ARL-TR-2976 MAY 2003

Numerical Simulations of Supersonic Flow Over

an Elliptic Section Projectile With Jet Interaction

Jubaraj Sahu

Approved for public release; distribution is unlimited.

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Army Research Laboratory

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____________________________________________________________________________

ARL-TR-2976 May 2003

____________________________________________________________________________

Numerical Simulations of Supersonic Flow Over an Elliptic

Section Projectile With Jet Interaction

Jubaraj Sahu

Weapons & Materials Research Directorate

____________________________________________________________________________

Approved for public release; distribution is unlimited.

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U.S. Army Research Laboratory

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Sahu, J. (ARL)

Numerical Simulations of Supersonic Flow Over an Elliptic Section Projectile With Jet 

Interaction

chimera computational fluid dynamics projectile and missile aerodynamics structured grids unstructured grids 

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Jubaraj Sahu

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ARL-TR-2976

Approved for public release; distribution is unlimited.

Computational fluid dynamics (CFD) approaches were used to compute the supersonic flow fields and aerodynamic forces and 

moments on an elliptic projectile with jet interaction. Steady state numerical results have been obtained for the jet interaction 

problem at a supersonic Mach number, Mach = 4.0, and several angles of attack from 0° to 12° via Navier-Stokes computational 

techniques. The jet modeled in this problem is a supersonic helium jet exhausted into the free stream flow at a high pressure. 

Computed CFD results show the qualitative features and strong flow interaction between the jet and the free-stream flow. In 

general, very good agreement of the computed aerodynamic coefficients with the experimental data was achieved for all angles 

of attack investigated for the “jet-on” conditions. The results show the predictive capabilities of CFD techniques for supersonic 

flow over elliptic projectiles with jet interaction.

1L1612618AH80
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v

Contents

List of Figures v

Acknowledgments vii

1. Introduction 1

2. Solution Techniques 2

2.1 CFD++ Flow Solver ....................................... 2

2.2 Chimera Composite Grid Scheme .............................. 4

3. Computational Grids 4

4. Results 9

5. Concluding Remarks 16

6. References 17

List of Figures

Figure 1. H3P78 projectile .......................................... 5

Figure 2. Full grid for viscous computations, jet on .......................... 5

Figure 3. Expanded view of the grid in the base region, jet on.................... 6

Figure 4. Circumferential cross section of the grid at the base.................... 6

Figure 5. Expanded view of the jet grids projected onto the projectile surface ......... 7

Figure 6. Expanded view of the grid near the jet with nozzle modeling: (a) top view,

(b) side view ............................................. 8

Figure 7. H3P78 projectile showing the jet locations ......................... 9

Figure 8. Computed helium concentration contours near the base region, angle of attack,

 = (a) 0°, (b) 4°, (c) 8°, and (d) 12°, M = 4.0........................ 10

Figure 9. Computed surface pressure contours, jet on, angle of attack, = (a) 0°,

(b) 4°, (c) 8°, and (d) 12°, M = 4.0 ............................... 12

Figure 10. Experimental surface pressure measurement points, M = 4.0 .............. 13

Figure 11. Surface pressure comparison along the centerline of symmetry, M = 4.0 ...... 13

Figure 12. Surface pressure comparison along the centerline of jet, M = 4.0 ........... 14

Figure 13. Normal force coefficient, M = 4.0 ............................... 14

Figure 14. Pitching moment coefficient, M = 4.0 ............................ 15

Figure 15. Application factor, M = 4.0 ................................... 15
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vii

Acknowledgments

The authors wish to thank D. M. Orchard, Qinetiq, United Kingdom (UK); E. Fournier,

Defence Research Establishment, Valcartier, Canada; and J. A. Edwards, Defence Evaluation

and Research Agency, UK, for all their help in providing the experimental data to validate the

computed results. Special thanks to D. M. Orchard for all the discussions and assistance in the

analysis of the data. The authors wish to thank S. R. Chakravarthy and his colleagues of

Metacomp Technologies for all their help with the application of CFD++ code to this problem.

The scientific visualization work of R. Angelini of the U.S. Army Research Laboratory (ARL)

and the computational support of ARL’s Major Shared Resource Center are greatly

appreciated.
viii

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1

1. Introduction

The advancement of computational fluid dynamics (CFD) has had a major impact on projectile

design and development [1 through 4]. Improved computer technology and state-of-the-art

numerical procedures enable solutions to complex, three-dimensional (3-D) problems associated

with projectile and missile aerodynamics. In general, these techniques produce accurate and

reliable numerical results for projectiles and missiles at small angles of attack. Modern

projectiles and missiles are expected to experience moderate to large angles of attack during

flight. Of particular interest is the accurate determination of supersonic and hypersonic flow

over elliptic projectiles at moderate angles of attack. The flow field for such projectiles with

non-axisymmetric cross sections is complex, especially in the presence of jets used to maneuver

these projectiles. The work presented in this report was initiated as part of The Technical

Cooperation Program (TTCP) effort with participants from Canada, the United Kingdom, and the

United States and was aimed at assessing the capabilities of Euler and Navier-Stokes solvers

currently available to research scientists for supersonic flow over elliptic projectiles for both “jetoff” and “jet-on” conditions [5,6]. The TTCP research effort has also focused on the wind tunnel

testing as well as free flight testing of these projectiles. Different aspects of computational

techniques such as grid generation, algorithms, turbulence modeling, and flow field visualization

have been addressed by the group.

Earlier, inviscid solutions were obtained for H-series projectiles by the zonal Euler solver

(ZEUS) graphical user interface (GUI) code [7]. Since H-series projectiles are not

axisymmetrical, the projectile surface was generated by an auxiliary program and written as a set

of discrete points to a file. The projectile surface was read into ZEUS GUI with the user-defined

surface option. Pitch plane symmetry was used for most computations. Computations of the H3

projectile and its variations (with and without flares and strakes) were performed with the Euler

ZEUS code at M = 8.2 and several angles of attack between 0° and 15°. A comparison was made

of stabilization by strakes and flares for a different H-series projectile. The computations indicated

that although the flares gave increased drag, they were still substantially more effective in

providing stability than strakes alone. Recently, CFD techniques have been applied for the

numerical prediction of supersonic flow over the elliptic H3P78 projectile [8].

Calculations for the H3P78 projectile were performed with the ZEUS Euler code and two

Navier-Stokes flow solvers: the zonal Navier-Stokes flow (ZNSFLOW) [9] solver and CFD++

[10, 11], at several supersonic Mach numbers between 2.5 and 4.0 and several angles of attack

from 0° to 12° for the jet-off conditions. Computed aerodynamic coefficients were found to be

in very good agreement with the experimental data in all cases. The present research focuses on

the application of advanced CFD techniques for accurate numerical prediction of supersonic flow

over the elliptic H3P78 projectile with jet interaction. Numerical computations for the H3P78
2

projectile have been performed for the jet-on conditions by CFD++ code to study the interaction

of a helium jet with a free stream, M = 4.0, flow at several angles of attack.

A description of the computational techniques is presented, followed by a description of the

applications of these techniques to the H3P78 projectile. Results for this configuration are

presented at Mach 4 and several angles of attack (0° to 12°) at various supersonic speeds.

Computed data have been compared with experimental data provided by the Defence Evaluation

and Research Agency (DERA) [5], United Kingdom (UK), and obtained at Defence Research

Establishment, Valcartier, Canada [12].

2. Solution Techniques

2.1 CFD++ Flow Solver

The basic numerical framework in which the proposed scheme is implemented is termed the

unified grid, unified physics, and unified computing framework. These have been implemented

in a software suite called CFD++ [10, 11], and the user is referred to these references for details

of the basic numerical framework. Here, only a brief synopsis of this framework and

methodology is given.

The 3-D, time-dependent Reynolds-averaged Navier-Stokes (RANS) equations are solved by the

following finite volume method:

+ [ − ] =

V V dV dA dV

t

W F G H (1)

in which W is the vector of conservative variables, F and G are the inviscid and viscous flux

vectors, respectively, H is the vector of source terms, V is the cell volume, and A is the surface

area of the cell face.

The numerical framework of CFD++ is based on the following general elements:

1. unsteady compressible and incompressible Navier-Stokes equations with turbulence

modeling (unified physics);

2. unification of Cartesian, structured curvilinear, and unstructured grids, including

hybrids (unified grid);

3. unification of treatment of various cell shapes, including hexahedral, tetrahedral, and

triangular prism cells (3-D), quadrilateral and triangular cells (two-dimensional) and linear

elements (one-dimensional) (unified grid);
3

4. treatment of multi-block patched aligned (nodally connected), patched nonaligned

and overset grids (unified grid);

5. total variation diminishing discretization based on a new multi-dimensional

interpolation framework;

6. Riemann solvers to provide proper signal propagation physics, including versions for

preconditioned forms of the governing equations;

7. consistent and accurate discretization of viscous terms via the same multidimensional polynomial framework;

8. point-wise turbulence models that do not require knowledge of distance to walls;

9. versatile boundary condition implementation which includes a rich variety of

integrated boundary condition types for the various sets of equations; and

10. implementation on massively parallel computers based on the distributed memory

message-passing model that uses native message-passing libraries or message-passing interfaces,

parallel virtual machine, etc. (unified computing).

The code has brought together several ideas about convergence acceleration to yield a fast

methodology for all flow regimes. The approach can be labeled as a “preconditioned implicit

relaxation” scheme. It combines three basic ideas: implicit local time stepping, relaxation, and

preconditioning. Preconditioning the equations ideally equalizes the eigenvalues of the inviscid

flux Jacobians and removes the stiffness arising from large discrepancies between the flow and

sound velocities at low speeds. The use of an implicit scheme circumvents the stringent stability

limits suffered by their explicit counterparts, and successive relaxation allows cells to be revised

as information becomes available and thus aids convergence.

The code has recently added the ability to deal with multi-block meshes with various types of

inter-block connectivities. Multi-dimensional interpolation more accurately represents local

behavior of flow-dependent variables. While the formal order of accuracy need not be any

higher, this approach leads to practically higher accuracy on relatively coarse meshes. The

multi-dimensional interpolation framework helps us deal easily with inter-block connectivities as

well. Second order discretization was used for the flow variables and the turbulent viscosity

equation. The turbulence closure has been based on topology-parameter-free formulations.

These models are ideally suited to unstructured bookkeeping and massively parallel processing

because of their independence from constraints related to the placement of boundaries and/or

zonal interfaces. Recent contributions to these models include the following:

a. improved behavior of the dissipation rate transport equation by explicit sensitization

to non-equilibrium flow regions, and
4

b. enhanced near-wall characteristics and elimination of ad hoc formulations through the

introduction of time scale realization.

2.2 Chimera Composite Grid Scheme

The chimera overset grid technique greatly adds to the number of applications to which the

CFD++ solver can be applied. The Chimera overset grid technique, which is ideally suited to

complex configurations and multi-body problems [1 through 4, 13, 14, 15], involves the

generation of independent grids about each body or component and then oversetting them onto a

base grid to form the complete model. An advantage of the overset grid technique is that it

allows computational grids to be obtained for each body component separately and thus makes

the grid generation process easier. Because each component grid is generated independently,

portions of one grid may lie within a solid boundary contained within another grid. Such points

lie outside the computational domain and are excluded from the solution process. Equation 1 has

been modified to accommodate chimera overset grids that allow the possibility of having

arbitrary holes in the grid. The set of grid points that forms the border between the hole points

and the normal field points is called inter-grid boundary points. We revise these points by

interpolating the solution from the overset grid that created the hole. Values of the interpolation

coefficients needed for this revision are automatically provided by a separate algorithm.

3. Computational Grids

Zonal multi-block grids were generated for computations of jet interaction flow fields. These

structured multi-block grids have one-to-one overlaps at the zonal boundaries and are H-type

grids. The H3P78 projectile can be seen in Figure 1. The initial grid used for these computations

was a two-zone grid (see Figure 2) consisting of 1.8 million grid points. The Zone 1 grid along

the projectile body has 251 longitudinal points, 59 normal points, and 91 circumferential points,

with an H-type grid at the nose of the projectile. The base grid, Zone 2, is an H-grid consisting

of 50 longitudinal points, 113 normal points, and 91 circumferential points. The minimum

spacing at the wall is 6.0E-05 mm (1.0E-06 calibers).

An expanded view of the base region grid is shown in Figure 3. This figure also shows a jet grid

overset onto the after-body grid of the projectile. Figure 4 shows a circumferential cross section

of the computational grid at the base of the projectile. It clearly shows the elliptical cross section

of the body.

For the jet-on cases, each of the multi-block grids was generated separately. For ease of grid

generation, the chimera overset gridding technique (described earlier) was used to model the jet.

The projectile body grid was generated first. The chimera technique allows the jet to be gridded

separately. Two additional grid zones were created to model the jet. The dimensions for each
5

zone are 21 x 20 x 40 and 10 x 10 x 40, in the longitudinal, circumferential, and normal

directions, respectively. These two zones were then added to the projectile grid for the jet-on

calculations, adding about 20,000 points to each grid. One of the jet grids is a cylindrical grid

that covers the actual jet and extends beyond (see Figure 5). The second one is a rectangular grid

placed within the actual jet and overset onto the other grid primarily to avoid the grid singularity

along the centerline of the jet. An expanded view of the jet grids projected onto the projectile

surface is shown in Figure 5. The jet grids and the body grids are all overset to form the

complete mesh system. The chimera procedure results in hole boundaries (not shown here) in

the body grid, which are attributable to the jet, and transfers information between the jet grids

along these hole boundaries. The outer boundaries of the jet grids also receive information

interpolated from the body mesh.

Figure 1. H3P78 projectile.

Figure 2. Full grid for viscous computations, jet on.
6

Figure 3. Expanded view of the grid in the base region, jet on.

Figure 4. Circumferential cross

section of the grid at the

base.
7

Figure 5. Expanded view of the jet grids projected onto the projectile surface.

A single unstructured grid was generated with 1.8 million grid points for the same problem. In

addition, another mesh was generated for the jet-on calculations where the inside of the actual

nozzle is modeled (see Figure 6). This is a single zone unstructured grid consisting of about 3.8

million grid points. The grid points are clustered in the near the vicinity of the jet. Also, another

grid consisting of a total of 4.6 million points was generated (not shown here) with even more

points added in the longitudinal direction in the vicinity of the jet, especially ahead of the jet.

The grid blocking used to generate the full grid was left unchanged. Again, the minimum

spacing at the wall was selected to yield y+ of about 1.0 in the boundary layer.
8

(a)

 (b)

Figure 6. Expanded view of the grid near the jet with nozzle

modeling: (a) top view, (b) side view.
9

4. Results

Steady state numerical computations made by viscous Navier-Stokes methods were performed to

predict the flow field and aerodynamic coefficients on the H3P78 elliptic projectile for jet-on

conditions. Three-dimensional numerical computations have been performed for the H3P78

projectile with jet interaction by the CFD++ code at a supersonic Mach number of 4.0 and

several angles of attack from 0° to 12°. The real gas version of the CFD++ code was used and

the governing equations included air and helium as species. A point-wise two-equation

turbulence model was used and integrated all the way to the wall. Because of symmetry, only

one of the two helium jets has been modeled in the computations to save computer time. The

total pressure, density, and velocity of the jet were set to 21400 Pa, 0.229 kg/m3, and 872 m/s,

respectively. Again, the projectile geometry and a set of experimental wind tunnel data for

validation of the computations were supplied by DERA, UK [12]. Figure 7 shows the model

geometry and the jet locations.

Figure 7. H3P78 projectile showing the jet locations.

A longitudinal cut at the jet centerline was selected and used to show the concentration of helium

in that plane containing the jet centerline (see Figure 8) for different jet pressures. Here, black

represents zero helium concentration (100% air), and yellow represents high helium

concentration. At the jet exit, the helium concentration is 1.0. This figure clearly shows the

helium jet interacting with the free-stream flow, the mixing of the two species, and the extent to

which it is transferred by convection downstream into the wake region. The size of this

interaction region increases with increasing angles of attack. Also, the jet is seen to negotiate

more with the lee side free-stream flow at higher angles of attack, resulting in steeper jet angle.

This figure also shows the computed surface pressure contours for the different angle-of-attack

cases.
10

(a)

(b)

(c)

(d)

Figure 8. Computed helium concentration contours

near the base region, angle of attack, =

(a) 0°, (b) 4°, (c) 8°, and (d) 12°, M= 4.0.
11

A circumferential view of the surface pressures on the projectile after-body is shown in Figure 9

for various angles of attack. Here, the low pressure region is indicated in blue, and the high

pressure region is indicated in red. The red region on the lee side shows the effect of the jet

upstream from and onto the incoming free-stream flow. It clearly shows the strong effect of the

jet in all directions for this jet-on case. The surface pressure in front of the jet is increased while

the surface pressure downstream from the jet is lower. The upstream influence of the jet is found

to increase with increasing angles of attack. The jet affects the pressure as far as the centerline

of symmetry, indicating the strong interaction of the two jets in that area. The flow upstream

from the jet shock in the flare section is almost unaltered from = 0° to 4°. At higher angles of

attack, one can notice lower pressure on the lee side in that area. It clearly shows the asymmetry

(with respect to the jet centerline) in the low pressure region behind the jet at higher angles of

attack.

Computed surface pressures have been obtained along the centerline of symmetry and along the

centerline of the jet itself. These surface pressures are used to study the effect of the

aerodynamic interference resulting from the jet interaction with the free-stream flow. Computed

surface pressures have been compared with available experimental data. Figure 10 shows the 3-

mm jet holes and the experimental measurement points for surface pressures. Figure 11 shows

the comparison of the computed surface pressures with the data measured along the centerline of

symmetry for various angle-of-attack cases. The computed results here are shown as lines, and

the data are shown as symbols. Both CFD and the data show a pressure rise; however, the

numerical predictions indicate a somewhat stronger jet-to-jet interaction than is indicated by the

data at lower angles of attack ( = 0° and 4°). At higher angles of attack, the extent of this

interaction is decreased, and the computed results are in good agreement with the data. The

pressure rise is much less pronounced with increasing angles of attack ( = 8° and 12°). The

computed results presented here used the unstructured single mesh (see Figure 6). A finer mesh

with more grid points clustered in front of the jet was also used in the computations. The

computed results were found to be very similar, with no significant changes in the flow field. It

is believed that the discrepancy at lower angles of attack is not attributable to the number of

mesh points used in the computations.

A comparison of the computed surface pressures along the centerline of the jet for various angleof-attack cases is shown in Figure 12. Again, computed results have been compared with the

available data. CFD results here at all angles of attack from = 0° to 12° agree very well with

the experimental data. Both CFD and the data clearly show the expected pressure rise ahead of

the jet. The extent of upstream influence ahead of the jet is seen to increase with the increase in

angle of attack. Also, this figure shows the lower pressures downstream from the jet (pressure

less than the free-stream static pressure). This level of lower pressure downstream from the jet is

again very similar to what was measured in the experiment. Overall, the computed flow field

around the projectile and the jet showed similar characteristics as those observed in the

experiment.
12

(a)

(b)

(c)

(d)

Figure 9. Computed surface pressure contours,

jet on, angle of attack, = (a) 0°, (b)

4°, (c) 8°, and (d) 12°, M = 4.0.
13

Figure 10. Experimental surface pressure measurement points, M = 4.0.

0

1

2

3

4

5

6

7

8

370 375 380 385 390 395 400

Distance from nose (mm)

p/p

0 deg. incidence

2 deg. incidence

4 deg. incidence

8 deg. incidence

12 deg. incidence

jet centre line

cfd-a0

cfd-a4

cfd-a8

cfd-a12

Figure 11. Surface pressure comparison along the centerline of symmetry, M = 4.0.

Computed aerodynamic forces and moments were determined from the flow field results and are

shown in Figures 13 and 14. Figure 13 shows the normal force coefficient as a function of angle

of attack. Both CFD and the experiment show the normal force coefficient to increase with

increasing angle of attack. In general, the CFD results are in agreement with the measured data.

CFD results obtained by the chimera multi-block grids seem to match the data very well at low

angles of attack; however, there is a small discrepancy in the comparison at high angles of attack.

The reverse is true with the CFD results obtained with a single grid with and without nozzle

modeling. Modeling the nozzle and computing the nozzle exhaust flow did not seem to change

the results from the solution obtained without the nozzle modeled. Figure 14 shows the pitching

moment coefficient as a function of angle of attack. Here, the pitching moment coefficient is
14

referenced to the nose of the projectile. Both CFD and the experiment show the pitching

moment to decrease with increasing angle of attack. There is a small discrepancy in the

comparison except at low angles of attack, where the chimera solution matches fairly well with

the data. Again, the single grid solutions with and without the modeling of the nozzle were

essentially the same.

Figure 12. Surface pressure comparison along the centerline of jet, M = 4.0.

-0.5

0

0.5

1

1.5

0 5 10 15

Angle of Attack (degrees)

CN

Experiment

CFD - Chimera

CFD - Single grid

CFD - with nozzle

Figure 13. Normal force coefficient, M = 4.0.

Figure 15 shows the amplification factor as a function of angle of attack. The amplification

factor is defined as the ratio of the sum of the jet force and the jet interaction force to the jet

force alone. As shown in Figure 15, this factor is almost constant in the chimera solution. The
15

experimental data show a small increase in the amplification factor with increasing angle of

attack. This trend can also be clearly observed in the computed results obtained with the single

grid CFD with and without nozzle modeling. The nozzle modeling shows a small improvement

in the comparison of computed results with the data.

-6

-4

-2

0

2

4

0 5 10 15

Angle of Attack (degrees)

C

M

Experiment

CFD - Chimera

CFD - Single grid

CFD - with nozzle

Figure 14. Pitching moment coefficient, M = 4.0.

0

1

2

3

4

5

0 2 4 6 8 10 12

Angle of Attack (degrees)

Amplification Factor

Experiment

CFD - Chimera

CFD - Single grid

CFD - with nozzle

Figure 15. Amplification factor, M = 4.0.
16

5. Concluding Remarks

CFD approaches were used to compute the supersonic flow fields and aerodynamic forces and

moments on elliptic projectiles with jet interaction. Steady state numerical results have been

obtained at a supersonic Mach number, Mach = 4.0, and several angles of attack from 0° to 12°

for the jet-on conditions by an unstructured Navier-Stokes flow solver. The jet-on cases

simulated the interaction of a helium jet with a free-stream M = 4.0 flow. In general, very good

agreement of the computed aerodynamic coefficients with the experimental data was achieved at

all angles of attack investigated for jet-on conditions. CFD results for the jet-on cases showed

the qualitative features and strong flow interaction between the jet and the free-stream flow

similar to those observed in the experiment. Computed surface pressures along the jet centerline

compared much better than those along the line of symmetry. Computed normal force and

pitching moment coefficient matched fairly well with the experimental data. The results showed

the predictive capabilities of CFD techniques for supersonic flow over elliptic projectiles with jet

interaction.
17

6. References

1. Sahu, J., Heavey, K.R., Ferry, E.N. Computational Fluid Dynamics for Multiple Projectile

Configurations. Proceedings of the 3rd Overset Composite Grid and Solution Technology

Symposium, Los Alamos, NM, October 1996.

2. Sahu, J., Heavey, K.R., Nietubicz, C.J. Time-Dependent Navier-Stokes Computations for

Submunitions in Relative Motion. Proceedings of the 6th International Symposium on

Computational Fluid Dynamics, Lake Tahoe, NV, September 1995.

3. Sahu, J., Heavey, K.R., Nietubicz, C.J. Computational Modeling of SADARM

Submunition Separation. Journal of Computer Modeling and Simulation in Engineering,

July 1997, 2, 267-283.

4. Sahu, J., Heavey, K.R., Ferry, E.N. Computational Modeling of Multibody Aerodynamic

Interference. Journal of Advances in Engineering Software Apr-Jul 1998, Elsevier

Sciences, 29 No. 3-6, 383-388.

5. Orchard, D., Fournier, E., Dupuis, A., Edwards, J. Wind Tunnel Tests on the H3P78,

Power Law, Elliptic Section Flared Projectile from Mach 2.5 to 4 inch, American Institute

of Aeronautics and Astronautics (AIAA) August 2001 Paper No. 2001-4321, Montreal,

Canada.

6. Fournier, E., Orchard, D. Testing of a Novel Maneuvering Projectile in the DREV Trisonic

Wind Tunnel, Technical Memorandum Report DREV TM-2000-108, Defence Research

Establishment, Valcartier, Canada, July 2000.

7. Edge, H.L., Clarke, J. Graphical User Interface for ZEUS, ARL-TR-1093, U.S. Army

Research Laboratory: Aberdeen Proving Ground, MD, June 1996.

8. Sahu, J., Heavey, K.R., Edge, H.L. Numerical Computations of Supersonic and

Hypersonic Flow over Elliptical Projectiles, AIAA August 2001 Paper No. 2001-4320,

Montreal, Canada.

9. Edge, H.L., Sahu, J., Sturek, W.B., Pressl, D.M., Heavey, K.R., Weinacht, P., Zoltani,

C.K., Nietubicz, C.J., Clarke, J., Behr, M., Collins, P. Common High Performance

Computing Software Support Initiative (CHSSI) Computational Fluid Dynamics (CFD)-6

Project Final Report: ARL Block-Structured Gridding Zonal Navier-Stokes (ZNSFLOW)

Solver Software. ARL-TR-2084, U.S. Army Research Laboratory: Aberdeen Proving

Ground, MD, February 2000.

10. Peroomian, O., Chakravarthy S., Goldberg, U.C. A “Grid-Transparent” Methodology for

CFD, AIAA 1997, Paper 97-07245.
18

11. Peroomian, O., Chakravarthy S., Palaniswamy, S., Goldberg, U.C. Convergence

Acceleration for Unified Grid Formulation using Preconditioned Implicit Relaxation, AIAA

1998, Paper 98-0116.

12. Orchard, D., Fournier, E., Dupuis, A., Edwards, J. Wind Tunnel Tests on the H3P78,

Power Law, Elliptic Section Flared Projectile with Jet Interaction, AIAA August 2001,

Paper No. 2001-4322, Montreal, Canada.

13. Steger, J.L., Dougherty, F.C., Benek, J.A. A Chimera Grid Scheme, Advances in Grid

Generation, edited by K. N. Ghia and U. Ghia, ASME FED-5, June 1983.

14. Benek, J.A., Donegan, T.L., Suhs, N.E. Extended Chimera Grid Embedding Scheme With

Application to Viscous Flows. AIAA 1987, Paper No. 87-1126-CP.

15. Meakin, R., Wissink, A. Unsteady Aerodynamic Simulation of Static and Moving Bodies

Using Scalable Computers, AIAA-99-3302-CP, 14th AIAA Computational Fluid Dynamics

Conference, Norfolk, VA, June 1999.

16. Goldberg, U.C., Peroomian, O., Chakravarthy S. A Wall-Distance-Free K-E Model With

Enhanced Near-Wall Treatment, ASME Journal of Fluids Engineering 1998, 120, 457-462.
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