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Chapter 2 Theoretical Formulation In this chapter, the governing equations of the inverse design theory will be pre- sented. It will be shown that these will reduce to a set of coupled partial differential equations involving the stream function 4, the periodic velocty potential 4, the blade camber fi and the splitter camber f2. The boundary conditions associated with these equations are described. A brief discussion on the use of an axisymmetric blockage distribution to account for the effects of the blade thickness is also given. 2.1 Governing Equations The flow through the turbine wheel is assumed to be steady, irrotational, inviscid, and non-heat conducting. It follows then that the flow is both homenthalpic and homentropic, or that the rothalphy (H*) and the entropy (S) are constant throughout the flow field. The governing equations (i.e., the conservation of mass, momentum, and energy, and the equation of state) then assume the forms: V.(pW) =0 Wx =0 H = H + 1W2 122 = H* + 1 W2 = H + 2222 p p T PT PT T V2 -wrVe = constant (2.1) (2.2) (2.3) (2.4) where p, p, T denote pressure, density and temperature, respectively. V is the absolute velocity, and W is the relative velocity, i.e., the velocity in the rotating frame (W = V - rwe). Hr, H*, H are the rothalpy (rotary total enthalpy), rotary static enthalpy and static enthalpy, respectively. - denotes the ratio of specific heats.PDF Image | Radial Inflow Splitter Blades in Three-Dimensional
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