Case 3.1: Turbulent Flow over a 2D Multi-Element Airfoil. Summary of Results. Marco Ceze
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1 Case 3.1: Turbulent Flow over a 2D Multi-Element Airfoil Summary of Results Marco Ceze (mceze@umich.edu) 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 1/14
2 Case description Objective: Test high-order methods in turbulent flow conditions over a complex geometry. Outputs of interest are lift and drag. Flow conditions: M = 0.2 at α = 16. Re = based on c ref = , fully turbulent. Gas properties: γ = 1.4 and Pr = Constant viscosity. 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 2/14
3 Geometry and provided mesh 4070 quartic elements generated via agglomeration. Outer boundary located 50 to 100 chord-lengths away from airfoil. 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 3/14
4 Participants codes and meshes Bergamo: k ω Turbulence model and Sutherland s law for viscosity. DG, hierarchical orthonormal basis on reference domain. van Leer-Hänell splitting for inviscid flux, BR2 for viscous discretization. Full p-muitigrid, backward-euler smoothing, PETSc (GMRES) linear solver. 12-node, quad-mesh with 35 to 100 chord-lengths farfield distance. Runs performed on 32 to 64 cores. Michigan: SA turbulence model. 2 sets of runs: constant and variable viscosity. DG, Lagrange basis on reference domain. Roe solver for inviscid flux, BR2 for viscous discretization. CPTC with in-house GMRES and line-jacobi preconditioner. EXPur for CFL evolution. HOW mesh. Runs performed on 60 cores. 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 4/14
5 Participants codes and meshes DLR: k ω Turbulence model. DG, hierarchical polynomial basis on physical space. Roe solver for inviscid flux, BR2 for viscous discretization. PTC with GMRES linear solver, hp-multigrid preconditioner. SER for CFL evolution. 2 curved meshes with far field of 35c to 100c and 44c to 50c. Runs performed in serial. TsAGI: EARSM turbulence model, Sutherland s law for viscosity. DG, hierarchical polynomial basis defined on physical space. Roe solver for inviscid flux, BR2 for viscous discretization. 5-step Runge-Kutta with full hp-multigrid. Hanging-node quad linear mesh. Runs performed on 16 cores. 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 5/14
6 Drag convergence versus DOFs drag Bergamo, coarse mesh, p ref = 3 5 Bergamo, fine mesh, p ref = 2 3 UM Drag based hp UM Drag based hp, error corrected UM Drag based iso h, p1 UM Drag based iso h, p1, error corrected DLR, p = 1, Bergamo mesh DLR, p = 2, Bergamo mesh DLR, p = 1, DLR mesh DLR, p = 2, DLR mesh TsAGI, p = 1, TsAGI mesh TsAGI, p = 2, TsAGI mesh TsAGI, p = 3, TsAGI mesh Reference DLR, FV, Tri mesh ndof^( 1/2) 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 6/14
7 Drag convergence versus workunits drag Bergamo, coarse mesh, p ref = 3 5 Bergamo, fine mesh, p ref = 2 3 UM Drag based hp UM Drag based hp, error corrected UM Drag based iso h, p1 UM Drag based iso h, p1, error corrected DLR, p = 1, Bergamo mesh DLR, p = 2, Bergamo mesh DLR, p = 1, DLR mesh DLR, p = 2, DLR mesh TsAGI, p = 1, TsAGI mesh TsAGI, p = 2, TsAGI mesh TsAGI, p = 3, TsAGI mesh Reference DLR, FV, Tri mesh workunits 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 7/14
8 Lift convergence versus DOFs lift Bergamo, coarse mesh, p ref = 3 5 Bergamo, fine mesh, p ref = 2 3 UM Lift based hp UM Lift based hp, error corrected UM Lift based iso h, p1 UM Lift based iso h, p1, error corrected DLR, p = 1, Bergamo mesh DLR, p = 2, Bergamo mesh DLR, p = 1, DLR mesh DLR, p = 2, DLR mesh TsAGI, p = 1, TsAGI mesh TsAGI, p = 2, TsAGI mesh TsAGI, p = 3, TsAGI mesh Reference DLR, FV, Tri mesh ndof^( 1/2) 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 8/14
9 Lift convergence versus workunits lift Bergamo, coarse mesh, p ref = 3 5 Bergamo, fine mesh, p ref = 2 3 UM Lift based hp UM Lift based hp, error corrected UM Lift based iso h, p1 UM Lift based iso h, p1, error corrected DLR, p = 1, Bergamo mesh DLR, p = 2, Bergamo mesh DLR, p = 1, DLR mesh DLR, p = 2, DLR mesh TsAGI, p = 1, TsAGI mesh TsAGI, p = 2, TsAGI mesh TsAGI, p = 3, TsAGI mesh Reference DLR, FV, Tri mesh workunits 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 9/14
10 C p distribution Cp Ref. Solution (Langer - DLR) UM Lift-based hp UM Lift-based iso-h (p=1) UM Drag-based hp UM Drag-based iso-h (p=1) TsAGI (p = 1) TsAGI (p = 2) TsAGI (p = 3) Bergamo (p = 3) Bergamo (p = 5) DLR (p = 2) Xs 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 10/14
11 C f distribution Cf 0.06 Ref. Solution (Langer - DLR) UM Lift-based hp UM Lift-based iso-h (p=1) UM Drag-based hp UM Drag-based iso-h (p=1) TsAGI (p = 1) TsAGI (p = 2) 0.04 TsAGI (p = 3) Bergamo (p = 3, coarse) Bergamo (p = 5, fine) DLR (p = 2) Xs 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 11/14
12 C f distribution abs(cf) Ref. Solution (Langer - DLR) UM Lift-based hp UM Lift-based iso-h (p=1) UM Drag-based hp UM Drag-based iso-h (p=1) TsAGI (p = 1) TsAGI (p = 2) TsAGI (p = 3) Bergamo (p = 3, coarse) Bergamo (p = 5, fine) DLR (p = 2) Xs 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 12/14
13 Conclusions? Constant or variable viscosity? Turbulence model likely affects the grid-converged values of drag and lift. How about we fix the domain geometry? hp-adaptation provides large savings in terms of degrees-of-freedom. Too much scatter in workunits to draw conclusions (post-processing error or actual difference?). Should we revise the procedure for computing workunits? Good agreement between participants for C p distribution. Disparity in sign definition of C f but absolute values are in reasonable agreement, except on the flap. How about defining a common procedure for computing the sign of C f? 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 13/14
14 Suggestions for next time Modify case definition to variable viscosity with Sutherland s law and T ref. = 288K. A reference IGES geometry file was generated and provided by Marco Ceze with both the airfoil and the far-field geometries. This file should be used for in-house mesh generation. Linear and high-order triangular and quadrilateral meshes were generated by Marco Ceze and they are provided in GMsh format. Please try to use these meshes to facilitate comparisons in future workshops. Please use the sign of the x-component of the shear stress as the sign for C f. 2 nd International Workshop on High-Order CFD Methods, May 27-28, Cologne, Germany C3.1 14/14
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