By Ginsparg P.

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**Example text**

1. (a) Pressure wave, (b) shock wave formation Fig. 2. Shock wave model, P means pressure, r density, T temperature, w or u velocity, subscript 1: ahead and 2: behind the shock wave, respectively Assuming a standing shock wave which is really propagating in an ideal gas with a velocity of w1 and a flow behind the shock wave has a velocity w2, as illustrated in Fig. 1 Shock Waves 47 E1, I1: energy and enthalpy of the gas in front of the shock wave, respectively E2, I2: energy and enthalpy of the gas behind the shock wave, respectively a1, a2: sound velocities of the gas in front of and behind the shock wave, respectively Cp, Cv: specific heats of the gas under constant pressure and constant volume, respectively g = Cp/Cv: ratio of specific heats we can obtain some relations between the variables described earlier according to the three conservation laws of flow and the state of the ideal gas.

As this photograph shows, the ignition takes place at a few points, from which flames propagate in the whole space. The induction period of ignition is thus different corresponding to the part of the mixture. 1 Probability of Ignition Behind Shock Waves45 In order to investigate a spontaneous ignition in a combustible mixture, it is first necessary to bring the mixture suddenly into a state in which an ignition can take place, namely, to raise the temperature as quickly as possible. For this purpose it is convenient to apply a shock tube and ignite the mixture behind the reflected shock wave in the shock tube, where the mixture is heated to a temperature between several hundred to a few thousand centigrade in a few microseconds without any influential flow.

Therefore, the observation of the gas behind a shock wave reflected from the tube end is more favorable, as the gas scarcely flows and besides pressure as well as temperature is much higher than those behind the incident shock wave. 18) c +1 2c M 2 -1 c -1 e c -1 1 o 3- c 2 d M 12 + c -1 ne 2M 12 + c -1 o T5 T5 T2 T1 = T2 T1 = 3c -1 3- c e c -1 M 12 - 2 oe 2M 12 + c -1 o 2 c +1 e c -1 o M 12 . 19) According to these equations the pressure, temperature, and density of the gas behind the reflected shock wave can be calculated from the initial state of the gas and the Mach number of the incident shock wave, considering the ratio of specific heats g corresponding to the gas temperature at each step.

### Applied conformal field theory by Ginsparg P.

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