Interdisciplinary Applied Mathematics

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Also included in the plot are the pressure distributions for corresponding compressible no-slip flows. The curvature in pressure distribution is more pronounced for the no-slip compressible flows than for rarefied flows.

• Therefore, rarefaction effects reduce the curvature in pressure distribution.

For rarefied air flow (Kn = 0.3) presented in Figure 4.3, the curvature in pressure distribution is more pronounced for high pressure ratios. For cases with П < 1.2, the pressure drop is practically linear, resembling an incompressible flow. To identify the effect of rarefaction in reducing the curvature effects in pressure distribution we plot deviations from the linear pressure drop    (i.e.,    corresponding incompressible    flow)    for    П =    2.58    in    Figure    4.3

(right). The outlet pressure in these simulations is fixed to be atmospheric. The Knudsen number is varied by changing the channel thickness (h). Corresponding values of h, Re (based on mass flowrate per channel width), Kno, and inlet and outlet Mach numbers (M; and Mo, respectively) are given in Table 4.1. It is clear that the stronger the rarefaction effects, the smaller the deviation from the linear pressure distribution (compare cases 3, 2, and 1). This finding contradicts the conclusions in (Pong et al., 1994), where the deviation from linear distribution for helium microflow is reported to be larger than the corresponding pressure distribution for nitrogen. This was attributed to the increase in the rarefaction effects for helium flow compared to the nitrogen flow. The curvature in pressure distribution for no-slip compressible flow increases with increasing inlet Mach number. For the same pressure ratio, the wider channel (case 1) corresponds to higher mass flowrate than the other cases. It also has larger inlet and outlet Mach numbers at the channel centerline, resulting in larger curvature even for the no-slip case compared to the other cases. The simulations also show a shift of the locus of maximum deviation from linear profile toward the inlet of the channel as the rarefaction effects are increased.

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