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A single ellipsoid curve and the surge line b (x,y) surge lin e a corrected mass flow, mdotcorr=mdot sqrt(T1)/p1 Figure 16: An ellipsoid curve based on equation (5.2.4) The values of the a parameters are first taken from the compressor map and the parameter z is at first parameterized with a linear increase with speed, as done in Perez (2001). To get the b parameter we use the ellipsoid equation with a known input, the point (x, y) from the map, where the curve crosses the surge line. With the values of x and y we can calculate b. Now the ellipsoid curve is matched with the given data at least in one point. Unfortunately the values of a and z are not good enough to give accurate results all along the curve. Instead manually adjustments are made to the parameters a and z for each speed to minimize (via visual inspection) the deviations between the ellipsoid curves and data from the map. There is no need for the ellipsoid curves to fit outside the actual operating range; instead emphasis is put on matching the data as good as possible within the operating range. As can be seen in figure 17 below, the model curves differ a lot from the data outside this range. Now each speed from the map is modelled by equation (5.2.4), uniquely determined by its parameters a, b, c and z. In order to generate a continuous mapping for all possible speeds, a polynomial function is fitted for each parameter a, b and z. The calculations were done in Matlab using the polyfit command. The polynomials are of an order between 4 and 7, depending on the nature of the data. With the polynomials, the parameters can during the simulation be evaluated for a continuous set of speeds from 21 000 rpm to 74 000 rpm like this: a=pa(1)⋅ncorr4 +pa(2)⋅ncorr3 +pa(3)⋅ncorr2 +pa(4)⋅ncorr+pa(5) (5.2.5) where pa is a vector containing the polynomial coefficients from the polyfit function and ncorr is the corrected speed. The other parameters b and z are evaluated in the same manner. 27 pressure ratio, p2/p1PDF Image | Modelling of Microturbine Systems
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