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Appl. Sci. 2020, 10, 4168 6 of 26 after the 2D analysis with values taken as spanwise averages of quantities at hub, mean and tip sections. Rotational speed and mass flow rate are also automatically inherited from the project database but are altered for off-design simulations. Like other CFD tools, AxCFD solves decomposed Reynolds-Stress-Averaged Navier Stokes (RANS) equations with time-averaged density, pressure and energy conservation, and mass-averaged velocity equations in discretised fluid domains. Passage mesh creation is required before any aerodynamic assessment of the turbine. The way of defining the size and number of the mesh elements in AxCFD is through mesh quality, a value ranging between 1 (coarsest) and 10 (finest). A mesh sensitivity study is performed, with results discussed in Section 3.3.1, to allow for a compromise between accuracy (mesh refinement) and computational time. Structured HO-type mesh elements with the same quality in hub-to-shroud and blade-to-blade directions are used in all cases with additional parameters for mesh adjustment; values are taken based on recommendations by SoftInWay. The meshing zones defined by points on leading edge (LE) and trailing edge (TE) are modified manually over the blade profile contour for hub and tip sections. A mesh quality check is performed; good quality elements are described as those with no Jacobian determinant less than 0.3 and no (or minimal) angle parameter less than 12◦. The k-ω SST turbulence model is used for its suitability in viscous turbomachinery simulations based on previous experience [23–25], with a medium turbulence intensity of 5%. The first order upwind scheme is employed due to convergence difficulties when using second-order. Slightly fluctuating trends and considerably high value criteria for some residuals in the range of 10−5 are accepted for simulations of similar applications shown in [26,27], but convergence is also checked against inlet/outlet mass imbalance of within 0.2%. AxCFD also allows calculations over 2D spanwise fluid domain sections via axi-symmetric modelling which is used of off-design performance map generation. 3. Results 3.1. Cycle Modelling Before proceeding to process modelling of the fully modified cycle and using it as a basis for turbine design, it is reasonable to try and understand if there are any cycle benefits which can be credited to the removal of turbine cooling beyond that of reducing design complexities. From a practical point, a comparison between thermodynamically-identical cycles is conducted where cooling is the only limiting distinction. 3.1.1. Cooled Cycle Comparison In an attempt to compare the performance of an uncooled cycle (the target cycle of this work) to a cooled one, like-for-like working conditions are applied. Conditions of the optimised cycle model from the work of Scaccabarozzi et al. are adopted [10] which are compared against the data from IEA GHG report [9]. Optimisation work, to achieve maximum cycle efficiency target, was carried out by the authors of [10] after performing a sensitivity analysis on the most relevant cycle-affecting parameters. The thermal energy of the feedstock is kept the same as in the cited works by setting the natural gas inlet flow rate to 16.52 kg/s. For the sake of comparison, the uncooled turbine is assumed to be capable of operating at a full-size (≈700–800 MW) power scale. The comparison between a number of cycle performance results is viewed in Table 2. Generally there is good agreement in the results with some discrepancies that can be attributed to the differences in minor quantitative assumptions, and because of using two compression stages instead of four [10] which lowers the power required to drive the compressors. The absence of turbine cooling gives a higher turbine outlet temperature which implies a lower temperature drop across the turbine contributing to a lower turbine specific work. However, the higher combustion flow rate, required to reach the desired temperature of the cycle, balances the drop in turbine specific work. Overall, the cyclePDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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