The influence of wall heat transfer on the expansion following a C-J detonation wave

Abstract

Numerous investigations have shown that the wave velocity of a self-sustaining detonation is less than the ideal Chapman-Jouguet (C-J) value and that the deficit increases with decreasing tube diameter. Moreover, in small diameter tubes, the pressure gradient in the expansion behind the wavefront is steeper than that predicted by isentropic relations. Estimates of these deviations from ideality by the nozzle model of Fay, based on a viscous boundary-layer displacement, only partly account for the observed values.Numerical integration by Skinner of the non-steady equations of motion of the burned gases, assuming the Reynolds' analogy to hold between friction and heat transfer, shows that a growing region behind the front becomes time-steady as the wave recedes from its plane of origin. This prediction is confirmed in the present work by gas velocity measurements. An approximate solution of the non-steady equation is derived that is valid near the front and which allows a simple criterion to be stated for the attainment of a steady profile.Wall heat transfer measurements are described using platinum resistance gauges coated with silicon monoxide to suppress the effect of ionization. Transfer rate measurements near the wavefront of oxy-hydrogen waves agree well with the calculations of Sichel and David for the situation obtaining near the C-J plane. The value of the friction coefficient derived from the heat transfer data is used to compute the pressure and gas velocity profiles; these profiles are found to be in satisfactory accord with the observational values.

Effect of Heat Loss on Pulse-Detonation-Engine Flow Fields and Performance

“…Edwards' experiments were the first to correlate the effect of heat losses to the large gas velocity and pressure deficits observed behind the detonation wave. 5 Edwards's pressure, velocity, and heat-flux measurements confirmed the earlier analyses of Sichel and David 6 and Skinner 7 of the influence of heat losses on the Taylor expansions behind detonation waves. 8 Similar observations on the departure of measured pressure profiles from the ideal isentropic solution were made subsequently in a number of studies.…”

“…In this case, an engineering model for the physical effect of boundary losses can be modeled via a volumetric heat-loss source term in the one-dimensional governing equations of gasdynamics, similar to Edwards et al's and Skinner's approaches. 5,7 This assumption signifies that the boundary losses are communicated to the entire cross section of the tube instantaneously. This one-dimensional formulation is clearly not valid close to the detonation wave front because the detonation front involves rates of energy release occurring on much faster timescales than the lateral gasdynamic relaxation, equivalent to energy removal from the bulk flow.…”

“…20 The stagnation temperature is equivalent to the recovery temperature for unity Prandtl number, and it takes into account the temperature increase of a fluid element caused by the adiabatic compression when the fluid velocity is decreased in the boundary layers. 20 Similar to Edwards et al 5 and Skinner, 7 we assume the heattransfer coefficient C h proportional to the heat capacity of the gas ρc p and particle velocity difference between the gas and the wall.…”

Shock Waves, Explosions, and Detonations

“…Indeed, experiments show that the rarefaction behind the front is stronger than expected and depends on the tube (Edwards et al 1963(Edwards et al , 1970. X-shaped waves are observed by Fay and Opel (1958) and Edwards et al .…”

The influence of heat transfer and friction on the impulse of a detonation tube

“…Skinner [23] analyzed the flow field in the tube onedimensionally by the method of characteristics and by applying a Reynolds analogy to the non-steady Taylor expansion to investigate the influence of the heat flux and shear stress. Edwards et al [24] experimentally observed the pressure and velocity deficits behind the detonation wave caused by the effect of heat losses. Edwards' pressure, velocity, and heat flux measurements confirmed the analysis models of Sichel and David [20] and Skinner [23].…”