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

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

This current and comprehensive book provides an updated treatment of molecular gas dynamics topics for aerospace engineers, or anyone researching high-temperature gas flows for hypersonic vehicles and propulsion systems. It demonstrates how the areas of quantum mechanics, kinetic theory, and statistical mechanics can combine in order to facilitate the study of nonequilibrium processes of internal energy relaxation and chemistry. All of these theoretical ideas are used to explain the direct simulation Monte Carlo (DSMC) method, a numerical technique based on molecular simulation. Because this text provides comprehensive coverage of the physical models available for use in the DSMC method, in addition to the equations and algorithms required to implement the DSMC numerical method, readers will learn to solve nonequilibrium flow problems and perform computer simulations, and obtain a more complete understanding of various physical modeling options for DSMC than is available in other texts.

Nonequilibrium Gas Dynamics and Molecular Simulation

Exact relationship is developed that connects the vibrational relaxation number, ZvDSMC, used in the direct simulation Monte Carlo method and that employed in continuum simulations. An approximate expression for ZvDSMC is also derived that is cost-effective and applicable when translational temperature is larger than vibrational temperature.

Vibrational relaxation rates in the direct simulation Monte Carlo method

The majority of implementations of the Direct Simulation Monte Carlo (DSMC) method of Bird do not account for vibration-dissociation coupling. Haas and Boyd have proposed the vibrationally-favored dissociation model to accomplish this task. This model requires measurements of induction distance to determine model constants. A more general expression has been derived that does not require any experimental input. The model is used to calculate one-dimensional shock waves in nitrogen and the flow past a lunar transfer vehicle (LTV). For the conditions considered in the simulation, the influence of vibration-dissociation coupling on heat transfer in the stagnation region of the LTV can be significant.

Direct simulation with vibration-dissociation coupling

The Direct Simulation Monte Carlo method of Bird is used to investigate the characteristics of low density hypersonic flowfields for typical aerobrakes during Martian atmospheric entry. The method allows for both thermal and chemical nonequilibrium. Results are presented for a sixty-degree spherically blunt cone for various nose radii and altitudes.

Monte Carlo simulation of entry in the Martian atmosphere

The generalized hard sphere model which incorporates the effects of attraction and repulsion is used to predict flow measurements in tests involving extremely low freestream temperatures. For the two cases considered, a Mach 26 nitrogen shock and a Mach 20 nitrogen flow over a flat place, only rotational excitation is deemed important, and appropriate modifications for the Borgnakke-Larsen procedure are developed. In general, for the cases considered, the present model performed better than the variable hard sphere model.

David B. Hash

Papers

Rates of thermal relaxation in direct simulation Monte Carlo methods

Direct simulation with vibration-dissociation coupling

Monte Carlo simulation of entry in the Martian atmosphere

Monte Carlo simulation of entry in the Martian atmosphere

Direct simulation of diatomic gases using the generalized hard sphere model