991},
Key = {92081333000}
}
@article{89080328741,
Author = {Hall, KC and Crawley, EF},
Title = {Calculation of unsteady flows in turbomachinery using the
linearizedEuler equations},
Journal = {Aiaa Journal},
Volume = {27},
Number = {6},
Pages = {777-787},
Publisher = {American Institute of Aeronautics and Astronautics
(AIAA)},
Year = {1989},
Month = {January},
url = {http://dx.doi.org/10.2514/3.10178},
Keywords = {Flow of Fluids--Unsteady Flow;Shock Waves;Mathematical
Models;},
Abstract = {A method for calculating unsteady flows in cascades is
presented. The model, which is based on the linearized
unsteady Euler equations, accounts for blade loading, blade
geometry, shock motion, and wake motion. Assuming that the
unsteadiness in the flow is small, the unsteady Euler
equations are linearized about the mean flow to obtain a set
of linear variable-coefficient equations that describe the
small-amplitude harmonic motion of the fluid. These linear
equations are discretized on a computational grid via a
finite-volume operator and solved directly, subject to an
appropriate set of linearized boundary conditions. An
important feature of the present analysis is the use of
shock fitting to determine steady and unsteady shock
positions. Use of the Euler equations in conjunction with
the Rankine-Hugoniot shock-jump conditions correctly models
the generation of entropy and vorticity at shocks. Results
of this method are presented for both channel and cascade
flows. Unsteady flows produced by blade motion (the flutter
problem) and incoming disturbances (the gust-response
problem) are predicted. A comparison of the present unsteady
flow predictions to those of semi-analytical and
time-marching numerical methods shows good agreement.
Furthermore, the linearized Euler method requires
substantially less computational time than the time-marching
procedures. © 1989 American Institute of Aeronautics and
Astronautics, Inc., All rights reserved.},
Doi = {10.2514/3.10178},
Key = {89080328741}
}
@article{84060105214,
Author = {Crawley, EF and Hall, KC},
Title = {Optimization and mechanisms of mistuning in
cascades},
Journal = {Journal of Engineering for Gas Turbines and
Power},
Volume = {107},
Number = {2},
Pages = {418-426},
Publisher = {ASME International},
Address = {Amsterdam, Neth},
Year = {1985},
Month = {January},
url = {http://dx.doi.org/10.1115/1.3239742},
Keywords = {FANS;},
Abstract = {An inverse design procedure has been developed for the
optimum mistuning of a high bypass ratio shroudless fan. The
fan is modeled as a cascade of blades, each with a single
torsional degree of freedom. Linearized supersonic
aerodynamic theory is used to compute the unsteady
aerodynamic forces in the influence coefficient form at a
typical blade section. The mistuning pattern is then
numerically optimized using the method of nonlinear
programming via augmented Lagrangians. The objective of the
mistuning is to achieve a specified increase in aeroelastic
stability margin with a minimum amount of mistuning. It is
shown that a necessary but not sufficient condition for
aeroelastic stability is that the blades be selfdamped. If
this condition is met, an optimized mistuning pattern can be
found that achieves a given stability margin for a much
lower level of mistuning than is required for the alternate
mistuning pattern. However, small errors in the
implementation of the optimum mistuning pattern severely
reduce the anticipated gains in stability margin. These
small errors are introduced by the manufacturing process and
by the approximation of the optimum mistuning pattern by
patterns of a few discrete blade frequencies. Alternate
mistuning, which requires only two blade frequencies, is
shown to be relatively insensitive to errors in
implementation. © 1985 by ASME.},
Doi = {10.1115/1.3239742},
Key = {84060105214}
}
@article{85060069260,
Author = {Crawley, E. F. and Hall, K. C.},
Title = {OPTIMIZATION AND MECHANISMS OF MISTUNING IN
CASCADES.},
Journal = {Journal of Engineering for Gas Turbines and Power,
Transactions of the ASME},
Volume = {107},
Number = {2},
Pages = {418 - 426},
Year = {1985},
Keywords = {TURBOMACHINERY - Blades;FANS - Mathematical Models;ROTORS -
Performance;AERODYNAMICS;},
Abstract = {An inverse design procedure has been developed for the
optimum mistuning of a high bypass ratio shroudless fan. The
fan is modeled as a cascade of blades, each with a single
torsional degree of freedom. Linearized supersonic
aerodynamic theory is used to compute the unsteady
aerodynamic forces in the influence coefficient form at a
typical blade section. The mistuning pattern is then
numerically optimized using the method of nonlinear
programming via augmented Lagrangians. The objective of the
mistuning is to achieve a specified increase in aeroelastic
stability margin with a minimum amount of mistuning. It is
shown that a necessary but not sufficient condition for
aeroelastic stability is that the blades be
self-damped.},
Key = {85060069260}
}
@article{fds289836,
Author = {Crawley, EF and Hall, KC},
Title = {OPTIMIZATION AND MECHANISMS OF MISTUNING IN
CASCADES.},
Journal = {American Society of Mechanical Engineers
(Paper)},
Year = {1984},
Month = {January},
Key = {fds289836}
}
@article{fds289837,
Author = {Crawley, EF and Hall, KC},
Title = {OPTIMIZATION AND MECHANISMS OF MISTUNING IN
CASCADES.},
Journal = {American Society of Mechanical Engineers
(Paper)},
Year = {1984},
Month = {January},
Key = {fds289837}
}
@article{84090160375,
Author = {Hall, KC and Johnson, WM},
Title = {Accurate centroid tracking},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {363},
Pages = {106-113},
Publisher = {SPIE},
Address = {San Diego, CA, USA},
Year = {1983},
Month = {August},
url = {http://dx.doi.org/10.1117/12.934167},
Keywords = {REMOTE SENSING;},
Abstract = {The object of this work was to develop analytical tools for
describing errors associated with mosaic array centroiding.
As an example of a current problem, a Monte Carlo simulation
of a point source tracking problem was implemented. Then for
a given noise and image model, the accuracy of the image
tracking was evaluated. In general the various causes for
error in the centroid estimate were pixel geometry, device
and background noise, and energy spillage outside window.
Both mean errors (bias) and distribution about the mean
(variance) were studied. The conclusions were: • Various
sources of centroid estimation errors were developed. • A
Monte Carlo simulation of track position estimation was
evaluated for various scenarios. • Multiple measurements
could be shown to provide resolution of a fraction of a
pixel. © 1983 SPIE.},
Doi = {10.1117/12.934167},
Key = {84090160375}
}
@article{5415394,
Author = {Hall, K.C. and Hall, S.R.},
Title = {Minimum induced power requirements for flapping
flight},
Journal = {J. Fluid Mech. (UK)},
Volume = {323},
Pages = {285 - 315},
Year = {25},
Keywords = {biomechanics;fluid dynamics;fluid oscillations;optimisation;vortices;},
Abstract = {The Betz criterion for minimum induced loss is used to
compute the optimal circulation distribution along the span
of flapping wings in fast forward flight. In particular, we
consider the case where flapping motion is used to generate
both lift (weight support) and thrust. The Betz criterion is
used to develop two different numerical models of flapping.
In the first model, which applies to small-amplitude
harmonic flapping motions, the optimality condition is
reduced to a one-dimensional integral equation which we
solve numerically. In the second model, which applies to
large-amplitude periodic flapping motions, the optimal
circulation problem is reduced to solving for the flow over
an infinitely long wavy sheet translating through an
inviscid fluid at rest at infinity. This three-dimensional
flow problem is solved using a vortex-lattice technique.
Both methods predict that the induced power required to
produce thrust decreases with increasing flapping amplitude
and frequency. Using the large-amplitude theory, we find
that the induced power required to produce lift increases
with flapping amplitude and frequency. Therefore, an optimum
flapping amplitude exists when the flapping motion of wings
must simultaneously produce lift and thrust},
Key = {5415394}
}
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