Shock temperature change across

Properties of the gas, such as the velocity, pressure, density and temperature, change by large amounts across the narrow shock wave. Although mass, energy and momentum are conserved across a shock wave, entropy is not. Entropy is created by a shock from supersonic to subsonic flow. The above analysis, comprising equations 6.95 to 6.100 and 6.101 to... 

A detonation shock wave is an abrupt gas dynamic discontinuity across which properties such as gas pressure, density, temperature, and local flow velocities change discontinnonsly. Shockwaves are always characterized by the observation that the wave travels with a velocity that is faster than the local speed of sound in the undisturbed mixtnre ahead of the wave front. The ratio of the wave velocity to the speed of sound is called the Mach number. 

It is obvious that the entropy change will be positive in the region Mi > 1 and negative in the region Mi < 1 for gases with 1 < y < 1-67. Thus, Eq. (1.46) is valid only when Ml is greater than unity. In other words, a discontinuous flow is formed only when Ml > 1. This discontinuous surface perpendicular to the flow direction is the normal shock wave. The downstream Mach number, Mj, is always < 1, i. e. subsonic flow, and the stagnation pressure ratio is obtained as a function of Mi by Eqs. (1.37) and (1.41). The ratios of temperature, pressure, and density across the shock wave are obtained as a function of Mi by the use of Eqs. (1.38)-(1.40) and Eqs. (1.25)-(1.27). The characteristics of a normal shock wave are summarized as follows ... 

Consider the propagation of a one-dimensional normal shock wave in a gas medium heavily laden with particles. Select Cartesian coordinates attached to the shock front so that the shock front becomes stationary. The changes of velocities, temperatures, and pressures of gas and particle phases across the normal shock wave are schematically illustrated in Fig. 6.12, where the subscripts 1, 2, and oo represent the conditions in front of, immediately behind, and far away behind the shock wave front, respectively. As shown in Fig. 6.12, a nonequilibrium condition between particles and the gas exists immediately behind the shock front. Apparently, because of the finite rate of momentum transfer and heat transfer between the gas and the particles, a relaxation distance is required for the particles to gain a new equilibrium with the gas. 

Figure 6.12. Schematic flow relations across a plane shock wave in gas-solid suspensions (a) Changes of velocities across a plane shock wave (b) Changes of temperatures across a plane shock wave (c) Change of pressure across a plane shock wave.

The change in temperature across the normal shock front at any position in time and space is represented by the equation... 

It should be noted that the term shock waves refers to a pressure wave of large amplitude that arises from sharp and vioient disturbances when the velocity of wave propagation exceeds the veiocity of sound propagation. Characteristicaiiy, an abrupt change of the medium properties (e.g., pressure, stress, density, particie velocity, temperature, etc.) takes piace in a limited space across the shock wave (Schetz and Fuhs, 1996 Shapiro, 1953 Anderson, 1982 Saad, 1992). In the case described in this chapter, the physicai phenomenon of shock wave is restricted to one-dimensional plane wave propagation, in which properties of air in the resonant tube of the wave generator... 

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