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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.

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

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  1. PARALLEL COMPUTATIONS OF 3D UNSTEADY COMPRESSIBLEEULER 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

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 movementswhen solving unsteady aerodynamic problems. • Parallel computation performance was studied. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  8. MPCCI Control Process GID=0 LID=N/A CODE II Process 1 GID=i+1 LID=0 CODE I: Process 1 GID=1 LID=0 CODE II Process 2 GID=i+2 LID=1 CODE I: Process 2 GID=2 LID=1 MPCCI CODE II Process j GID=i+j+1 LID=j-1 CODE I: Process i GID=i LID=i-1 MPCCI communications ID settings 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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  10. Q3 Q4 Q2 Q1 u v Qt Quadrilateral element interpolations 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Δt Un Step n Pn Δt Un+1 Step n+1 Time integration Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Deform the CFD mesh Map the displacements to CSD virtual surface mesh Finish Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  19. Computational Fluid Dynamics Solver - USER3D (Cont.) The cell volume can be calculated by • 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  20. 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: Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  21. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  22. Computational Structural Dynamics Solver – SAP4 (Cont.) • A Newmark-family of time integration scheme is used to obtain the solution at the (n+1) time step: Initial Condition: For Flutter Analysis Either or Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  23. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  24. In the present application: • n processors are used for CFD solution • One processor for CSD solution • One processor for communication management with MPCCI Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  25. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  26. TEST CASES (Cont.) MODE 1 MODE 2 SAP4 Modal Shape MODE 3 MODE 4 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  27. TEST CASES (Cont.) Mode 1 Mode 2 ANSYS Modal Shape Mode 3 Mode 4 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  28. TEST CASES (Cont.) • Steady Solution of the Rigid Body Steady State Transonic Flow at M∞ = 0.96 and M∞ = 1.141 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  29. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  30. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  31. 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. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  32. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  33. TEST CASES (Cont.) Deformed Mesh Undeformed Mesh Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  34. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  35. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  36. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  37. TEST CASES (Cont.) Deformed Mesh Undeformed Mesh Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  38. 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 Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  39. Mach=0.957, Vf = 0.349 , U∞=14400 inch/s TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  40. TEST CASES (Cont.) • Mach=0.957, Vf = 0.250 , U∞=10200 inch/s Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  41. TEST CASES (Cont.) • Mach=0.957, Vf = 0.262 , U∞=10800 inch/s Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  42. TEST CASES (Cont.) • Comparison of Results Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  43. TEST CASES (Cont.) • Initial Velocity Effect Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  44. 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 M∞ = 1.58, angle of attack (AOA) = 0.0. Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  45. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  46. 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 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

  47. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  48. TEST CASES (Cont.) Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  49. 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 Efficiency E is defined as Zhenyin Li, Master’s Thesis Defense, July 19, 2002

  50. TEST CASES (Cont.) 144,216 nodes and 706,105 cells Zhenyin Li, Master’s Thesis Defense, July 19, 2002

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