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and Smith arithmetically sum the losses due to each of these shocks to obtain the total shock loss. The bow shock loss is modeled using the entropy rise which is a function of the leading edge radius, solidity, chord, and inlet relative Mach number and flow angle. The normal and oblique shock losses are also functions of inlet relative Mach number and are calculated empirically using curve fits of experimental 2-D cascade data. Koch and Smith also include a model for losses caused by the presence of a mid- span damper. This model essentially uses a method similar to those used in calculating losses over airfoils and uses the Horner (Koch, 1976) drag coefficient calculation. The drag was assumed to come from two sources: mid-span damper profile drag and interference drag generated between the mid-span damper and the rotor blades. The drag coefficients are then arithmetically summed into a total drag coefficient and then used to calculate entropy generation. Based on the entropy generation, mid-span damper loss may be obtained. There are essentially three methods of calculating the total off-minimum-loss for transonic flows. The first method calculates a minimum-loss separately then uses the empirical loss equation similar to Equation 2.15. ω =ωmin+a[i−i*]2 (2.15) A form of Equation 2.15 is used by Cetin, Creveling (1968), and Hearsey. This solution method is highly empirical, with the parameter (a) being a function of inlet relative Mach number, flow angle, and blade geometry. The second method of calculating the total off-minimum-loss sums a constant profile loss to the shock loss that is a function of inlet relative flow angle and relative Mach number. Bloch (1996) is one of the most fundamentally based models available, and includes a bow shock as well as a passage shock due to a combination of normal and oblique shocks within the blade passage. The Bloch model is based on actual shock structures found in 2-D cascade Schlieren photographs of changing shock geometry due to varying back pressure over the started choke regime and varying the inlet angle over 17PDF Image | Gas Turbine Design Axial Flow Compressors
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