The Ideal Constant Volume Limit of Pulsed Propulsion
AIR FORCE RESEARCH LAB EDWARDS AFB CA SPACE AND MISSILE PROPULSION DIV
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A constant volume limit of pulsed propulsion is formulated which applies when blow down times are much longer than characteristic wave transit times in the combustion chamber. Under this limit, the combustion chamber is approximated as being time varying but spatially uniform, and the nozzle is approximated as being one dimensional but quasi-steady. Some analytical solutions for this limit with fixed expansion ratio nozzles are explored for the isentropic blow down of a constant ideal gas. The results are compared with a variable expansion ratio case where the expansion ratio is continuously varied to match the pressure ratio during blow down. The major conclusions are that constant volume devices should optimize at approximately file same mixture ratios as constant pressure devices, and that using fixed expansion ratio results in only a modest impulse penalty, not exceeding 3 for the cases examined, compared to using a variable expansion ratio, as long as the fixed expansion ratio has been optimized to produce the maximum possible impulse for the blow down.
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