The present study addresses the influence of convective heat losses on the flowfield and performance of pulse detonation engines (PDE). We investigate the simplest PDE configuration of a single-cycle straight detonation tube open at one end. The gasdynamics are modeled by a simple one-dimensional formulation and solved by the method of characteristics. Previous heat-flux measurements obtained in hydrogen-air and hydrogen-oxygen detonation experiments are used to calibrate the convective heat-flux model. The results are compared with previous experiments in hydrogen, propane, and ethylene mixtures with either oxygen or air. The present model is found in very good agreement with experiment and reveals how the influence of heat losses is manifested on the pressure profiles inside the detonation tube. It is shown that the nondimensional tube length L/D, where D is tube diameter, governs the amount of losses, the rate of pressure decay at the thrust wall, and hence the specific impulse. The present study reveals that the specific impulse losses vary quasi-linearly with L/D, reaching a deficit of approximately 20% in tube geometries of L/D = 50.
Nomenclature
A= π D 2 /4, tube cross-sectional area A s = π DL, tube internal surface area subject to convective heat losses C = c/c CJ , nondimensional sound velocity C f = friction coefficient C h = heat-transfer coefficient c = sound velocity c p = specific heat at constant pressure D = tube diameter g = gravitational acceleration h = specific enthalpy I SP = specific impulse L = tube length p = pressure Q = total energy available during one cycle inside the tube q = heat loss rate per unit mass q = wall heat flux averaged in space and time over one cycle q c = heat of combustion per unit mass of mixture R = ideal-gas constant S = s/γ R, nondimensional entropy s = specific entropy T = temperature T 0 = {1 + [(γ − 1)/2](u 2 /c 2 )}T , stagnation temperature t = time from detonation initiation at the closed end of the tube U = u/c CJ, nondimensional particle velocity u = particle velocity u w = wall velocity V = π D 2 L /4, volume inside the tube V CJ = detonation velocity x = distance from the closed end of the tube