Interdisciplinary Applied Mathematics

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The density contours obtained with SMILE for Ret = 270 are plotted in Figure 6.36 (Ivanov et al., 1999). The dashed lines show corresponding results from the program GASP (Aerosoft Inc., Blacksburg Virginia, 1996) based on the compressible Navier-Stokes equations. Corresponding Mach line contours and differences between continuum and rarefied flows are shown in Figure 6.37. In Figure 6.38 a comparison is included with Rothe’s experimental data that shows good agreement with the simulations but deviations from the ideal case.


Ivanov et al. (1999) have also examined the performance of a micronozzle with an about 27-micron throat and 15° diverging half-angle. It was designed so that at p0 = 10 atm gave 1 mN thrust at stagnation temperature TO = 297 K. The stagnation pressure was varied from 1 to 10 atm, and correspondingly, the Reynolds number varied from 130 to 1300. This tenfold increase in Ret results in specific impulse efficiency change from 90% to 95% compared with the ideal case. A typical result obtained by Ivanov et al. is shown in Figure 6.39 in terms of the specific impulse along the micronozzle axis. Again, comparisons between continuum and atomistic predictions are made, similar to those for the results for the Rothe nozzle. Simulations pre-

FIGURE 6.37. Rothe nozzle (Ret = 270): Mach isocontours based on atomistic (solid line: SMILE) and continuum (dashed line: GASP) simulations. (Courtesy of M. Ivanov).

FIGURE 6.38. Temperature distribution along the Rothe nozzle axis based on atomistic (SMILE) and continuum (GASP) simulations (Ret = 270). (Courtesy of M. Ivanov.)


diet that Isp is greater than the ideal for low Reynolds number (Ret = 130), which is a nonphysical result. Even at large pressures there seems to be a large effect of rarefaction. For low pressure, the maximum Isp occurs upstream of the nozzle exit. As pointed out by Ivanov et al.(1999), this is due to relatively long diverging section which leads to excessive viscous losses. A shorter expansion nozzle would be advantageous, and would also reduce back-flow contamination due to plume at the nozzle exit.

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