Title: PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING
1PARALLEL COMPUTATIONS OF 3D UNSTEADY
COMPRESSIBLEEULER EQUATIONS WITH STRUCTURAL
COUPLING
- Masters Candidate
- Zhenyin Li
- Advisor Dr. H. U. Akay
- Department of Mechanical Engineering
- Computational Fluid Dynamics Laboratory
- Indiana University Purdue University Indianapolis
- July 19, 2002
2Outline
- 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
3Introduction 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.
4Studies 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.
5AEROELASTIC COUPLING ALGORITHM
- A basic procedure to obtain an aeroelastic
solution includes following steps
- Get pressure on CFD mesh nodes from flow
calculation - Pass the load information to CSD domain
- Calculate nodal displacements with CSD code
- Feedback the structure deformation to CFD domain
- Deform the CFD mesh
- Repeat steps 1 through 5
6AEROELASTIC COUPLING ALGORITHM (Cont.)
- 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
Process II
CFD fluid solver
CSD structure solver
Application Interface
Application Interface
MPCCI
MPCCI Configuration
7AEROELASTIC COUPLING ALGORITHM (Cont.)
- The current version of MPCCI works well with
Message Passing Interface (MPI)-based parallel as
well as serial computing programs.
8AEROELASTIC COUPLING ALGORITHM (Cont.)
- 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.
9AEROELASTIC COUPLING ALGORITHM (Cont.)
- 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
10AEROELASTIC COUPLING ALGORITHM (Cont.)
- Information Exchange Pressure and displacements
need to be exchanged during the coupling process.
Q3
u
Q2
v
Q1
w
w
u
v
Qt
Triangular element interpolations
11AEROELASTIC COUPLING ALGORITHM (Cont.)
Virtual CSD Surface Mesh
Mid-surface Structural Mesh
Fu
Real Surface
Mc
Central Surface
Fc
CFD surface Mesh Match Virtual CSD Surface Mesh
Fb
Central surface transformations
12AEROELASTIC COUPLING ALGORITHM (Cont.)
- Time Integrations of Coupled System
- Here, the same ?t is used for fluid and structure
Fluid
Solid
Pn-1
Step n-1
?t
Un
Step n
Pn
?t
Un1
Step n1
Time integration
13Construct CFD Mesh
Steady State Solution for rigid body
Construct CSD virtual surface mesh
Calculate new CFD flow field
Put pressure on virtual surface
Extract fluid surface mesh
MPCCI
Calculate dynamic forces on CSD virtual surface
mesh
Calculate node pressure on surface mesh
Transform the dynamic forces to structure mesh
and solve equilibrium equation
Put the displacements on surface mesh
MPCCI
Map the displacements to CSD virtual surface mesh
Deform the CFD mesh
Finish
14Computational Fluid Dynamics Solver - USER3D
- A parallel finite-volume based unstructured
Euler solver - Serial version of User3D was developed by Oktay
(1994) - Parallel version of User3D was developed at CFD
Laboratory at IUPUI (2000) - This solver was validated in previous studies.
15Computational Fluid Dynamics Solver - USER3D
(Cont.)
- Governing Equations for USER3D
- The Arbitrary Lagrangian-Eulerian
formulation of the three-dimensional
time-dependent inviscid fluid-flow equations is
expressed in the following form -
- 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
16Computational 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.
- An implicit time integration scheme is used to
solve flow field at each time step.
17Computational Fluid Dynamics Solver - USER3D
(Cont.)
- Mesh-Movement Algorithm
- 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.
Stiffness K
Displacement
18Computational Fluid Dynamics Solver - USER3D
(Cont.)
- Limitation of the current scheme
- The spring technology needs a large amount of
CPU time and memory - The small size cells near the inner boundary can
not afford large amplitude motion
- A simple dual-zone smoothing approach is proposed
to improve the performance of the current spring
system
II
Region I The inner zone is moving rigidly with
the body Region II The outer zone is deformed
by general mesh deformation method .
I
19Computational Fluid Dynamics Solver - USER3D
(Cont.)
- The characteristic boundary conditions are
applied to outer far field of flow by using
Riemann invariants on farfield boundaries - For the moving boundaries, the velocities should
be taken into account -
20Computational Fluid Dynamics Solver - USER3D
(Cont.)
- Geometric Conservation Law
- The geometry conservation equation is required
to solve simultaneously with other conservation
equations.
where Ws denotes the local velocity on the
boundary surface S
- The cell volume can be calculated by
21Computational Structural Dynamics Solver SAP4
- The finite element discrete aeroelasticity
element equation for a structural system can be
written as
M, C and K are system mass, damping and
stiffness matrix
- For static analysis, equation can be rewritten as
- For dynamic analysis, equation can be rewritten
as
22Computational Structural Dynamics Solver SAP4
(Cont.)
- Mode superposition method
1. Get the generalized eigenvalue solution
2. Use first n modes to simulate structural
response
3. Get the generalized displacement solution
23Computational Structural Dynamics Solver SAP4
(Cont.)
- A Newmark-family of time integration scheme is
used to obtain the solution at the (n1) time
step
Initial Condition For Flutter Analysis Either
or
24TEST CASES
- Aeroelastic Research Wing (AGARD Wing 445.6)
1.208 ft
5.2 ft
45O
1.833 ft
AGARD wing 445.6 panel dimensions
The CFD grid consists of 147,547 cells and 26,228
nodes. The CFD wing surface has 2020 elements
and 1077 nodes
25- In the present application
- n processors are used for CFD solution
- One processor for CSD solution
- One processor for communication management with
MPCCI
26TEST CASES (Cont.)
- Modal Analysis of Wing 445.6
Table 5.2 Modal frequencies of AGARD wing 445.6
Comparison of AGARD wing 445.6 modal frequencies
27TEST CASES (Cont.)
MODE 1
MODE 2
SAP4 Modal Shape
MODE 3
MODE 4
28TEST CASES (Cont.)
Mode 1
Mode 2
ANSYS Modal Shape
Mode 3
Mode 4
29TEST CASES (Cont.)
- Steady Solution of the Rigid Body
- Steady State Transonic Flow at M8 0.96 and M8
1.141
30TEST CASES (Cont.)
31TEST CASES (Cont.)
32TEST CASES (Cont.)
Rigid Body Result
- Static Aeroelastic Analysis at Mach 0.8
- 1. The coupling iteration starts from the
steady-state solution of the rigid body. - 2. In practice, a load factor is used to control
the force loaded on the structural system. - 3. An alternate approach also performed here is
using dynamic analysis to simulate steady case.
33TEST CASES (Cont.)
The tip deflection at the trailing edge was
computed to be 0.40 inch which is very close to
0.39 inch from MDICE
34TEST CASES (Cont.)
Deformed Mesh
Undeformed Mesh
35TEST CASES (Cont.)
36TEST CASES (Cont.)
- Dynamic Aeroelastic Analysis Mach 0.8, AOA 1.0
degree - 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
37TEST CASES (Cont.)
38TEST CASES (Cont.)
Deformed Mesh
Undeformed Mesh
39TEST CASES (Cont.)
Dynamic instability where-by the system extracts
energy from the free 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
40TEST CASES (Cont.)
- Mach0.957, Vf 0.349 , U814400 inch/s
41TEST CASES (Cont.)
- Mach0.957, Vf 0.250 , U810200 inch/s
42TEST CASES (Cont.)
- Mach0.957, Vf 0.262 , U810800 inch/s
43TEST CASES (Cont.)
44TEST CASES (Cont.)
45TEST CASES (Cont.)
- Parallel Aerodynamic Studies
- A 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 M8 1.58,
angle of attack (AOA) 0.0.
46TEST CASES (Cont.)
47TEST CASES (Cont.)
- This case is the basic finner performing a
sinusoidally pitching motion about its center of
gravity. The angle of attack varies as
For this test case, the reduced frequency k
2.53165, freestream Mach number M8 1.58, the
mean angle of pitching am 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
48TEST CASES (Cont.)
49TEST CASES (Cont.)
50TEST CASES (Cont.)
- Parallel Efficiency Study
- The parallel efficiency study performed here is
based on Indiana Universitys IBM SP clusters and
Compaq Linux clusters. - The speedup is defined as
Efficiency E is defined as
51TEST CASES (Cont.)
144,216 nodes and 706,105 cells
52TEST CASES (Cont.)
- 144,216 nodes and 706,105 cells
53Conclusions
- 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
researchers 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.
54Conclusions (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.
55Future 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.
56Future 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.
57Acknowledgement
- 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.
58Question?