An analytical model for the impulse of a single-cycle pulse detonation tube has been developed and validated against experimental data. The model is based on the pressure history at the thrust surface of the detonation tube. The pressure history is modeled by a constant pressure portion, followed by a decay due to gas expansion out of the tube. The duration and amplitude of the constant pressure portion is determined by analyzing the gasdynamics of the self-similar ow behind a steadily moving detonation wave within the tube. The gas expansion process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, speci c impulse, and thrust. Comparisons are given with estimates of the speci c impulse based on numerical simulations. Impulse per unit volume and speci c impulse calculations are carried out for a wide range of fuel-oxygen-nitrogen mixtures (including aviation fuels) of varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. The trends observed are explained using a simple scaling analysis showing the dependency of the impulse on initial conditions and energy release in the mixture. = time taken by the rst re ected characteristic to reach the thrust surface t 3 = time associated with pressure decay period t ¤ = time at which the rst re ected characteristic exits the Taylor wave U CJ = Chapman-Jouguet detonation velocity u = ow velocity u e = exhaust velocity u 2 = ow velocity just behind detonation wave V = volume of gas within detonation tube X F = fuel mass fraction ® = nondimensional parameter corresponding to time t 2 = nondimensional parameter corresponding to pressure decay period°= ratio of speci c heats 1P = pressure differential 1P 3 = pressure differential at the thrust surfacé = similarity variablȩ = cell size 5 = nondimensional pressure ½ e = exhaust density ½ 1 = initial density of reactants ¿ = nondimensional time ct=L Á = equivalence ratio
= pendulum mass P = pressure P env = environment pressure P lip = pressure on lip at exit of tube P TS = pressure on thrust surface in detonation tube interior P 1 = initial pressure of reactants P 2 = Chapman-Jouguet pressure P 3 = pressure of burned gases behind Taylor wave p = pitch of spiral obstacles S = wetted surface area of tube's inner diameter T 1 = initial temperature of reactants t = time U CJ = Chapman-Jouguet detonation velocity V = internal volume of detonation tubē = ratio of N 2 -to-O 2 concentration in initial mixture°= ratio of speci c heats in combustion products 1x = horizontal pendulum displacemenţ = cell size ½ 1 = density of combustible mixture at the initial temperature and pressure ¿ = wall shear stress
An analytical model for the impulse of a single-cycle pulse detonation engine has been developed and validated against experimental data. The model analyzes the pressure differential at the thrust surface of the detonation tube. The pressure inside the tube is modeled with a constant pressure region and a blowdown process. A careful study of the gas dynamics inside the tube enables the derivation of a similarity solution for the constant pressure part. The blowdown process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, specific impulse, and thrust. Impulse per unit volume and specific impulse calculations are carried out for a wide range of fueloxygen-nitrogen mixtures (including aviation fuels) varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. Comparisons with numerical simulation estimates of the specific impulse are given. φ equivalence ratio ρ 1 initial density of reactants
= pendulum mass P = pressure P env = environment pressure P lip = pressure on lip at exit of tube P TS = pressure on thrust surface in detonation tube interior P 1 = initial pressure of reactants P 2 = Chapman-Jouguet pressure P 3 = pressure of burned gases behind Taylor wave p = pitch of spiral obstacles S = wetted surface area of tube's inner diameter T 1 = initial temperature of reactants t = time U CJ = Chapman-Jouguet detonation velocity V = internal volume of detonation tubē = ratio of N 2 -to-O 2 concentration in initial mixture°= ratio of speci c heats in combustion products 1x = horizontal pendulum displacemenţ = cell size ½ 1 = density of combustible mixture at the initial temperature and pressure ¿ = wall shear stress
A simplified flowpath analysis of a single-tube airbreathing pulse detonation engine is described. The configuration consists of a steady supersonic inlet, a large plenum, a valve, and a straight detonation tube (no exit nozzle). The interaction of the filling process with the detonation is studied, and it is shown how the flow in the plenum is coupled with the flow in the detonation tube. This coupling results in total pressure losses and pressure oscillations in the plenum caused by the unsteadiness of the flow. Moreover, the filling process generates a moving flow into which the detonation has to initiate and propagate. An analytical model is developed for predicting the flow and estimating performance based on an open-system control volume analysis and gasdynamics. The existing single-cycle impulse model is extended to include the effect of filling velocity on detonation tube impulse. Based on this, the engine thrust is found to be the sum of the contributions of detonation tube impulse, momentum, and pressure terms. Performance calculations for pulse detonation engines operating with stoichiometric hydrogen-air and JP10-air are presented and compared to the performance of the ideal ramjet over a range of Mach numbers. Nomenclature
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