Boundary layer calculation in gas flows in micronozzles

摘要

Tasks performed by small space vehicles (SSVs) require orbit and position correction of the space vehicle in outer space. Strict requirements for SSV precision position control necessitate the development of microengines equipped with micronozzles to ensure ultra-small thrust values (about 1 mN). A distinguishing feature of the gas flow in micronozzles is the decisive effect of the boundary layer. The paper introduces a method for calculating the laminar and turbulent boundary layer in micronozzles. The increased non-uniformity of the velocity in the flow cross-section and the increased pressure gradients result in the unreliable gas-dynamic calculation for micronozzles using potential-flow methods. The paper shows the practicability of applying the calculation method based on the flow separation into an isentropic core and a viscous boundary layer with the use of the boundary-layer momentum integral equation. When calculating the boundary layer, the methods of the theory of viscous fluid motion are used, and when calculating the potential flow, the methods of the potential flow theory are used. Considering that, due to the extremely small size of micronozzles, it is possible to reliably determine by experiment the integral parameters of gas and not the local ones, the comparison of the calculation results with the experimental results shows their good convergence. In this paper, we solve the problem of determining the flow rate coefficient in micronozzles based on geometric parameters, by building an averaged mathematical model of the gas flow in micronozzles, taking into account the influence of the boundary layer and the particular physics of the gas flow. The method of mathematical modeling proposed in the paper and calculation results can be used to optimize the output characteristics when designing microengines with ultra-small thrust values and reduce the time spent for testing such microengines.