Aerodynamic Analysis of a Rocket Configuration With Grid Fin

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AbstractCFD simulations have been carried out on a rocket configuration with a flared base using PARAS code at various Machnumbers. This configuration has propulsive motor nozzles projected to the flow at the middle and grid fins are provided at the end. Theviscous turbulent flow studies have been carried out to generate aerodynamic coefficients and load distribution with and without grid fins.The computed aerodynamic coefficients obtained through CFD agree within 10% of the reported wind tunnel test data for Apollo EscapeVehicle. The variation of aerodynamic coefficients with Mach number is on the expected lines. At transonic Mach number, the flows getchocked and normal shock is formed inside the grid fins, causing considerable increase in drag and reduction in grid fin effectiveness. Gridfins are very effective to improve the stability in subsonic and supersonic regimes.

Keywords Grid Fins, PARAS-3D, Aerodynamic coefficients

Nomenclature

Symbol Quantity UnitsD Diameter m

M Mach number

Angle of attack deg

CM Moment coefficient

CN Normal force coefficient

CA Axial force coefficient

SdCN/d(x/D) Load distribution along x-axis m2

X Longitudinal distance m

S Reference area m2

I. INTRODUCTION

Grid fins are relatively new aeromechanic technology used for providing the required static margin during sustainer phase ofa rocket. The design of these grid fins allow an effective aerodynamic control device stowed along with the sustainer body with aminimum increase in the overall dimensions. This will give very small disturbance to the flow over the main vehicle. A grid fin isan unconventional lifting and control surface consisting of an outer frame supporting an inner grid of intersecting small chordplanar surfaces [1]. Most advantage of the grid fins are,desired when kept folded during flight regime and deployed whenever itis required. The drag of the grid fin can be minimized with the proper design of the inner grid [2]. Computational fluid dynamic(CFD) techniques to calculate the viscous flow around grid fins were recently demonstrated [3], [4]. Unlike conventional planarfins which experience maximum normal force coefficient during transonic regime, a grid fin experiences lesser normal forcecoefficients which is commonly referred as Transonic bucket[5].

The main objective of this study is to analyze the effect of grid fin over a rocket configuration. Section two of this paperpresents geometry details and computational approach carried out using PARAS-3D. Section three gives the details of the studiescarried out at different Mach numbers and the results.

* J Sreenivasulu., Sci./Engr SC, Aerodynamics Design Division, Vikram Sarabhai Space Center, Thiruvananthapuram, kerala, India-69502.

(e-mail: [email protected] or [email protected]). Dr. Patil M M, Sci./Engr SG, Aerodynamics Design Division, Vikram Sarabhai Space Center, Thiruvananthapuram, kerala, India-69502.

(e-mail: [email protected])$A E Sivaramakrishnan, Head, Aerodynamics Design Division, Vikram Sarabhai Space Center, Thiruvananthapuram, kerala, India-69502.(e-mail: [email protected])

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Aerodynamic Analysis of a Rocket Configuration with Grid Fin

J Sreenivasulu*, Dr. Patil M M and A E Sivaramakrishnan

Proceedings of the 37th National & 4th International Conference on Fluid Mechanics and Fluid Power

December 16-18, 2010, IIT Madras, Chennai, India.

FMFP10 - HS - 14


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II. COMPUTATIONAL APPROACH

A. Geometry generationThe CFD simulation is used to determine the stability and aerodynamic coefficients on a rocket configuration with and

without grid fin. The rocket configuration used in the CFD study consists of a nose followed by a cylinder of diameter 1D withpropulsive nozzles at the end of the cylinder, followed by a towered interstage which ends up with a flare. This configuration hasa flared base of diameter 4.5625D, four rockets are attached on the flare circumferentially equi distance and four grid fins arelocated at the base of vehicle. The total length of configuration is 16.8275D. Figure 1 shows the rocket configuration with grid fin

and Figure 2 shows the rocket configuration without grid fin used in this study.

Each grid fin has a height of 1.25D, span of 0.703D and chord length of 0.1875D. Each grid fin consists of 7x4 panelsand each panel of thickness 0.01875D.

B. Flow SolverThe study has been carried out using Computational Fluid Dynamics (CFD) through an in house developed code

PARAS-3D. PARAS-3D is versatile tool for analyzing various type of flow with multiple free streams. The Reynolds AveragedNavier-Stokes (RANS) equations are solved. The turbulent flows are simulated using k- model in association with modified wallfunctions. The explicit finite volume method is used for solution of RANS equations. The time integration has done using Eulerscheme. The inviscid fluxes are computed using an approximate Riemann solver. Viscous flux terms are computed using centraldifferencing scheme

C. Grid GenerationThe PARAS code uses the Cartesian grids. The grid is generated by means of an adaptive Cartesian mesh technique. The

overall flow domain for subsonic flow analysis is 60 D on all sides with flow symmetry. Initially a coarse grid with approximately8.5 million cells is used. During flow simulation the grids are refined and finally a finer grid of 11 million cells is arrived at.Figure 3 shows the section of 3D grid for M less than 1. In order to capture the flow features, appropriate cluster was used tomake finer grid near the body. For supersonic study, the flow domain is 6D upstream and 60D on other sides. The initial coarsegrid contained nearly 8.5 million cells and the final finer grid turned out to be 18 million cells. Figure 4 shows the section of 3Dgrids for M greater than 1. The boundary conditions are implemented with the dummy cells. Computational grid at the close upview of grid fin is shown in Figure 5

D. ConvergenceComputations were initiated by specifying initial value to the entire domain. During computations, forces and moments are

monitored. Figure 6 shows the typical converged curves for CA, CN and CM at Mach number 0.8 and angle of attack of 40 for a

rocket configuration with grid fin.

E. Grid Independence TestThe grids are refined at different levels during computation. Results are obtained for the coarse and finer grids. The result of

the grid independence study at M=0.8 and angle of attack of 40 for a rocket configuration without grid fin is shown in Figure 7.These show the results are within 2.5%.

III RESULTS & DISCUSSION

Computations were performed to analyze the flow over a rocket configuration with and without grid fins under jet-off andjet-on conditions. For different Mach numbers, the jet pressure ratio used in simulations are given in Table 1. Computations havebeen carried out at various Mach numbers and attitude at 4 deg. angle of attack.

Table 1: Jet pressure ratio of jet-on condition

Mach number Jet pressure ratio

0.6 8.72

0.8 11.5

1.2 21.39

2 53.54


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A. Validation

The viscous simulation tool used in this study is validated using existing wind tunnel test data [6]. The Apollo configurationis chosen for this purpose since extensive wind tunnel data are available for comparison.

The flow analysis at Mach number of 0.7 and angle of attack of 50 is carried out at wind tunnel test flow conditions.The static margin is calculated from nose tip. The comparison of aerodynamic coefficients is given in Table 2. The computednormal force coefficient is 10% higher than experimental data. The moment coefficient is 2% lower than experimental values.

Table 2: Validation results of Apollo vehicle at M=0.7 and =50

Literature Computed Difference

CM -0.0932 -0.09513 2.02%

CN 0.1837 0.1655 -9.9%

Static Margin(interms of D)

0.5086 0.576 0.0674

B. Aerodynamic characterization of a rocket configuration with and without grid fin

Figure 8 shows the variation of static margin with Mach number for a rocket configuration with and without grid fin. Rocketwith and without grid fin configurations are simulated under jet-off and jet-on conditions. In presence of jet, center of gravity ofthe rocket configurations moves towards base. Jets improve the static margin at lower Mach numbers. Both the configurations

have minimum static margin of 1D. Grid fins are effective in subsonic and supersonic Mach numbers. At transonic Machnumbers rocket configuration with grid fin has less static margin than rocket configuration without grid fin.

Figure 9 to Figure 12 show the load distribution over a rocket configuration with and without grid fin for various Mach numberunder jet-off and jet-on conditions. It is seen from the figures that the flow is smooth till the nozzle region. Also a sharp rise in theload distribution is seen at the nozzle region under jet-off condition. The load distribution behind the nozzle is smooth andincreases at the flare and then decreases due to the change in the flare angle. At the grid fin location the load distributionincreases. At transonic Mach numbers the load distribution due to the grid fins decreases is shown in Figure 11. At transonicMach number, the flow gets choked and normal shock is formed inside the grid fins, causing considerable increase in drag andreduction in grid fin effectiveness [5]. At supersonic Mach number grid fins are very affective to increase the load distribution isshown in Figure 12.

IVCONCLUSION

Aerodynamic coefficients and load distribution over a rocket configuration with and without grid fin has been generated. Thevariation of aerodynamic coefficients with Mach number is on the expected lines. Both the configurations have a static margin of1D. At transonic Mach number, the flow gets chocked due to normal shock formed inside the grid fins, causing considerableincrease in drag and reduction in grid fin effectiveness. Grid fins are very effective to improve the stability in subsonic andsupersonic regions.

ACKNOWLEDGEMENT

Authors are thankful to Dr. George Joseph., GD, ADTG and Sri. S.V Sharma, Deputy Director, Aeronautics Entity, VSSCfor their guidance and encouragement for this work. We also thankful to Sri. Rakesh C K, HSP, VSSC for his support ingeometry modeling. Authors thankful to Dr. T Jayachandran, Head, FMTD for kindly agreeing to review the paper and for thevaluable suggestions.

REFERENCES

[1] Karl S. Orthner and Ensign, Aerodynamic Analysis of Lattice Grid Fins in Transonic Flow AFIT/GAE/ENY/04-J09[2] Miller, M. S., and Washington, W. D., An Experimental Investigation of Grid Fin Drag Reduction Techniques, AIAA Paper 94-1914-

CP, Jun. 1994.[3] DeSpirito, J., Edge, H. L., Weinacht, P., Sahu, J., and Dinavahi, S. P. G., Computational Fluid Dynamics Analysis of a Missile With

Grid Fins, Journal of Spacecraft and Rockets, Vol. 38, No. 5, 2001, pp. 711718.[4] DeSpirito, J., and Sahu, J., Viscous CFD Calculations of Grid Fin Missile Aerodynamics in the Supersonic Flow Regime, AIAA Paper

2001-2057, Jan. 2001[5] Wm. David Washington and Mark S Millar., Experimental investigation of grid fin aerodynamics-A synopsis of nine wind tunnel and

three flight tests, RTO AVT symposium on Missile Aerodynamics, Sorrento, Italy, 11-14 May 1998[6] William C. Moseley, Jr. and James G.Honros., Aerodynamic Stability Characteristics of the Apollo Launch Escape Vehicle, NASA, TN

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Figure 1 Rocket configuration with grid fin

Figure 2 Rocket configuration without grid fin

Figure 3 Section view of 3D grid for M1

Figure 5 Computational grids at the close up of grid fin

Figure 6 Convergence history at M=0.8, =40 for a Rocketconfiguration with grid fin

Nozzle

0 25 50 75 100 1258

9

10

11

12

No. ofcells

in million

0

6

12

18

24

30

CM

0

1

2

3

4

5

CN

0

6

12

18

CA

No. of cellsin millionC

MC

NC

A

No. of Iterations/1000

CA,CN

andCM

M=0.8, =40

and jet-off


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Figure 7 Grid independence test at M=0.8, =40 for a Rocketconfiguration without grid fin

Figure 8 Variation of static margin with Mach number for a Rocketconfiguration with and without grid fin

Figure 9 Load distribution over a Rocket configuration with and

without grid fin at M=0.6 and =40







-1.5

-1.0

-0.5

0

0.5

1.0

1.5

0 2 4 6 8 10 12 14 16 18

with grid finwithout grid fin

Longitudinal Distance (x/D)

SdCN

/d(x/D),m

2

M=0.6, =40

an Jet off

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

0 2 4 6 8 10 12 14 16 18


Longitudinal distance (x/D)

SdCN/d

(x/D),m

2

M=0.8, =40, Jet-off

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

0 2 4 6 8 10 12 14 16 18


Mach number

SdCN

/d(x/D),m

2

M=1.2, =40

and jet-off

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

0 2 4 6 8 10 12 14 16 18



SdC

N/d(x/D),m

2

M=2.0, =40

and jet-on

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

without grid fin (jet-on)

with grid fin (jet-on)without grid fin (jet-off)with grid fin (jet-off)

Mach Number

StaticMargin(intermsofD)

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

0 2 4 6 8 10 12 14 16 18

Fine gridCoarse grid


SdCN

/d(x/D),m

2

M=0.8, =40

and jet-off

Aerodynamic Analysis of a Rocket Configuration With Grid Fin

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