Effect of wall on impulse of solid propellant driven millimeter-scale thrusters

An analytic model is presented for evaluating the decrement in impulse due to wall effects in millimeter-scale solid propellant driven thrusters. The model assumes a thin flame sheet moving with constant velocity along the thruster axis. Both frontend ignition (FEI) and backend ignition (BEI) are considered. The decrement in impulse due to plenum heat loss and the nozzle wall boundary layer is evaluated,as a function of thruster geometric scale r and a flame speed parameter V-f = t(p)/t(s), where t(s) and t(p) are characteristic:times for steady-state flame propagation and for pulsed dow operation, respectively For the case of deflagration waves (V-f << 1), the plenum heat loss in BEI devices and the nozzle boundary layer loss in FEI devices,vary as (rV(f))(-1/2). Thus, relatively large dame speeds are needed in millimeter-scale thrusters to avoid significant impulse loss. In a numerical example, three out of six prospective high dame speed propellants had losses of about 10% or less. Hence, millimeter-scale thrusters appear viable with regard to wall loss. However, experimental confirmation of fabrication techniques, ignition techniques, and propellant performance is needed.