G. A. Bird

Breakdown of translational and rotational equilibrium in gaseous expansions

The direct simulation Monte Carlo method has been used to study the breakdown of translational equilibrium in steady cylindrical and spherical expansions of hard sphere and Maxwell molecules. The study of spherical expansions was extended to the combined translational and rotational breakdown in a gas of rough sphere molecules. The breakdown of translational equilibrium in a complete one-dimensional rarefaction wave in a hard sphere gas was also investigated. In all cases, the breakdown of equilibrium was found to coincide with a constant value of the ratio of the logarithmic time derivative of density following the motion of the fluid to the collision frequency in the gas. This value is proposed as an empirical breakdown criterion for use in engineering studies of systems which involve low-density expansions from continuum to highly rarefied conditions. The onset of nonequilibrium was marked by the divergence of the separate kinetic temperatures based on the molecular velocity components parallel and normal to the flow direction. The parallel temperature in a steady expansion gradually froze to a constant value, in qualitative agreement with experiment and with analytical studies employing the BGK model. The rate of decay of the temperature based on the normal velocity components was greater than the isentropic rate for hard sphere molecules, but less than it was for Maxwell molecules.

Direct Simulation and the Boltzmann Equation

The direct simulation Monte Carlo method for the numerical solution of problems in rarefied gas dynamics is described and discussed. It is shown that the procedures adopted in this method can be directly related to the Boltzmann equation and that the two are entirely consistent. It is concluded that the results obtained from the method constitute a solution of the Boltzmann equation.

Definition of mean free path for real gases

Attention is drawn to the inconsistency in the conventional procedure for the definition of a mean free path in a real gas through the classical hard sphere result. It is shown that the variable cross‐section hard sphere, or VHS, model can be used to define a mean free path that properly accounts for the temperature exponent of the coefficient of viscosity of the gas. In addition, the VHS model is shown to have advantages over the classical inverse power law models for numerical and analytical studies.

Recent advances and current challenges for DSMC

Abstract The current status of the direct simulation Monte Carlo (or DSMC) method is reviewed with particular emphasis on its range of validity, the extent of its validation against experiment, and the new molecular models that have been developed in the context of DSMC modelling. The growing number of DSMC applications to the study of flow instabilities are discussed and results are presented for new calculations of unsteady axially symmetric and three-dimensional Taylor-Couette flows. The axially symmetric cases exhibit a transition at a critical Reynolds number from an eventual steady laminar flow to a permanently unsteady flow.

Aspects of the Structure of Strong Shock Waves

The direct simulation Monte Carlo method has been used to study the structure of strong shock waves in a gas of point center of repulsion molecules. The values obtained for the maximum density slope thicknesses agree with the predictions of the Mott‐Smith method. The results for the effect of molecular model on the rate of change of this thickness with shock Mach number are in agreement with the common prediction of the Mott‐Smith and Navier‐Stokes theories. The velocity distribution function within the wave is illustrated by computer display photographs with the molecules represented as dots in the plane of longitudinal and lateral velocity. This also gives qualitative support to the bimodal model. However, it is found that the density profile has a significant degree of asymmetry, contrary to the bimodal prediction. Results are also presented for the profiles of the higher moments of the distribution function.

Rates of thermal relaxation in direct simulation Monte Carlo methods

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...

Nonequilibrium radiation during re-entry at 10 km/s

The direct simulation Monte Carlo method, including a real air model with thermal radiation, is applied to the flows associated with the two sets of measurements that are directly relevant to the projected aeroassisted orbital transfer vehicle. The first is a shock tube measurement of the radiation from a 10 km/s shock wave in air that was made at AVCO in 1962. The second is the flight data that was obtained from the Project Fire re-entry test vehicles in 1964. The calculations for both cases were made with a program that models the one-dimensional flow along a stagnation streamline. The shock standoff distance for the Fire vehicle was obtained from the theoretical studies that were associated with its launch. The simulation employed a partly phenomenological model for the nonequilibrium radiation. It was found that the results from the calculation were consistent with the measured radiation in each case, and also with the convective heat transfer data for the Fire vehicle. The uncertainties associated with the spectral absorptance and recombination probability at the surface appear to be as serious as those associated with the reaction rates.

Direct simulation of transitional flow for hypersonic reentry conditions

This paper presents results of flowfield calculations for typical hypersonic reentry conditions encountered by the nose region of the Space Shuttle Orbiter. Most of the transitional flow regime is covered by the altitude range of 150 to 92 km. Calculations were made with the Direct Simulation Monte Carlo (DSMC) method that accounts for translational, rotational, vibrational, and chemical nonequilibrium effects. Comparison of the DSMC heating results with both Shuttle flight data and continuum predictions showed good agreement at the lowest altitude considered. However, as the altitude increased, the continuum predictions, which did not include slip effects, departed rapidly from the DSMC results by overpredicting both heating and drag. The results demonstrate the effects of rarefaction on the shock and the shock layer, along with the extent of the slip and temperature jump at the surface. Also, the sensitivity of the flow structure to the gas-surface interaction model, thermal accommodation, and surface catalysis are studied.

The DS2V/3V Program Suite for DSMC Calculations

There is a need for general purpose DSMC codes that can be readily applied by non‐specialist users to a wide variety of practical problems. The specifications that should be met by such programs are outlined and the currently available programs are noted. The DS2V program for two‐dimensional and axially‐symmetric flows and the DS3V program for three‐dimensional flows are described in some detail. The “V” in the program names is to indicate the interactive visual characteristic of the programs. Both programs run in a time‐accurate mode and the flow sampling may be of the unsteady flow or, if a steady flow is established at sufficiently large times, of the steady flow. The gas model includes internal degrees of freedom, gas phase chemical reactions, and surface reactions. The initial state may include flow discontinuities that permit the study of shock tube flows and free shear flows. Solid surfaces may move in their own plane, a typical application being a rotating body in an axially‐symmetric flow. Altern...

The Q-K model for gas-phase chemical reaction rates

The quantum-kinetic, or Q-K, model is based on the quantum vibration model that is employed in the computation of gas flows at the molecular level by the direct simulation Monte Carlo (DSMC) method. The Q-K procedure for dissociation is physically realistic within the context of the vibration model in that the reaction occurs upon the selection of the vibrational level that corresponds to dissociation. An analogous, but entirely phenomenological, procedure has been presented for endothermic exchange and chain reactions. These procedures for the endothermic reactions have been well validated, but the existing procedures for the corresponding exothermic reactions have proved to be problematic. This paper presents new procedures for the exothermic reactions that are computationally efficient and provide a near exact match with the equilibrium constant of statistical mechanics. The Q-K model does not depend on the availability of continuum rate coefficients. Instead, the simplicity of the new DSMC procedures ...