Contact discontinuity

It is important to note that the state determined by this analysis refers only to the pressure (or normal stress) and particle velocity. The material on either side of the point at which the shock waves collide reach the same pressure-particle velocity state, but other variables may be different from one side to the other. The material on the left-hand side experienced a different loading history than that on the right-hand side. In this example the material on the left-hand side would have a lower final temperature, because the first shock wave was smaller. Such a discontinuity of a variable, other than P or u that arises from a shock wave interaction within a material, is called a contact discontinuity. Contact discontinuities are frequently encountered in the context of inelastic behavior, which will be discussed in Chapter 5. 

Contact discontinuity A spatial discontinuity in one of the dependent variables other than normal stress (or pressure) and particle velocity. Examples such as density, specific internal energy, or temperature are possible. The contact discontinuity may arise because material on either side of it has experienced a different loading history. It does not give rise to further wave motion. 

As a consequence of implicit mass conservation, the gas-dynamic conservation equations, expressed in Lagrangean form, can describe contact discontinuities. To prevent oscillating behavior in places where shock phenomena are resolved in the... 

Nontrace isothermal systems give the adsorption effect (i.e., significant change in fluid velocity because of loss or gain of solute). Criteria for the existence of simple waves, contact discontinuities, and shocks are changed somewhat [Peterson and Helfferich, J. Phys. Chem., 69,1283 (1965) LeVan et al., AIChE J. 34, 996 (1988) Frey, AIChE L, 38,1649(1992)]. 

If the flow rate is increased so that Peclet number Pe l, then there is a timescale at which transversal molecular diffusion smears the contact discontinuity into a plug. In Taylor (1993), Taylor found an effective long-time axial diffusivity proportional to the square of the transversal Peclet number and occurring in addition to the molecular diffusivity. After this pioneering work of Taylor, a vast literature on the subject developed, with over 2000 citations to date. The most notable references are the article (Aris, 1956) by Aris, where Taylor s intuitive approach was explained through moments expansion and the lecture notes (Caflisch and Rubinstein, 1984), where a probabilistic justification of Taylor s dispersion is given. In addition to these results, addressing the tube flow with a dominant Peclet number and in the absence of chemical reactions, there is... 

Note that the solution to the problem obtained by taking the simple section average develops a physically incorrect contact discontinuity. Also our upscaled problem gives a good approximation for the original 2D problem, which is not the case with the simple mean. 

There are two types of discontinuity surfaces contact surfaces and shock fronts. There is no flow between regions separated by a contact surface, while shock fronts are crossed by the flow. A contact surface moves with the fluid and separates two zones of different density and temperature, but the same pressure. The normal component of the flow velocity is the same on both sides of a contact discontinuity... 

Accdg to Ref 66, p 137, actually occurring oneadimensional flows often contain uniform and simple wave flow regions, shocks and contact discontinuities which move toward or thru one another. The interference of one type of flow with another leads to complex patterns re quiring the general solutions of the conservation equations... 

Since shock discontinuities move at supersonic speed into the fluid ahead, shocks overtake contact discontinuities and rarefaction waves. Since shocks move sub-sonically with respect to the fluid behind them, a shock will be overtaken by a shock or rarefaction behind it. When two shocks moving toward each other collide, two shocks moving away from each.other are produced together with two regions of different entropy separated by a contact discontinuity thru the point of collision. 

If a shock collides with a contact discontinuity between two fluids, a shock is sent ahead into ths 2nd fluid and a shock or rarefaction wave is reflected back into the 1st fluid. The kind of reflection depends on relative fluid densities and sound speeds and on the initiating shock strength (Ref 66, p 137)... 

Ejection from the GRB progenitor of a mass Mo with initial Lorentz factor To results in two shocks propagating asunder from the contact discontinuity. The forward shock moves into the external gas and has a much greater compression ratio at its front than the other, reverse shock, which passes through the ejected matter. As the shocked external gas has a temperature much higher than that in the vicinity of the reverse shock, we neglect the losses in the ejecta. 

Particles are precipitated at the bottom of the container and in some time three areas with precise borders (Fig. 8.7, b) can be distinguished in the volume. The pure liquid layer is located on the top, followed by the suspension layer (note that the top border of the second layer shifts downwards with time), and finally, the last layer consists of solid sediment. After a certain time r all particles will precipitate from the liquid into the sediment, the suspension will be completely separated into the pure liquid, and the solid sediment layer and the process of sedimentation will be brought to completion by the establishment of sedimentation balance (Fig. 8.7, c). The boundaries between layers are characterized by jumps of density and known as contact discontinuities. Let us determine the velocities of motion of discontinuity surfaces. Consider the motion of the top border of the second layer in Fig. 8.7. Denote by u the velocity of the border s motion directed downwards. Following a common practice in hydrodynamics, choose the system of coordinates attached to the moving surface. In this system, the surface of discontinuity is motionless. Denote the values of parameters before the jump (above) by the index 1, and behind the jump (below) - by the index 2 (Fig. 8.8, a). 

Since the diameters of bubbles range from Di to D2, at t > 0 there are three regions in the considered volume (Fig. 24.1), divided by flat surfaces of contact discontinuities (these surfaces are already familiar to us from the similar problem of suspension sedimentation (Section 8.5)). Consider a plane (z, t) (Fig. 24.2) and straight lines... 

The theory of laser schlieren system schlieren system is that reflecting the first order partial derivative with the change of refractive index in flow field and it can capture the shock wave and contact discontinuity. To combustion flow field with self-luminous light, the light given in flow field and illuminant will both cause film exposion. 

If we assume that we observe only one phase boundary when Vq and are specified in the different phases, it is plausible to employ the one-parameter (denoted as ) family of solutions of Fig. 3.1 in the isothermal case and Fig. 3.2 in the nonisothermal case when the initial data are appropriate. In these figures all the intermediate states (vl,v, Vr, etc.) are constants. The abbreviations F.W., B.W., C.D., and P.B. stand for forward wave, backward wave, contact discontinuity, and phase boundary, respectively. The forward and backward waves consist of a shock or a rarefaction wave. In the isothermal case this one-parameter family of solutions was discussed first time in [13]. We take to be Vl - Vq in the isothermal case and Ul - Ug in the nonisothermal case. Then the decay of entropy (the entropy rate) is given by... 

All phenomena of explosive, combustion and detonation are transient and accompanied by the generation and motion of acoustic, shock and blast waves. Therefore, for imaging shock fronts, the frame exposure time should not exceed 10 s. To describe the wave motion and the contact discontinuity displacement the frame number should be close to 10. 

Fig. 11.33 Diagram of wave front propagation within a working part A - incident shock wave B - contact discontinuity C - centered rarefaction wave D - reflected shock wave 1 - undisturbed air 2 - air compressed by incident shock wave 3 - combustible gas flowing out of the high pressure pipeline 4 -undisturbed combustible gas 5 - air compressed behind the reflected shock wave 2 and 5 K - gas mixture state in the vicinity of the contact discontinuity [40, 47]...

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