Subsonic region

At z>0 the flow is subsonic. The chemical reaction rate is given in terms of a single variable, the concentration of unreacted molecules. Radial, tangential and axial perturbations of the velocity, pressure, density and concentration are introduced in the subsonic region. The small flow perturbations are assumed to be superimposed... 

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). 

Figure 10.11 compares the flow transient calculated by ASVAM with the standard transient calculated by SVHIM. ASVAM, like VHIM, relies implicitly on the C value to characterize valve flow in the subsonic region via the calculation of AT, and then Kp. As a result, ASVAM underestimates the flow by about 3% at the beginning of the transient in the same way as VHIM. But ASVAM produces essentially the same value as SVHIM for flow by time = 15 seconds. In fact, ASVAM predicts sonic flow in the valve at time = 16 seconds, a second in advance of SVHIM, but the difference in flow is very small. 

Figure 18.18 (left) exhibits the calculated gas flow field from an individual gas jet at atomization pressure po = 0.5 MPa (polPa = 5). The diameter at the nozzle exit is 3 mm. The simulation is conducted based on the 2D axisymmetric geometry (see Fig. 18.15). Five cells with shocks can be found after the nozzle exit. Figure 18.18 (right) exhibits the velocity distribution at the centre line of the jet. The experimental data were obtained by laser Doppler anemometry (LDA) [26]. A good agreement is achieved between experimental data and numerical simulation results, for example in the location and number of shock cells, the calculated length of the supersonic core of the jet and the decay rate of the gas velocity in the subsonic region. Only the amplitudes of the velocity fluctuation differ between experiment and simulation the peak in velocity values behind the shock is more intense than those measured in the experiment. The experimental deviation may be caused by the behaviour of the tracer particles used for LDA measurements. These small but still inertial tracer particles cannot follow the steep velocity gradients across a shock exactly. The k-co SST model indicates a better performance than the standard k-e model.

Sect. 1.10 if we restrict the discussion to the subsonic case. For subsonic velocities, /(co) can be expanded as a Taylor expansion in the velocity, where each term is a rational function of the moduli, as required by the argument in Sect. 1.10. We will see in the next section that the situation becomes more complex above the subsonic region. Taking the inverse Fourier transform of (7.2.3 a) gives... 

In commercial practice, powdered explosives on an ammonium nitrate basis are used in most cases. Typical detonation velocities are between 1800 and 3500 m/s depending on the metal system to be bonded. The lower detonation velocity range is preferred for many metal systems in order to minimize the quantity of solidified melt associated with the bond-zone waves (12). In addition, subsonic detonation velocity explosives are required for the parallel cladding technique in order to avoid attached shock waves in the coUision region, which preclude formation of a good bond. 

Witze Am. In.st. Aeronaut. Astronaut. J., 12, 417-418 [1974]) gives equations for the centerline velocity decay of different types of subsonic and supersonic circular free jets. Entrainment of surrounding fluid in the region of flow establishment is lower than in the region of estabhshed flow (see Hill, J. Fluid Mech., 51, 773-779 [1972]). Data of Donald and Singer (T/V7/1.S. In.st. Chem. Eng. [London], 37, 255-267... 

Regions III and IV give expansion waves, which are the low-velocity waves already classified as deflagrations. That these waves are subsonic can be established from the relative order of magnitude of the numerator and denominator of Eq. (5.6a), as has already been done in Chapter 4. 

In Fig. 5.5, the flow configuration and velocity and temperature distributions at the time instant of 12.5 s are depicted. Even though the flow is subsonic, due to the high Reynolds number, the flow structure in the region upstream of the solid propellant is minimally affected by the time-dependent boundary shape due to phase change. However, the thermal characteristics near the propellant interface show clear signs of time dependency, indicating that the mass flux of... 

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 ... 

Region I Pi> Pj supersonic flow to subsonic flow, strong detonation... 

Region IV p > pj subsonic flow to subsonic flow, weak deflagration... 

Region IV p2 > Pk subsonic flow to subsonic flow, weak deflagration Region V P2 < Tk supersonic flow to supersonic flow, strong deflagration... 

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