Interdisciplinary Applied Mathematics

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(Bayt, 1999).

6.6.1 Micropropulsion Analysis


Micropropulsion subsystems consist primarily of thrusters, but they also contain other MEMS components such as valves, tanks, and pressure regulators. In this section, we consider the performance of a micronozzle that primarily determines the performance of the micropropulsion system. A micronozzle has a converging section, a throat, and an expanding section similar to the De Laval nozzles used in macro domain applications (see Figure 6.30). The value of Reynolds number at the nozzle throat is important, since it determines the viscous flow losses. It is defined as


Ptcs dt Po ’


where cs is the speed of sound, dt is the throat diameter, and the subscript “0” refers to stagnation conditions. It is proportional to the stagnation pressure p0, i.e.,



Ret


where the exponent (n) depends on the gas type. For low values of Ret the efficiency of the nozzle is low, and since the targeted low values of thrust are obtained readily at low Reynolds number, this becomes a difficult design problem. Let us consider the thrust force given by


Ft <x. po At,


where At    is the    throat area.    If    the    throat    is circular,    then At ~    d2,    and


thus to obtain lower thrust levels, say by a factor of 100, the nozzle size has to be reduced by a factor of 10. On the other hand, the Reynolds number scales linearly with the diameter, and thus the induced losses are not as great.

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