N.S. Eqs. DSMC. Euler Eqs. Knudsen Number. 0.01. 0.1. 1. 10. 100. Inviscid. Free-molecule. The Boltzmann Equation. Equations of Flow and Rarefaction. The Boltzmann equation is expressed in terms of the N particle distribution function in 6N dimensional phase space - PowerPoint PPT Presentation
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• 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, o Continuum, Kn ≤ ~ 0.01 o Transitional, DSMC , Kn ≥ ~ 0.01 • Flows around spacecraft, rockets, micro-propulsion Equations of Flow and Rarefaction DSMC Knudsen Number 0.01 0. 1 1 10 10 0 Inviscid Free-molecule Euler Eqs. N.S. Eqs. The Boltzmann Equation
Transcript
• 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,
• 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
DSMCKnudsen Number
0.01 0.1 1 10 100Inviscid Free-molecule
Euler Eqs.
N.S. Eqs.
The Boltzmann Equation
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 n•exp(-E/kT)
Divert Attitude Control System - Degree of plumewrap-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/s5 km/s3 km/s
Grid at the multi-nozzle exit plane x=0Computational 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)
Comparison of Plume - Body Flow Interactions (Temperature Distributions)
An Improved CO2, H2O 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, 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
Non-Equilibrium Radiation Distribution Program (NERD)
V=3.5
km/s
Reentry Bow-Shock Applications*
*CFD calculations, courtesey of Dr. M. Wright.
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
