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Most studies of vortex shedding from a circular cylinder in a gas flow have assumed the no-slip condition on the cylinder surface. To investigate the effect of slip, we simulate vortex shedding using molecular gas dynamics (direct simulation Monte Carlo method) and computational fluid dynamics (incompressible Navier-Stokes equations with a slip boundary condition) and find the results of both methods to be in reasonable agreement. The critical accommodation coefficient below which vortex shedding ceases is found for Reynolds numbers of 60-100 at a Mach number of 0.3. Conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

Moving‐boundary algorithms for the Direct Simulation Monte Carlo (DSMC) method are investigated for a microbeam that moves toward and away from a parallel substrate. The simpler but analogous one‐dimensional situation of a piston moving between two parallel walls is investigated using two moving‐boundary algorithms. In the first, molecules are reflected rigorously from the moving piston by performing the reflections in the piston frame of reference. In the second, molecules are reflected approximately from the moving piston by moving the piston and subsequently moving all molecules and reflecting them from the moving piston at its new or old position.

Direct Simulation Monte Carlo (DSMC) simulations are used to develop a shear‐stress/velocity‐slip boundary condition for Navier‐Stokes (NS) simulations of low‐speed isothermal Couette flow. In this boundary condition, the wall shear stress equals the product of the difference between the gas and wall velocities and a momentum transfer coefficient. This momentum transfer coefficient depends on two dimensionless parameters that determine its behavior in the near‐continuum and transitional regimes, respectively. For a given gas, these parameters are determined by comparing the NS Couette‐flow shear‐stress expression to DSMC shear‐stress values for free‐molecular to near‐continuum pressures with three values of the accommodation coefficient. The parameter values for argon, helium, nitrogen, air, and inverse‐power‐law (IPL) interactions from hard‐sphere to Maxwell lie within narrow ranges. For the hard‐sphere interaction, the DSMC‐based results are in excellent agreement with previously published analytical ap...

A set of Direct Simulation Monte Carlo (DSMC) chemical‐reaction models recently proposed by Bird and based solely on the collision energy and the vibrational energy levels of the species involved is applied to calculate non‐equilibrium chemical‐reaction rates for atmospheric reactions in hypersonic flows. The DSMC non‐equilibrium model predictions are in good agreement with theoretical models and experimental measurements. The observed agreement provides strong evidence that modeling chemical reactions using only the collision energy and the vibrational energy levels provides an accurate method for predicting non‐equilibrium chemical‐reaction rates.

The Direct Simulation Monte Carlo (DSMC) method is widely considered to be both an accurate and general method for simulating non‐continuum gas flows and a computationally intense method because of its molecular nature. Recently, the originator of the method proposed a new variant of DSMC, termed “sophisticated DSMC.” This new DSMC algorithm aims at improving the computational efficiency of DSMC without losing the accuracy of the original algorithm. In this paper the accuracy and convergence of the new DSMC method are investigated for one‐dimensional combined Couette‐Fourier flow. The primary convergence metrics studied, in harmony with previous work, are the ratios of the DSMC‐calculated thermal conductivity and viscosity to their corresponding infinite‐approximation Chapman‐Enskog theoretical values. As discretization errors are reduced, the sophisticated DSMC values are shown to approach the theoretical values to high precision. The convergence behavior of sophisticated DSMC is compared to that of stan...

Thermal accommodation coefficients have been determined for a variety of gas‐surface combinations using an experimental apparatus developed to measure both the pressure dependence of the conductive heat flux and the variation of gas density between parallel plates separated by a gas‐filled gap. Effects of gas composition, surface roughness and surface contamination have been examined with this system, and the behavior of gas mixtures has also been explored. Results are discussed in comparison with previous parallel‐plate experimental studies as well as numerical simulations.

Bird’s Direct Simulation Monte Carlo (DSMC) method is used to compute the molecular velocity distribution of a nonequilibrium monatomic gas to compare with Chapman‐Enskog (CE) theory. The gas is confined between two parallel, fully accommodating walls, which either are motionless and have unequal temperatures (Fourier flow) or are moving tangentially and oppositely and have equal temperatures (Couette flow). Molecules with inverse‐power‐law potentials from hard‐sphere through Maxwell are examined. For Fourier and Couette flow with small heat‐flux or shear‐stress Knudsen numbers, DSMC reproduces the CE thermal conductivity, viscosity, and Sonine‐polynomial coefficients outside the Knudsen layers. For Fourier flow with larger heat‐flux Knudsen numbers, the thermal conductivity continues to agree with the CE value, but systematic differences in the Sonine‐polynomial coefficients are observed and are quantified in terms of the heat‐flux Knudsen number for hard‐sphere and Maxwell interactions. Thus, DSMC can determine the state of a gas when CE theory does not apply and can be used to assess other analytical or numerical methods purporting to solve the Boltzmann equation.

The convergence behavior of Bird’s Direct Simulation Monte Carlo (DSMC) method is explored for near‐continuum, one‐dimensional Fourier flow. An argon‐like, hard‐sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using a one‐dimensional code based on Bird’s DSMC prescription. The convergence metric is taken as the ratio of the DSMC‐calculated bulk thermal conductivity to the infinite‐approximation, Chapman‐Enskog (CE) theoretical value. The convergence rate is monitored with respect to three parameters: time step, cell size, and number of computational molecules per cell. For a sufficiently large number of computational molecules, the DSMC discretization error is observed to decrease quadratically with time step and cell size, in good agreement with previous predictions based on Green‐Kubo theory. When all three parameters are finite, the observed convergence behavior is complex. As numerical errors are systematically reduced, the DSMC‐calculated conductivity is shown to approach the theoretical CE value to within 0.02%, showing that the present implementation of Bird’s DSMC algorithm provides an excellent representation of continuum, CE heat conduction.

Numerical calculations are presented for the thermophoretic force acting on a motionless, spherical particle suspended in a quiescent, rarefied gas between parallel plates of unequal temperature. The rarefied‐gas heat flux and temperature profiles are calculated with the Direct Simulation Monte Carlo (DSMC) method, which provides a time‐averaged, spatially resolved approximation to the molecular velocity distribution. A force Green’s function is used to calculate the spatial and pressure dependence of the thermophoretic force directly from the computed velocity distribution.

An approach is presented to compute the force on a spherical particle in a rarefied flow of a monatomic gas. This approach relies on the development of a Green’s function that describes the force on a spherical particle in a delta‐function molecular velocity distribution function. The gas‐surface interaction model in this development allows incomplete accommodation of energy and tangential momentum. The force from an arbitrary molecular velocity distribution is calculated by computing the moment of the force Green’s function in the same way that other macroscopic variables are determined. Since the molecular velocity distribution function is directly determined in the DSMC method, the force Green’s function approach can be implemented straightforwardly in DSMC codes. A similar approach yields the heat transfer to a spherical particle in a rarefied gas flow. The force Green’s function is demonstrated by application to two problems. First, the drag force on a spherical particle at arbitrary temperature and ...

This paper deals with the evaluation of thermal radiation from hypersonic shock waves in real air, using the Direct Simulation Monte Carlo Method. The method uses the Maximum Entropy method to calculate the chemical and ionising reactions and measured and calculated cross sections to calculate the excitation probability without assuming equilibrium distribution for the electronic states. The new method is validated against experimental results from a one dimensional test case in real air at Mach 29. The radiation from the shock layers formed in front of a Mars-net type re-entry vehicle flying at a number of altitudes and speeds is also examined.

The ellipsoidal-statistical Bhatnagar–Gross–Krook (ES-BGK) kinetic model is investigated for steady gas-phase transport of heat, tangential momentum, and mass between parallel walls (i.e., Fourier, Couette, and Fickian flows). This investigation extends the original study of Cercignani and Tironi, who first applied the ES-BGK model to heat transport (i.e., Fourier flow) shortly after this model was proposed by Holway. The ES-BGK model is implemented in a molecular-gas-dynamics code so that results from this model can be compared directly to results from the full Boltzmann collision term, as computed by the same code with the direct simulation Monte Carlo (DSMC) algorithm of Bird. A gas of monatomic molecules is considered. These molecules collide in a pairwise fashion according to either the Maxwell or the hard-sphere interaction and reflect from the walls according to the Cercignani–Lampis–Lord model with unity accommodation coefficients. Simulations are performed at pressures from near-free-molecular to near-continuum. Unlike the BGK model, the ES-BGK model produces heat-flux and shear-stress values that both agree closely with the DSMC values at all pressures. However, for both interactions, the ES-BGK model produces molecular-velocity-distribution functions that are qualitatively similar to those determined for the Maxwell interaction from Chapman–Enskog theory for small wall temperature differences and moment-hierarchy theory for large wall temperature differences. Moreover, the ES-BGK model does not produce accurate values of the mass self-diffusion coefficient for either interaction. Nevertheless, given its reasonable accuracy for heat and tangential-momentum transport, its sound theoretical foundation (it obeys the H-theorem), and its available extension to polyatomic molecules, the ES-BGK model may be a useful method for simulating certain classes of single-species noncontinuum gas flows, as Cercignani suggested.