Single-Cycle Impulse from Detonation Tubes with Nozzles

Experiments measuring the single-cycle impulse from detonation tubes with nozzles were conducted by hanging the tubes in a ballistic pendulum arrangement within a large tank. The detonation-tube nozzle and surrounding tank were initiallyfilledwith air between 1.4 and 100kPa in pressure simulating high-altitude conditions.A stoichiometric ethylene–oxygen mixture at an initial pressure of 80 kPa filled the constant-diameter portion of the tube. Four diverging nozzles and six converging–diverging nozzleswere tested. Two regimes of nozzle operationwere identified, depending on the environmental pressure. Near sea-level conditions, unsteady gas-dynamic effects associated with the mass of air contained in the nozzle increase the impulse as much as 72 % for the largest nozzle tested over the baseline case of a plain tube. Near vacuum conditions, the nozzles quasi-steadily expand the flow, increasing the impulse as much as 43 % for the largest nozzle tested over the baseline case of a plain tube. Competition between the unsteady and quasi-steady-flow processes in the nozzle determine the measured impulse as the environmental pressure varies. Nomenclature A = area C = combustible mixture mass D = diameter F = force g = gravitational acceleration h = enthalpy per unit mass I = impulse Isp = mixture-based specific impulse I0sp = mixture-based specific impulse of the plain tube K = model proportionality constant L = tube length M = mass _m = mass flow rate N = tamper mass P = pressure T = temperature t = time UCJ = Chapman–Jouguet detonation velocity u = average velocity u = velocity V = volume Y = species concentration = density = nozzle half-angle Subscripts C = converging portion of the nozzle D = diverging portion of the nozzle i = nozzle inlet state throat = state at the throat of the converging–diverging nozzle TS = thrust surface t = stagnation properties x = nozzle exit state 0 = state of the environment 3 = state in the stagnant flow region behind the Taylor wave I