1. The Boltzmann equation is expressed in terms of the N particle distribution function in 6N dimensional phase space The Euler and Navier-Stokes Equation may be derived from the Boltzmann equation The direct simulation Monte Carlo (DSMC) is a numerical method for solving the Boltzmann equation, under the assumption of the binary collisions Kn = Knudsen number = /l ref  = mean free path, l ref = reference length, oContinuum, Kn ≤ ~ 0.01 oTransitional, DSMC, Kn ≥ ~ 0.01 Flows around spacecraft, rockets, micro-propulsion devices, and spores can all be modeled by DSMC because they have similar Kn Equations of Flow and Rarefaction DSMC Knudsen Number 0.010.1110100 InviscidFree-molecule Euler Eqs. N.S. Eqs. The Boltzmann Equation

2. Spacecraft Divert Attitude Control System - Statement of the Problem Calculations show that DSMC modeling of continuum – thruster flows expanding into space/high altitude near- vacuums is accurate Rocket-borne optical seeker needs an accurate assessment of background levels to assess S/N Background radiation  nexp(-E/kT)

3. Divert Attitude Control System - Degree of plume wrap-around sensitive to interceptor speed and altitude 80 km 120 km 160 km Mach Number Contours at Different Altitudes - 5 km/s OH Number Density Contours at Different Velocities - 120 km 8 km/s 5 km/s 3 km/s

4. Grid at the multi-nozzle exit plane x=0 Computational domain is divided into three main zones: (1) axisymmetric part of the body (blue+yellow), (2) aft body (red), and (3) multi- nozzle plume region (green) Zone dimensions: (1) body : 100  60 and 130  60 cells. (2) aft body : 120  140  65 cells. (3) marching zone: 150  140  65 cells (to 150 m). CFD - Navier-Stokes Atlas Plume Calculations Computational Grid - Multi-zone Approach

5. With body Without body Comparison of Plume - Body Flow Interactions (Temperature Distributions)

6. An Improved CO 2, H 2 O and Soot Infrared Radiation Model for High Temperature Flows Motivation: Shock layers and rocket plumes exhibit non-equilibrium (non- LTE) flow due to high speeds and/or low densities Soot, CO 2 and H 2 O are major radiators in the IR spectrum SOCREF works simulated nozzles and plume flow for Atlas rocket engines Sounding rocket experiments supply spectral data looking through the hypersonic bow shock Non-LTE radiation model, accurate line-line values at high temperatures, using Voight line-shape Integrated soot and molecular radiation Parallel-processing, using HITRAN database format: HITRAN – Missing transitions for temperatures over 500K HITEMP – Data files for CO, CO 2, H 2 O and OH at temperatures up to 1000K or 1500K. CDSD-1000 – High-temperature absorption line data for CO 2. Validated for temperatures > 4000K Non-Equilibrium Radiation Distribution Program (NERD)

7. V=3.5 km/s Reentry Bow-Shock Applications* *CFD calculations, courtesey of Dr. M. Wright.

8. NERD Plume Radiation Applications - Atlas Navier-Stokes CFD (GASP) modeling, 21 vs 40 km altitudes Soot overlay method used to transport particles, oxidation defined by Hiers Model NERD predicted imagery and spectra sensitive to particulate and gas radiation 40 km 21 km 40 km