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CURVE FITTING 4 0 Because of the degradation of the data matrix in the variation of exhaust pressure, pressure ratio had to be the first variable considered in the curve fitting process. Since different values of exhaust pressure were obtained for each combination of speed and inlet quality, there are not sufficient groups of data with consistent pressure ratio to allow other variables to be considered first. Mass flow rate reaches an asymptote a t high pressure ratio for any combination of speed and inlet quality. In addition, the mass flow rate has a theortical value associated with no leakage flow at a pressure ratio of one. A hyperbola forced through this point can thus be used to describe the variation in mass flow rate with pressure ratio. The important quality of the hyperbola in this application is that it approaches an asymptote in y for large values of x. The transformed equation: - rn= ((PR -1) / (a+b(PR)) +mt Where: PR is the pressure ratio m i s t h e mass flow rate(lbm/sec) Here, rnt is the theoretical mass flow rate given by mt = (ViN) (vf + vfgxi) Where: Vi is the theoretical intake volume( ft3-min/rev-sec) N i s t h e engine speed(RPM) vf is the specific volume of saturated liquid(l20 psia) vfg is the specific volume difference across the vapor dome(120 psia) x1 is the inlet quality The other term in the equation represents the leakage rate. The leakage rate goes to zero as the pressure ratio decreases to I one and reaches an asymptote of l/b as the pressure ratio becoines large. A transformation involving ln(PR) instead of PR-1 was attempted because it appeared to have more physical meaning. This approach did not produce a good correlation and was (PR -1) /(m was used to obtain equations of the form: . mt) =a+b(PR)PDF Image | EMPIRICAL MODELING OF A LYSHOLM HELICAL SCREW EXPANDER
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