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Aerodynamic Drag Prediction Using Unstructured Mesh Solvers

Aerodynamic Drag Prediction Using Unstructured Mesh Solvers. Dimitri J. Mavriplis National Institute of Aerospace Hampton, Virginia, USA. Overview. Introduction Physical model fidelity Grid resolution and discretization issues

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Aerodynamic Drag Prediction Using Unstructured Mesh Solvers

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  1. Aerodynamic Drag Prediction Using Unstructured Mesh Solvers Dimitri J. Mavriplis National Institute of Aerospace Hampton, Virginia, USA VKI Lecture Series, February 3-7, 2003

  2. Overview • Introduction • Physical model fidelity • Grid resolution and discretization issues • Designing an efficient unstructured mesh solver for computational aerodynamics • Drag prediction using unstructured mesh solvers • Conclusions and future work VKI Lecture Series, February 3-7, 2003

  3. Overview • Introduction • Importance of Drag Prediction • Suitability of Unstructured Mesh Approach • Physical model fidelity • Inviscid Flow Analysis • Coupled Inviscid-Viscous Methods • Large-Eddy Simulations (LES and DES) VKI Lecture Series, February 3-7, 2003

  4. Overview • Grid resolution and discretization issues • Choice of discretization and effect of dissipation • Cell centered vs. vertex based • Effect of discretization variations on drag prediction • Grid resolution requirements • Choice of element type • Grid resolution issues • Grid convergence VKI Lecture Series, February 3-7, 2003

  5. Overview • Designing an efficient unstructured mesh solver for computational aerodynamics • Discretization • Solution Methodologies • Efficient Hardware Usage VKI Lecture Series, February 3-7, 2003

  6. Overview • Drag prediction using unstructured mesh solvers • Wing-body cruise drag • Incremental effects: engine installation drag • High-lift flows • Conclusions and Future Work VKI Lecture Series, February 3-7, 2003

  7. Introduction • Importance of Drag Prediction • Cruise: fuel burn, range, etc… • High-lift: Mechanical simplicity, noise • High accuracy requirements • Absolute or incremental: 1 drag count • Specialized computational methods • Wide range of scales • Thin boundary layers • Transition VKI Lecture Series, February 3-7, 2003

  8. Introduction • Issues centric to unstructured mesh approach • Advantages and drawbacks over other approaches • Accuracy, efficiency • State-of-the art in aerodynamic predictions • De-emphasize non-method specific issues • Validation/ verification • Drag integration VKI Lecture Series, February 3-7, 2003

  9. CFD Perspective on Meshing Technology • Sophisticated Multiblock Structured Grid Techniques for Complex Geometries Engine Nacelle Multiblock Grid by commercial software TrueGrid.

  10. CFD Perspective on Meshing Technology • Sophisticated Overlapping Structured Grid Techniques for Complex Geometries Overlapping grid system on space shuttle (Slotnick, Kandula and Buning 1994)

  11. Unstructured Grid Alternative • Connectivity stored explicitly • Single Homogeneous Data Structure VKI Lecture Series, February 3-7, 2003

  12. Characteristics of Both Approaches • Structured Grids • Logically rectangular • Support dimensional splitting algorithms • Banded matrices • Blocked or overlapped for complex geometries • Unstructured grids • Lists of cell connectivity, graphs (edge,vertices) • Alternate discretizations/solution strategies • Sparse Matrices • Complex Geometries, Adaptive Meshing • More Efficient Parallelization VKI Lecture Series, February 3-7, 2003

  13. Unstructured Meshes for Aerodynamics • Computational aerodynamics rooted in structured methods • High accuracy and efficiency requirements • Unstructured mesh methods 2 to 4 times more costly • Mitigated by extra structured grid overhead • Block structured • Overset mesh • Parallelization • Accuracy considerations • Validation studies, experience • Unstructured mesh solvers potentially more efficient than structured mesh alternatives with equivalent accuracy VKI Lecture Series, February 3-7, 2003

  14. Physical Model Fidelity • State-of-the-art in drag prediction: RANS • Entire suite of tools available to designer • Useful to examine capabilities of other tools • Lower fidelity – lower costs • Numerous rapid tradeoff studies • Higher fidelity – higher costs • Fewer detailed analyses • Situate RANS tools within this suite VKI Lecture Series, February 3-7, 2003

  15. Physical Model Requirements(Unstructured Mesh Methods) VKI Lecture Series, February 3-7, 2003

  16. Unstructured Mesh Euler Solvers • Inviscid flow unstructured mesh solvers well established – robust • No viscous effects • No turbulence/transition modeling • Isotropic meshes • Good commercial isoptropic mesh generators • Good convergence properties VKI Lecture Series, February 3-7, 2003

  17. Example: Euler Solution of DLR-F4 Wing-body Configuration • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS VKI Lecture Series, February 3-7, 2003

  18. Example: Euler Solution of DLR-F4 Wing-body Configuration • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS VKI Lecture Series, February 3-7, 2003

  19. Example: Euler Solution of DLR-F4 Wing-body Configuration • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS • 1.65 million vertices VKI Lecture Series, February 3-7, 2003

  20. Euler vs. RANS Solution Euler Solution (235,000 pts) RANS Solution (1.65M pts) • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS VKI Lecture Series, February 3-7, 2003

  21. Euler vs. RANS Solution • Exclusion of viscous effects • Boundary layer displacement • Incorrect shock location • Incorrect shock strength • Supercritical wing sensitive to viscous effects • Euler solution not useful for transonic cruise drag prediction VKI Lecture Series, February 3-7, 2003

  22. Coupled Euler-Boundary Layer Approach • Incorporate viscous effects to first order • Boundary layer displacement thickness • More accurate shock strength/location • Retain efficiency of Euler solution approach • Isotropic tetrahedral meshes • Fast, robust convergence VKI Lecture Series, February 3-7, 2003

  23. Coupled Euler-Boundary Layer Approach • Stripwise 2-dimensional boundary layer • 18 stations on wing alone • Interpolate from unstructured surface mesh • Transpiration condition for simulated BL displacement thickness VKI Lecture Series, February 3-7, 2003

  24. Euler vs. RANS Solution Euler Solution (235,000 pts) RANS Solution (1.65M pts) • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS VKI Lecture Series, February 3-7, 2003

  25. Euler-IBL vs. RANS Solution Euler-IBL Sol. (235,000 pts) RANS Solution (1.65M pts) • 235,000 vertex mesh • (ICEMCFD tetra) • Fully tetrahedral mesh • Convergence in 50 cycles • (multigrid) • 3 minutes on 8 Pentiums • 50 times faster than RANS VKI Lecture Series, February 3-7, 2003

  26. Coupled Euler-Boundary Layer Approach VKI Lecture Series, February 3-7, 2003

  27. Coupled Euler-Boundary-Layer Approach • Vastly improved over Euler alone • Correct shock strength, location • Accurate lift • Reasonable drag • More sophisticated coupling possible • 25 times faster than RANS • Neglibible IBL compute time • Convergence dominated by coupling • Parameter studies • Design optimization VKI Lecture Series, February 3-7, 2003

  28. LES and DES Methods • RANS failures for separated flows • Good cruise design involves minimal separation • Off design, high-lift • LES or DES as alternative to turbulence modeling inadequacies • LES: compute all scales down to inertial range • Based on universality of inertial range • DES: hybrid LES/RANS (near wall) • Reduced cost VKI Lecture Series, February 3-7, 2003

  29. LES and DES: Notable Successes • European LESFOIL program • Marie and Sagaut: LES about airfoil near stall • DES for massively separated aerodynamic flows • Strelets 2001, Forsythe 2000, 2001, 2003 • Two to ? Orders of magnitude more expensive than RANS • Predictive ability for accurate drag not established • RANS methods state-of-art for foreseeable future VKI Lecture Series, February 3-7, 2003

  30. Grid Resolution and Discretization Issues • Choice of discretization and effect of dissipation (intricately linked) • Cells versus points • Discretization formulations • Grid resolution requirements • Choice of element type • Grid resolution issues • Grid convergence VKI Lecture Series, February 3-7, 2003

  31. Cell Centered vs Vertex-Based • Tetrahedral Mesh contains 5 to 6 times more cells than vertices • Hexahedral meshes contain same number of cells and vertices (excluding boundary effects) • Prismatic meshes: cells = 2X vertices • Tetrahedral cells : 4 neighbors • Vertices: 20 to 30 neighbors on average VKI Lecture Series, February 3-7, 2003

  32. Cell Centered vs Vertex-Based • On given mesh: • Cell centered discretization: Higher accuracy • Vertex discretization: Lower cost • Equivalent Accuracy-Cost Comparisons Difficult • Often based on equivalent numbers of surface unknowns (2:1 for tet meshes) • Levy (1999) • Yields advantage for vertex-discretization VKI Lecture Series, February 3-7, 2003

  33. Cell Centered vs Vertex-Based • Both approaches have advantages/drawbacks • Methods require substantially different grid resolutions for similar accuracy • Factor 2 to 4 possible in grid requirements • Important for CFD practitioner to understand these implications VKI Lecture Series, February 3-7, 2003

  34. Example: DLR-F4 Wing-body (AIAA Drag Prediction Workshop) VKI Lecture Series, February 3-7, 2003

  35. Illustrative Example: DLR-F4 • NSU3D: vertex-based discretization • Grid : 48K boundary pts, 1.65M pts (9.6M cells) • USM3D: cell-centered discretization • Grid : 50K boundary cells, 2.4M cells (414K pts) • Uses wall functions • NSU3D: on cell centered type grid • Grid: 46K boundary cells, 2.7M cells (470K pts) VKI Lecture Series, February 3-7, 2003

  36. Cell versus Vertex Discretizations • Similar Lift for both codes on cell-centered grid • Baseline NSU3D (finer vertex grid) has lower lift VKI Lecture Series, February 3-7, 2003

  37. Cell versus Vertex Discretizations • Pressure drag • Wall treatment discrepancies • NSU3D : cell centered grid • High drag, (10 to 20 counts) • Grid too coarse for NSU3D • Inexpensive computation • USM3D on cell-centered grid closer to NSU3D on vertex grid Concentrate exclusively on Vertex-Discretizations VKI Lecture Series, February 3-7, 2003

  38. Grid Resolution and Discretization Issues • Choice of discretization and effect of dissipation (intricately linked) • Cells versus points • Discretization formulations • Grid resolution requirements • Choice of element type • Grid resolution issues • Grid convergence VKI Lecture Series, February 3-7, 2003

  39. Discretization • Governing Equations: Reynolds Averaged Navier-Stokes Equations • Conservation of Mass, Momentum and Energy • Single Equation turbulence model (Spalart-Allmaras) • Convection-Diffusion – Production • Vertex-Based Discretization • 2nd order upwind finite-volume scheme • 6 variables per grid point • Flow equations fully coupled (5x5) • Turbulence equation uncoupled VKI Lecture Series, February 3-7, 2003

  40. Spatial Discretization • Mixed Element Meshes • Tetrahedra, Prisms, Pyramids, Hexahedra • Control Volume Based on Median Duals • Fluxes based on edges • Single edge-based data-structure represents all element types Fik = F(uL) + F(uR) + T |L| T-1 (uL –uR) - Upwind discretization - Matrix artificial dissipation VKI Lecture Series, February 3-7, 2003

  41. Upwind Discretization • First order scheme • Second order scheme • Gradients evaluated at vertices by Least-Squares • Limit Gradients for Strong Shock Capturing

  42. Matrix Artificial Dissipation • First order scheme • Second order scheme • By analogy with upwind scheme: • Blending of 1st and 2nd order schemes for strong shock capturing VKI Lecture Series, February 3-7, 2003

  43. Entropy Fix L matrix: diagonal with eigenvalues: u, u, u, u+c, u-c • Robustness issues related to vanishing eigenvalues • Limit smallest eigenvalues as fraction of largest eigenvalue: |u| + c • u = sign(u) * max(|u|, d(|u|+c)) • u+c = sign(u+c) * max(|u+c|, d(|u|+c)) • u – c = sign(u -c) * max(|u-c|, d(|u|+c)) VKI Lecture Series, February 3-7, 2003

  44. Entropy Fix • u = sign(u) * max(|u|, d(|u|+c)) • u+c = sign(u+c) * max(|u+c|, d(|u|+c)) • u – c = sign(u -c) * max(|u-c|, d(|u|+c)) d = 0.1 : typical value for enhanced robustness d = 1.0 : Scalar dissipation - L becomes scaled identity matrix • T |L| T-1 becomes scalar quantity • Simplified (lower cost) dissipation operator • Applicable to upwind and art. dissipation schemes VKI Lecture Series, February 3-7, 2003

  45. Discretization Formulations • Examine effect of discretization type and parameter variations on drag prediction • Effect on drag polars for DLR-F4: • Matrix artificial dissipation • Dissipation levels • Entropy fix • Low order blending • Upwind schemes • Gradient reconstruction • Entropy fix • Limiters VKI Lecture Series, February 3-7, 2003

  46. Effect of Artificial Dissipation Level • Increased accuracy through lower dissipation coef. • Potential loss of robustness

  47. Effect of Entropy Fix for Artificial Dissipation Scheme • Insensitive to small values of d=0.1, 0.2 • High drag values for large d and scalar scheme

  48. Effect of Artificial Dissipation VKI Lecture Series, February 3-7, 2003

  49. Effect of Low-Order Dissipation Blending for Shock Capturing • Lift and drag relatively insensitive • Generally not recommended for transonics

  50. Comparison of Discretization Formulation (Art. Dissip vs. Grad. Rec.) • Least squares approach slightly more diffusive • Extremely sensitive to entropy fix value

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