By Prabhu Lal Bhatnagar
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Extra info for Nonlinear Waves in One-Dimensional Dispersive Systems
In both the methods, however, the temperature of the mixture is changed often so slowly that some reactions can take place during the period of temperature change. Applying shock waves, we can change the temperature and density of the mixture within a few microseconds. Such shock waves can be produced in a shock tube having a very simple construction and applied easily to investigate the ignition of combustible mixtures. 1 Shock Waves A pressure wave usually propagates in a medium with a velocity near the sound velocity corresponding to the medium state, since it is compressed almost isentropically and relatively slowly, as shown in Fig.
5 shows an example of shock diagrams in a shock tube. 0m means the position of the membrane in the shock tube. When the diaphragm bursts, the shock wave propagates along the line 0m−S1, while the front of the rarefaction wave travels in the opposite direction into the high-pressure driver gas along the line 0m−R1 with the sound velocity. After a certain expansion period the tail of the rarefaction wave propagates along the line 0m−R2. The contact surface propagates along the line 0m−S2 with the same velocity as the flow velocity of w2.
The contact surface propagates along the line 0m−S2 with the same velocity as the flow velocity of w2. The reflected shock propagates along the line S1−S2 which is separated into two waves S2−S3 and S2−R1S1 after collision with the contact surface at S2. 19) is kept only in the region 5 in this diagram. Its duration period and region are namely limited. In order to keep the state behind the reflected shock waves much longer, tailored shock waves can be applied, in which the contact surface after the collision of the incident shock with the reflected one stands still, namely, S2−S4 line is 6 Stochastic Ignition Theory The ignition is also a distinctly irreversible process and has many stochastic phenomena in it.