FUGSE

If the FUGSE is used to model flow of a non-diatomic gas through the valve, it should be borne in mind that the value of Cg is dependent on the specific-heat ratio, y, according to equation (9.14), and that the value of Cg given will be Cg(lA). Hence, substituting from equation (9.15) into equation (9.14), the Cg at any other specific-heat ratio, y, will be given by ... 

Appendix 4 gives a detailed comparison of the FUGSE with the nozzle-based model of gas flow through the... 

The historical dominance of US valve manufacturers has led to valve characteristics often being given in standard US units (US gallons, standard cubic feet per hour, etc.). A particularly important influence because of its extensive research into and testing of control valves was the Fisher Controls Company of Marshalltown, Iowa (now part of Fisher-Rosemount Ltd.) This appendix converts the basic liquid-flow equation from US to SI units. The appendix then goes on to derive Fisher s Universal Gas-Sizing Equation ( FUGSE ) from the basic liquid-flow equation and shows how this may be converted into SI units. 

A3.5 Gas flow at intermediate pressure drops the Fisher Universal Gas Sizing Equation (FUGSE)... 

The FUGSE blends the liquid-flow algorithm for high-pressure ratios with a choking equation valid at low valve pressure ratios by using a sine function, the argument of which is chosen to be proportional to the square root of the fractional pressure drop, =... 

A4.3) reducing to the choked gas equation (9.2). But while the FUGSE will be valid at either end of the range of pressure ratios, the fact that the sine function joins the extremes in a conveniently smooth manner does not guarantee that the formula will be accurate at intermediate values. This appendix examines how closely the FUGSE matches direct data and the nozzle-based method for calculating control valve gas flow. 

Meanwhile the FUGSE predicts the onset of choked flow in the valve when the two terms on the right-hand side of equation (A4.4) ate equal ... 

Valve pressure ratio at the onset of choking versus squared friction coefficient comparison of the FUGSE with Fisher... 

An increasing divergence is evident after this point, and it is noticeable that the FUGSE does not reproduce the important direct data point (1.0, 0.5283). 

Figure A4.3 shows /fugse and /nv against valve pressure ratio, pi p, when the friction coefficient is Cfgh = 1.25, typical of a globe valve. The FUGSE function predicts flows significantly smaller than the nozzle-valve function as the valve pressure ratio falls below about 0.9. The FUGSE function does not predict choked flow until Pi p has fallen to about O.IS, approximately a third of the valve pressure ratio.

Ftgur A4.2 Comparison of noule-valve and FUGSE flow functions for friction coefficients, Cr, of 0.7 and 1.0. 

Figure A4.3 Comparison of nozzle-valve and FUGSE functions when the friction coefficient, O. is 1.25.

The FUGSE has the merit of mathematical simplicity (especially in the SI form of equations (A4.3) and (A4.4)). Further, provided allowance is made for the change in limiting gas conductance, Cg, when non-diatomic gases are being passed (equation (9.56)),... 

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