Interdisciplinary Applied Mathematics

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pressure ratio cases. The numerical predictions for helium flow are consistent with the high-order formula. Both the rarefied air flow (Kn = 0.075) and the    no-slip    air flow    show    deviations    from    the    high-order    formula,    es


pecially for high pressure ratios. The numerical predictions show less mass flowrate than that predicted by the formula. The reason is the pronounced compressibility effects caused by the inertial terms in the Navier-Stokes equations, which were neglected in the derivation of equation (4.8).


Next we examine the pressure distribution along a channel; the experimental results in (Liu et al., 1993; Pong et al., 1994), show a nonlinear pressure distribution. In Figure 4.3 (left) we plot the pressure distribution for air flow for different values of pressure ratios П obtained from simulation.


(4.9)


P,„/P„„t


FIGURE 4.1.    Variation    of    normalized    mass    flowrate    as    a    function    of    pressure


ratio. The experimental data (MIT) are from (Arkilic et al., 1994).


FIGURE 4.2. Variation of mass flowrate normalized with no-slip mass flowrate as a function of pressure ratio. The experimental data (MIT) are from (Arkilic et al., 1994).


TABLE 4.1. Data for air flow simulations for various channel dimensions.


Case


h(p m)


Re


Kn0


П


Mi


Mo


1


0.923


3.367


0.0


2.574


0.091


0.247


0.923


4.144


0.075


2.576


0.116


0.279


2


0.615


1.522


0.0


2.583


0.064


0.168


0.615


2.036


0.110


2.585


0.083


0.198


3


0.226


0.208

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