David B. Hash

Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods

A planar Couette flow is simulated using several different interface conditions in a hybrid technique in which the direct simulation Monte Carlo (DSMC) method and the Navier-Stokes equations are coupled. Comparison of computational times and accuracy of the different methods are made to determine the best approach for further study. It is concluded that the Marshak condition, in which the properties at the interfaces between the continuum and rarefied regions are determined from flux conservation equations, is the best technique in terms of accuracy and run-time performance. When coupling NavierStokes and DSMC solvers, the use of a Maxwellian distribution to represent the particle velocity distribution hi the Navier-Stokes region yields unacceptable errors.

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...

A generalized hard‐sphere model for Monte Carlo simulation

A new molecular model, called the generalized hard‐sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard‐sphere (VHS) model of Bird [Rarefied Gas Dynamics, edited by S. S. Fisher (AIAA, New York, 1981), Part 1, p. 239] and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo (DSMC) methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier–Stokes calculations.

Role of boundary conditions in Monte Carlo simulation of MEMS devices

A study is made of the issues surrounding prediction of microchannel flows using the direct simulation Monte Carlo method. This investigation includes the introduction and use of new inflow and outflow boundary conditions suitable for subsonic flows. A series of test simulations for a moderate-size microchannel indicates that a high degree of grid under-resolution in the streamwise direction may be tolerated without loss of accuracy. In addition, the results demonstrate the importance of physically correct boundary conditions, as well as possibilities for reducing the time associated with the transient phase of a simulation. These results imply that simulations of longer ducts may be more feasible than previously envisioned.

Direct simulation with vibration-dissociation coupling

In the investigation of hypersonic rarefied flows, it is important to consider the effects of thermal nonequilibrium.on the dissociation rates. Because the vibrational mode requires a finite time to relax, vibrational energy may not be available for dissociation immediately behind the shock. In this way, the dissociation of the preshock species can be delayed for a significant portion of the hypersonic shock layer. 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 (VFD) model to accomplish this task. Their model made use of 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 important.

Improved Modeling of Shock Layer Radiation in Air

An update of NEQAIR is presented and used to compare with experiment in the presence of thermal equilibrium. The updates included boundbound transition probabilities of C, N, and O, Stark broadening expressions, cross sections for bound-free transitions and additional transitions bands for N2. Moreover, the role of carbon contamination is examined. Some improvements are indicated but gaps remain between experiment and computation in the ultraviolet region of the spectrum. The discrepancies are not a result of ignoring the carbon contaminant.

THE GHS INTERACTION MODEL FOR STRONG ATTRACTIVE POTENTIALS

A new version of the generalized hard sphere (GHS) model is presented that is valid for interactions where both repulsion and attraction of the colliding particles are important. The parameters of the cross section for scattering of heavy particles interacting through a 12‐6 Lennard–Jones potential are given for collisions involving like and unlike particles.