The Constant Volume Limit of Pulsed Propulsion for a Constant Gamma Ideal Gas

The constant volume (CV) limit of pulsed propulsion was explored theoretically, where the combustion chamber was approximated as being time-varying but spatially uniform, while the nozzle flow was approximated as being one dimensional but quasi-steady. The CV limit was explored for the isentropic blow down of a constant y ideal gas for fixed expansion ratios and for variable expansion ratios which were adjusted to match the pressure ratio at all times. The CV limit calculations were notable in that all the fixed expansion ratio results could be expressed as analytical solutions. The CV limit was then compared with two relevant constant pressure (CP) cycles. Among the several conclusions were that using a fixed expansion ratio nozzle during a CV blow down did not exert more than a 3% performance penalty over using a variable expansion ratio nozzle as long as the fixed expansion ratio nozzle was optimized for the blow down. Another major conclusion was that, while the impulse produced by a CV device could significantly exceed that of a CP device operating at the fill pressure of the CV device at elevated ambient pressures (e.g. , I atm), the impulse produced by a CP device could actually exceed, albeit only slightly, the impulse produced by a CV device when the ambient pressure was near zero, such as would occur in the near vacuum conditions in space. Nomenclature A - area c - speed of sound CF - thrust coefficient cp - specific heat at constant pressure F - thrust g(Y) - eq. (4) / - impulse rate of mass flow Mach number velocity pressure