drag prediction using automatic hexahedra grid generation ... · grid convergence study of ih=0...

1

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 WorkshopJune 20-21, 2009. San Antonio, TX.

2

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)

3

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

4

Input parameters

Domain (max and min of x, y, z)Max and min cell size on the surfaceLayer parameter (thickness of first layer, expansion factor)

Automatic operation using very few control parameters

5

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 .

6

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

7

Feature capturing Feature capturing

STL data

Grid surface

Without feature capturing

With feature capturing

8

Setting of gridding parameters

Upper surface of main wing

Setting parameter Coarse Medium FineMax cell size on solid surface 5 in 5 in 5 inMin 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 1.25Thickness 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 inGridding Guidelines

9

Setting of gridding parameters

Upper surface of main wing

Setting parameter Coarse Medium FineMax cell size on solid surface 5 in 5 in 5 inMin 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 1.25Thickness 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 inGridding 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)

10

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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Coarse Medium Fine

Coarse Medium Fine



Node count 3,213,783 11,055,602 36,601,899

Cell count 3,644,942 12,654,764 41,630,191





+2+3

Wing tip of main wing

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Coarse Medium Fine

Coarse Medium Fine



Node count 3,213,783 11,055,602 36,601,899

Cell count 3,644,942 12,654,764 41,630,191





+2+3

Tail wing

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Coarse Medium Fine

Coarse Medium Fine



Node count 3,213,783 11,055,602 36,601,899

Cell count 3,644,942 12,654,764 41,630,191





+2+3

Cross-section of main wing at eta=0.50

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Coarse Medium Fine

Coarse Medium Fine



Node count 3,213,783 11,055,602 36,601,899

Cell count 3,644,942 12,654,764 41,630,191





+2+3

Trailing edge of main wing at eta=0.50

5-6 nodes are located across the TE base.

The total thickness of prism layer is decreasing.

15

Flow Solver Configuration

TAS-code(Tohoku University Aerodynamic Simulation code)

Mesh: Unstructured gridDiscretization: Cell vertex, finite volume methodFlux: HLLEW (Harten-Lax-van Leer-Einfeldt-Wada)Accuracy: Second order by a linear reconstruction with

Venkatakrishnan’s limiter and U-MUSCLTime integration: LU-SGSTurbulence 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)

17

1.1 Grid convergence study

0.420.430.440.450.46

0.470.480.490.500.510.52

0.53

0.022 0.024 0.026 0.028 0.03 0.032CD

CL Coarse

MediumFine

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)C

D

HexaGrid+TAS

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

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1.2 Downwash study

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=-2iH=0iH=2No tail

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5

AoA

CL


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

CM

CL

iH=0iH=-2iH=2No tail

0

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


=CD-CL2/πAR

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Trim Drag

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

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=-2iH=0iH=2No tailTrimed

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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=0.4CL=0.45CL=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

22

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+TASMEGG3D+TASUPACS

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

_pre

ssure


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


CD_total

CD_pressure CD_skin-friction

Grid convergence study of iH=0 modelat CL=0.500, M=0.85

Large sensitivity of grid sizeHexaGrid+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

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1


η=0.95

η=0.50

η=0.20η=0.30

Eta=0.2

Eta=0.5

Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5

Eta=0.95Eta=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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-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1


η=0.95

η=0.50

η=0.20η=0.30

Eta=0.2

Eta=0.5

Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5





Eta=0.5

25


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1


η=0.95

η=0.50

η=0.20η=0.30

Eta=0.2

Eta=0.5

Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5





26


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1


η=0.95

η=0.50

η=0.20η=0.30

Eta=0.2

Eta=0.5

Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5





Eta=0.95

27


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

x/c

Cp


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1


η=0.95

η=0.50

η=0.20η=0.30

Eta=0.2

Eta=0.5

Eta=0.95

Eta=0.30

Eta=0.2 Eta=0.5





28

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

HexaGrid MEGG3D UPACS

Smeared in the spanwisedirection

Smeared due to the coarse grid

Clearly captured(LE resolution is not sufficient)

29

Angle sweep (iH=0, medium grid)

0

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+TASUPACS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5

AoA

CL



30

Stalled flow at AoA of 4deg

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5

AoA

CL


HexaGrid

MEGG3D

UPACS

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

31

Conclusion

Capability and limitation of HexaGridAutomatic method, prism layer, feature capturing, mainly hexahedral element GoodCoarse 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.


Larger separation is observed in the case of HexaGrid.

drag prediction using automatic hexahedra grid generation ... · grid convergence study of ih=0...

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