Interdisciplinary Applied Mathematics

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temperature fields obtained by the DSMC program and p,Flow are shown in Figure 6.14. The temperature of the gas molecules in the DSMC are determined by combination of the translational, rotational, and vibrational energy of the diatomic nitrogen molecules. Since the overall gas temperature is not far from ambient, the vibrational energy mode is negligible here. The temperature contours calculated by both methods are quantitatively the same. Elevated temperatures occur near the recirculation zone (2.8 < x < 4.5). This phenomenon can be attributed to the viscous dissipation effects, i.e., the term


d


dX3


(&jiui)


in equation (2.16). A detailed analysis of viscous dissipation terms in the Navier-Stokes equations may be necessary for quantification of the viscous heating effects. The flow separation and recirculation zones predicted by the continuum and atomistic simulations agree well. The flow is locally transonic at the step expansion. This is due to the acceleration of the fluid and reduction of the static temperature of the fluid near the step expansion.


In Figures 6.15 and 6.16 we plot the streamwise variations of the pressure and streamwise velocity, obtained at five different y/h locations. The values of pressure and velocity are nondimensionalized with the corresponding freestream dynamic head and the local sound speed, respectively. The specific y/h locations    are    selected    to    coincide    with    the    DSMC    cell    centers to


avoid interpolation or extrapolation of the DSMC data, and are given in Table 6.1. In Figures 6.15 and 6.16 we first observe an increase in static pressure at C and TW locations near the entrance at x/h = 0.86. Such an increase in pressure is accompanied with deceleration of the fluid near the walls, while a sudden decrease of fluid temperature near the walls is

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