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Drag Prediction Using Automatic Hexahedra Grid Generation Method - - PowerPoint PPT Presentation

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4th AIAA CFD Drag Prediction Workshop June 20-21, 2009. San Antonio, TX. Drag Prediction Using Automatic Hexahedra Grid Generation Method Atsushi Hashimoto, Keiichi Murakami, Takashi Aoyama, Mitsuhiro Murayama, Kazuomi Yamamoto Japan

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Drag Prediction Using Automatic Hexahedra Grid Generation Method

Atsushi Hashimoto, Keiichi Murakami, Takashi Aoyama, Mitsuhiro Murayama, Kazuomi Yamamoto Japan Aerospace Exploration Agency (JAXA)

4th AIAA CFD Drag Prediction Workshop June 20-21, 2009. San Antonio, TX.

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Objective

The objective of this study is evaluation of an automatic hexahedra grid generator, HexaGrid.

Contents

Features of HexaGrid

  • Grid generated by HexaGrid

Flow solver (TAS) Results

  • Comparison with JAXA’s other results.

(MEGG3D+TAS, Gridgen+UPACS)

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Features of HexaGrid

  • Unstructured mesh based on Cartesian mesh
  • Handles complex geometry
  • Automatic operation (very few control parameters)
  • Predominantly hexahedral element
  • Input multi-component geometry in STL format
  • Run on ordinary PC and

JSS (JAXA Supercomputer System).

HexaGrid : Automatic grid generator based on hexahedral grid

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Input parameters

  • Domain (max and min of x, y, z)
  • Max and min cell size on the surface
  • Layer parameter (thickness of first

layer, expansion factor)

Automatic operation using very few control parameters

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Mesh Refinement Control

  • Start with one big element (= computational domain)
  • Cartesian grid is generated by means of successive local refinement
  • Each refinement divides a cell isotropically into eight child cells
  • Refine the element using 3 criteria
  • Each criterion has a target element size (user-defined)

(1) Region refined by solid surface (user defines max cell size) (2) Region refined by solid surface with large curvature (user defines min cell size) (3) Refinement box (user defines box position and cell size) We do not use the refinement box for simplicity in this study .

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Prismatic grid generation

Grid surface snapped to solid surface Prismatic grid generation Grid smoothing

Thickness of first layer and expansion factor are given by the input parameters

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Feature capturing Feature capturing

STL data Grid surface

Without feature capturing With feature capturing

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Setting of gridding parameters

Upper surface

  • f main wing

Setting parameter Coarse Medium Fine Max cell size on solid surface 5 in 5 in 5 in Min cell size on solid surface 5 in 1.25 in (=5/22) 0.625 in (=5/23) Expansion ratio of prism layers 1.25 1.25 1.25 Thickness of first prism layer 9.85E-4 in 9.85E-4 in 9.85E-4 in Cubic domain size 100 Cref 100 Cref 100 Cref Reference Chord length = 275.80 in Gridding Guidelines

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Setting of gridding parameters

Upper surface

  • f main wing

Setting parameter Coarse Medium Fine Max cell size on solid surface 5 in 5 in 5 in Min cell size on solid surface 5 in 1.25 in (=5/22) 0.625 in (=5/23) Expansion ratio of prism layers 1.25 1.25 1.25 Thickness of first prism layer 9.85E-4 in 9.85E-4 in 9.85E-4 in Cubic domain size 100 Cref 100 Cref 100 Cref Reference Chord length = 275.80 in Gridding Guidelines 0.1% of local chord at LE, TE 0.11-0.47in for the main wing (Gridding Guidelines) 10-50 times larger grid size (Coarse grid) 3-10 times larger grid size (Medium grid) 1.5-6 times larger grid size (Fine grid)

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Grids generated with HexaGrid

Coarse Medium Fine

Coarse Medium Fine Number of refinement process 13 15 16 Number of prism layers 35 29 26 Node count 3,213,783 11,055,602 36,601,899 Cell count 3,644,942 12,654,764 41,630,191 Boundary node count 105,686 295,394 757,593 Boundary face count 106,272 297,697 762,131 Prismatic cell count 1,932,525 7,145,542 17,752,826 3.5M (Coarse), 10M (medium), 35M (fine) are required by the guideline.

+2 +3 Body/main wing juncture Feature line is clearly captured

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Grids generated with HexaGrid

Coarse Medium Fine

Coarse Medium Fine Number of refinement process 13 15 16 Number of prism layers 35 29 26 Node count 3,213,783 11,055,602 36,601,899 Cell count 3,644,942 12,654,764 41,630,191 Boundary node count 105,686 295,394 757,593 Boundary face count 106,272 297,697 762,131 Prismatic cell count 1,932,525 7,145,542 17,752,826 3.5M (Coarse), 10M (medium), 35M (fine) are required by the guideline.

+2 +3 Wing tip of main wing

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Grids generated with HexaGrid

Coarse Medium Fine

Coarse Medium Fine Number of refinement process 13 15 16 Number of prism layers 35 29 26 Node count 3,213,783 11,055,602 36,601,899 Cell count 3,644,942 12,654,764 41,630,191 Boundary node count 105,686 295,394 757,593 Boundary face count 106,272 297,697 762,131 Prismatic cell count 1,932,525 7,145,542 17,752,826 3.5M (Coarse), 10M (medium), 35M (fine) are required by the guideline.

+2 +3 Tail wing

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Grids generated with HexaGrid

Coarse Medium Fine

Coarse Medium Fine Number of refinement process 13 15 16 Number of prism layers 35 29 26 Node count 3,213,783 11,055,602 36,601,899 Cell count 3,644,942 12,654,764 41,630,191 Boundary node count 105,686 295,394 757,593 Boundary face count 106,272 297,697 762,131 Prismatic cell count 1,932,525 7,145,542 17,752,826 3.5M (Coarse), 10M (medium), 35M (fine) are required by the guideline.

+2 +3 Cross-section of main wing at eta=0.50

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Grids generated with HexaGrid

Coarse Medium Fine

Coarse Medium Fine Number of refinement process 13 15 16 Number of prism layers 35 29 26 Node count 3,213,783 11,055,602 36,601,899 Cell count 3,644,942 12,654,764 41,630,191 Boundary node count 105,686 295,394 757,593 Boundary face count 106,272 297,697 762,131 Prismatic cell count 1,932,525 7,145,542 17,752,826 3.5M (Coarse), 10M (medium), 35M (fine) are required by the guideline.

+2 +3 Trailing edge of main wing at eta=0.50 5-6 nodes are located across the TE base. The total thickness

  • f prism layer is

decreasing.

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Flow Solver Configuration

TAS-code

(Tohoku University Aerodynamic Simulation code) Mesh: Unstructured grid Discretization: Cell vertex, finite volume method Flux: HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) Accuracy: Second order by a linear reconstruction with Venkatakrishnan’s limiter and U-MUSCL Time integration: LU-SGS Turbulence model: Spalart-Allmaras (SA) As for the SA model, the trip term and the ft2 function are not

  • included. A modified production term is used.
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Results

Cp contours (M=0.85, CL=0.50, Medium Grid)

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1.1 Grid convergence study

0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.022 0.024 0.026 0.028 0.03 0.032 CD CL Coarse Medium Fine

0.0270 0.0275 0.0280 0.0285 0.0290 0.0295 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 5.E-05 1/(Gridsize)^(2/3) CD HexaGrid+TAS

M=0.85, CL=0.50 Coarse, medium, fine grids

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1.2 Downwash study

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.015 0.025 0.035 0.045 0.055 CD CL iH=-2 iH=0 iH=2 No tail 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 2 3 4 5 AoA CL iH=-2 iH=0 iH=2 No tail 0.1 0.2 0.3 0.4 0.5 0.6 0.7

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 CM CL iH=0 iH=-2 iH=2 No tail 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.015 0.02 0.025 0.03 0.035 Idealized CD CL iH=-2 iH=0 iH=2 No tail

=CD-CL

2/πAR

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Trim Drag

TRIMMED DRAG POLAR => Interpolate iH at fixed CL to calculate CM_TOT = 0.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.015 0.025 0.035 0.045 0.055 CD CL iH=-2 iH=0 iH=2 No tail Trimed

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2 Mach sweep study

CD at CL=0.4, 0.45, and 0.5 for M=0.7-0.87

0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.7 0.75 0.8 0.85 0.9 Mach number CD CL=0.4 CL=0.45 CL=0.5

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Comparison with other results

MEGG3D + TAS Gridgen + UPACS Multi-block structured grid Tetra unstructured grid HexaGrid + TAS Hexa unstructured grid

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Grid convergence study

0.0265 0.0270 0.0275 0.0280 0.0285 0.0290 0.0295 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 5.E-05 1/(Gridsize)^(2/3) CD HexaGrid+TAS MEGG3D+TAS UPACS 0.0140 0.0145 0.0150 0.0155 0.0160 0.0165 0.0170 0.0175 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 5.E-05 1/(Gridsize)^(2/3) CD_pressure HexaGrid+TAS MEGG3D+TAS UPACS 0.012 0.0121 0.0122 0.0123 0.0124 0.0125 0.0126 0.0127 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 5.E-05 1/(Gridsize)^(2/3) CD_friction HexaGrid+TAS MEGG3D+TAS UPACS

CD_total CD_pressure CD_skin-friction Grid convergence study of iH=0 model at CL=0.500, M=0.85 Large sensitivity of grid size HexaGrid+TAS results are between MEGG3D+TAS and UPACS. (The results of HexaGrid are comparable to the manual methods.)

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Cp distribution (Medium, iH=0, CL=0.5)

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 HexaGrid+TAS MEGG3D+TAS UPACS

η=0.95 η=0.50 η=0.20 η=0.30

Eta=0.2 Eta=0.5 Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5 Eta=0.95 Eta=0.3 (tail)

HexaGrid results agree well with the other results. The shock wave in the middle of wing is well captured with HexaGrid. The suction peak is smaller than the others at the wing tip due to the coarse LE grid.

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Cp distribution (Medium, iH=0, CL=0.5)

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 HexaGrid+TAS MEGG3D+TAS UPACS

η=0.95 η=0.50 η=0.20 η=0.30

Eta=0.2 Eta=0.5 Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5 Eta=0.95 Eta=0.3 (tail)

HexaGrid results agree well with the other results. The shock wave in the middle of wing is well captured with HexaGrid. The suction peak is smaller than the others at the wing tip due to the coarse LE grid.

Eta=0.5

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Cp distribution (Medium, iH=0, CL=0.5)

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 HexaGrid+TAS MEGG3D+TAS UPACS

η=0.95 η=0.50 η=0.20 η=0.30

Eta=0.2 Eta=0.5 Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5 Eta=0.95 Eta=0.3 (tail)

HexaGrid results agree well with the other results. The shock wave in the middle of wing is well captured with HexaGrid. The suction peak is smaller than the others at the wing tip due to the coarse LE grid.

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Cp distribution (Medium, iH=0, CL=0.5)

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 HexaGrid+TAS MEGG3D+TAS UPACS

η=0.95 η=0.50 η=0.20 η=0.30

Eta=0.2 Eta=0.5 Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5 Eta=0.95 Eta=0.3 (tail)

HexaGrid results agree well with the other results. The shock wave in the middle of wing is well captured with HexaGrid. The suction peak is smaller than the others at the wing tip due to the coarse LE grid.

Eta=0.95

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Cp distribution (Medium, iH=0, CL=0.5)

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 x/c Cp HexaGrid+TAS MEGG3D+TAS UPACS

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 HexaGrid+TAS MEGG3D+TAS UPACS

η=0.95 η=0.50 η=0.20 η=0.30

Eta=0.2 Eta=0.5 Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5 Eta=0.95 Eta=0.3 (tail)

HexaGrid results agree well with the other results. The shock wave in the middle of wing is well captured with HexaGrid. The suction peak is smaller than the others at the wing tip due to the coarse LE grid.

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Wing tip Cp contours (CL=0.5, medium grid)

HexaGrid MEGG3D UPACS

Smeared in the spanwise direction Smeared due to the coarse grid Clearly captured (LE resolution is not sufficient)

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Angle sweep (iH=0, medium grid)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.015 0.025 0.035 0.045 0.055 CD CL HexaGrid+TAS MEGG3D+TAS UPACS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 AoA CL HexaGrid+TAS MEGG3D+TAS UPACS

HexaGrid results agree well with the other results.

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Stalled flow at AoA of 4deg

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 AoA CL HexaGrid+TAS MEGG3D+TAS UPACS

HexaGrid MEGG3D UPACS The separation line and pattern are largely affected by the grid topologies.

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Conclusion

  • Capability and limitation of HexaGrid
  • Automatic method, prism layer, feature capturing,

mainly hexahedral element Good

  • Coarse LE and TE grids Not good
  • HexaGrid results agree well with the other grids (tetra

unstructured grid, multi-block structured grid).

HexaGrid can automatically generate grids comparable

to manual methods.

  • The shock wave in the middle of wing is well captured

with HexaGrid.

  • Larger separation is observed in the case of HexaGrid.