ASVAM

Applying this approximate method required the estimation of suitable values for the flow coefficient, bo, which is a function of the total frictional loss in velocity heads, Kj, and the pressure ratio, p p. The polynomial approximations of equations (6.66) to 

and the pressure ratio, Pv P over the upstream section. At the beginning of the transient, b po bo although the two diverge as 7- increases substantially with time. 

The valve inlet pressure, p i, has been calculated on the basis of the fourth estimate of Pvt/P, n =4 in equation (10.60). The valve inlet pressure, and the valve outlet pressure, p, calculated under ASVAM trace a very similar path to that shown 

The latter course has been adopted in this example. The following equations may be used to calculate a fixed value of bo (see Section 6.8)  

Note that the calculation of the valve inlet pressure, p , needed for determining sonic flow, is made on the basis of the first estimate of the ratio p /p.  

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An approximate meth, the Average Specific Volume Approximation Method (ASVAM), is also presented, based on the Long-Pipe Approximation described in Chapter 6. This approximate method retains much of the accuracy of the SVHIM, but has the advantage of yielding a direct estimate of flow. 

Gas flow through an installed valve - Average Specific Volume Approximation Method (ASVAM)... 

This final method is based on the approximate methods for calculating compressible flow in a pipe, as described in Sections 6.8, 6.9 and Appendix 2, and in a valve, as described in Section 9.11.2. The major approximation made is that the specific volume of the gas in large stretches of pipework can be represented adequately by a notional average specific volume. The benefit of ASVAM is that it can be programmed to avoid implicit loops, and hence the associated problems of convergence in the main equations, while maintaining a very reasonable accuracy. 

The equations underlying ASVAM will now be set down for the plant arrangement of Figure 10.1. First we calculate the frictional loss in velocity heads in the same way as laid down for VHIM in Section 10.2 for the upstream section of pipe, the downstream section and the valve (equations (6.58), (7.36) and (7.25)), and then find the total frictional head loss, Kt, from equation (10.1). 

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 10.12 Pressure upstream of valve and at pipe outlet (ASVAM).

The average specific volume at this condition is found to be Vflw = 0.1131 mVltg, and the value of bo is bo = 0.8333. Replacing the variable value of bo with this constant value in ASVAM, but making no other changes, produces the mass flow transient shown in Figure 10.13. 

ASVAM is an essentially explicit approximation to VHIM. ASVAM benefits from the extensive offline computations carried out to define both the critical pressure ratio, P3c/Pi. as a function of the fric-tionsd loss in velocity heads, Kr, and also the shape of the bo versus Kt and Pa/pi surface. It is much quicker and less complicated than VHIM as a result. 

ASVAM has the distinct advantage that it avoids convergence problems, since its only iteration occurs in a minor loop, where the number of passes may be fixed in advance. ASVAM is therefore a very attractive option for the modeller. 

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