Charles R. Lilley

A macroscopic chemistry method for the direct simulation of gas flows

In most chemistry methods developed for the direct simulation Monte Carlo (DSMC) technique, chemical reactions are computed as an integral part of the collision simulation routine. In the macroscopic chemistry method developed here, the simulation of collisions and the simulation of reactions are decoupled; reactions are computed independently, after the collision routine. The number of reaction events to perform in each cell is calculated using the macroscopic reaction rates k+, k- and equilibrium constant K*, calculated from the local macroscopic flow conditions. The macroscopic method is developed here for the symmetrical diatomic dissociating gas. For each dissociation event, a single diatomic simulator particle is selected with a probability based on its internal energy, and is replaced by two atomic particles. For each recombination event, two atomic particles are selected at random, and are replaced by a single diatomic particle. The dissociation energy is accounted for by adjusting the translational thermal energies of all particles in the cell. The macroscopic method gives density profiles in agreement with experimental data for the chemical relaxation region downstream of a strong shock in nitrogen. In the non-equilibrium regions within the shock, and along the stagnation streamline of a blunt cylinder in rarefied flow, the macroscopic method gives results in excellent agreement with those obtained using the most common conventional DSMC chemistry method in which reactions are calculated during the collision routine. The number of particles per computational cell has a minimal effect on the results provided by the macroscopic method. Unlike most DSMC chemistry methods, the macroscopic method is not limited to simple forms of k+, k- and K*. Any forms may be used, and these may be any function of the macroscopic conditions. This is demonstrated by using a two-temperature rate model, and a form of K* with a number density dependence. With the two-temperature model, the macroscopic method gives densities in the post-shock chemical relaxation region that also agree with the experimental data. For a form of K^* with a number density dependence, the macroscopic method can accurately reproduce chemical recombination behavior. In a primarily dissociative flow, the number density dependence of K* has very little effect on the flow. The macroscopic method requires slightly less computing time than the most common DSMC chemistry method.

Modified Generalised Hard Sphere Collision Model for Direct Simulation Monte Carlo Calculations

The generalised hard sphere collision model (GHS) was introduced by Hassan and Hash [Physics of Fluids A, v5(3), 738-744 (1993)] and is a generalization of the Sutherland collision model suggested by Kuscer [Physica, v158, 784-800 (1989)]. Despite its superior modelling of realistic gas viscosities, compared to the Variable Hard Sphere collision model, the GHS model is rarely used because of its great computational expense compared to the VHS model. We show here how a slight modification of the GHS model makes it no more than 15% more computationally expensive than the VHS model, while retaining its superior viscosity modelling. All that is required is that the collision probability be limited for collision speeds approaching zero, rather than increase to infinity as it does for the original GHS model. A particularly simple modification is to use a Maxwell collision cross-section (equal probabilities) for collision energies less than the attractive energy of a realistic molecular model (characteristic temperature T* approximate 90 - 150 K). For temperatures above T*, the GHS viscosity is retained, while for temperatures less than T* the viscosity is slightly different from the GHS viscosity, but arguably more realistic.