Rarefaction fan

Figure 2.8. An x-t diagram of a piston interacting with a compressible fluid. At the origin, the piston begins moving at constant velocity, generating a shock wave. At tj, the piston stops abruptly, generating rarefaction fan. Snapshots of wave profiles at times t2 and 3 are shown.

On the x-t diagram we show the leading- and trailing-edge velocities, and sometimes throw in a few values in between to show this is a rarefaction. This x-t representation is called the rarefaction fan. Figure 19.6 shows this as a example based on the square pulse we previously saw in Figure 19.4... 

Figure 19.6 The rarefaction fan on an x-t plane. (If the entire rarefaction fan does not play a significant role in the problem at hand, then just plot the leading edge of the rarefaction.)...

Fig. 6.9. Representation of events in a shock tube. The locations of the shock front, the contact surface and the rarefaction fan in the driven and driver sections of the tube after an interval t following the bursting of the diaphragm are marked.

Figure 17. 575 nm PVN + 440 nm PMMA stacked film shocked to 18 GPa. The 1624 cm peak is PVN VasfNCtz) and the 1728 cm peak is PMMA s carbonyl stretch. Arrows denote timings to, shock enters PVN ti, shock has fiilly transited PVN t2, shock has transited PMMA and rarefaction begins t3, head of the rarefaetion fan reaches PVN/PMMA interface t4, head of the rarefaction fan reaches PVN/Al interface. 

Two rarefaction fans are separated by a region of constant critical state. The tail... 

For simplicity, we have shown an expansion wave in which the pressure is linearly decreasing with time. This, in general, is not the case. The release behavior depends on the equation of state of the material, and its structure can be quite complicated. There are even conditions under which a rarefaction shock can form (see Problems, Section 2.20 Barker and Hollenbach, 1970). In practice, there are many circumstances where the expansion wave does not propagate far enough to fan out significantly, and can be drawn as a single line in the x t diagram. 

In the study of Fan, et al. [If], a numerical simulation of gaseous flows in microchannels by the DSMC was carried out. Several unique features were obvious to maintain a constant mass flow, the mean streamwise velocity at the walls was found to increase to make up for the density drop caused by the pressure decrease in the flow direction, which is in contrast to the classical PoisueUe flow. In addition, the velocities at the walls were found to be nonzero and to increase in the streamwise direction, which highlights the slip-flow effect due to rarefaction. The results of the DSMC simulations were validated by an analytical solution in the slip regime. It was observed that the two results showed remarkable agreements. 

Two different methods for introducing a shock wave (which may or may not subsequently turn into a detonation wave) into the target AB material have been used. The first employs a thin, inert A2 solid flyer plate, which is launched at a velocity +2up towards the target, resulting in an initial particle velocity of +Up into the sample (and one of -t/p into the flyer plate, due to the virtually perfect impedance match of A2 and AB). If chemical reactions have not begun by the time the rarefaction (release-wave) fan from the rear end of the flyer plate overtakes the initial unreactive shock (a time proportional to the flyer plate thickness), then the shock wave decays and eventually fails to propagate. 

Fig. 10.32 Diagram of the flow behind the detonation complex in a layer of a combustible mixture (a) [54] and the explosion products velocity field, (b) [55] 1 - combustible mixture 2 - noncombustible surrounding 3 - attached oblique wave 4 - contact surface between explosion products and surrounding interface 5 - fan of attached and reflected rarefaction waves (Prandtl-Meyer expansion fan)...

Angles of product flow rotation ro and attached oblique wave angle 0 are calculated based on the flow characteristics [54]. The explosion products expand in a rarefaction wave fan attached to the detonation complex for Pe3, pressure, and further, in the system of reflected rarefaction waves, to P, - pressure. 

The diagram of wave-front motions behind the membrane in the duct is known and, by analogy with the classical shock tube [43], is presented in Fig. 11.33. If it is assumed that the membrane is removed instantaneously, then we have the classical case of a membrane rupture and a flat topped shock wave generated in the low-pressure section (air at condition 1) ahead of the membrane. A centered rarefaction wave C travels back to the combustion gas at condition 4. The solution of the problem for parameters of the incident and rarefaction waves is known [43]. As a rule, before the membrane rupture, Tj = 74. The air temperature T2 behind the incident wave at condition 2 and expanding the gas temperature behind the rarefaction wave fan at condition 3 are calculated using the following expressions ... 

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