Constant volume limit of pulsed propulsion for a constant gamma ideal gas

The constant volume (CV) limit of pulsed propulsion is explored theoretically, where the combustion chamber is approximated as being time varying but spatially uniform, and the nozzle flow is approximated as being 1D but quasi-steady. Isentropic blowdown of a constant gamma ideal gas is assumed. Notably, all of the fixed expansion ratio results can be expressed as analytical solutions. Using an appropriately selected fixed expansion ratio nozzle was found not to result in more than a 3 percent performance penalty over using a variable expansion ratio nozzle optimized at all times for the instantaneous ratio of chamber to ambient pressure. It was also found that an optimized CV device produces more impulse than an optimized constant pressure device operating at the fill pressure of the CV device, for all ambient pressures except in a vacuum. However, the latter conclusion applies to optimum expansion ratios, which are infinite in a vacuum. Caution is required in applying the latter conclusion to the finite expansion ratios of real devices. (Author)