Stationary shock wave

Though the form of the Rankine-Hugoniot equation, Eqs. (1.42)-(1.44), is obtained when a stationary shock wave is created in a moving coordinate system, the same relationship is obtained for a moving shock wave in a stationary coordinate system. In a stationary coordinate system, the velocity of the moving shock wave is Ml and the particle velocity is given by u = u M2. The ratios of temperature, pressure, and density are the same for both moving and stationary coordinates. 

These three equations of conservation may be looked upon as defining any three of the four variables p, p, U, u in terms of the 4th, if it is assumed that the equation of the medium, f(p,p,T)=0, as well as the dependence of internal energy of any pair of these variables of state is known. Therefore, the properties of a stationary shock wave follow from the knowledge of the velocity of the piston maintaining the wave, which is also the material (particle) velocity, u... 

When the surface has attained its terminal velocity Vbf we shall have a stationary shock wave propagating with constant velocity Vu into the gas, followed by a growing column of heated, shocked gas between the surface and the shock front that is moving with the constant velocity Vb of the surface. 

Fig.C-2 Pressure profile of a stationary shock wave in a gas. In the laboratory coordinates, the motion of the shock front is from right to left.

We shall present some quantitative relations for stationary shock wave with complete condensation. Continuity condition and momentum conservation law define the expressions for the wave velocity and the liquid velocity... 

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

In materials that support shock waves, the sound speed increases with pressure. It is this same property that causes rarefactions to spread out as they progress. In Fig 2.6(b), an unloading wave is shown propagating into a stationary material with some initial pressure Pq. This time, we consider the evolution of two small decompressional disturbances. The first disturbance moves at the local sound speed of a, into its surroundings, which have begun... 

It was further stated that the energy of the shock.wave is continuously expended in the irreversible heating of a compressible substance and, therefore, a stationary shock... 

Nauk (UkrainRSR) 1966(7), 871-74 CA 65, 19919 (1966) "Criterion of Uni-dimensional Instability of Gas Detonations (The criterion was derived by using Zel dovich-Von Neumann model, which represents a detonation wave in an ideal gas as a stationary complex consisting of a shock wave and the front of an instantaneously occurring reaction with a characteristic induction time that follows the shock wave at a definite distance. The results showed that the criterion assumes the form dependent... 

Detonation, Pseudo. Phenomenon of pseudo detonation was observed by Pangburn et al (Ref 1, p 7) during comparison of combustion modes in intermittent jet engines. The same phenomenon is also known as unstable double discontinuity or latent combustion phase Dunkle (Ref 2, p lie), under the heading "Coalescence of Shock and Combustion Waves , stated that if both shock wave front and combustion wave front move at the same velocity, the rapid photography camera frame in which the shock wave front is stationary and the frame in which the flame front is stationary are the same. This, however, is not always rhe case. 

Theory of Detonation of Explosives , pp 948-60 in Kirk Othmer 5(1950). It includes Theory of shock wave (pp 949-52) Rankine-Hugoniot equation (951) Theory of stationary deton wave (952-55) Calcn of deton para-... 

Fig. 7.2. Diagram of the PDS-1000/He, a stationary particle bombardment machine that is connected to a helium gas container. Controlled by adjustable valves, the gas stream (He) terminates in an acceleration tube, which is mounted on the top of a target chamber. This chamber is closed by a door and set under vacuum shortly before bombardment. When gas flows into the acceleration tube, the rupture disc bursts releasing the shock wave into the lower part of the tube. The gas pressure then accelerates the macrocarrier sheet containing the microprojectiles on its lower surface. The net-like stopping screen holds the macrocarrier sheet back and serves to block the shock wave, while the microprojectiles slip through the pores of the grid and continue on towards their final target.

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. 

Fields of interest adsorption, catalysis, cavitation, nuclear and thermonuclear weapons, shock waves, nuclear physics, particle physics, astrophysics, physical cosmology, and general relativity. Andrei Sakharov named him a man of universal scientific interests and Stephen W. Hawking said to Zel dovich Before I met you here, I believed you to be a collective author , like Bourbaki. See also Zel dovich theory in -> nucleation, subentry -> non-stationary nucleation, and -> Roginskii-Zeldovich kinetics in adsorption kinetics. 

Fig. 3.1 Schematic representation of the detonation process and the shock-wave structure (a) as well as the shock adiabat for an explosive and the detonation products (detonation in a stationary state) (b).

In a stationary detonation wave, the shock front is followed by a zone of chemical reaction which can be considered as an ordinary stationary-state combustion wave propagating through the denser and hotter gases behind the shock front (Fig. XIV.7). Such a combustion wave is characterized by a pressure decrease and a temperature increase across the flame front. Because of this and because, in the stationary state, the flame front must follow the shock front at a fixed distance, the model of the moving surface is not quite adequate to describe a stationary detonation/ A further difference between the two is that, whereas in the mechanical shock the surface velocity Vb was an independent parameter at the disposal of the experimenter, in the detonation the chemical composition of the reacting gases is the collective parameter which replaces vt and is the means by which the experimenter can control the detonation velocity. 

The crack opening can be determined (p = 1), if the fringe order n is known. This method has been used in investigations of stationary cracks to determine static and dynamic stress intensity factors, the latter being induced by a shock wave. 

Fig. 9. Radial trajectories of several mass elements of the core of a 15 M star versus time after bounce. The trajectories are plotted for each 0.02 M up to 1 M , and for each 0.01 M outside this mass. The thick dashed line indicates the location of the shock wave. The prompt shock stalls within 100 ms after reaching 150 km, and recedes down to below 100 km. No sign of a revival of the shock that possibly leads to a successful D(elayed-)CCSN is seen either, even after 300 ms. Instead, a stationary accretion shock forms at several tens of km. A PNS is seen to form, reaching 1.6 M around 1 s after bounce (from [19])...

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