Results from the 3rd Drag Prediction Workshop using the

NSU3D Unstructured Mesh Solver

Dimitri J. MavriplisUniversity of Wyoming

Overview

• Description of Meshes • Description of NSU3D Solver

– Sample performance– Preliminary Sensitivity Evaluations

• WB and WBF Results• W1 and W2 Results

– Including runs performed at Cessna on 2nd family of grids

• Conclusions

General Gridding Guidelines

• Grid Convergence Cases:

– DLR F6 WBF• 3 grid levels required

– DLR F6 WB • Medium grid required, coarse/fine optional

– Wing1 and Wing2• Four grid levels required

General Gridding Guidelines• Grid Resolution Guidelines

– BL Region• Y+ < 1.0, 2/3, 4/9, 8/27 (Coarse,Med,Fine,VeryFine)• 2 cell layers constant spacing at wall• Growth rates < 1.25

– Far Field: 100 chords – Local Spacings (Medium grid)

• Chordwise: 0.1% chord at LE/TE• Spanwise spacing: 0.1% semispan at root/tip• Cell size on Fuselage nose, tail: 2.0% chord

– Trailing edge base:• 8,12,16,24 cells across TE Base (Coarse,Med,Fine,Veryfine)

General Gridding Guidelines

• Grid Convergence Sequence– Grid size to grow ~3X for each level refinement

• 1.5X in each coordinate direction (structured)– Maintain same family of grids in sequence

• Same relative resolution/topology/growth factors– Sample sizes (DLR F6 WBF):

• 2.7M, 8M, 24M pts (structured grids)• Unstructured grids should be similar

– Cell based vs. Node Based Unstructured solvers– 5 to 6 times more tetrahedra per nodes– 2 times more prisms than nodes

Available (Posted) Unstructured Grids

• VGRID (NASA Langley)– Node-Based grids NASA(W1,W2,WB,WBF)– Node-Based grids Cessna (W1,W2)– Cell Centered Grids Raytheon (WB,WBF)

• ANSYS Hybrid Meshes• Centaur (DLR, adapted) (Node Based)• AFLR3 (Boeing) (Cell Centered)• TAS (JAXA) (Node Based)• GridPro (Block-Structured/Unstructured)

VGRID NASA (Node Based)

• WB:– Coarse : 5.3M pts– Medium: 14.3M pts– Fine: 40.0M pts (> 200M cells)

• WBF:– Coarse: 5.6M pts– Medium: 14.6M pts– Fine: 41.1M pts ( > 200M cells)

VGRID Node Centered (NASA)

VGRID Node Centered (NASA)

VGRID Node Centered (NASA)

NSU3D Description• Unstructured Reynolds Averaged Navier-

Stokes solver– Vertex-based discertization– Mixed elements (prisms in boundary layer)– Edge data structure– Matrix artificial dissipation

• Option for upwind scheme with gradient reconstruction

– No cross derivative viscous terms• Thin layer in all 3 directions• Option for full Navier-Stokes terms

Solver Description (cont’d)• Spalart-Allmaras turbulence model

– (original published form)– Optional k-omega model

Solution Strategy• Jacobi/Line Preconditioning

– Line solves in boundary layer regions• Relieves aspect ratio stiffness

• Agglomeration multigrid– Fast grid independent convergence rates

• Parallel implementation– MPI/OpenMP hybrid model

• DPW runs: MPI on local cluster and on NASA Columbia Supercomputer

Grid Generation• Runs based on NASA Langley supplied

VGRIDns unstructured grids• Tetrahedra in Boundary Layer merged into

prismatic elements

• Grid sizes up to 41M pts, 240M elements

Sample Run Times• All runs performed on NASA Columbia Supercomputer

– SGI Altix 512cpu machines– Coarse/Medium (~15Mpts) grids used 96 cpus

• Using 500 to 800 multigrid cycles– 30 minutes for coarse grid– 1.5 hrs for medium grid

– Fine Grids (~40M pts) used 248 cpus• Using 500 to 800 multigrid cycles

– 1.5 to 2 hrs hrs for fine grid

– CL driver and constant incidence convergence similar– WB cases hard to converge (not entirely steady)

Scalability

• Near ideal speedup for 72M pt grid on 2008 cpus of NASA Columbia Machine

(~10 minutes for steady-state solution)

NSU3D Sensitivity Studies

• Sensitivity to Distance Function Calculation Method

• Effect of Multi-Dimensional Thin-Layer versus Full Navier-Stokes Terms

• Sensitivity to Levels of Artificial Dissipation

Sensitivity to Distance Function

• All DPW3 Calculations done with Eikonal equation distance function

Sensitivity to Navier-Stokes Terms

• All DPW3 Calculations done with Multidimensional Thin-Layer Formulation

Sensitivity to Dissipation Levels

• Drag is grid converging• Sensitivity to dissipation decreases as expected• All Calculations done with low dissipation level

WBF Convergence (fixed alpha)

• “Similar” convergence for all grids• Force coefficients well converged < 500 MG cycles

WBF Convergence

• Medium Grid (15M pts): Fixed alpha

WBF Convergence

• Medium Grid (15M pts): Fixed CL

WBF Convergence

• Similar convergence (Fixed CL or alpha)

WBF: Grid Convergence Study

• CP at wing break station (y/b=0.411)

WBF: Grid Convergence Study

• CP at wing break station (y/b=0.411)

WBF: Grid Convergence Study

• CP at wing break station (y/b=0.411)

WBF: Grid Convergence Study

• CF at wing break station (y/b=0.411)

WBF: Grid Convergence Study

• Good fairing design (coarse grid: 5M pts)

WBF: Grid Convergence Study

• Good fairing design (medium grid: 15M pts)

WBF: Grid Convergence Study

• Good fairing design (fine grid: 40M pts)

WBF: TE Separation

• Coarse grid: 5M pts

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CP at wing break station (y/b=0.411)

WBF: Drag Polar

• CFX at wing break station (y/b=0.411)

WBF: Drag Polar

• Full Polar run on all 3 grids (5, 15, 40M pts)

WBF: Drag Polar

• Full Polar run on all 3 grids (5, 15, 40M pts)

WBF: Moment

• Full Polar run on all 3 grids (5, 15, 40M pts)

WBF: Moment

• Full Polar run on all 3 grids (5, 15, 40M pts)

WB Convergence (fixed alpha)

• Separated Flow, unsteady shedding pattern• Smaller residual excursions with fewer MG levels• Moderate CL variations

WB Medium Grid

• Plot Min and Max unsteady CL values

WB Medium Grid

• Plot Min and Max unsteady CL values• Good overlap in polar– suitable drag values

WB Medium Grid

• Plot Min and Max unsteady CL values• Less overlap in CM

WB Medium Grid

• CP Values at Break Station (y/b=0.411)

WB Medium Grid

• CFX Values at Break Station (y/b=0.411)

WB Grid Convergence

• CP Values at Break Station (y/b=0.411)

WB Grid Convergence

• CFX Values at Break Station (y/b=0.411)

WB Grid Convergence

• Separation Pattern (Coarse grid : 5M pts)

WB Grid Convergence

• Separation Pattern (Medium grid : 5M pts)

WB Grid Convergence

• Separation Pattern (Fine grid : 40M pts)

WB TE Separation Pattern

• (Coarse grid : 5M pts)

Grid Convergence (WB+WBF)

• Grid convergence apparent (particularly for WBF)

Grid Convergence (WB+WBF)

• Some cancellation apparent: WBF less uniformly converging

Grid Convergence (WB+WBF)

• Grid Convergence Ranked 8th in Vassberg Fig. of Merit:– Best for unstructured solvers ….. Importance of uniform family of grids

Grid Convergence (WB+WBF)

• Grid convergence apparent (in this measure)

Grid Convergence (WB+WBF)

• Grid convergence apparent (in this measure)

WBF-WB Differences

• Medium grid comparisons

WBF-WB Differences

• Medium grid comparisons

WBF-WB Differences

• Medium grid comparisons

Grid Convergence of Drag Increment

• Consistent with one group of DPW3 Entries

Conclusions

• WBF appears to be grid converging• WB case is complex

– Previous results showed importance of grid topology

– New DPW3 grids are once again different• DPW1,2,3 pushing s.o.f of grid resolution

– DPW1: 1.6M pts– DPW2: 3M pts to 10M– DPW3: 5M to 40M pts

VGRID NASA (Node Based)• W1:

– Coarse : 1.8M pts– Medium: 4.5M pts– Fine: 11.5M pts– SuperFine: 36.9M pts

• W2:– Coarse: 1.9M pts– Medium: 4.7M pts– Fine: 11.9M pts– SuperFine: 38.5M pts

VGRID NASA (Cessna)• W1:

– Coarse : 0.98M pts– Medium: 2.4M pts– Fine: 6.1M pts– SuperFine: 12.7M pts

• W2:– Coarse: 0.95M pts– Medium: 2.3M pts– Fine: 5.9M pts– SuperFine: 12.4M pts

VGRID Node Centered (NASA)

W1 Convergence (fixed alpha=0.5)

• “Similar” convergence for coarse/med grids• Apparent unsteadiness in residual for finest grid• Force coefficients well converged < 500 MG cycles for all grids

W1 Grid Convergence Study

• CP at station 5:

W1 Grid Convergence Study

• CP at station 5:

W1 Grid Convergence Study

• CP at station 5:

W1 Grid Convergence Study

• CP at station 5:

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W1 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Convergence Study

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

W2 Grid Polar Sweep (Fine Grid)

• CP at station 5

Streamlines at 0.5 degrees (W1)

Streamlines at 0.5 degrees (W2)

W1-W2 Grid Polar Comparison(Fine Grid)

W1-W2 CL-Incidence Comparison(Fine Grid)

W1-W2 Moment Comparison (Fine Grid)

W1-W2 Grid Convergence Study

•Apparently uniform grid convergence

W1-W2 Grid Convergence Study

•Good grid convergence of individual drag component

W1-W2 Grid Convergence Study

•Ranked 1st by Vassberg Figure-of-Merit

W1-W2 Grid Convergence Study

W1-W2 Grid Convergence Study

W1-W2 Results

• Discrepancy between UW and Cessna Results

W1-W2 Results

• Despite uniform grid convergence: Results on 2 grid families not converging to same values

W1-W2 Results

• Removing effect of lift-induced drag : Results on both grid families converge consistently

65M pt mesh Results

• 10% drop in CL at AoA=0o: closer to experiment• Drop in CD: further from experiment• Same trends at Mach=0.3• Little sensitivity to dissipation

Summary

• W1-W2 appear to be in asymptotic grid convergence range– Cd difference ~ 1 count at 0.5 degrees

• Grids are getting finer …..40M pts ~1 hr on NASA Columbia Supercomputer

• Drag decomposition useful in providing better drag estimates on coarser grids