Thermodynamic Calculations of Hydrogen-Oxygen Detonation Parameters for Various Initial Pressures

Abstract

Composition, temperature, pressure and density behind a stable detonation wave and its propagation rate have been calculated for seven hydrogen-oxygen mixtures at 1, 5, 25 and 100 atm initial pressure, and at an initial temperature of 40 C. For stoichiometric mixtures the calculations also include an initial temperature of 200 C. According to these calculations the detonation velocities of hydrogen-oxygen mixtures increase with increasing initial pressure, but decrease slightly when the initial temperature is raised from 40 to 200 C. The calculated detonation velocities agree satisfactorily with values determined experimentally. These values will be published in the near future.T HE CALCULATIONS are based on the assumption that complete thermodynamic and chemical equilibrium is established in the wave. Dissipating effects such as viscosity, heat transfer by conduction and radiation, and chemical reaction rate phenomena are disregarded. The calculations were carried out for hydrogen-oxygen mixtures using a rigorous method developed by Edse (l). 3 Other gaseous reactants will be treated in a future paper.The detonation parameters are derived from the Hugoniot equation for the reacted gas mixture in equilibrium, and from the condition that the detonation velocity is the minimum wave velocity of the possible velocities for the given state of the combustible gas.^Thus the results are based on the Chapman-Jouguet point at which the velocity of the reacted gas relative to the detonation wave is equal to the equilibrium sonic speed (2) in the reacted gas behind the wave. These conditions can be calculated more readily than those for a frozen speed of sound for which the ratio of the specific heats k must be calculated (3). Method of CalculationAssuming that only the neutral species of H 2 0, H 2 , 0 2 , OH, 0 and H occur in the detonation wave of hydrogenoxygen mixtures, the Hugoniot equation can be written Pa Vt

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“…Therefore, trial and error (e.g., Bollinger and Edse, 1961) or Newton-Raphson iteration (e.g., Zelenik and Gordon, 1962;Gordon and McBride, 1971) methods have been used to calculate the thermodynamic jump conditions numerically. Sheng and Sislian (1983) studied the wave interaction between an oblique shock and a detonation wave using a two-gamma gasdynamic discontinuity analysis where values of downstream specific heat ratio and combustion heat release were considered as known quantities.…”