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Radial Inflow Splitter Blades in Three-Dimensional

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Radial Inflow Splitter Blades in Three-Dimensional ( radial-inflow-splitter-blades-three-dimensional )

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Chapter 3 The Numerical Technique This chapter discusses the numerical technique to solve all the governing equations subjected to the appropriate boundary conditions described in chapter 2. A more com- prehensive discussion can be found on the original work by Yang (see Ref.1, Chap.5). 3.1 Grid Generation Although the problem under consideration is a three-dimensional flow, the periodic nature of the flow has made it possible to use Fourier Series to represent the flow variables in the circumferential direction. As a result, we have to generate only a two- dimensional mesh in the meridional plane. Given the profile of the hub and shroud, we can generate a mesh by two means. The first method is the Algebraic method which is the simpler one. We can cast the expression for (r, z) coordinates in terms of the mapping coordinates (e, r7) as r(e, 7) = [r(IMAXI) + r ( ,J) - 1) )] + [r(I,JMAx)7 + r(,l)(1 - 7 2(3.1) z(,) = I[z(IMAX,J)e + Z(1J) (1- and the mapping coordinates (e, 7) are given by Z(I,JMAX) 2 ) + _= I-1 IMAX-1 J-1 - JMAX-1 + Z(,1)(1 - )] Because the equations are linear, no numerical iteration is needed. The second one is the Elliptic method. We solve two elliptic equations for mapping coordinates e and r, which are err + 1zz = P(, ?7) (3.3) 1,7rr + ezz = Q(ei7) (3.2)

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