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Gas Turbine Design Axial Flow Compressors

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Gas Turbine Design Axial Flow Compressors ( gas-turbine-design-axial-flow-compressors )

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Modern transonic compressors have variable area annuli which force the engine modeler to account for changes in fluid flow properties as a function of radius when converting from a 2-D to a 3-D flowfield. As a result, a new definition of loss is required as well. The difference between definitions of loss for 2-D and 3-D flowfields is that the 3-D loss ω 3D uses the ideal exit total pressure Ptr2ideal as opposed to the inlet total pressure Pt1 used in Equation 2.7 for the 2-D case (see Equation 2.9). ω= 3D (2.9) The change in reference total pressure from Ptr2ideal to Ptr1 is a result of assuming isentropic flow of a perfect gas along a streamline with no loss, heat transfer, or irreversible work. Constant rothalpy is a key requirement that allows the assumption of isentropic flow between state points (1) and (2) as shown in Figure 2.4 (Lieblein Chapter 7, 1965). Equation 2.10 shows the thermodynamic relationship between Pt2ideal and Pt1 which accounts for the centripetal effect of a radius change such as that shown in Figure 2.4. Pt2 ideal Pt1 = {1+ γ-1 2 * (Ω r2)2 γ R Tt1 1 γ /(γ-1) [1-(r/r)2]} 2 Ptr2 ideal - Ptr2 Ptr1 - P1 12 (2.10) r x Figure 2.4 Meridional View of Radius Change due to Variable-Area Annulus 10

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