Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube

Abstract

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

Pulse Detonation Assessment for Alternative Fuels

“…However, we would point out that the analytical results are based on a simplified method, while the experimental results are also subject to error bars due to measurement and other uncertainties, and the predicted detonation speed is supported by published higher fidelity CFD results [49]. For acetylene, also, our predicted detonation velocity matches exactly a separate published experimental measurement [47] and agrees within 6% with the same analytical analysis [48], such that our model predictions fall within the bounds of these few other available published findings. We believe this suggests that our adopted methodology is an appropriate one, at least for such an initial investigation of biofuel alternatives, which are all predicted to have a very closely similar (3% variation) higher detonation velocity.…”

“…Only the results for acetylene and kerosene fuels could be validated in this way. Model results for acetylene fuel were compared with the experimental data of Turns [47] and an analytical study by Wintenberger [48], while comparisons for kerosene fuel were made with the analytical study of Wintenberger [48] and the time-dependent Computational Fluid Dynamics (CFD) of Yungster [49], as well as experimental work conducted by Cheatham [50] for a range of fuel droplet sizes. The detonation velocity is taken at the von Neumann spike, while pressure rise is taken as time-averaged.…”

Numerical Study and Performance Evaluation for a Pulse Detonation Engine with an Exhaust Nozzle (1st Report: Estimation on Performance using a Detailed Reaction Model)

“…This value is reported as a different value. For example, Zitoun et al, 15) Wintenberger et al, 16) and Kailasanath 1) proposed K ¼ 5:3, 4.8 and 4.65, respectively. Though the above researchers proposed K as an empirical value, Endo et al 17) proposed an approximate solution without empirical parameters.…”

“…Many researchers 1,[15][16][17][18] have reported that the thrust of a simplified PDE with a straight tube with a filling fraction of 1.0 is predicted by the following Eq. (1):…”

Exhaust of Underexpanded Jets from Finite Reservoirs

“…The time of arrival of the first characteristic of the reflected expansion head (and the boundary of the simple region) can be obtained via a similarity solution [24]. This solution accounts for the interaction of the reflected head with the incident wave (see Fig.…”