Equations of Flow and Rarefaction

1. N.S. Eqs. DSMC Euler Eqs. Knudsen Number 0.01 0.1 1 10 100 Inviscid Free-molecule The Boltzmann Equation Equations of Flowand Rarefaction • 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 = /lref, = mean free path, lref = reference length, • Continuum, Kn ≤ ~ 0.01 • Transitional, DSMC , Kn ≥ ~ 0.01 • Flows around spacecraft, rockets, micro-propulsion devices, and spores can all be modeled by DSMC because they have similar Kn

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

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

4. CFD - Navier-Stokes Atlas Plume Calculations Computational Grid - Multi-zone Approach 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).

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

6. An Improved CO2, H2O and Soot Infrared Radiation Model for High Temperature Flows Non-Equilibrium Radiation Distribution Program (NERD) Motivation: • Shock layers and rocket plumes exhibit non-equilibrium (non-LTE) flow due to high speeds and/or low densities • Soot, CO2 and H2O 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, CO2, H2O and OH at temperatures up to 1000K or 1500K. • CDSD-1000 – High-temperature absorption line data for CO2. Validated for temperatures > 4000K

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