Interdisciplinary Applied Mathematics

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A typical result for the specific impulse obtained using DSMC (Ketsde-ver et al., 1998) is shown in Figure 6.33 at two different temperatures as a function of Knudsen number. A comparison is made with results from a micronozzle with a 20 pm throat, and inlet and outlet have ratios 16.8 and 19.8, respectively. The micronozzle results were obtained with the continuum-based program GASP (Aerosoft Inc., Blacksburg Virginia, 1996), which solves the compressible Navier-Stokes equations. GASP overpredicts values of specific impulse Isp, since rarefaction effects typically cause lower values of Isp.

6.6.2 Rarefaction and Other Effects


There are several phenomena that affect the performance of micronozzle, including rarefaction, viscosity, three-dimensionality, roughness, nonequilibrium, and plume contamination. The relative effect of a specific phenomenon depends primarily on the thrust level targeted. Therefore, to make these contributions clearer we will refer to specific designs available in the literature.


We start with the DRIE-fabricated planar micronozzles of (Bayt, 1999) and (Bayt and Breuer, 2000). A baseline configuration has a nozzle throat of 20 pm, expansion ratio 25:1, etch depth 300 pm, and a nozzle divergence angle of    20°.    In    the    ideal    case    of    no    losses,    such    a thruster    operating    at


stagnation pressure of p0 = 100 psi will produce thrust of Ft = 7 mN at specific impulse Isp = 75 secs, while at p0 = 14.7 psi the thrust reduces to Ft    = 1    mN.    However,    these ideal    operating    points    will    be affected    by


losses. For    example,    viscous    losses could    be    substantial    at    p0 =    14.7    psi,


where the corresponding Reynolds number is 300, and less so at p = 300 psi, where the corresponding Reynolds number is 2040. In fact, significant performance degradation was reported in (Bayt, 1999; Bayt and Breuer, 2000), for Re < 1500 for most of the designs that they tested with nitrogen as the propellant. Table 6.3 (taken from (Bayt, 1999)) summarizes results of different micronozzles at similar thrust levels and in the same Reynolds number range.

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