We address direct simulation Monte Carlo (DSMC) implementation of phenomenological models of the rotational relaxation process suitable for an arbitrary gas mixture composed of atomic and quantized diatomic species. The macroscopic relaxation process is parametrized by a constant or temperature-dependent collision number Zr such as that of Parker [Phys. Fluids 2, 449 (1959)]. The energy redistribution properties predicted by such a model at the collision level are compared with a recent quasiclassical state-to-state model. Modified forms of the constant collision number, and thus constant relaxation probability, serial quantized Borgnakke–Larsen algorithm [Phys. Fluids A 5, 2278 (1993)] and the null collision SICS-D algorithm [Phys. Fluids A 4, 1782 (1992)] are shown to be equivalent. The generalization to an energy-dependent relaxation probability [Phys. Fluids 6, 4042 (1994)] leads to a systematic bias toward delayed relaxation, due to approximations inherent in the analytical formulation. The error induced in the predicted relaxation behavior as a function of temperature is approximately equivalent in magnitude to a previously proposed, but unrelated, correction factor [Phys. Fluids 6, 2191 (1994)], and also to the variation in the temperature-dependent Parker collision number over a wide range of conditions. Comparisons between DSMC and state-to-state calculations of the rotational distribution function in a relaxing bath quantify the microscopic limitations of the phenomenological model. Finally, a direct comparison of DSMC results with experimental shock layer measurements demonstrates that the energy-dependent relaxation model has a negligible advantage over the constant probability model when the collision number is chosen judiciously.
Experiments were performed to investigate single-phase heat transfer from a smooth 12.7 × 12.7 mm2 simulated chip to a two-dimensional jet of dielectric Fluorinert FC-72 liquid issuing from a thin rectangular slot into a channel confined between the chip surface and nozzle plate. The effects of jet width, confinement channel height, and impingement velocity have been examined. Channel height had a negligible effect on the heat transfer performance of the jet for the conditions of the present study. A correlation for the convective heat transfer coefficient is presented as a function of jet width, heater length, flow velocity, and fluid properties. A self-contained multichip cooling module consisting of a 3 × 3 array of heat sources confirmed the uniformity and predictability of cooling for each of the nine chips, and proved the cooling module is well suited for packaging large arrays of high-power density chips.
Several common models for dissociation reactions in direct simulation Monte Carlo calculations are analyzed quantitatively under general equilibrium and nonequilibrium conditions. The models differ in the degree to which the internal energy of the colliding particles contributes to the probability of dissociation. Test calculations in an equilibrium bath show that the temperature dependence of the predicted equilibrium rate constant, a commonly used measure of accuracy, is dominated by the collision selection algorithm, rather than the details of the dissociation model, and is thus a poor measure of physical validity or accuracy. The distribution of internal energy states of molecules selected for dissociation under the bath conditions, as used for analysis here, is a preferred means to assess accuracy, and is available qualitatively from existing theory. Recent state-specific quasi-classical trajectory calculations allow for quantitative assessment for certain molecules. Certain singularities present in a recent threshold dissociation model [Phys. Fluids 8, 1293 (1996)] are mediated by recourse to the full threshold equations. Sensitivity studies are performed to show the effect of the details of the numerical implementation. A simple generalization of a Weak Vibrational Bias model [Phys. Fluids 6, 3473 (1994)] is suggested to include rotational favoring. The present analysis provides a means to generate quantitatively a two-temperature rate constant, commonly applied in continuum models, for arbitrary conditions. Calibrated simulations which differ only in the dissociation model are performed for the hypersonic stagnation streamline problem to confirm the order of magnitude decrease in dissociation relative to a standard nonfavored model under conditions of large nonequilibrium.
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