## TWO PHASE RAREFIED PLUME SIMULATION

The primary goal of this project is the development of an efficient
numerical method for modeling high altitude rocket exhaust plume flows,
in which a solid particulate phase is suspended within the gas-phase
exhaust constituents. Solid particles, particularly soot and aluminum
oxide (Al_{2}O_{3}), are commonly found in plume flows from liquid or solid-propellant
rockets, and may have significant effects on both the overall
efficiency of the propulsion system and on the plume radiation
signature. Al_{2}O_{3} particles expelled from
solid-propellant rocket motors may account for up to 50% of the mass
flux at the nozzle exit, so that consideration of the particle
properties – as well as the complex interaction between the solid and
gas phases – is often crucial for accurate modeling of the plume. In a
typical plume flow, significant exchange of momentum and energy will
occur in the near-field region just beyond the nozzle, where the gas
will tend to increase the velocity and reduce the temperature of the
particles, and the particle phase will have the opposite effects on the
gas. The interphase energy transfer is due to some combination of
convective/conductive energy exchange through nonreactive collisions,
combustion energy exchange through reactive collisions, and radiative
heat transfer. Mass transfer between the phases may also occur in this
region, primarily through either particle evaporation or combustion.

Processes within the particle phase may include phase change (from liquid to solid states), breakup, agglomeration, as well as intraphase collisions and radiative heat transfer. Depending on the altitude, complex shock structures may form downstream of the nozzle, extending the region in which these effects are important. Further downstream, radiation becomes the primary means of heat loss for the particle phase, and the particles will either achieve ballistic trajectories (at very high altitudes) or reach a nearly equilibrium state with the surrounding gas.

At present, numerical methods for modeling two phase plume flows are restricted to relatively low altitudes, where quasi-equilibrium gas assumptions allow for the gas phase to be simulated using Computational Fluid Dynamics (CFD) based methods. At higher altitudes, where the gas becomes rarefied and CFD solutions are highly inaccurate, the Direct Simulation Monte Carlo (DSMC) method tends to give the best combination of accuracy and efficiency in modeling the gas. In this method, the gas is simulated as a collection of computational molecules, each of which represents a large number of actual gas molecules or atoms. Molecule movement and collisions are decoupled from each other during each simulation time step, but are physically consistent with the Boltzmann equation (the governing equation for gas dynamics from gas-kinetic theory) and allow the bulk properties of the gas to be accurately determined.

For this project, a two phase version of the existing DSMC code MONACO (created by our group, and under Prof. Boyd at Cornell University) is being developed to allow for accurate modeling of high altitude two phase plume flows. The particle phase is simulated using a Lagrangian tracking method similar to that used for the gas phase (for details see "Evaluation of a Monte Carlo Model For Two Phase Rarefied Flows" by J. Burt and I. Boyd, AIAA paper 2003-3496) and momentum and energy transfer from the gas to the particles is determined using a scheme (also described in this paper) developed by Gallis et al. at Sandia National Laboratory. In order to model the reciprocal transfer of momentum and energy from the particles to the gas, a new scheme (explained in a paper to be presented in Reno, NV in January 2004) has been developed, based on statistical and analytical models of specular and diffuse collision processes between solid a sphere and a locally free-molecular surrounding gas. In order to maximize the efficiency of the code, a series of interphase coupling parameters (described in the same paper) are periodically evaluated in each grid cell and used to determine whether certain physical processes are insignificant and can therefore be neglected in the calculations. Numerical models for other phenomena mentioned above – including particle phase change, combustion, and radiation – are also under development. In addition, the Message Passing Interface (MPI) is being implemented in the code, in order for very large scale computationally intensitive simulations to be run on multi-processor parallel computers. The ultimate goal is to run axisymmetric or three-dimensional simulations of plumes from large multi-nozzle rockets, for which the required computational domain may approach 1 km in length.

Figure 1. Contours of average gas and particle velocity in the near-field
region of a plume flow for a small (0.12 m nozzle exit diameter)
solid-propellant rocket motor expelling into a vacuum. Gas velocity
contours are displayed on the upper portion of the figure. Gas and
particle streamlines are also shown. Values are in SI units (m/s).

Figure2. Contours of gas translational and average particle temperatures for
the same flow as above. Note an increase in the gas temperature just
beyond the nozzle exit, due to the presence of the particle phase.