Rayleigh piston

The Rayleigh particle is the same particle as the Brownian particle, but studied on a finer time scale. Time differences At are regarded that are small compared to the time in which the velocity relaxes, but, of course, still large compared to the duration of single collisions with the gas molecules. Thus the stochastic function to be considered is the velocity rather than the position. It is sufficient to confine the treatment to one dimension this is sometimes emphasized by the name Rayleigh piston . 0... 

Exercise. The transition probability per unit time for the velocity V of a Rayleigh piston in a gas is... 

Fig. 27. Hugoniots from piston driven two-dimensional simulations assuming Model II (top) and III (bottom). The inserts show snapshots of the unsupported detonations that result in these models soon after initiation. The straight lines drawn are Rayleigh lines...

To calculate the resolved reaction zone and the stability of detonations, we wish to use a piston that is as close to the steady-state piston as possible, so that the deviations from the steady-state will be as small as the mesh used will permit. To accomplish this for any desired detonation velocity, the piston velocity was initially set equal to the particle velocity of the undecomposed condensed explosive that corresponds to the detonation (shock) velocity. The piston compresses and heats the explosive next to it, and a certain amount of reaction occurs. The intersection of the Rayleigh line, as shown in Figure 1.2 with the corresponding Hugoniot is used to determine the proper piston velocity for the next time step. The piston velocity computed in this manner approximates the steady-state piston. A detailed description of the method used to compute the steady-state piston is presented in Appendix A. 

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