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PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING

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... presented in terms of velocity index Vf which is defined as ... Mach=0.957, Vf = 0.349 , U=14400 inch/s. Zhenyin Li, Master's Thesis Defense, July 19, 2002 ... – PowerPoint PPT presentation

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Title: PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLE EULER EQUATIONS WITH STRUCTURAL COUPLING


1
PARALLEL 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

2
Outline
  • 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

3
Introduction 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.

4
Studies 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.

5
AEROELASTIC 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

6
AEROELASTIC 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
7
AEROELASTIC COUPLING ALGORITHM (Cont.)
  • The current version of MPCCI works well with
    Message Passing Interface (MPI)-based parallel as
    well as serial computing programs.

8
AEROELASTIC 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.

9
AEROELASTIC 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
10
AEROELASTIC 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
11
AEROELASTIC COUPLING ALGORITHM (Cont.)
Virtual CSD Surface Mesh
  • Exchanging Quantities

Mid-surface Structural Mesh
Fu
Real Surface
Mc
Central Surface
Fc
CFD surface Mesh Match Virtual CSD Surface Mesh
Fb
Central surface transformations
12
AEROELASTIC 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
13
Construct 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
14
Computational Fluid Dynamics Solver - USER3D
  • Background of 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.

15
Computational 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

16
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.
  • An implicit time integration scheme is used to
    solve flow field at each time step.

17
Computational 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
18
Computational 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
19
Computational Fluid Dynamics Solver - USER3D
(Cont.)
  • Boundary Conditions
  • 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

20
Computational 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

21
Computational 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

22
Computational 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
23
Computational 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

24
TEST 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

26
TEST 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
27
TEST CASES (Cont.)
MODE 1
MODE 2
SAP4 Modal Shape
MODE 3
MODE 4
28
TEST CASES (Cont.)
Mode 1
Mode 2
ANSYS Modal Shape
Mode 3
Mode 4
29
TEST CASES (Cont.)
  • Steady Solution of the Rigid Body
  • Steady State Transonic Flow at M8 0.96 and M8
    1.141

30
TEST CASES (Cont.)
31
TEST CASES (Cont.)
32
TEST 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.

33
TEST 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
34
TEST CASES (Cont.)
Deformed Mesh
Undeformed Mesh
35
TEST CASES (Cont.)
36
TEST 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

37
TEST CASES (Cont.)
38
TEST CASES (Cont.)
Deformed Mesh
Undeformed Mesh
39
TEST CASES (Cont.)
  • Flutter Analysis

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
40
TEST CASES (Cont.)
  • Mach0.957, Vf 0.349 , U814400 inch/s

41
TEST CASES (Cont.)
  • Mach0.957, Vf 0.250 , U810200 inch/s

42
TEST CASES (Cont.)
  • Mach0.957, Vf 0.262 , U810800 inch/s

43
TEST CASES (Cont.)
  • Comparison of Results

44
TEST CASES (Cont.)
  • Initial Velocity Effect

45
TEST 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.

46
TEST CASES (Cont.)
47
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

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

48
TEST CASES (Cont.)
49
TEST CASES (Cont.)
50
TEST 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
51
TEST CASES (Cont.)
144,216 nodes and 706,105 cells
52
TEST CASES (Cont.)
  • 144,216 nodes and 706,105 cells

53
Conclusions
  • 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.

54
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.

55
Future 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.

56
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.

57
Acknowledgement
  • 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.

58
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