Interdisciplinary Applied Mathematics

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Ml < 1, the maximum possible value is Kn < 0.1.


Next, we simulate nitrogen flow in a backward-facing step using the DSMC method (see Section 15.1). The DSMC simulations employed a total of 28, 000 equally    spaced cells    (700    cells    in    the    streamwise    and    40    cells


in the cross flow direction). The simulations employed 420,000 simulated molecules, and the results are sampled for 1 x 105 time steps. Numerical convergence is verified by monitoring the mass balance, with the maximum errors being approximately 1%. Inlet section to the channel is also included in the simulation, with the inlet located at x/h = 0.86. A uniform flow stream corresponding to M = 0.45 approaches the inlet of the channel


TABLE 6.1. Abbreviation, location, and corresponding symbols for the stream-wise cuts taken in the step geometry. The TW and BW locations correspond to the DSMC    cell centers    adjacent    to    the    walls, and    can    be    treated    as the wall


quantities.


Abbreviation


Description


Location


Symbol


BW


Bottom Wall


y/h = 0.01675


Solid Triangle


BC


Bottom Center


y/h = 0.25


Hollow Square


C


Center


y/h = 0.48325


Hollow Circles


CE


Center of Entrance


y/h = 0.75


Solid Circles


TW


Top Wall


y/h = 0.9875


Solid Circles


with a free-stream static temperature of T = 330 K. All wall surfaces are maintained at 300 K. The Reynolds number of the simulations based on the mass flowrate per unit width is Reyf = 80, the Knudsen number at the channel outlet    is    Kno    =    0.04,    and    the    Prandtl    number is Pr =    0.7.    The

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