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Appl. Sci. 2020, 10, 4168 12 of 26 Table 8. Performance results for 3D CFD mesh sensitivity study using two different boundary condition definitions. Number of Elements [-] ηtt [%] 72.66 73.48 69.77 ηtt [%] 76.28 73.01 69.87 ηts [%] 67.50 67.98 63.17 ηts [%] 70.42 67.21 63.05 Boundary Condition: m ̇ in & Pout P0in [bar] W ̇ [MW] 224 83.97 281 93.16 282 102.2 BoundaryCondition:P0in &Pout 51,110 209,308 971,613 Number of Elements [-] m ̇ [kg/s] 51,110 377.3 209,308 375.2 971,613 372.5 W ̇ [MW] 81.48 101.3 108.5 The finest mesh of 971,613 elements is used for flow visualisation. The y+ on the rotor surfaces is ≤2; it is harder to obtain low values of the non-dimensional distance on the stator and rotor shroud because of the high Reynolds number (Re ≈1.7 × 107, given that the fluid has a high density). The range of y+ values on all surfaces is between 0.14–200 (200 being the highest acceptable limit of y+ as referred to SoftInWay manual recommendations). Cerdoun et al. [33] also noted high values of y+ in specific regions of the CFD mesh (0.3–92.2). Lower y+ can be obtained by further increasing mesh element count but owing to the licensing restrictions of AxCFD and the limited computational resources available to run the simulations, the mentioned values are accepted. H-O grid topologies are used in both the stator and rotor domains for smooth alignment with the flow direction, and refinement made in regions near blade walls and leading/trailing edges to account for high normal gradients [34]. Inlet/outlet mass imbalance, monitoring of total-to-total efficiency stabilisation, and root mean square residuals of mass, density, pressure and turbulence equations (k and ω) are used as criteria to assess solution convergence. For lower mesh densities, the residual values are set at ≤10−6 but for finer meshes, residuals require more iterations to reach steady higher values. This is observed in similar works by Wei [26] where increased residual values are accepted for off-design conditions and for finer mesh simulations. 3.3.2. Design Point Turbine Analysis Performance data obtained from the numerical 3D turbulent simulations is listed in Table 9 which can be compared to the 2D analysis results found in Table 7. Global variables of mass flow, power, and non-dimensional parameters all show good agreement; the small difference in thermodynamic properties between the analyses outcomes (enthalpies and temperatures) lead to a greater difference in power output. The total pressure at turbine outlet is 62.9 bar with a total temperature of 975 K which are both slightly higher than the values initially anticipated. The most pronounced discrepancy can be observed in the values of efficiencies that can reach 20%. This change is not fully uncommon with comparisons of 15% efficiency difference between meanline design and CFD results noted by Sauret et al. [35] in their design of a R134A radial turbine, and almost 24% efficiency difference reported by Meijboom [23] between 1D design and 3D CFD modelling for a supercritical CO2 radial turbine. The source of this variance can be attributed to a number of factors, the turbine 3D blade geometries not being fully optimised, and the effects of three-dimensional viscous losses and tip clearance not accounted for in earlier analysis stages. The current design corresponds to an intermediate development stage and requires further adjustment based on the following observations made hereafter.PDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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