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The equation in the open literature most commonly used to calculate minimum- loss deviation angle is shown in Equation 2.14. δ* = m θ /σb (2.14) c In Equation 2.14, (δ*) is the minimum-loss deviation angle, (mc) is an empirical relation that is usually a function of exit relative flow angle or stagger angle, (θ) is the blade camber angle, (σ) is the solidity, and (b) is the solidity exponent. The solidity exponent (b) is set to 0.5 in the Carter correlation (Cohen, 1987). Since the Carter correlation was developed for 2-D cascades, Cetin (1987) added empiricism to it in order to adjust the minimum-loss deviation angle calculated by the Carter correlation for 3-D flows. Along with the minimum-loss deviation angle calculated from Equation 2.14, the Hearsey model also included a correction factor due to the velocity ratio. In the current evaluation, three components are used to model minimum-loss. These components are the profile loss caused by blade boundary layers, the profile loss caused by the mid-span damper, and the shock loss. In calculating the blade profile loss, all correlations use a technique originally developed by Lieblein (1957), using a diffusion factor which is a function of maximum inlet relative velocity, and inlet and exit relative velocities. The maximum velocity is determined empirically and is a function of circulation, compressibility effects, and blade geometry. Once the momentum thickness is calculated using the diffusion factor, one may apply a compressible mixing loss due to mixing in the wakes. The compressible mixing loss uses that from Stewart (1955). Swan (1961) took the Lieblein diffusion factor and empirically extended it as a function of blade span to apply to a compressor blade. Koch and Smith (1976), who had the most comprehensive model, performed operations similar to Lieblein, but better accounted for viscosity by including Reynolds number and surface friction effects. The Hearsey model differed from Lieblein in that it contained a correction for profile loss at inlet relative Mach numbers greater than the critical inlet relative Mach number. 15PDF Image | Gas Turbine Design Axial Flow Compressors
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