Results from the 3 rd Drag Prediction Workshop using the NSU3D Unstructured Mesh Solver Dimitri J. Mavriplis University 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 2 nd 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)

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 8 th 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 1 st by Vassberg Figure-of-Merit

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 C L at AoA=0 o : closer to experiment Drop in C D : 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