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Mathematics 2020, 9, 50 14 of 30 Mathematics 2020, 8, x FOR PEER REVIEW 15 of 34 Figure 14. Computational fluid domains for stator and rotor. Figure 14. Computational fluid domains for stator and rotor. Navier–Stokes equations that are discretized by a finite volume approach are inte- 5. Finite Element Analysis (FEA) grated into the current study. These equations are applied to solve for velocity, pressure and temperature associated with a moving fluid. Navier–Stokes equations describe the Rotors in radial inflow turbines experience aerodynamic and mechanical loads. Therefore, it is conservation of mass, momentum and energy, as shown in Equations (21)–(23), respectively. essential to investigate the mechanical integrity of such components. In addition, rotor blades in The Reynolds’s average Navier–Stokes (RANS) equations are also used to account for the conventional radial turbines are usually radially fibered (zero inlet blade angle) to minimize bending turbulence in the flow. These equations are solved to obtain the time-averaged properties stresses. However, since backswept blades are used in the current study, the centrifugal stresses at of the flow without the need for resolution of the turbulent fluctuations. the leading edge must be analyzed and checked carefully. The purpose of the current analysis is to identifythelimitsofbladetipdeformationan∂dρtotal∂vonMisesstressesusingANSYSStaticStructure. + ρ.uj = 0 (21) Theresultedmaximumstressanddisplaceme∂nttsh∂oxuldnotexceedthematerialtensilestrengthand j the running tip clearance (0.6 mm [31]). The running tip clearance is the clearance between the rotor ∂ ∂∂p∂τij and the casing. Figure 15 shows the specified fixed support and direction of rotation. (ρ.ui)+ ρ.uj.ui =− + +ρfi (22) ∂t ∂xj ∂xi ∂xj ∂(ρ.h)+ ∂ρ.u.h=∂P+u∂P+τ∂ui−∂qj+W +q (23) ∂t ∂xj j ∂t j∂xj ij∂xj ∂xj ext H 5. Finite Element Analysis (FEA) Rotors in radial inflow turbines experience aerodynamic and mechanical loads. There- fore, it is essential to investigate the mechanical integrity of such components. In addition, rotor blades in conventional radial turbines are usually radially fibered (zero inlet blade angle) to minimize bending stresses. However, since backswept blades are used in the current study, the centrifugal stresses at the leading edge must be analyzed and checked carefully. The purpose of the current analysis is to identify the limits of blade tip deforma- tion and total von Mises stresses using ANSYS Static Structure. The resulted maximum stress and displacement should not exceed the material tensile strength and the running tip clearance (0.6 mm [31]). The running tip clearance is the clearance between the rotor and the casing. Figure 15 shows the specified fixed support and direction of rotation. Figure 15. Specified boundary conditions for the finite element analysis (FEA), fixed support (a) and rotational speed and its axis (b).PDF Image | Generation of 3D Turbine Blades for Automotive ORC
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