cfd computational modeling of nearfield to farfield plume expansion aiaa-2007-5704.pdf

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AIAA 2007-5704

Computational Modeling of Nearfield to Farfield

Plume Expansion

D.B. VanGilder *, C.C. Chartrand†, J. Papp‡, R. Wilmoth§, and N. Sinha**

Combustion Research and Flow Technology, Inc., Pipersville, PA, 18947

A hybrid continuum/non-continuum methodology is being developed to model flows in

which rarefaction effects are important while the continuum approach is accurate for parts

of the flowfield. Depending on altitude, rocket and missile exhaust plume expansion can be

modeled using a combination of continuum, direct simulation Monte Carlo (DSMC), or free-

molecular (FM) techniques. The ability to automatically couple these techniques allows for

efficient and accurate modeling of length scales on the orders of km’s from the nozzle exit

plane, and parametric studies can easily be performed. The methodology is demonstrated

for an axisymmetric (0 angle of attack) and a 3D (>0 angle of attack) missile configuration.

For the latter calculations, the DSMC solution is coupled to an outer DSMC simulation and

a FM code. The Automatic Efficient Generalized Interface Surface Toolkit (AEGIS Toolkit)

which enables the coupling between the continuum and DSMC codes is described.Extensions to the methodology for particulates and unsteady flow phenomena are among the

capabilities.

I. Introduction

omputational modeling of rocket and missile exhaust plumes requires accurate physical models andsophisticated numerical methods. The nearfield plume can be modeled using conventional continuum-based

CFD codes. As this flow expands, it becomes more rarefied. At high altitudes, the interaction of this plume with a

rarefied freestream requires modeling the intermolecular interactions more directly. In this region, the directsimulation Monte Carlo (DSMC) method is appropriate. When the flow is more rarefied, a free-molecular

approximation is sufficient.

C

Hybrid CFD-DSMC simulations of the plume flowfield typically consist of a continuum nearfield simulated

using continuum-based CFD methods while the rarefied farfield is treated using DSMC methodology. Rarefiedflow modifications are implemented into the continuum flow solver to extend its range of applicability to higheraltitudes and more rarefied conditions, in order to further reduce the computational effort on the non-continuum

solver. An interface surface is generated using some type of continuum/non-continuum breakdown criteria.

Continuum flow values are then interpolated onto this surface and utilized as an inflow boundary for the DSMCsimulation.

Particulates from solid motors are also of interest for high-altitude plume flow characteristics and plume

radiance. Past efforts to simulate particles within the rarefied regime have decoupled the particulate simulation from

the rarefied gas simulation1. Now the particulates are included in both the CRAFT CFD® code and the DAC/PDAC

codes.

This paper describes a unique Automatic Efficient Generalized Interface Surface Toolkit (AEGIS Toolkit) that has been developed for separating continuum and rarefied non-continuum regions along a “continuum breakdown

surface”. It has been designed and tested to automatically generate an interface surface based on a CRAFT CFD® 2-3

solution and output this surface with appropriate properties in the format needed by the Direct Simulation MonteCarlo (DSMC) Analysis Code (DAC) developed at NASA Johnson 4. However, the methodology and the

procedures used are general. This methodology has been shown previously for zero angle of attack at high altitudeswhere axisymmetric calculations are sufficient 5. The present study includes a generic missile flying at high altitude

* Research Scientist, 6210 Keller’s Church Rd, Pipersville, PA, AIAA Member.† Research Scientist, 6210 Keller’s Church Rd, Pipersville, PA, AIAA Member.‡ Senior Research Scientist, 6210 Keller’s Church Rd, Pipersville, PA, AIAA Member.§ Principal Research Scientist, 124 Burnham Place, Newport News, VA, AIAA Associate Fellow.** Vice President and Technical Director, 6210 Keller’s Church Rd, Pipersville, PA, AIAA Associate Fellow.

American Institute of Aeronautics and Astronautics

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at a moderate angle of attack. Since the non-zero angle of attack breaks the symmetry, full 3D simulations are

required. Thus, 3D CRAFT CFD® and DAC calculations are performed. Application of the AEGIS toolkit to this

3D problem is described. The coupling of two DAC flow regions is also described. This coupling allows for a

larger farfield domain without the inefficiencies encountered in a single large DSMC calculation. Results from

coupling DAC results to a free-molecular code are also presented.

II.

Methodology

A. CRAFT CFD® Navier-Stokes Solver

The Navier Stokes calculations described in this work are performed using the CRAFT CFD® code

2. CRAFT

CFD® uses is a finite-volume, second or third order upwind Roe TVD formulation. A number of options are

available for thermophysical modeling of high-speed flows, turbulence modeling, and multiphase modeling

(Eulerian or Lagrangian). Some CRAFT CFD® features are presented in Table 1. Features related to rarefied flowsinclude the addition of a surface slip model and non-local thermal equilibrium (NLTE) using a Landau-Teller

relaxation rate based on Millikan and White relaxation times 6.

Table 1. Current Features of CRAFT CFD® Code

NUMERICS/PARALLEL

PROCESSING

• 1D/2D/AXI/3D Finite-Volume Discretization

• Implicit, ADI and L/U, Higher-Order Upwind (Roe/TVD) Formulation• Fully Implicit Source Terms/Boundary Conditions

• PNS Spatial Marching Capability

• Domain-Decomposition Parallel Architecture with MPI

• Shared Memory Parallelism

• Preconditioning Extensions

GRID FEATURES

• Grid Dynamics to Account for Moving Boundaries

• Grid Patching/Blanking for Complex Geometries

• Solution-Adaptive Gridding and Grid Embedding

• Noncontiguous Grid Interfacing with Flux Preservation Across Domains

THERMO-CHEMISTRY

• Multi-Component Real Gas Mixtures

• Finite-Rate Chemistry/Arbitrary Number of Species and Reactions

• Fully Implicit Source Term Linearization

MULTIPHASE FLOW • Non-equilibrium Particle/Droplet Solvers (Eulerian and Lagrangian Formulations)

TURBULENCE• k ε /EASM Formulations with Compressibility/Vortical Upgrades

• LES Subgrid Scale Models – Algebraic and One-equation

RAREFIED FLOW

• Slip Boundary Conditions

• Vibrational non-local thermal equilibrium energy modeling

B. DAC/PDAC DSMC Solver

The Direct Simulation Monte Carlo (DSMC) Analysis Code or DAC is utilized to perform DSMC calculationsin the present work. The DAC package was primarily developed by LeBeau et al. 4 and is a collection of programs

that are used in the analysis of rarefied flows for either three-dimensional or axisymmetric geometries. DACfollows the standard DSMC methodology 7 where simulated molecules, each representing many real molecules, are

statistically tracked as they travel through the computational volume and undergo collisions with each other and

with solid surfaces. A grid is used in the computational volume in order to facilitate the selection of nearest

neighbor collision pairs and in order to obtain statistical samples for macroscopic flowfield quantities.The computational grid is divided into a Cartesian network of Level 1 cells, with equally spaced cells in each

coordinate direction 8. The cell size is typically defined by the user as the maximum size needed to resolve the flow,approximately the mean free path of the freestream. For regions of higher gas density, each Level 1 cell can be

independently refined an additional level. These Level 2 cells are themselves a Cartesian grid imbedded in each

Level 1 grid cell with equal spacing in each coordinate direction, so directional bias can be maintained. The Level 2


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grid refinement is required to provide accuracy by maintaining collision modeling cells on the order of a mean free

path. A new feature in DAC allows the refinement to be relaxed by using the nearest neighbor collision pairing 9.

Automatic grid adaptation varies the number of Level 2 cells in each parent Level 1 cell based on the previous

solutions density. Grid adaptation allows features such as the plume induced separation and plume edge to be

realized as opposed to the original coarse grid solution. The main DAC features are presented in Table 2.Extensions to DAC, called PDAC, include particulate and unsteady flow capabilities.

Table 2. Features Of DAC

• Implements the Direct Simulation Monte Carlo Technique for 3D and Axisymmetric

Simulations

• Tracks Molecular Motion Deterministically and Molecular Collisions Probabilistically

• General Boundary Conditions for Wide Range of Problems

• Domain-Decomposition Parallel Architecture with MPI

• Distributed Memory Parallelism

• Pre-Processor and DSMC Codes Can Be Run In Scalar or Parallel Modes

NUMERICS/

PARALLEL

PROCESSING

• Automatic, Dynamic Load Balancing

• Automatic Flowfield Grid Generation Using Two-Level Embedded Grid Technology

• Automatic Flowfield Grid Adaptation Based on Previous SolutionGRID FEATURES

• Unstructured Grid Definitions of Complex 3D Geometries Embedded Within CartesianFlowfield Grid Framework

• Multi-Component Real Gas Mixtures

• Translational, Rotational, and Vibrational Non-Equilibrium Energy Exchange

• Finite-Rate Non-Equilibrium Chemistry/Arbitrary Number of Species and Reactions

• Chemical Reactions Modeled on Molecular Level Via Probabilistic Kinetic Theory

• Limited Reactions Sets Provided But Additional Sets Can Be Added by User

THERMO-

CHEMISTRY

• Extended Reaction Sets for Missile Plume and Divert Jets

1. Particulate Extensions

The one-way coupled version of PDAC implements the same empirical drag and heat transfer models as CRAFT

CFD®, and details of the PDAC implementation are given in Reference [5]. PDAC performs post-DSMC analysisof the particulate transport based on a previous hybrid continuum-DSMC simulation.

Two-way coupled methods that allow particle to gas momentum and energy transfer as well have been explored.Reference [10] describes a heat-bath model and compares it to the model by Burt and Boyd (BBG) 11 using a 1D

code for a simple two-phase equilibrium test problem. It is assumed in both of these methods that the number

density of solid particulates is much different than the number density of gas molecules such that different scalefactors, i.e., number of real particles represented by each simulation particle, are required to scale the simulated

densities to the real densities. For typical mass loadings (typically a few percent or less) of micron-sized Al2O3

particles, this assumption is generally true. For example, the number densities of gas molecules are typically of the

order 1010 times greater than the solid particle number densities due to the large difference in mass per particle

compared to the molecular mass. Therefore, direct simulations with a single number density scale factor for

molecules and particles would be impractical since they would require the total number of simulation molecules and

particles to be greater than 1010 in order to provide adequate statistics.

The BBG model, described in Reference [11], uses the Gallis free-molecular analysis, modified to account forinternal degrees of freedom in the gas molecule, to transfer energy to the particle. An analogous procedure is used

for drag. The method to treat gas-particle collisions that transfer momentum and energy from the particle to the gas

is analogous to that used for gas-gas collisions in a typical DSMC calculation. However, with different gas and particle weighting factors, it is shown to conserve energy and momentum on average. The heat-bath model is an

alternate approach that was developed to ensure detailed balance on a macroscopic level within each simulation cell

during each time step. In this method, the energy transferred from the gas to the particle is “stored” in a heat bath

and later distributed to (subtracted from) the gas molecules. During each time step, the energy transferred to the

solid particle is calculated in the same manner as in the BBG model. However, the total energy transferred to

particles within a cell is stored and the particle temperatures are updated as in the BBG model. A proportional


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amount of energy is subtracted from each gas molecule ( p

p

g

N E

N Δ∑ ) such that the total energy is conserved. Kinetic

(translational) and internal energy contributions are computed separately such that the method maintains the proper

partitioning of energy between modes. While this macroscopic approach does not simulate the detailed non-

equilibrium effects of gas-particle collisions provided by the BBG method, it has been found in representative teststhat the actual change in energy per gas molecule per time step is typically a very small fraction of the total energy

per molecule (<1%). Furthermore, the change in molecular energy is randomly redistributed among other gasmolecules through gas-gas collisions.

2. Unsteady Extensions

The development of an unsteady, hybrid continuum-DSMC method would allow modeling of transient plume

phenomena. However , it presents a considerable challenge. A one-way coupled unsteady hybrid approach has beenreported previously 12 with application to a simple spherical expansion. That study used a simple one-dimensional,

spherically-symmetric unsteady DSMC code developed by Bird which produced results comparable to those for a

continuum calculation. The study demonstrated that hybrid coupling could be accomplished by simply providing

the temporal solution from the continuum solution as a boundary condition to the DSMC code at a fixed spatiallocation and continuing the DSMC calculation out to larger distances from the spherical boundary.

Substantial progress has been made in extending this methodology to PDAC. While DAC does not contain

explicit unsteady capability, the DSMC methodology is inherently unsteady, and DAC can be run in a time-accurate

mode on the first-level uniform grid. However, to achieve adequate statistical sampling, a very large number ofsimulated molecules would be required in each cell, and even fairly simple unsteady problems would requiresignificant computational resources. Therefore, the first step in the development of an unsteady version of PDAC

has been to incorporate ensemble averaging of the flowfield properties at discrete time intervals. In essence, the

simulation is repeated a number of times with different random number seeds and using a relatively small number ofsimulation molecules. The samples are then accumulated at specific times or time intervals to obtain adequate

statistics. The approach allows for additional samples to be added to the previous aggregate. Additions to PDAC

which permit interpretation of a time-varying source and/or wall boundary conditions in a more general manner

have been incorporated in order to couple to an unsteady continuum code. The boundary condition input was

modified to permit time variation of each of the source properties on all surfaces. The variation can be given by aspecified function or by values that are read from a file. Capabilities to initialize the flow to specified starting

conditions, such as freestream or ambient conditions, have also been developed.

C. AEGIS Toolkit

Although a hybrid continuum/DSMC coupling technique has been developed and utilized in many applications

in the past, the process of generating the interface surface can still be cumbersome and inefficient.

Oversimplification of the interface surface(s) through the use of common shapes (ellipsoids, cones, spheres, etc.)

saves time in surface generation but often impacts the computational effort and/or accuracy, especially if thedetermined breakdown region is complex. Consequently, a simplified surface that does not fit the desired

breakdown contour may either encompass too much continuum flow resulting in an inefficient DSMC simulation, or

encompass too much rarefied flow resulting in an inaccurate boundary condition for the DSMC simulation. In an

effort to address these issues, the unique Automatic Efficient Generalized Interface Surface Toolkit (AEGIS

Toolkit) has been developed to automatically generate an interface surface that separates the continuum and rarefied

non-continuum regions where the continuum assumption is less accurate.

As the name implies, the AEGIS Toolkit contains a set of procedures designed to efficiently proceed from acontinuum solution to DSMC initialization. A summary of the process is described in Figure 1 while the key

components are described in Table 3. This toolkit is an extension of the Arbitrary Breakdown Surface Generation(ABSG) technique described previously 5 where it was applied to axisymmetric plumes and simplified separationzones. However, the AEGIS Toolkit has been extended beyond the basic ABSG methodology to accommodate

more generalized flow features, interface regions, and interface (breakdown) parameters.


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Table 3. AEGIS Component Descriptions

Component DescriptionBreakDn Interface parameter generator

GDM2D/GDM3D Triangulated surface generator based on cost minimization relative to user defined

constraints and interface parameter

GTSOps Interface to GNU Triangulated Surface toolkit Boolean functions

Interp Tool to interpolated flow results onto interface surfaceGenDACSD Generate DAC Surface Definition file (may also interpolate)

Figure 1. Schematic Of AEGIS Operation.

At the heart of the AEGIS Toolkit is still the Geometrically Deformed Model (GDM).methodology13

. Thismethodology employs a cost minimization algorithm based on image (breakdown parameter), topology (surfaceelasticity), and deformation (forcing function) parameters to produce a continuous and water-tight triangulated

surface. Symbolically, the procedure can be thought of as a balloon expanding within a cage. As the balloon is

inflated (deformation), it gradually takes on the shape of the cage while the surface elasticity (topology) of the

balloon prevents it from leaking out any of the holes. Eventually, a point is reached where the balloon cannot

expand without violating any of the constraints and the final surface is produced. Because the methodology canaccommodate discontinuous image functions (the cage with openings) and the smoothness is maintained as a

constraint, an appropriate coupling boundary surface can be obtained from an often times complex and

discontinuous field function.Although the GDM process can easily generate an interface surface, this surface is initially free-floating, fully

three-dimensional, and not tied to any geometric (body) surface. The earlier ABSG methodology utilized simplified

procedures to stitch the final GDM surface to a body, typically a nozzle exit, as well as take advantage of any

symmetry. Consequently, the process was very specialized and not prone to modification to more generalizedfeatures. To alleviate this deficiency, the AEGIS Toolkit implements some of the capabilities of the GNUTriangulated Surface (GTS) toolkit 14.

The GTS toolkit is an Open Source Free Software that contains numerous features for the triangulation of 2D

parameterized surfaces and, more importantly, for performing boolean manipulation of these surfaces, such asunions, intersections, and differences. Such a methodology is utilized by AEGIS to perform such actions as merge a

body to GDM surface, merge a GDM surface to another GDM surface, symmetry cutting, etc., efficiently and, more

importantly, automatically. Unfortunately, the GTS Boolean process often produces collinear or very skewedtriangular elements which have to be extricated. Presently a procedure of either point removal or edge shifting is

performed to accomplish this task.

Define InterfaceParameter

Generate

Surface

GTSOperations

GenerateDACSD

Interpolate

ContinuumSolution

DACSimulation AEGIS

Toolkit


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An example of the image identification and surface generation process is shown in Figure 2 through Figure 4.

The process begins by choosing an appropriate image constraint that will define the location of breakdown. This

may be the Bird breakdown parameter or similar such variable. In this case, the parameter is the density of a plume

species. As can be seen, the surface is discontinuous and contains a gap due to the multi-block nature of the solution

(Figure 2a). Once an appropriate image is determined, the GDM process begins by introducing a seed surfacewithin the image constraint (Figure 2 b). Through the deformation process, the initial seed surface grows until it is

constrained by the image (Figure 2c through Figure 2e). As can be seen by the comparison of the final surface with

the image constraint, the fit is quite good. Due to the topological constraint, the points do not ‘leak’ out from thegaps.

(a) (b) (c)

(d) (e) (f) Comparison to image constraint

Figure 2. Demonstration Of Surface Generation Using GDM Methodology Within AEGIS Toolkit.

After completion of the surface generation, there is a gap between the body and the intended body interface(Figure 3a). Because DAC requires a water-tight surface grid, this gap must be removed and the surface stitched to

the body. This is accomplished through the GTS boolean operator tool within AEGIS. The user can choose from

several basic interface shapes and operations in order to generate the final interface surface. In this case, the

interface points along the nozzle lip are defined along with a normal direction and cone angle in order to generate

the initial cone surface (Figure 3 b). The GTS union operation is then performed to produce the fully integratedinterface surface (Figure 3c).

At this point, the surface is technically water-tight. However, the GTS operation tends to create an excessive

amount of element skewness as it strictly applies the Boolean operation (Figure 4a). This cell skewness can result innear zero area cells that are not degenerate but collinear. Such elements cause difficulty with DAC’s pre-processing

program (PREDAC). Consequently, after the GTS process, highly skewed cells are extricated using the various

methods shown in Figure 4 b. The final result of this process is shown in Figure 4c. As can be seen, the skewed

cells are removed and the topology of the region is much improved. The only thing left at this point is to interpolate

any flow results onto inflow surfaces and export the data in the desired DSMC file format.

Application of the AEGIS Toolkit to a straight back plume and divert jet are shown in Figure 5 and Figure 6 respectively. In both these cases, the Bird parameter is chosen as the image constraint. Due to its derivative nature,

the iso-surface can be very discontinuous, which is especially evident in the divert jet case. However, the AEGIS

Toolkit has no problem generating the final interface surface. The AEGIS Toolkit has also been applied to a re-entry vehicle geometry 15.


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(a) (b) Generic cone geometry (c) GTS boolean operation

Figure 3. Generating of interface to body using GTS Toolkit.

(a) (b) (c)

Figure 4. Demonstration Of Cell Modification To Remove Skewed Elements.

(a) (b)

Figure 5. Application Of AEGIS To Straight-Back Plume.


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(a) Initial Bird parameter (b) GDM seed surface

(c) GDM growth (d) Final GDM surface

(e) Forward view GDM surface (f) GTS operation

(g) Final interface surface

Figure 6. Application of AEGIS to divert jet.

D. DAC-to-DAC

For length scales of interest, 100’s of meters to kilometers from the missile exit plane, the plume number densitydecreases by several orders of magnitude. Continuum methods are needed for the inner core, then, DSMC modeling

is appropriate for rarefied regions in which the collisions are still important. Eventually, a free-molecular

approximation is sufficient. Given the requirements of a sufficient molecule count for collisions and statistics and

the scaling of grid cells to the mean free path, the size of the intermediate “DSMC” region can require substantial

computational size and times. DAC has a 2-level grid structure, so that grid resolution can vary with densities. Thisstructure also allows for time step and the real-to-simulated molecule ratios to vary between cells. Thus, the

collisional behavior is better captured. However, this approach becomes less computationally efficient as the

variations in density for the domain increase. For example, the fluxing of molecules across cell boundaries withdifferent ratios and time steps requires cloning and destroying of molecules. A simple approach to address this issue

is to couple the DSMC domain to another (outer) DSMC domain analogous to the CFD to DSMC coupling. An


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automated procedure has been developed to take the inner PDAC (or DAC) solution and put density, velocity, and

temperatures onto a new triangulated surface for an outer PDAC (or DAC) calculation. PDAC has an optional

feature that permits each species of a source flow to have its own rotational and/or vibrational temperature specified.

This multi-temperature feature is necessary to ensure that the non-equilibrium flow characteristics (that the DSMC

method captures) are propagated to the outer DSMC domain.At high altitudes, as the plume expands collisions become less significant and a free-molecular (FM) description

is adequate at sufficient distances from the nozzle exit. For example, the steady-state density field resulting from a

mass flow rate with bulk velocity ue is given by:m&

[ ]2 2sin 2 2 2 2

2

cos 1( ) cos exp( cos ) ( cos ) 1 ( cos )

2

sm x e s s s erf s

A r

θ β φ ρ θ θ θ π

π

− ⎧ ⎫= − + + +⎨ ⎬⎩ ⎭

&rθ (1)

where β is 1

2 RT , s is the speed ratio β*ue, θ is the angle between ue and x, and φ is the angle between the nozzle

exit plane and x 16. Similarly, other flow properties such as velocity and temperature can be obtained from various

moments of solution. Thus, the mass, momentum, and energy fluxes across a DSMC or CFD domain boundary can be used for a FM calculation of the farfield plume. A FM code that calculates these properties on a Cartesian grid

using the projection of an inflow in the DAC surface format (which is described by properties on a triangulated

surface) has been used in this study.

III. Results

As a demonstration of the methodology described in the previous section, a generic missile configuration at an

altitude where the freestream is sufficiently rarefied is chosen. Thus, the direct simulation Monte Carlo technique is

appropriate for plume and freestream interactions, while the plume near the missile is captured using the continuummethod. A zero angle of attack case is simulated, so that axisymmetric calculations can be performed. A more

detailed discussion of axisymmetric results has been reported previously 5 Additional simulations were performed

for a moderate angle of attack in order to demonstrate the application to a 3D problem. For these simulations, the

inner PDAC solutions were then coupled to a free-molecular code and to an outer PDAC calculation.

The axisymmetric results are shown in Figure 7a and Figure 7 b. The upper parts of both figures include the

CRAFT CFD® solution inside the interface boundary (highlighted in black) along with the PDAC solution that uses

the values on the interface boundary as input. Results for both translational temperature and number density show a

continuity of solution across the boundary. Discrepancies in temperature reflect the attention given to modeling the

shock layer and its interaction with the plume in the DSMC calculation. It was found that at high altitudes that the plume “core” calculated by CFD is insignificantly influenced by the freestream. The number density contours in

Figure 7 b are in good agreement.

a) Translational temperature: upper PDAC /lowerCRAFT CFD®

b) Number density: upper PDAC /lower CRAFTCFD®

Figure 7. Temperature And Number Density Contours Comparing CRAFT CFD® And PDAC For

Axisymmetric Case.


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A comparison of CRAFT CFD® and PDAC results for the 3D case are shown in Figure 8a and Figure 8 b. The

interface boundary is included, and the CFD solution is enclosed within it. Again the continuity of solution across

the boundary is maintained. A slight decrease in density across this boundary near the missile’s nozzle can be seen.

The one-way coupling assumption is less accurate when the flow is mostly tangential to the boundary, which is the

case in this region. However, this difference becomes negligible for farfield values.

a) Translational temperature b) Number density

Figure 8. Temperature And Number Density Contours Comparing CRAFT CFD® And PDAC For 3D Case.

These 3D inner PDAC solutions were then coupled to an outer PDAC simulation. Some sample results are

shown in Figure 9-Figure 13. The contours for each figure are for the symmetry plane (z=0). The number density

and velocity contours (Figure 9, Figure 10, and Figure 11) indicate that the method is properly propagating the fluxof the gas across interface boundaries. Figure 12 and Figure 13 show the translational and rotational temperatures at

the lower “y” boundary. These figures indicate the importance of preserving the non-equilibrium information.

Although additional effort is needed in determining the proper resolution at the interface boundary, the close-upviews do show better agreement when the multiple temperature feature is used. The overall temperature, which is a

weight by mode of translational and internal energies, is generally less that the translational temperature due to

dissociation of the diatomic molecules and the lower relaxation rate of the internal modes. Therefore, the single

temperature used is low compared to the inner translational temperature (see Figure 12 b). The rotational

temperature differences (Figure 13a and b) are not as significant here. However, vibrational temperatures were

found to be quite different in the shock layer. Thus, preserving these values from one DSMC calculation to theother is important.

Figure 9. Number Density

Contours.

Figure 10. U-Velocity Contours. Figure 11. V-Velocity Contours.

.


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(a) (b)

Figure 12. Translational Temperature Contours For a) Multi-Temperature And b) Single Temperature.

(a) (b)

Figure 13. Rotational Temperature Contours For a) Multi-Temperature And b) Single Temperature.

This simple technique for DAC-to-DAC coupling does a good job of preserving flux across the boundaries for a

plume expansion problem. Using the multiple temperature option also allows the internal energy to be properlyrepresented. Depending on the level of detail needed, this approach is likely sufficient for describing a plume

expansion. However, a macroscopic approach which enforces an equilibrium distribution may not accurately

describe the distribution functions, especially in a multiple species flow. Applications in which detailed energydistributions are important may require a microscopic approach. By setting up molecule files which capture a

representative sample of molecules from the inner solution, the outer solution can sample these files to introducemolecules. These molecules would then do a reasonable job of preserving the distribution across the interface as

long as a sufficient number of molecules needed to maintain proper flux conservation is used. This value is

proportional to the scaling of the number of real molecules to simulated molecules and the change in time stepacross the interface. This approach has been used successfully by Bird 7.

Figure 14a-c show results from coupling the inner PDAC simulation to a free-molecular calculation that projects

the solution to 1 km from the nose of the missile. In order to avoid the discontinuity at the boundaries caused by the1/r 2 dependence inaccuracies for r~0, a surface was chosen slightly inside the DSMC domain. The number density

and velocities are well-captured in most of the flow. It is important to note that the anomalies near the DSMC

boundary have no effect on the FM solution in the farfield, since each grid point strictly depends on summing the

contributions from each source at the coupling surface. In fact, a grid is not required at all for the FM solution, and

a FM farfield solution could be obtained at an arbitrary single or set of points.Differences can be seen in much of the outer region compared to the outer PDAC calculation. The FM solution

represents the plume and its interaction with the freestream only before the interface boundary. This outer result

does not include the freestream contribution or its interaction with this “inner” flow. This explains the discontinuity

across the upper “y” boundary for v-velocity in Figure 14c. Since the flow velocity is directed away from the higher“y” region, there is a very low density there. Thus, the average v-velocity is skewed. Inclusion of the freestream

contribution would give a more realistic flowfield here, however this contribution would be duplicative at other

places in the flowfield, eg. in the +x-direction. The DSMC solution is more accurate for the farfield, because it

captures this freestream contribution directly and the collisions that occur. For proper treatment, the coupling between the DSMC and FM should be based on a local Knudsen number.


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a) Number density b) U-velocity

c) V-velocity

Figure 14. DSMC-To-FM Contours At Symmetry Plane.

IV.

Conclusion

The coupling of the CRAFT CFD® continuum flow solver and the DAC DSMC flow solver has been

demonstrated for a 3D application. The development of the Automatic Efficient Generalized Interface SurfaceToolkit (AEGIS Toolkit) has enabled 3D and/or complex interface surfaces to be created and appropriate properties

output for the surface with minimal user intervention. The coupling methodology has been applied to a high altitude

missile configuration. To capture the farfield plume structure, these solutions are then coupled to an additional

DSMC simulation or a free-molecular calculation using scripts to automate the process. Thus, a method for

modeling the nearfield to farfield plume expansion using the best appropriate model in each region has beendeveloped. Extensions for particulates and unsteady flow phenomena are also available which can be important

when simulating high altitude plume flowfields.

Acknowledgments

Portions of this work were funded by ARDECOM.

References1 Papp, J. L., Yellin, K. A., and Dash, S. M., “Plume and Divert Jet Effects on Missile Flowfields at Higher

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2 York, B.J., Kenzakowski, D.C., Lee, R.A., and Dash, S.M., "Upgrades to CRAFT Code for Simulation ofDucted Launcher/Plume Interactions," 1997 JANNAF EPTS & SPIRITS Users Group Joint Meeting, Lockheed

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