1 PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING EULER EQUATIONS WITH STRUCTURAL COUPLING Master’s Candidate Zhenyin Li Advisor: Dr. H. U. Akay Department of Mechanical Engineering Computational Fluid Dynamics Laboratory Indiana University Purdue University Indianapolis July 19, 2002
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PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING
PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING. Master’s Candidate Zhenyin Li Advisor: Dr. H. U. Akay Department of Mechanical Engineering Computational Fluid Dynamics Laboratory Indiana University Purdue University Indianapolis July 19, 2002. - PowerPoint PPT Presentation
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PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLEPARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLEEULER EQUATIONS WITH STRUCTURAL COUPLINGEULER EQUATIONS WITH STRUCTURAL COUPLING
Master’s Candidate
Zhenyin LiAdvisor: Dr. H. U. Akay
Department of Mechanical Engineering Computational Fluid Dynamics Laboratory
Indiana University Purdue University IndianapolisJuly 19, 2002
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 2/57
3D Unsteady Compressible Euler Equations with Structural Coupling
OutlineOutline
Introduction to Fluid-Structure Coupling
Fluid-Structure Coupling Procedure
Computational Fluid Dynamics Solver – USER3D
Computational Structural Dynamics Solver– SAP4
Test Cases
Conclusions and Recommendations
Acknowledgements
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 3/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Introduction to AeroelasticiyIntroduction to Aeroelasticiy
“Aeroelasticity is the phenomenon which exhibits appreciable reciprocal interactions (static or dynamic) between aerodynamic forces and the deformations induced in the structure of a flying vehicle, its control mechanisms, or its propulsion system.” Bisplinghoff (1975)
Two major concerns in aeroelasticity are stability and response problem.
Experiments and computer simulations are two basic ways to reveal the characteristic of various phenomena in aeroelasticity study.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 4/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Studies done in this researchStudies done in this research
Develop a procedure based coupling of on independent CFD (Computational Fluid Dynamics and CSD (Computational Structural Dynamics) solvers to resolve static and dynamic aeroelasticity problems.
The developed procedure was demonstrated by AGARD wing 445.6.
A dual zone mesh movement method developed for large mesh movements when solving unsteady aerodynamic problems.
Parallel computation performance was studied.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 5/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Mesh-based Parallel Code Coupling Interface (MPCCI), is used to exchange information between CFD and CSD codes and administer both in-code and out of code communications
Process I
CFDfluid solver
Application Interface
Process II
CSDstructure solver
Application Interface
MPCCI
MPCCI Configuration
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 7/57
3D Unsteady Compressible Euler Equations with Structural Coupling
A global communication ID (GID) is assigned to each of the processes involved in the coupled computation, and a local communication ID (LID) is assigned to the processes of the current code.
MPCCI Control ProcessGID=0 LID=N/A
CODE I: Process 1GID=1 LID=0
CODE I: Process 2GID=2 LID=1
CODE I: Process iGID=i LID=i-1
CODE II Process 1GID=i+1 LID=0
CODE II Process 2GID=i+2 LID=1
CODE II Process jGID=i+j+1 LID=j-1
MPCCI
MPCCI communications ID settings
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 9/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Any CSD/CFD code must define its coupling region at the initial stage. The coupling regions do not need to be identical in either size of the region or the density of the elements.
Fluid Model Solid Model
MPCCI
Non-matching meshes
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 10/57
3D Unsteady Compressible Euler Equations with Structural Coupling
The Arbitrary Lagrangian-Eulerian formulation of the three-dimensional time-
dependent inviscid fluid-flow equations is expressed in the following form:
0ˆ}{ dSnFdVQt
Where Q is the vector of conserved flow variables
F is the normal component of the convective flux vector
N is the unit normal vector to the boundary
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 16/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Computational Fluid Dynamics Solver - USER3D (Cont.)Computational Fluid Dynamics Solver - USER3D (Cont.) The time integration employed in the flow solver is the cell-
centered finite volume formulation. The volume-averaged values are adopted to represent the flow variables.
t
VQdSnQF
t
VQ
nn
nn }{)(}{
An implicit time integration scheme is used to solve flow field at each time step.
dSnQFR
Q
RI
t
VA
t
VQRQA
nn
n
nnn
nnnnn
)(}{
}{
}{][][
}{}{}{][
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 17/57
3D Unsteady Compressible Euler Equations with Structural Coupling
The mechanism of this method is that any two neighboring nodes in the mesh are connected by a spring and the spring stiffness is inversely proportional to the distance of the two nodes.
2/1222 ])()()[( ijijijm zzyyxxk
m
mni
m
mni
m
mni k
zkz
k
yky
k
xkx 111 ,,
Stiffness K
Displacement
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 18/57
3D Unsteady Compressible Euler Equations with Structural Coupling
In this section, the previous steady-state solution is used as a sudden load at time zero. The wing motion is entirely determined by the structural response. The time increment is 1.0e -4
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 37/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 38/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Deformed Mesh
Undeformed Mesh
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 39/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Flutter Analysis
Dynamic instability where-by the system extracts energy from thefree stream flow producing a divergent response. The computed flutter characteristics are presented in terms of velocity index Vf which is defined as
Stable
Neutral
Unstable
bUV f /
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 40/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 41/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Mach=0.957, Vf = 0.250 , U∞=10200 inch/s
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 42/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Mach=0.957, Vf = 0.262 , U∞=10800 inch/s
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 43/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Comparison of Results
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 44/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Initial Velocity Effect
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 45/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Parallel Aerodynamic StudiesA standard research configuration for missile geometries, is studied under forced pitching conditions. The computational mesh used consists of 144,216 nodes and 706,105 cells, 24 Blocks
The steady case was performed with M∞ = 1.58, angle of attack (AOA) = 0.0.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 46/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 47/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
This case is the basic finner performing a sinusoidally pitching motion about its center of gravity. The angle of attack varies as:
)sin()( tt pm For this test case, the reduced frequency k = 2.53165, freestream Mach number M∞ = 1.58, the mean angle of pitching αm = 0.0 degree and the amplitude of pitching is 10 degrees. The results were obtained using 2000 steps per cycle of the motion. The time increment of 2e-4 was used
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 48/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 49/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 50/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
Parallel Efficiency Study The parallel efficiency study performed here is based on Indiana University’s IBM SP clusters and Compaq Linux clusters. The speedup is defined as
UNIX LINUX
Model IBM RISC System / SP6000
POWER3+ Thin Node
Compaq ProLiant 1850R rack-
mounted compute
nodes
CPU(Each Node)
4 CPU, 375MHz clock cycle
Dual Intel 400 MHz Pentium II processors
Memory 2GB 256 MB
Cache 8MB 512 KB
Network 10/100Mb "Fast" Ethernet (100 TX)
pp TTS /1
Efficiency E is defined as
pSE p /100
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 51/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)
144,216 nodes and 706,105 cells
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 52/57
3D Unsteady Compressible Euler Equations with Structural Coupling
TEST CASES (Cont.)TEST CASES (Cont.)144,216 nodes and 706,105 cells
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 53/57
3D Unsteady Compressible Euler Equations with Structural Coupling
ConclusionsConclusions
A loosely coupled procedure is developed by using parallel Euler equations solver USER3D and finite element structural solver SAP4. The advantage of current method is to provide a flexible and easy implementation for coupling CFD and CSD codes without a large amount of works in existing codes.
In steady aeroelastic problems, due to the limitation of mesh deformation scheme, a load factor was used to increase the load gradually. The results are quite consistent with other researcher’s work. Using dynamic aeroelastic solutions with damping the results of static problem is also validated.
Dynamic aeroelastic problems were solved using the coupled CFD-CSD procedure. Significant aeroelastic effects were observed in this study.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 54/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Conclusions (Cont.)Conclusions (Cont.)
Flutter analysis was implemented by choosing initial perturbation of the structural system and examining whether the initial perturbation will decay, grow or maintain neutral conditions to determine the flutter conditions. The results compared well with previous works and experimental results.
A dual-zone dynamic mesh system was successfully employed to solve unsteady aerodynamic problems. High computational efficiency was obtained.
Both steady-state solution scheme and unsteady solution showed good speedup and efficiency for multi-block cases.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 55/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Future WorksFuture Works
The present dynamic grid scheme can prevent two nodes colliding with each other. And the dual-zone scheme can only deal with known motion. This scheme works well with small motion or large simple motion such as sinusoidal motion. Problems will occur when solving aeroelastic problems with large motion.
Time increment in the present scheme is same on both CFD and CSD solvers. But, CSD solver usually requires larger time increments than the CFD solver. In the future work, the effect of time sub-cycle should be studied. Another problem in current scheme is only that only the CFD code is a parallel code. In the future study, a parallel CSD code may be required to improve the computational efficiency, especially for large structures such as a complete aircrafts or missiles.
The information exchange between CFD and CSD solvers is based on bi-linear interpolations. Although its accuracy is enough for the current problem, a more complex interpolation scheme maybe required for future applications.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 56/57
3D Unsteady Compressible Euler Equations with Structural Coupling
Future Works (Cont.)Future Works (Cont.)
One remaining problem in this procedure is that MPCCI requires that each sub process must define its own coupling region, but some CFD blocks which are partitioned by GD do not include such coupling regions. As the result, the current procedure may be limited to a few blocks which depend on how GD divides a grid.
Although reasonable results are obtained for flutter analysis, there are still some differences between the present results and experiments. One possible way to improve the accuracy is to refine the mesh to get more accurate fluid solutions. Another way to improve the accuracy is by improving the present bilinear interpolation scheme to get more accurate quantities exchanging.
Zhenyin Li, Master’s Thesis Defense, July 19, 2002 57/57
3D Unsteady Compressible Euler Equations with Structural Coupling
AcknowledgementAcknowledgement
First, I would like to thank my advisor and committee chairman, Dr. Hasan U. Akay. His invaluable guidance helped me in realizing this research throughout the course of my studies.
I also would like to extend my thanks to Dr. Hasan U. Akay and Dr. Erdal Oktay for giving me the opportunity to work on this research project; to Dr. Akin Ecer for providing me the opportunity to use the facilities of the CFD Laboratory and serving in my thesis committee; and to Dr. Andrew T. Hsu for serving in my thesis committee.
Valuable assistance from Mr. Resat U. Payli contributed a lot to the computational work in this research to which I am grateful.
Finally, I would thank to my lovely wife, Jing, without her, none of this would have been possible.
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3D Unsteady Compressible Euler Equations with Structural Coupling