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Missile Configuration Test Cases

byPeter Cross John CarterRon Schultz

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Purpose of Study• Evaluate the accuracy of the Star-CCM+ CFD package in predicting the

aerodynamic coefficients of supersonic missile configurations– Longitudinal coefficients

• Axial Force, Normal Force, Pitching Moment

– Lateral coefficients• Side Force, Rolling Moment, Yawing Moment

– Invest “reasonable” level of effort in generating meshes and setting up cases– Consider both conventional & unconventional missile configurations– Conduct study over large range of angles of attack– Include configurations with large control deflections

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Missile Configurations Studied

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Missile Configuration Overview• Tandem Control Missile

– “Generic” missile design• Independent tail & canard control surfaces• Test data available for both “+” & “x” orientations

– Simulation conditions• Mach: 2.5• Alpha sweep: 0 - 28 in 2 increments• Control deflections: various combinations up to 20

– Experimental data• Tests conducted by A. B. Blair in Langley Unitary Plan Wind Tunnel in 1993• Data is unpublished, obtained from Floyd Wilcox, NASA Langley• Referenced & used in AIAA 2002-0275

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Star-CCM+ Case Setup• Initial “baseline” configuration

– Import geometry– Select mesh & physics models

• Used coupled flow solver• K-omega turbulence model with All y+ wall treatment

– ~6+ surface mesh user iterations• Even more if using surface wrapper tool

– ~3+ volume mesh user iterations– Set boundary / initial conditions– Set reports / monitors / plots / etc.

• Control deflection configuration– Built upon baseline configuration– ~3 surface mesh user iterations– ~1 volume mesh user iteration

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Star-CCM+ Meshing• Set up mesh on surfaces

– Want refined mesh in areas of high curvature or detail• Nose, leading edge, fins, etc

– Want larger cells in other areas to reduce cell count• Body, domain boundaries, etc

– Want smooth growth rate in cell size• Set up “feature curves”

– To preserve sharp edges or other important geometry features• Set up prism layer mesh to capture boundary layer

– Wall cell thickness to give desired Y+• All y+ 1 < y+ < 30• Low y+ y+ < 0.4 (y+ < 5 recommended )• High y+ 15 < y+ < 40 (30 < y+ < 100 recommended )

– Prism layer thickness, # of cell layers, stretch ratio• Volume mesh generated automatically by program

– Can get large cells where small cells are desired & vice versa• Add “volume sources” to refine mesh in certain areas

– Can get poor cells in interfaces between volume sources or between volume source and prism layer mesh

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Mesh: Tandem Control Missile “+”

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Mesh: Tandem Control Missile “x”

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Star-CCM+ Run Metrics• Tandem control missile in “+” configuration

– Half model– Approximately 1.5M cells– Meshing time

• <5 minutes surface mesh• ~30 minutes volume mesh

– Solution time• ~3 hours per alpha (~600-700 iterations)• Full alpha sweep in <48 hours

• Tandem control missile in “x” configuration– Half model– Approximately 2.0M cells– Meshing time

• <5 minutes surface mesh• ~50 minutes volume mesh

– Solution time• ~6 hours per alpha (~1200 iterations)• Full alpha sweep in <72 hours

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Computing Environments

• “Boxcluster” (primary)– 4 nodes– 1 dual-core Intel Core 2 Duo E6850 processor @ 3.00 GHz per node– 8 GB memory per node– ~270 iterations per hour for 1.5M cells

• “Falcon” (AFRL HPC Cluster)– Used for additional solving power– Used 6 nodes (out of 1024)– 2 single-core AMD Opteron processors @ 2.8 GHz per node– 4 GB memory per node– ~260 iterations per hour for 1.5M cells

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Tandem Control Missile “+” Configuration

Canard: 0 / Tail: 0

Canard: 0 / Tail: -20

Canard: 20 / Tail: -20

Canard: 20 / Tail: 0

Canard: 10 / Tail: 10

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Flow Field: T.C.M “+”, α = 10

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Flow Field: T.C.M “x”, α = 10

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0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Axi

al F

orce

Coe

ffici

ent

Run 47Run 1003Star-CCM+ 0/0Run 1015Star-CCM+ 0/-20Run 1010Star-CCM+ 20/0Run 1046Star-CCM+ 20/-20Run 53Star-CCM+ 10/10

T.C.M. “+” Results: Axial Force

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-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Nor

mal

For

ce C

oeffi

cien

t Run 47Run 1003Star-CCM+ 0/0Run 1015Star-CCM+ 0/-20Run 1010Star-CCM+ 20/0Run 1046Star-CCM+ 20/-20Run 53Star-CCM+ 10/10

T.C.M. “+” Results: Normal Force

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-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Pitc

hing

Mom

ent C

oeffi

cien

t

Run 47Run 1003Star-CCM+ 0/0Run 1015Star-CCM+ 0/-20Run 1010Star-CCM+ 20/0Run 1046Star-CCM+ 20/-20Run 53Star-CCM+ 10/10

Tandem Control Missile “+” Configuration

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Tandem Control Missile “x” Configuration

Canard: 0 / Tail: 0

Canard: 20 / Tail: 0 Canard: 0 / Tail: -20

Canard: 10 / Tail: -10 Canard: 20 / Tail: 20

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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Axi

al F

orce

Coe

ffici

ent Run 1004

Star-CCM+ 0/0Run 1044Star-CCM+ 0/-20Run 1037Star-CCM+ 20/0Run 1020Star-CCM+ 10/-10Run 1039Star-CCM+ 20/20

T.C.M. “x” Results: Axial Force

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-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Nor

mal

For

ce C

oeffi

cien

t Run 1004Star-CCM+ 0/0Run 1044Star-CCM+ 0/-20Run 1037Star-CCM+ 20/0Run 1020Star-CCM+ 10/-10Run 1039Star-CCM+ 20/20

T.C.M. “x” Results: Normal Force

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-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

-5 0 5 10 15 20 25 30

Angle of Attack, degrees

Pitc

hing

Mom

ent C

oeffi

cien

t

Run 1004Star-CCM+ 0/0Run 1044Star-CCM+ 0/-20Run 1037Star-CCM+ 20/0Run 1020Star-CCM+ 10/-10Run 1039Star-CCM+ 20/20

T.C.M. “x” Results: Pitching Moment

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Elliptic Missile

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Missile Configuration Overview

• Elliptic Missile– Unconventional missile concept

• Body has elliptical cross section• Mono-wing design• Tail surfaces in “x” configuration with 30 dihedral

– Simulation conditions• Mach: 2.5• Alpha sweep: 0 - 28 in 2 increments• Beta sweeps: 0 - 10 in 2 increments

– at alpha 0 & 10

• Control deflections: none

– Experimental Data• NASA Technical Memorandum 74079, 1977• NASA Technical Memorandum 80055, 1979

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Mesh: Elliptic Missile (Original)

Cut plane through mesh

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Elliptic Missile Original Mesh (3.7M Cells)

Inadequate mesh refinement in this region

Obtain excessive mesh refinement in this region

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Meshing Issues: Elliptic Missile

Cut plane through mesh (automatic cell size)

Symmetry plane (cell size controlled by surface mesh).

Mesh grows more quickly than desired away from surfaces.

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Elliptic Missile Original Mesh (3.7M Cells)

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Elliptic Missile Improved Mesh (3.8M Cells)

Volume sources placed around fins.

Placed “Interface” surface around missile to slow mesh growth rate near missile body.

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Mesh: Elliptic Missile (Improved)

Cut plane through mesh

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Mesh: Elliptic Missile (Original)

Cut plane through mesh

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Flow Field: Elliptic Missile, α = 10 β = 0

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Flow Field: Elliptic Missile, α = 0 β = 10

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0.00

0.05

0.10

0.15

0.20

0.25

0.30

-5 0 5 10 15 20 25 30 35

Angle of Attack, degrees

Axi

al F

orce

Coe

ffici

ent

ExperimentStar-CCM+Remesh

Elliptic Missile Results: Axial Force

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-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

-5 0 5 10 15 20 25 30 35

Angle of Attack, degrees

Nor

mal

For

ce C

oeffi

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t

ExperimentStar-CCM+Remesh

Elliptic Missile Results: Normal Force

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-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

-5 0 5 10 15 20 25 30 35

Angle of Attack, degrees

Pitc

hing

Mom

ent C

oeffi

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ExperimentStar-CCM+RemeshAdjusted

Elliptic Missile Results: Pitching Moment

If WTT reference center is shifted 0.16” aft of reported location, Star-CCM+ results match experimental data well.

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Elliptic Missile Results: Rolling Moment

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

-6 -4 -2 0 2 4 6 8 10 12

Sideslip Angle, degrees

Rol

ling

Mom

ent C

oeffi

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Experiment, Alpha = 0Star-CCM+, Alpha = 0Remesh, Alpha = 0Experiment, Alpha = 10Star-CCM+, Alpha = 10

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-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

-6 -4 -2 0 2 4 6 8 10 12

Sideslip Angle, degrees

Side

For

ce C

oeffi

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Experiment, Alpha = 0Star-CCM+, Alpha = 0Remesh, Alpha = 0Experiment, Alpha = 10Star-CCM+, Alpha = 10

Elliptic Missile Results: Side Force

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-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

-6 -4 -2 0 2 4 6 8 10 12

Sideslip Angle, degrees

Yaw

ing

Mom

ent C

oeffi

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Experiment, Alpha = 0Star-CCM+, Alpha = 0Remesh, Alpha = 0Experiment, Alpha = 10Star-CCM+, Alpha = 10

Elliptic Missile Results: Yawing Moment

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Results• Axial force

– Consistently under-predicted, similar to other CFD tools.– Trends captured well– Good mesh independence– No clear benefit for using low- or high-y+ wall treatments at these resolutions

• Normal force and Pitching moments (all configurations)– Extremely good correlation between Star-CCM+ results and experimental data– Very Good prediction of control surface effectiveness

• Roll & yaw moments, side force (elliptic missile only)– Worse correlation between Star-CCM+ results and experimental data– Due to neglecting base component or poor mesh? Difficult to predict

separation over body?• Including base component did not impact results• Improving volume mesh did not improve results• Other distribution of prism layer cells? larger prism layer? Other turbulence models?

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Self-Critique• “Reasonable” level of effort used in setting up all simulations

– Typical time & effort used to generate meshes and set up cases– Additional effort was put into generating the various improved meshes for the

elliptic missile, but did not appear to be beneficial• Second mesh used for elliptic missile “improved” from original mesh

– Original mesh gave good results, despite appearance– “Improvements” did not appear to affect results– Mesh could probably be further improved

• Quality of mesh depended on missile geometry– Tandem control missile meshed easily– Elliptic missile was more troublesome, possibly due to:

• Lack of symmetry plane surface• Variable curvature of missile body • Multiple close surfaces with varying surface cell sizes.

• Only SST k-omega turbulence model was used– Default settings – A different turbulence model or different settings might improve axial force

predictions

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Conclusions• Accuracy of Star-CCM+ solution for missile geometries was very good

– Normal force, axial force, & pitching moment predicted well– Control Effectiveness predicted well.– Elliptic missile test case raises questions about secondary forces & moments

• Possibly due to poor quality or inaccurate experimental data• Additional test geometries need to be evaluated before a good assessment can be made

• Geometry Wrapping and Automatic Mesh Really Work!– Limited ability to directly control volume mesh– Meshes can be generated quickly with minimal effort

• Half models with symmetry planes seem to generate “better” meshes than full models.– Some configurations may require significant tweaking to obtain good mesh

• Easy-to-use code, good productivity, gentle learning curve– Excellent user interface– Accurate simulations can be set up quickly by individuals with aero background but with

limited CFD experience– Ability to visualize solution while running solver very useful– Beware the Black Box User!

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Acknowledgements

• Thanks due to:– CD-Adapco

• For providing the use of the computing cluster and software on which this study was performed

– AFRL MSRC• For the use of the “Falcon” computer, which was used to run some of the

cases for this study

– Peter Cross (China Lake)• Did the bulk of work for this study

– Ron Schultz (China Lake)• Directed this effort and provided his many years of CFD experience

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Questions?