Interdisciplinary Applied Mathematics

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of 2.5-5 mm and a chamber pressure less than 1 atm, with the Reynolds number in the range 55 to 550. The subsonic and supersonic portions of the Rothe nozzle are cones with half-angles 30° and 20°, respectively, and with longitudinal radius    of    curvature    at    the    throat    equal    to half    of the    throat


radius. The gas in Rothe’s experiments was nitrogen at T = 300 K. In this axisymmetric nozzle, measurements of temperature and density were obtained along the centerline and along the radial directions at various stations (Rothe, 1971). At Re < 150, the exit temperature was increasing due to viscous shear force, causing the thermalization of flow energy. Alt hough this is not strictly a micronozzle, the availability of detailed experimental results (Rothe, 1971) has made this a benchmark case for validating DSMC programs before other micronozzles are tested.


In the following we present simulations performed by (Ivanov et al., 1999)

FIGURE 6.36. Rothe nozzle (Ret = 270): density isocontours based on atomistic (solid lines: SMILE) and continuum (dashed lines: GASP) simulations. (Courtesy of M. Ivanov.)


for throat Reynolds numbers in the range 120-270. The DSMC program SMILE developed by Ivanov and collaborators combines majorant and free cell schemes (see also Section 15.1). Each cell has its own interaction parameter that governs local collisions via an adaptive scheme. It employs two different grids, one for collisions and another one for sampling the gas dynamics parameters, with the latter having fewer cells than the former. In addition, other features such as spatial weights for axisymmetric domains that distribute molecules closer to the axis, adaptive and asynchronous domain decomposition, and particle doubling make SMILE a particularly effective program for simulating micronozzle flows. The last feature introduces successively an increased number of particles, so it accelerates convergence to stationary states.

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