Chimera Moving Body Methodology for Rolling Airframe Missile Simulation with Dithering Canards

L.H.Hal1

Dynetics, Inc. 1000 Explorer Blvd.

Huntsville, AL 35806 Email: les.hall@dvnetics.com

ABSTRACT

A numerical technique for predicting the aerodynamic characteristics of a rolling airframe missile is presented. The missile utilizes canards as forward control surfaces that are staggered with the tail fins. An overset Chimera technique is utilized to allow prescribed motion of the canards as the missile spins. Using the flow solver GASP, Version 4.0, three dimensional, viscous, time-accurate solutions are obtained for the spinning missile configuration while the canards dither. Variations in grid density and temporal accuracy are examined and compared with data from an aerodynamic prediction tool developed from wind tunnel data and semi- empirical methods. Results are also compared to data from an established semi-empirical tool, as well as to CFD predictions from another well known software package.

INTRODUCTION

The configuration modeled in this work is a rolling airframe missile. The system uses a single co-planer pair of canard control surfaces of directional control of the missile during flight. Because the canards dither in a bang-bang fashion, the missile must roll during flight to effect directional control in a required direction.

The rolling-while-controlling aspect of these missiles presents some unique problems in defining the aerodynamic characteristics of the system. Traditionally, in wind tunnel tests of missile configurations, data were taken statically. The wind tunnel model is placed in the wind tunnel at fixed or “static” orientations relative to the wind and with the control surfaces at fixed control detlections. Data were taken at each

orientatiodcontrol surface deflection; the orientatiodcontrol deflection is then changed slightly and data are recorded again. However, it has been shown that use of aerodynamic models developed from static wind tunnel tests for this class of system can prove unsatisfactory. It was determined that the missiles’ roll during flight influenced their aerodynamic characteristics.

Due to shortcomings of the aerodynamic models developed from the “static” wind tunnel tests for this class of problem, designers often opt to run “dynamic” wind tunnel tests. In these tests, the wind tunnel models are continuously rolled about their longitudinal axis. and the canard control surfaces are positioned in a time-varying fashion to emulate the operation of these control surfaces during flight. The results are aerodynamic coefficients averaged over many roll cycles.

Prediction of aerodynamic characteristics for this body offers an equally challenging problem when utilizing CFD. To model the body time accurate, rather than static, results in a computationally intensive simulation. For normal commanded maneuvers, assuming a repeatable canard pattern per revolution, the body still must be rotated a full revolution after all transient start-up effects are no longer present in the solution.

The current study takes advantage of a duel time stepping methodology to achieve relatively large physical time steps for the time accurate simulation. To accommodate the canard dither while maintaining a structured grid topology. a Chimera’ (overset) technique is employed. Each canard is modeled with an independent multi- block grid overset upon the background grid representing the missile body. The Chimera

Appmnxl for puhlic ~ I K I I S C .

1 American Institute of Aeronautics and Astronautics

20th AIAA Applied Aerodynamics Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-2801

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

approach requires a new hole cut and updating of zonal boundary coefficients each physical time step. However, efficient tree-based logic implemented in the search routines keeps the CPU time spent in the Chimera routine relatively small when compared to that of the flow solver.

The goal of this study was to demonstrate a technique and the requirements for time accurate, viscous simulation of rotating airframes with moving control surfaces. Effects of grid resolution and temporal accuracy upon integrated aerodynamic predictions are examined. Results are compared to those of other prediction tools of both semi-empirical and computational nature. This paper presents findings that are a continuation of work previously done on this configuration’. As il result, some work that was presented before is shown here for completeness.

GEOMETRY AND GRID GENERATION

The simulated configuration, shown in Figure I below, utilizes a single co-planer pair of canard control surfaces for directional control during flight. The missile has 4 tail fins spaced at 90 degree increments circumferentially around the body at a constant axial station. The geometry surface file was supplied in IGES file format and imported into the grid generation package GRIDGEN3.

Figure 3. Rear View of Geometry

Two three-dimensional structured chimera grids were constructed upon this geometry. A coarse mesh was created for the initial simulation. The grid consisted of 102 blocks containing 377,186 nodes. The overset canard grids each consisted of 8 blocks and 13,548 nodes, while the body was modeled utilizing 350,090 points in 86 blocks.

A high fidelity chimera grid was created to model the geometry that utilized an identical blocking topology as the coarse chimera grid. The grids consisted of 3,929,618 nodes. Details of the fine mesh are shown in Figures 4,5 and 6.

Figure 1. Spinning Missile Geometry

Another view of the missile surface is shown in Figure 2 , while Figures 3 shows details of the rear of the configuration.

Figure 4. Rear Fin Region For Fine Grid

Figure 2. Spinning Missile Geometry

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SOLUTION METHODOLOGY

Figure 5. Aft Section of Body for Fine Grid

Figure 6. Details of Overset Canard Mesh

FLOW SOLVER

The flow solver utilized for this study was the General Aerodynamic Simulation Program' (GASP), Version 4.0. GASP is a density-based flow solver that solves the integral form of the time-dependent Reynolds-Averaged Navier- Stokes equations in a general curvilinear coordinate system. The flow may be modeled inviscid, laminar or turbulent. Turbulence models supported include Baldwin-Lomax'. several variations of the k-E model6*', several variations of the k-omega m ~ d e l ~ . ~ and spalart allmaras'O. Both flux-vector and flux-difference schemes are available with higher-order limiters. The tlow solver supports structured/unstructured, hybrid, multi-block, blocked and chimera grid systems.

For this study, a' global iterative method was used to solve a fully implicit time integration methodology. Roe's scheme" was utilized, with third-order spatial accuracy and a min-mod limitert2. A laminar model was employed. Time- accurate solutions are achieved with both first and second order temporal accuracy. utilizing dual time ~tepping'~.

All dithering canard simulations were obtained utilizing an overset Chimera technique. GASP incorporates double-fringe interpolation across chimera boundaries where grid resolution is adequate, resorting to first order interpolation if necessary.

HARDWARE

All solutions were obtained on a Renegade platform executed and distributed over 23 PC Linux-based machines running in parallel. For the coarse solution, processor speed was 750 MHz for 15 machines, and 500 MHz for 8 machines. For the fine grid solution, the 15 750 MHz processors were replaced by 1200 MHz processors. GASP allows for load balancing so that each machine was assigned a work load based on CPU speed.

PROBLEM DESCRIPTION

Solutions were run for Mach 1.6 at 3 degree angle of attack. The missile body spin rate was 8.75 Hz. The cases demonstrated invoke a body spin rate such that the canard deflection history as a function of aerodynamic roll position repeats itself every roll cycle.

The two canards during the simulation exhibit identical motion. The canard deflection versus roll angle is shown for the coarse grid in Figure 7. A slight variation for prescribed canard motion was utilized for the fine grid solution, as shown in Figure 8.

3 American Institute of Aeronautics and Astronautics

20

1 15

d P -5

0 -10 E

-15

-20

Figure 7. Canard Prescribed Motion for Coarse Grid Simulation

20

15

10

2 5 0-5

6 0

; -5

8 -10

-15

-20

Figure 8. Canard Prescribed Motion for Fine Grid Simulation

EXPERIMENTAL DATA

Experimental data was available in the form of time averaged data over many roll cycles from wind tunnel measurement. In order to obtain aerodynamic predictions versus time without resorting to a full CFD solution, the Rolling Airframe Prediction Tool (RAPT) was developed. The predictions RAPT are used for comparison in this study, as the exact tested conditions from the tunnel were not duplicated with CFD. The reason is that a canard deflection history that is repeated versus roll orientation for each cycle was chosen, as it would computationally be too expensive otherwise. The model was derived primarily from wind tunnel data, with some reliance on semi-empirical methods when required. A brief summary of this tool is given.

RAPT was created to provide aerodynamic forces and moments as a function of instantaneous missile orientation to relative wind, relative velocity (Mach) and canard deflection angle. Several basic assumptions,

listed below, were made for development of the model and should be pointed out to explain how the model prediction would be expected to vary from CFD results.

RAPT Assumptions:

1. Differences between force and moment measurements are considered to be due to the action of the canards alone. The contribution of the canards to normal and side forces is strictly a linear function of the canard's angle of attack. The force contribution of the canard deflection is orthogonal to both the missile and the canard hinge line.

2.

3.

The above assumptions allow a missile aerodynamic coefficient to be written as:

Where;

C = Aerodynamic Coefficient C,,dy = Contribution to C from body (assumed constant) DELC =Constant to be solved for &d = Canard deflection angle Q = Aerodynamic Roll angle

Averaged over time, (Eqn 1) can be written as:

Carnap = Cwy + D E E COS Q).- (Eqn 2)

Due to the assumptions made, the only unknowns for Equation 2 are the coefficient contribution of the body and the constant DELC, as the canard history and averaged coefficient value are known from the wind tunnel test. Hence, solving Equation 2 for two different canard deflection histories at identical tunnel conditions results in two equations and two unknowns, allowing us to solve for CwY and DELC. Equation 2 can then be used to produce the unsteady coefficient prediction data which is compared to the CFD results. One important aspect of this model is due to the way it was developed, the average of 'the aerodynamic predictions over a roll cycle will always exactly match the measured tunnel average for a case in which that exact wind tunnel data does exist.

When considering how RAPT will compare to CFD results, most notable is assumption (1). While inclusive of force and moment contributions due to canard flow field disturbance impinging on the missile body and

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tail tins, the effect is averaged into to the data when the body loading is considered a constant. This should result in a smoothing of the prediction data produced from RAPT versus true physical behavior for discrete roll orientations over a roll cycle. In addition RAPT assumes instantaneous change in force and moment data upon canard deflection. While in reality that is closer to truth in the force computations, the moment data should see more of a variation due to canard flow field disturbance propagating down the body to the fins. This would be demonstrated by a lagging effect on the moment coefficient from canard deflection due to time required for the flow to travel from canards to fins. In addition, the disturbance from the canards would impact the fins at a different body roll orientation due to the high rate of spin of the missile. In the case of this problem, that body roll differential was on the order of several degrees.

Figure 10. Windward Surface of Canard

In summary, the data from RAPT to which the CFD is compared should be a close representative of the wind tunnel data, but not exact. Assumptions have been made to make the prediction for the conditions of which the CFD simulation models. These assumptions will result in some percentage error from truth which is believed to be small. but which does exist.

RESULTS

Coarse Grid Solution

Figure 11. Details of the Tail Region The steady state solution for all grids was obtained with the canards in the yaw plane. Figure 9 shows pressure contours for this solution. Details of the surface pressure in the canard and tail regions are shown in Figures 10 and 1 1, respectively.

An important requirement of this problem was the capturing of the vortices shed from the canards. It was suspected these vortices could impact the tail fins and have a significant effect upon the aerodynamic loads. It was known ahead of time that the coarse grid utilized in this study would not offer the fidelity to adequately capture and preserve these vortices. In addition, the surface spacing was not adequate to correctly resolve the boundary layer. The coarse grid study was undertaken to offer insight into how to most efficiently obtain this solution in areas such as convergence and examine time accuracy requirements. In addition, run times and memory requirements for the coarse solution would help dictate the size of the fine grid.

Figure 9. Steady State Solution

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The time accurate solution was begun with a rotation rate of 8.75 Hz instantaneously imparted to the body about the axial centerline. The simulation was run for 2 complete body revolutions. Using dual time stepping, a rotation of 3.15 degrees per time step was taken. The 3.15 degree rotation was decided upon after running and comparing a series of solutions with varying time step. Rotations of close to five degrees were achieved that still matched closely with solutions using a time step an order of magnitude less. Based on those results, the final time step seemed a reasonable choice and also coincided with a time step of 0.001 seconds Integrated normal force coefficient verses roll orientation is shown in Figure 12 for the second revolution of the body. The average over a roll cycle of the integrated CFD results and RAPT are also plotted. The normal force coefficient. average for RAPT was CN=0.6453, while the CFD average was CN=0.6934. It should be noted in the following figures, the scale for the canard deflection is not correct. The deflection is simply superimposed on the graph so that aerodynamic coefficient changes can be easily identified with the canard deflections.

Figure 12. Force Coefficient Data

Integrated pitching moment coefficient versus roll orientation is shown in Figure 13. The pitching moment is taken about some point near the body midsection for which the moment arm is small, and the moment consequently very sensitive to changes in the center of pressure resulting from the integrated force. The pitching moment coefficient average for the wind tunnel- was CM=.5187, while the CFD average was CM=.9179. While the difference of 0.4 is large in percentage for the averaged value, one must consider that due to the large variance in value of the pitching moment over the roll cycle, a

smaller percentage difference at each time step can result in a cumulative larger percentage error. For example, at the peak pitching moment values achieved close to 180 degree rotation, the percentage error reaches a maximum of approximately 18%. However, 18% error of a pitching moment with a peak value of six times the average over approximately 116 of the roll cycle can cause the final percent error on the pitching moment average to be large. In addition, this effect is compounded due to the small value for averaged pitching moment which results at the small angle of attack for this simulation. The trend for the coefficient is seen to be captured well from Figure 13. Considering these results were on a coarse grid intended to gain insight into the fine grid solution, the results were better than expected. As anticipated, the effects on ‘moment coefficient from canard deflection lag behind RAPT predictions for most of the roll cycle, where effects of the model are considered instantaneous.

Figure 13. Pitching Moment Coefficient Data

The factor speed up from running in parallel on 23 machines was 19.6. The time per iteration was 4.9 seconds, with average time per physical time step requiring approximately 14.2 minutes. The time per revolution was approximately 27 hours.

One question to be answered from the coarse grid study was approximately to what degree would the body be required to rotate before the flow would obtain a physical state after instantaneously imparting the roll to the body. It was thought that by the second revolution of the body, all trace of initial non-physical effects from the start-up would be removed from the flow field. Figures 14 and 15 compare force and moment coefficient data for the second revolution of the body versus a portion of the

6 American Iiistitute of Aeronautics and Astronautics

third revolution. After seeing a close match in the data between revolutions, the third revolution solution was truncated, and the second solution was considered to be inclusive of no start-up effects.

-nn-.h"

Figure 14. Normal Force Coefficient Data

4ngb of R o W m

Figure 15. Pitching Moment Coefficient Data

The above results were run with first order temporal accuracy. To examine the effect of running with a second order temporal accuracy, a second solution was obtained for the missile for over half a revolution. A comparison of normal force coefficient is shown in Figure 16. The differences in solution were considered small enough so that the fine grid solution was obtained first order in time. .

7

. . . . . . . .. . . ' a 1

I

~

American institute of Aeronautics and Astronautics

.IC.-

Figure 16. Normal Force Coefficient Data '

Fine Grid Solution:

The fine grid solution utilized a physical time step corresponding to 3.15 degrees of body rotation, as with the coarse grid simulation. A instantaneous roll rate of 8.75 Hz was imparted to the body at the beginning of the time accurate solution. The grid fidelity proved adequate to capture and preserve the vortices shed from the canards. Figure 17 shows the root and tip vortices from the canard depicted in a cutting plane of velocity magnitude. The surfaces of the body are shaded with pressure contours.

Figure 17. Vortices Shed from the Canards

As the canard angle of attack changes sign, so does the directionality of the 'vortex rotation. Figures 18 and 19 demonstrate this effect with the body at two different rotation angles, with the cutting planes showing velocity magnitude and the surfaces shaded with pressure. In figure 18, the body is at 117 degrees rotation, with the canards deflected at a negative 15 degrees. Figure 19 depicts the body at 162 degree roll and a positive 15 degree canard deflection.

vortex rotation is seen to change sign between the first two cutting planes. The canards are at maximum detlection in Figure 21, and seen again in transition i n Figure 22.

Figure 18. Vortices Shed from the Canards at . Negative Angle of Attack

Figure 20. Vortices Shed from the Canards with Body Rolled 72 degrees

Figure 19. Vortices Shed from the Canards at Positive Angle of Attack

To offer most efficient capturing of vortices with minimum grid requirement, the grid topology was such that points were packed tightly normal to the body between the body surface and a distance shortly outside of the tip of the canards and tail fins. The rationale was that the importance of capturing the vortex was for purpose of predicting vortex tail impingement. If the mesh outside of that region was exceedingly coarse, causing the vortex dissipate, it was felt it would not significantly affect the resultant aerodynamic loads on the body. Figures 20, 21, and 22 show the vortices at varying times in the solution represented by a series of cutting planes in the solution showing velocity magnitude. The body surfaces are shaded with pressure. In figure 20, the canards are in transition from positive to negative angle of attack, shown here at a negative 5 degrees deflection. As a result, the

Figure 21. Vortices Shed from the Canards with Body Rolled 189 degrees

Figure 22. Vortices Shed from the Canards with Body Rolled 290 degrees

Integrated normal force coefficient verses roll orientation is shown in Figure 23. The average over a roll cycle of the integrated CFD results and RAPT are also plotted. The normal force coefficient average for RAPT was CN=.6621, while the CFD average was CN=.6792.

8 Aineiican Institute of Aeronautics and Astrooautics

Figure 23. Normal Force Coefficient Data

The integrated pitching moment coefficient versus roll orientation is shown in Figure 24. The pitching moment coefticient average for RAPT was CM=.5821, while the CFD average was CM=.7093. It was felt this was in good agreement, considering the close proximity of. the moment reference point to the center of pressure, and the small angle of attack of this simulation.

I i

I 4

l 3 2

1

Ij 0

I -1

1 -3 ! -2

Figure 24. Pitching Moment Coefficient Data

A comparison of side force coefficient versus roll orientation is shown in Figure 25. The side force coefficient average for RAFT was CY=.04885, while the CFD average was CY=.04692.

A comparison of Yawing moment coefficient versus roll orientation is shown in Figure 26. The yawing moment coefficient average for RAPT was CLN=.3 129, while the CFD average was CLN=.5 365.

--RAPT +cFDFk*Glid -cnrdD.lrcm

0.8

0.6

0.4

0 2

4.2

-0.4

0.8

4.8

Figure 25. Side Force Coefficient Data

Figure 26. Yawing Moment Coefficient Data

A comparison of axial force coefficient versus roll orientation is shown in Figure 27. The axial force coefficient average for RAPT was CA=1.265, while the CFD average was CA=1.015. The difference in the two axial force predictions was fairly significant. However, it should be noted the base pressure was not measured in the wind tunnel, but rather estimated by using the semi-empirical tool, USAF DATCOM. This value was then used to modify the measured axial force to predict a value without the presence of the sting.

1.6

1 5

1 4

1 3

e l 1 2

1 1

I

0 9

0 8

~

Figure 27. Axial Force Coefficient Data

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Tabulated results of the averaged aerodynamic coefficients for the fine grid simulation and RAPT are provided in Table 1 .

Coefficient Normal Force (CN)

Side Force (CY)

to the 41e6 node mesh contained approximately 8e6 grid points. Refer to Real41 for further details of this work.

RAPT CFD .662 1 .6792

.04885 .04692 I PitchingMoment I ,5821 I .7093 - 1

(CM) I I Yawing Moment I .3 129 I S365

The comparison of results between these codes for this complex problem was of great interest. While the gridding technique utilized is similar, and solutions obtained from both codes were viscous, their exists distinct differences in the solution methodologies.

( C W I Axial Force (CA) I 1.265 I 1.015

Table 1. Averaged Aerodynamic Coefficients

Knowledge gained from running this problem first with a coarse grid resulted in a much more efficient. computation for the fine grid simulation. The factor speed up from running in. parallel on 23 machines was 20.07..The time per iteration was 43.95 seconds, with average time per physical time step requiring approximately 47.6 minutes. Convergence of each physical time step required an average of 65 iterations. For each of those iterations, an inner-iteration scheme is utilized, with an average of 6 to 10 Gauss Seidel iterations being performed, variant upon the number taken to converge to the specified tolerance of two orders. The computation time per revolution was approximately 90.5 hours.

METHODOLOGY COMPARISONS

For purpose of comparison between varying CFD codes on this class of problem, data from a simulation produced with the flow solver OVERFLOW-D'4 were obtained, which were not produced by this author. OVERFLOW-D is a general purpose Navier-Stokes solver which allows for relative motion between configuration components. As with GASP, the code uses a structured overset structured grid methodology. OVERFLOW-D is based on the well known NASA OVERFLOW code, but has been modified to accommodate moving body applications, allow solution adaptation, and run on scalable computers.

Results with OVERFLOW for this configuration were first obtained on a mesh of approximately 41eG nodes. This solution then served as a baseline for a grid density study. The final domain size used with OVERFLOW for subsequent solutions which offered close results

GASP utilizes an iterative technique to approximately solve the fully coupled first order Euler implicit time integration scheme. Several iterative techniques are available in GASP. For this problem, approximately 6 to 10 Gauss Seidel iterations were performed. OVERFLOW in turn implements a diagonalized scheme. Such algorithms only require the solution of scalar systems of equations, instead of block systems. This creates a significant speed up per iteration. In addition, GASP utilizes a dual-time-stepping algorithm, in which a larger physical time step may be taken. A second pseudo-time derivative is use for sub-iterations at each time step. Once the problem is converged in pseudo time, an accurate solution is obtained at the current physical time. For this case, the body was perturbed 3.15 degrees per time step, while that of OVERFLOW was approximately 0.03 degrees per time step. However, for OVERFLOW, taking such a small time step is a viable alternative due to the rapid time per iteration obtained for solving the scalar matrix. In addition, while terms are ignored when solving the scalar matrix, the miniscule time step taken would tend to eliminate error which otherwise might arise. GASP, while not discarding those terms, could introduce error if the chosen physical time step, which is not limited when dual time stepping, is too large. For the two methodologies, a computational time advantage is seen by GASP in the fact that the chimera coefficients are only computed for the outer time step, which occurs 114 times per revolution. If OVERFLOW were to compute the coefficients every time step, it would do so I200 times per revolution. It may not be necessary, however, to compute the hole cut every iteration step when the time step is so small. The rapid time per iteration seen by OVERFLOW due to solving the scalar matrix resulted in a time of solution nearly seven times faster than that of GASP when solved on a grid with the same number of points.

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The following figures plot predicted aerodynamic coefficients from the two codes, as well as RAPT prediction. Integrated normal force coefficient verses roll orientation is shown in Figure 28. The normal force coefficient average for RAPT was CN=.6621, CN=.6792 for GASP, and CN=.687 for OVERFLOW.

10

8

6

4

u 2

0

2

-4

4

Y

1.2

1

0.8

0.8

cI( 0.4

0 2

0

4 2 4.4

4* 1 I -- Figure 28. Normal Force Coefficient Data

Integrated pitching moment coefficient verses roll orientation is shown in Figure 29. The pitching moment coefficient average for RAPT was CM=.582, CM=.710 for GASP, and CM=.832 for OVERFLOW.

5

4

3

2

1 QI

1

-2

9

-4

-5

Figure 29. Pitching Moment Coefficient Data

Integrated side force coefficient verses roll orientation is shown in Figure 30. The side force coefficient average for RAPT was CY=.O49, CY=.O47 for GASP, and CY=.058 for OVERFLOW

Integrated yawing moment coefficient verses roll '

orientation is shown in Figure 3 1. The prediction for RAPT was CLN=.313, CLN=.537 for GASP, and CLN=.672 for OVERFLOW.

0.m

0.m

0.4

0.2

cy 0

4.2

4 .4

4.8

4.8

~~

Figure 30. Side Force Coefficient Data

I I -- I I

Angh of Rolnau (De@ L Figure 31. Yawing Moment Coefficient Data

Integrated axial force coefficient verses roll orientation is shown in Figure 32. The prediction for RAPT was CA=1.265, CA=1.015 for GASP, and CA=1.140 for OVERFLOW.

Tabulated results of the averaged aerodynamic coefficients for GASP, OVERFLOW, and RAPT are shown in Table 2.

J

Figure 32. Axial Force Coefficient Data

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Force (CY) Pitching

Yawing Moment (CLN)

Axial Force

.049

.582

.313

1.265

RAPT GASP OVERFLOW

.047 .058

.710 .832

-537 .672

1.015 1.140

Table 2. Averaged Aerodynamic Coefficients

It is difficult to draw any conclusion other than both methodologies are in good agreement with each other and RAPT predictions. The lack of significant difference in predicted coefficients for this case between codes indicates that the diagonlized scheme employed by OVERFLOW offers a feasible and less CPU intensive alternative to the block diagonal scheme of GASP. However, it should be noted that while the accuracy of predictions seems to be comparable, the number of points for the GASP solution was half that as utilized for OVERFLOW. This could indicate a methodology which requires fewer grid points to retain the same accuracy, a more efficient placement of grid points, or simply that fewer points could be used with the OVERFLOW solution without sacrificing accuracy. Due to difference in computing platforms, it is difficult to make an exact CPU time per solution between the codes. However, these comparable solutions were obtained approximately 3.5 times faster for OVERFLOW than that of GASP on equivalent hardware platforms.

Since completion of these simulations, GASP has improved &he Chimera routine such that the user may now specify on which physical time steps to cut the hole and perform the chimera coefficient computations. This is only necessary when the bodies are moving relative to each other. After testing the new version of GASP, it was determined this improvement would have resulted in approximately a 12% decrease in runtime for this simulation, requiring approximately 80 hours to complete on the specified platform.

COMPARISONS WITH SEMI-EMPIRICAL METHODS

Missile DATCOM is an aerodynamic prediction code that was developed to provide relative fast, economic estimates of the aerodynamic characteristics of missile configuration designs. It is an empirical tool that is based on component build-up techniques. The individual component aerodynamics are primarily derived from internal tabular databases and parametric descriptions of the components.

For the DATCOM modeling of the this missile, the vehicle was described as an axisymmetric body with two fin sets - the two forward canards and the four rear tail fins. The body was modeled using the DATCOM body option in ‘which longitudinal stations and the corresponding body radii are defined, from nose to tail. This input option allowed more fidelity in modeling the blunted nose on the missile. The two fin sets were model using the standard finset inputs that are based on the fin geometry, section thickness parameters, longitudinal fin location on the body, number of fin in each finset, and angular location around the body of the finset.

For this model, it was necessary to approximate the shape of the canards because their actual shape could not be exactly represented by the DATCOM fin input. The DATCOM description was a rectangular fin with the spanwise area distribution of the actual fin. For the rear fin. a protuberance option was used to reflect the drag of the platforms on which the fins are mounted. Also, a drag increment was introduced into the axial force data to account for the base drag of the rear fins. This technique was suggested by the DATCOM developers in previous modeling efforts. Two different boat-tail diameters were examined. The large boat-tail corresponds to the configuration on which the CFD solutions were obtained, while the small boat-tail represents an approximate 25% reduction in base area.

Figures 33 through 37 plot predicted aerodynamic coefficients from GASP, DATCOM, as well as RAPT predictions. Tabulated results for these predictions are shown in Table 3.

12 American liistitute of Aeronautics and Astronautics

.

Coef‘ficient RAPT CFD DATCOM Large

7 I

DATCOM Small

1 4

1 2

1

0.0

0 6

0.4

0.2

0

4.2 4.4

-0 0

(CY) Pitching Moment

(CM) Yawing Moment (CMN)

AxialForce (CA)

Figure 33. Normal Force coefficient Data

25821 .7093 1.2345 1321

3129 S365 3 3 2 3169

1.265 1.015 1593 1.566

I

5

4

3

2

a’ 0

-1

-2

-3

Figure 34. Pitching Moment Coefficient Data

0.8

0 4

0.2

c y 0

4.2

4.4

4 8

-0.8

Figure 35. Side Force Coefficient Data

The data from the DatCom predictions showed that the trends can be captured for this complex class of problem. However, the averaged results when compared to the Aerodynamic Model and CFJ3 results show a moderate under-prediction of the normal force coefficient, and a significant over-prediction of the pitching moment. However, error does arise due to the limited number of data points provided from DatCom solutions, as coefficients were provided only at 10 degree increments through the rotation.

-

-&mMOd* -CFD Fun (wd i o

8

0

4

2

0

4

4

a

d

Figure 36. Yawing Moment Coefficient Data

Figure 37. Axial Force Coefficient Data

I BoatTail [ BoatTail Normal I .6621 1 .6792 I S487 1 ,5530

13 American Institute of Aeronautics and Astronautics

SUMMARY AND CONCLUSIONS

A simulation technique obtaining viscous, time accurate solution of a high speed rotating airframe with moving control surfaces has been demonstrated. Running in parallel on a linux PC cluster of 23 machines with an average MHz rating of IOOO, a full revolution solution utilizing a mesh with approximately 4xe6 grid points can be obtained in approximately 80 hours. Results for aerodynamic coefficients have been compared against predictions from an aerodynamic prediction tool developed from wind tunnel data and semi-empirical methods. In addition, results were compared to another well- known CFD code and established semi-empirical tool. All results are in good agreement and confidence is instilled in the chosen software and methodology for this class of problem.

ACKNOWLEDGMENTS

Thanks to Mr. Gary Winn of Dynetics, Inc. for providing data from RAPT which he developed that was shown in this paper. Additional thanks to Mr. Neil Walker of Dynetics who provided all DATCOM results shown in this work.

REFERENCES

1. Benek, J.A., Buning, P.G. and Steger, J.L., “A 3D Chimera Grid Embedding Technique,” AIAA Paper 85-1523, 1985.

2. Hall, L.H., “Rolling Airframe Missile Aerodynamic Predictions Using a Chimera Approach for Dithering Canards”, AIAA 02- 0405,2002.

3. “Gridgen User Manual, Version 13,” Pointwise, Inc., Bedford, Tx, 1997.

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14 American institute of Aeronautics and Astronautics