▪ Abstract The principles of and procedures for implementing direct simulation Monte Carlo (DSMC) are described. Guidelines to inherent and external errors common in DSMC applications are provided. Three applications of DSMC to transitional and nonequilibrium flows are considered: rarefied atmospheric flows, growth of thin films, and microsystems. Selected new, potentially important advances in DSMC capabilities are described: Lagrangian DSMC, optimization on parallel computers, and hybrid algorithms for computations in mixed flow regimes. Finally, the limitations of current computer technology for using DSMC to compute low-speed, high–Knudsen-number flows are outlined as future challenges.

Direct Simulation Monte Carlo: Recent Advances and Applications

Thermal structure of the atmosphere of Jupiter was measured from 1029 km above to 133 km below the 1-bar level during entry and descent of the Galileo probe. The data confirm the hot exosphere observed by Voyager (∼900 K at 1 nanobar). The deep atmosphere, which reached 429 K at 22 bars, was close to dry adiabatic from 6 to 16 bars within an uncertainty ∼0.1 K/km. The upper atmosphere was dominated by gravity waves from the tropopause to the exosphere. Shorter waves were fully absorbed below 300 km, while longer wave amplitudes first grew, then were damped at the higher altitudes. A remarkably deep isothermal layer was found in the stratosphere from 90 to 290 km with T ∼ 160 K. Just above the tropopause at 260 mbar, there was a second isothermal region ∼25 km deep with T ∼ 112 K. Between 10 and 1000 mbar, the data substantially agree with Voyager radio occultations. The Voyager 1 equatorial occultation was similar in detail to the present sounding through the tropopause region. The Voyager IRIS average thermal structure in the north equatorial belt (NEB) approximates a smoothed fit to the present data between 0.03 and 400 mbar. Differences are partly a result of large differences in vertical resolution but may also reflect differences between a hot spot and the average NEB. At 15 4 bars, probe descent velocities derived from the data are consistently unsteady, suggesting the presence of large-scale turbulence or gravity waves. However, there was no evidence of turbulent temperature fluctuations >0.12 K. A conspicuous pause in the rate of decrease of descent velocity between 1.1 and 1.35 bars, where a disturbance was also detected by the two radio Doppler experiments, implies strong vertical flow in the cloud seen by the probe nephelometer. At p < 0.6 bar, measured temperatures were ∼3 K warmer than the dry adiabat, possible evidence of radiative warming. This could be associated with a tenuous cloud detected by the probe nephelometer above the 0.51 bar level. For an ammonia cloud to form at this level, the required abundance is ∼0.20 × solar.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JE01766

Thermal structure of Jupiter's atmosphere near the edge of a 5‐μm hot spot in the north equatorial belt

Statistical simulation of reactive rarefied flows - Numerical approach and applications

▪ Abstract Recent considerable progress in the field of rarefied hypersonic computational fluid dynamics (CFD) gives reason to address its evolution to an independent CFD branch that covers many fundamental and closely related applied problems of high-altitude aerothermodynamics of space vehicles. The primary purpose of this review is to describe the main numerical methods and real gas models for investigation of problems of rarefied hypersonic flows, and to review results that we believe demonstrate most clearly the achievements and capabilities of the field of rarefied hypersonic CFD in the last years.

Computational hypersonic rarefied flows

The Galileo probe deceleration module contained an experiment which measured the recession of the forebody heat shield during the ablative probe entry into the Jovian atmosphere. A detailed description of the experiment, reduction of the probe data, reconstruction of the heat-shield shape, and comparisons with preflight predictions are presented. Data quality is good during the second half of recession, but excessive noise levels at the onset of ablation prevented the experiment from meeting two of three performance requirements. The recession distribution is surprisingly dissimilar from preflight predictions. Measured recession was less than predicted near the stagnation point, but exceeded predictions over most of the frustum. (Author)

/pdf/galileo-probe-heat-shield-ablation-experiment-1npcs8zxen.pdf

Galileo Probe Heat Shield Ablation Experiment

For internal energy relaxation in rarefied gas mixtures, exact relationships are derived between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans’ equation. These expressions apply to the Borgnakke–Larsen model for internal energy exchange mechanics and are not limited to the assumption of constant Z. Although Jeans’ equation leads to adiabatic relaxation curves, which coalesce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke–Larsen selection probabilities depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, simulation results show that the common assumption P=1/Z is invalid, in general, and leads to considerably slower relaxation than stipulated by Z in Jeans’ equation. Moreover, inconsistent definitions of collision rates appearing in the literature can lead to considerable errors in DSMC models. Finally, for general gas mixtures, Borgnakke–Larsen DSMC kinetics match Jeans’ behavior exactly only when using a selection methodology, which prohibits multiple relaxation events during a single collision.

Rates of thermal relaxation in direct simulation Monte Carlo methods

A new model for reactive collisions is developed within the framework of a particle method, which simulates coupled vibration-dissociation (CVD) behavior in high-temperature gases. The fundamental principles of particle simulation methods are introduced with particular attention given to the probability functions employed to select thermal and reactive collisions. Reaction probability functions are derived which favor vibrationally excited molecules as reaction candidates. The new models derived here are used to simulate CVD behavior during thermochemical relaxation of constant-volume O2 reservoirs, as well as the dissociation incubation behavior of postshock N2 flows for comparisons with previous models and experimental data.

Models for direct Monte Carlo simulation of coupled vibration-dissociation

The use of the same symbol, Z, representing a ‘‘collision number’’ for thermal relaxation, has lead to confusion regarding its definition in the context of both continuum and particle simulations. Examination of the relaxation mechanics employed in particle simulations demonstrates that these definitions differ by a numerical factor that depends upon the intermolecular potential. Particle and continuum simulations employing appropriate definitions of Z lead to identical results during isothermal and adiabatic stationary relaxation.

Resolution of differences between collision number definitions in particle and continuum simulations

Aerodynamic loads upon the Magellan spacecraft during aerobraking through the atmosphere of Venus are computed at off-design attitudes with a direct simulation Monte Carlo (DSMC) particle method. This method is not restricted to the assumption of collisionless flow normally employed to assess spacecraft aerodynamics. Simulated rarefied flows at nominal altitudes near 140 km and an entry speed of 8.6 km/s were compared with simulated and analytic free-molecular results. Aerodynamic moments, forces, and heating for rarefied entry at all attitudes were 7-10% below free-molecular results. All moments acted to restore the vehicle to its nominal zeropitch, zero-yaw attitude. Suggested canting of the solar panels is an innovative configuration to assess gas-surface interaction during aerobraking. The resulting roll torques about the central body axis, as predicted in rarefied-flow simulations, were nearly twice that predicted for free-molecular flow, although differences became less distinct for thermal accommodation coefficients well below unity. In general, roll torques increased dramatically with reduced accommodation coefficients employed in the simulation. In the DSMC code, periodic free-molecule boundary conditions and a coarse computational grid and body resolution served to minimize the simulation size and cost while retaining solution validity.

Simulated Rarefied Aerodynamics of the Magellan Spacecraft During Aerobraking

Rarefied and free molecular flowfields corresponding to proposed aeropass maneuvers through the atmosphere of Venus by the Magellan spacecraft are computed with a vectorized particle simulation method. The significance of rarefaction and reaction effects are assessed and surface heat flux, drag coefficients, and flowfield properties are computed. A simple surface heat transfer model is coupled directly to the simulation and assumes that each surface element is in radiative equilibrium with deep space. This allows direct computation of surface temperature distributions rather than requiring prescribed isothermal boundary conditions. Uncoupled dual-node heat transfer models, which account for heat capacity and thermal conductivity within each structural component, permit more accurate determination of surface temperatures. Such temperatures restrict the allowable altitudes and entry speeds of the aeropass maneuvers, and must therefore be estimated accurately. Simulations with an entry velocity of 8600 m/s at altitudes between 125 and 140 km reveal that allowable surface temperatures occur only at the highest altitudes where the flowfield is appropriately modeled as free-molecular. Excessive surface heat flux occurs at lower altitudes where molecular collisions are significant.

Brian L. Haas

Papers

Rates of thermal relaxation in direct simulation Monte Carlo methods

Models for direct Monte Carlo simulation of coupled vibration-dissociation

Resolution of differences between collision number definitions in particle and continuum simulations

Simulated Rarefied Aerodynamics of the Magellan Spacecraft During Aerobraking

Particle simulation of rarefied aeropass maneuvers of the Magellan spacecraft