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load of the stage. Introducing the above dimensionless parameters into the equations of continuity, moment of momentum, and degree of reaction, the stage is fully defined by the following set of equations [1], 𝜈 𝑐𝑜𝑡𝑔𝛼 −𝑐𝑜𝑡𝑔𝛽 =𝜇𝜙 2 2 𝑐𝑜𝑡𝑔𝛼3 − 𝑐𝑜𝑡𝑔𝛽3 = 1 𝜙 𝜙2 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 1 + 2𝜆 [1 + 𝑐𝑜𝑡𝑔2𝛼3 − 𝜇2(1 + 𝑐𝑜𝑡𝑔2𝛼2)] 𝜆 = 𝜙(𝜇𝜈𝑐𝑜𝑡𝑔𝛼2 − 𝑐𝑜𝑡𝑔𝛽3) − 1 (5.2.a) (5.2.b) (5.2.c) (5.2.d) In which, α and β show the flow’s absolute and relative angles at stator and rotor, respectively (Figure 50). The above equations include 9 unknown parameters from which 5 of them should be assumed and the other 4 will be calculated by solving the Eq. 5.2a-d. All the mixture properties such as enthalpy, entropy, γ, Cp, etc at different pressures, temperatures, and fuel/air ratios are calculated using a FORTRAN gas table developed by Schobeiri [1]. At the inlet of each stage, the inlet conditions (i.e. pressure and temperature) are known from the previous stage. Based on the stage desired pressure ratio and a preliminary assumed isentropic efficiency, the exit pressure and temperature of the stage are calculated. The final isentropic efficiency is found after implementation of all individual losses [1]. In order to come up with the appropriate values for 5 of the unknown parameters in Eq. 5.2a-d, the stage geometry (i.e. mean diameter and blade height), rotational speed, and α2 values are specified. Moreover, μ and ν are calculated assuming average blade height and velocity at the middle section of the stage. The remaining 78PDF Image | DEVELOPMENT OF AN ULTRA-HIGH EFFICIENCY GAS TURBINE ENGINE (UHEGT
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