Interdisciplinary Applied Mathematics

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Re


r.eM


M


wy


For comparison purposes the predictions of incompressible version of p,Flow are also included in Figure 6.13. For large pressure ratios, locally transonic conditions are achieved. It is seen in Figure 6.13 that the separation distance increases nonlinearly with increased Rem , unlike the case of incompressible flow. The differences between the incompressible and compressible simulations become more dominant as the mass flowrate is increased further, corresponding to cases in which locally transonic conditions are achieved.


In Figure    6.13    we    also    include    predictions    of    p,Flow    for    rarefied flows


with Kno = 0.04. Here the value of the Knudsen number Kn is based on exit conditions. In the simulations we used the slip model given by equation (2.26), where the slip information is obtained at a distance A away from the wall surface. The exit pressure of the channels and the channel thickness were fixed in the simulations. Therefore, the value of Knudsen number Knis constant at the exit of the channel for all cases. However, the distribution of Kn    varies    from    simulation    to simulation    as    the    inlet    to    exit    pressure


ratio is varied. One limitation in the compressible flow simulations is the possibility of choking the flow in the channels. Here, we limit the simulations to subsonic cases, i.e.,


U


fpRT



M


< 1,


where the overbar conditions indicate quantities averaged across the channel. Therefore, the maximum possible Kn in the simulations can be estimated by


Kn



A


h



ph(RT2/Tr)i



77T5 pL U

~2~) Uph^RT)*





For a    nonnegligible    separation    region    we    need Reyf    >    10,    and    thus    for

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