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the hyperbola forced through a point(x1, yl), CURVE FITTING 39 Curve Fitting An empirical engine model was created by applying statistical curve fitting techniques to the test data. Methodology was developed for using such traditional curve fitting methods to obtain expressions in three or more variables. The equation forms considered were limited to transformations of the linear equation y = a + bx and the parabolic equation. Explicit expressions for power and mass flow rate in terms of pressure ratio, inlet quality and engine speed at an inlet pressure of 120 psia were obtained. The model was completed by combining the predictions for mass flow rate and power with a steam table to produce predictions for efficiency and exhaust quality. There is an extremely large number of equation forms which can be used to fit experimental data. In order to l i m i t the time involved in the modeling process, the types of equation considered for use in modeling were limited: An attempt was made t o employ only transformations of the linear equation y z a + bx[13, 141. These include: the expotential equation, the logarithmic equation, the power equation, y = aebx y = a +bln(x) y = axb y = ((x -xi) / (a + bx)) + y1 and the parabolic equation forced through a point(x1, yl), y = (yl -ax11 + (a -bx1)x + bx2 The regression coefficients for these equations were determined using the method of least squares. To reduce the chance of error and the time involved in this extensive task, a progranable calculator was employed. A s t a t i s t i c s software pack in the form of aROYwas used with an HP-41C. A peripheral printer was used to record and check the data entries.PDF Image | EMPIRICAL MODELING OF A LYSHOLM HELICAL SCREW EXPANDER
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