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~~ .- ... .-.......... ... . ......~ .. .._..-. .. CURVE FITTING ratio and was rejected. The x-intercepts were later adjusted to improve the fit. The power variation with pressure ratio was thus described by equations of the form: Power = (PR -PR1) / (a + b(PR)) Where: PR1 is the minimum pressure ratio required to turn the engine at a given speed Since there appears to be no significant variation of power with inlet quality, only one more step was required in the curve fitting process for power. The coefficients a, b and PR1 were related to the speed by the equations: a = aa + baN b = ab + bbN + cbN2 PR1 = exp(bcN) The parabolic variation in b with speed confirms that the power reaches a peak a s the speed increases. The reciprocal of asymptotic power(l/b) bottoms out at the peak in power with speed. < The correlation of the final version of the model was substantially improved by a subtle variation on the technique described. After coefficients associated with the first level of curve fitting were obtained, the coefficient a was related to the other variables as usual. Now, however, values of a were generated by the curve fitfora given speed and inlet quality. The original data were then used to force new curves through these values of a, obtaining new values of the coefficient b. Expressions for b in terms of the other variables were then obtained as before. This method could be used at all but the last level of the curve fit. The forcing technique reduced the effect of errant sets of coefficients, a and b, having self-negating but significant variations froa the rest of the coefficients. These sets of coeeficients may have best fit the particular set of data but wreaked havoc on subsequent curve fits. Values for the coefficients used in the final version of the model can be found in Table 4. 42PDF Image | EMPIRICAL MODELING OF A LYSHOLM HELICAL SCREW EXPANDER
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