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Each of the horizontal curves corresponds to one constant speed of rotation. The range is from 20 000 rpm up to 74 000 rpm. The area enclosed by the surge line and the choke line is the normal operating range for the compressor. On the left side of the surge line the pressure ratio decreases for decreasing mass flow, i.e. a positive pressure gradient. This can, for the lower speeds, already be seen on the immediate right side of the surge line. Surge is associated with a drop in the pressure ratio, i.e. the delivery pressure, which can lead to pulsations in the mass flow and even reverse it. It can cause considerable damage to the compressor, e.g. blade failure. The surge phenomenon is similar to wing stall of an airplane. Rotating stall is another dangerous event. It occurs when cells of separated flow form and block a segment of the compressor rotor. Performance is decreased and the rotor might be unbalanced, also leading to failures, Fox (1998). As the pressure ratio decreases and mass flow increases, the radial velocity of the flow must also increase, in order for the compressor to blow enough gas through it. At some point the compressor cannot accelerate the flow to high enough radial velocity for the given motor speed, then maximum mass flow is reached and choking is said to occur, Cohen (1996). The compressor map model must in one way or another represent the theoretical compressor map. One obvious method is taking the raw tables of data that produce the curves above and use them in a look-up table. Between data points bilinear interpolation can be used. This method was tested in the compressor model for the mass flow and the efficiency. Unfortunately it did not work, due to numerical problems, which will be discussed in the end of the compressor section. Another option is to fit continuous functions to the different curves and parameterize them so that the whole map can be continuously represented, even for different speeds. This has been done in Gustafsson (1998). The curves in the map above can be viewed as ellipsoid curves and can be represented with an ellipsoid equation: xz yz +=c a b (5.2.4) When the parameters a, b, c and z are varied, the form of the ellipsoid curve can be adjusted to fit any data curve from figure 15. The parameter a corresponds to the corrected mass flow at pressure ratio one (where the curve would cross the x-axis). Similarly the parameter b represents the pressure ratio at zero mass flow (where the curve would cross the y-axis). The parameter c is just an arbitrary constant usually taken to one. The parameter z represents the curvature of the curve. 26PDF Image | Modelling of Microturbine Systems
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