Subsonic discontinuity

Application of this procedure to inadvertently ignited safety valve discharges can involve a special problem. Certain combinations of pressure ratio and length of safety valve riser can result in choked flow, with a pressure discontinuity at the exit. The pressure of the jet then adjusts to atmospheric pressure in a system of shock waves or expansion waves over a distance of a few pipe diameters. These waves can affect the local mixing of the jet with the crosswind. Since the calculation procedure incorporates correlations for subsonic jets, it cannot be expected to be entirely accurate in this case. Nevertheless, since the wave system... 

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 ... 

We conclude that the growth of a new phase is controlled by the rate of dissipation at a moving kink. This dissipation is taking place at the microlevel and must be prescribed in order for the macro-description to be complete. The incompleteness of the continuum model manifests itself through the sensitivity of the solution to the singular (measure-valued) contributions describing fine structure of the subsonic jump discontinuities (kinks). 

Let the rear boundary of reaction wave move with.a specific velocity Up along the line P in the x,t-plane as in Fig 9 of Ref 2 (our Fig 1). Then initial data are prescribed along two lines. One is the x-axis, which is spacelike with. respect to the material behind it and carries the quantity u = 0 (if. the material is initially at rest), and p=p0. The other line is P, which is timelike, or subsonic to the gas flow, since it is identical with the path of the adjacent gas particles it carries velocity Up. The discontinuity of the reaction wave is represented by the line W. The deductions on uniqueness which. can be Used for non-reactive flow (See Ref 2, pp 136-37) cannot be applied here directly because of the interference of the unknown discontinuity W. 

The resulting flow transient calculated by ASVAM is shown in Figure lO.lOcompared with that of VHIM. The flows are almost identical over the subsonic region up to time = 16 seconds, and come back together again aher 18 seconds. It is noticeable that the discontinuity between subsonic valve flow and sonic valve flow that characterizes VHIM disappears under ASVAM. This is because of the transition in ASVAM takes a very simple form, namely the maximum selection of equation (10.62). 

VHIM is based on a simple transfer to the pipe-plus-valve case of the method outlined in Section 6.4 for calculating flow in a pipe. It will be less accurate than SVHIM in the subsonic-valve region because only the liquid valve coefficient, C , is used in this flow regime, rather than the more representative gas coefficient, Cg. This causes a small discontinuity to occur when sonic flow conditions are met in the valve, and the C characterization is superseded by a characterization based on Cg. The loss in accuracy compared with SVHIM is 3% or less, but VHIM retains the disadvantage that it requires an iterative solution. 

That such an event is not an isolated example and occurs with other azides has been shown in recent work by Chaudhri and Field [28]. They obtained a sequence in which crystals of silver and jS-lead azides were mounted side by side. In both cases initiation occurred at the interface, but also later when the water shock interacts with discontinuities near the ends of the crystals. Since the reaction fronts in the crystals were subsonic it was possible for the shocks in the crystals, as well as stress waves produced by reaction, to travel ahead. The waves were capable of fracturing the crystals (by, for example, a spall-type mecha-... 

---