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M Abidat, M K Hamidou, M Hachemi And M Hamel ∂(ρε) → μ ε +∇.ρεU=∇.μ+ t ∇ε + (C P-C ρε)(16) η P ∂t σ k 1εRNG k 2εRNG ε Where C =1.42−f, f=η1− (1+β η3)and η= k 1εRNG η η 4.38 RNG ρCμRNG ε Pk is the turbulence production and σκ = 1.00, σε = 1.30, C2εRNG = 1.68, βRNG =0.012are constants determined experimentally from a wide range of turbulent flows by Patankar and Spalding [12]. 3 NUMERICAL METHOD 3.1 Mesh Generation The flow solution in the mixed flow turbine volute, shown in figure 3, is obtained by a numerical finite volume method. The flow domain is discretised into finite volumes of tetrahedral elements. The ANSYS-ICEM software is used to build the volute geometry and to generate the unstructured mesh. During the mesh generation process, care has to be taken in the choice of the first grid spacing near wall boundaries to obtain a proper resolution of the boundary layer. As a result of the use of the wall function approach to model the flow near the wall in the RNG k − ε turbulence model, it is advised that the Y+ value for the near wall nodes has to be in the range of 20 to 100 [13]. 3.2 Numerical Method The integration, on the finite volumes, of the equations describing the turbulent flow results in a set of discrete equations. The terms of the differential equations on the volume interfaces are obtained by a first order upwind scheme or a high resolution (second order upwind scheme). The first order upwind scheme is generally used to obtain an approximate solution of the flow while the high resolution scheme is used to obtain the final solution. The pressure-velocity coupling is achieved using the SIMPLE algorithm of Patankar and Spalding [12] in conjunction with a momentum-interpolation technique similar to that of Rhie and Chow [14] to prevent pressure-field oscillations as a result of the non staggered, collocated grid arrangement. At the domain inlet, the flow is assumed subsonic, and therefore the total pressure and the total temperature in the stationary frame of reference as well as the flow direction are imposed. At the turbine outlet, where the flow is considered to be subsonic, instead of the static pressure, the mass flow rate is imposed. On the solid boundaries, a no slip condition is used.PDF Image | ANALYSIS OF RADIAL AND MIXED FLOW TURBINE VOLUTES
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