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

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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.