Gaseous-Propellant Microthrusters, I. Completion of Burn Prior to Venting

Abstract

We present results from an inviscid unsteady one-dimensional model of the discharge, from a cylindrical container into vacuum, of initially homogeneous, high-pressure, high-temperature ideal gas. In this study (Part I), the discharge is begun, by displacement of a diaphragm at one end of a cylindrical chamber, only after the burn of the contents is complete; in a companion study (Part II)-published separately, the venting is initiated during flame propagation across the reactive-gas mixture. Of particular interest are the integrals over time of the momentum and the mass discharged from the container exit, and the ratio of the momentum-discharge integral to the mass-discharge integral-this ratio is essentially the specific impulse. We address first the case of simple, nozzleless blowdown, in which the cross-sectional area of the container exit, A', is equal to the cross-sectional area (V/L) of the plenum of the cylindrical container; we consider the complete time evolution for the case of a massless diaphragm that plays no dynamical role, and just the early-time evolution for the case of a diaphragm with a mass that is finite relative to the mass of the gas initially stored in the container. We also address the case in which the area of the exit A' is significantly less than the cross-sectional area (V/L) of the plenum of the cylinder, say, [(A'/(V/L)]≤(1/4); for this case, acoustic waves equilibrate the thermodynamic state of the essentially quiescent gas in the plenum of the container, so that a quasisteady treatment suffices and, throughout the plenum, the pressure (upon neglect of acoustic oscillations) is taken to be spatially uniform, though temporally evolving. We suggest that the specific impulse as a function of time for intermediate values of the area ratio, i.e., for (1/4) < [(A'/(V/L)] < 1, may be obtained (for a given value of the isentropic ratio γ) by interpolation of results between the nozzleless-blowdown case [A'(V/L) = 1] and quasisteady cases [0 < (A'/V/L)] < 1/4]. Finally, in the context of a propulsion device attached to a payload in orbit, we briefly address tradeoffs (in the kinetic energy derived by the payload from combustion of the propellant of the microthruster) involving the relative mass of the combustion-chamber cap (diaphragm).