Determination of the Speed of Flames and the Temperature Distribution in a Spherical Bomb from Time-Pressure Explosion Records

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Abstract
A method has been developed for determining the velocity of flame relative to the mass movement of the gases, in a closed spherical bomb from an analysis of the time‐pressure record of the explosion. The speed of the flame can be evaluated at any moment during its progress from the center to the periphery of the bomb, as well as the temperature existing in the unburned phase, the temperature immediately behind the flame front, the temperature gradient from the latter point to the center of the bomb, and the pressure in the bomb at the same moment. Given a certain fraction burned of the total amount of gas, the volume occupied by the products can be determined for three conditions: (1) Before it has expanded against the rest of the unburned gas; (2) after it has expanded; and (3) when combustion is complete and it has been compressed by subsequent burning of gas nearer the periphery. Calculations of flame speeds, temperatures, etc., have been made and tabulated for explosions of mixtures of ozone and oxygen. The speed of flame increases from the center of the bomb to the wall. At the same time the pressure and temperature of the gas about to be burned increases. The temperature gradient in the gas from the center to the wall has been calculated when the combustion is complete. A complete diagrammatic description is given for one explosion. It is shown that the temperature gradient actually existing in the bomb does not affect the specific heat results obtained by the usual method of calculating the final temperature from the maximum pressure by means of the gas law. It is pointed out that the practical coincidence of the pressure curve with the zero line in the first part of the time‐pressure record is not due to a time lag between passage of the spark and ignition, but to the small fraction of gas which has burned during this time.

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