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T [K] 371 368 364 360 355 349 3. Results 3. Results CFD Validation CFD Validation out sin pin pout ρin [J/kgK] 1,343 [Pa] 366,619 [Pa] 366,040 [kg/m3] 9.35 1,347 366,040 292,470 8.54 7.42 1,349 292,470 247,050 7.42 6.27 1,352 247,050 201,090 6.27 5.11 1,355 201,090 156,400 5.11 3.99 1,360 156,400 115,050 3.99 2.95 Int. J. Turbomach. Propuls. Power 2020, 5, 19 ρout [kg/m3] 8.54 12 of 17 Figure 12. Velocity triangles for the first two rows. Figure 12. Velocity triangles for the first two rows. The configuration proposed in Figure 12 was simulated via a viscous turbulent CFD analysis, to The configuration proposed in Figure 12 was simulated via a viscous turbulent CFD analysis, to validate the proposed model. The blade shape was designed using Dunham’s parametric method [18] Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 12 of 16 validate the proposed model. The blade shape was designed using Dunham’s parametric method and the number of blades was selected using a modified Zweifel’s criterion [19,20], since ROTs have an [18] and the number of blades was selected using a modified Zweifel’s criterion [19,20], since ROTs axial blade shape. A MATLAB code based on the above parametric method was written to define the define the shape of the blades by interpolating over 1000 points chordwise; then the blade shape was have an axial blade shape. A MATLAB code based on the above parametric method was written to shape of the blades by interpolating over 1000 points chordwise; then the blade shape was imported in imported in SolidWorks and simulated by Ansys Fluent. SolidWorks and simulated by Ansys Fluent. For the CFD simulation a RANS model with a k–ε turbulence model was used. For this For the CFD simulation a RANS model with a k–ε turbulence model was used. For this preliminary preliminary design validation, the viscous sublayer was not resolved. Both two- and three- design validation, the viscous sublayer was not resolved. Both two- and three-dimensional simulations dimensional simulations were performed. The relative motion was simulated by the sliding mesh were performed. The relative motion was simulated by the sliding mesh method in the two-dimensional method in the two-dimensional case and by the Multiple Reference Frame (MRF) model in the three- case and by the Multiple Reference Frame (MRF) model in the three-dimensional case. dimensional case. A Conformal Mesh was generated using a growth rate of 1.045 in order to have a mesh continuity A Conformal Mesh was generated using a growth rate of 1.045 in order to have a mesh continuity as gradual as possible with triangular elements, except in the near-wall region where rectangular as gradual as possible with triangular elements, except in the near-wall region where rectangular elements provide better accuracy. A mesh sensitivity analysis was performed (see Figures 13 and 14) elements provide better accuracy. A mesh sensitivity analysis was performed (see Figures 13 and 14) to check the independency of the results from the mesh generated. The objective function for the mesh to check the independency of the results from the mesh generated. The objective function for the sensitivity was the total entropy. mesh sensitivity was the total entropy. Figure 13. Mesh quality before refinement. Figure 13. Mesh quality before refinement.PDF Image | Optimal Design of a Ljungstrom Turbine for ORC Power
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