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Appl. Sci. 2020, 10, 5069 8 of 20 loss models for sCO2 micro-scale axial turbines; these models were derived for air turbines and have not been validated yet for sCO2 turbines. Table 2. 100 kW supercritical carbon dioxide (sCO2) turbine design model validation. Performance Parameters ηtt ηts ζR ζN Verified [41] 0.903 0.835 0.108 0.070 Results 0.9058 0.8391 0.1077 0.0699 Difference [%] 0.31 0.48 0.28 0.14 Design Angles β3 β2 α2 α3 Verified [41] 42.3 63.9 70.7 5.70 Results 42.310 63.960 70.703 5.777 Difference [%] 0.024 0.094 0.004 1.340 5. Results and Discussion A parametric study is presented in this section to investigate the effect of the flow coefficient (φ), degree of reaction (Λ) and loading coefficient (ψ) on the turbine performance ηtt and design feasibility. Different turbine designs are generated assuming different values of the design parameters φ, ψ, Λ, based on the specified ranges in Table 1. Accordingly, a Smith chart is obtained as shown in Figure 4, which shows the normalised efficiency achieved for the sCO2 turbine with a degree of reaction and rotational speed of 0.5 and 150 kRPM respectively. Figure 4. Contour plot for normalised sCO2 turbine efficiency at Λ = 0.5 and 150 kRPM. It is observed that the highest normalised efficiencies are obtained at low flow and loading coefficients, as in the original Smith chart [25]. According to Figure 4, a design point can be selected as a starting point for the parametric study. Though one of the benefits of using sCO2 is having compact component designs, clearance losses will be proportionally larger compared to turbomachines of a comparable power rating owing to the high density of sCO2 and small turbine dimensions. Additionally, windage losses could be expected to be significant on the turbomachinery wheel surfaces compared to large-scale gas turbines as reported from the tests conducted by the Naval Nuclear Laboratory and the Tokyo institute of technology’s (TIT) [39,40]. Therefore, whilst windage losses are not accounted for in the current study, it is important to include these in the future. Likewise, losses due to surface roughness are not considered in this analysis owing to the simplicity of the implemented loss model. Thus, the mean-line model will be extended to include both roughness and windage effects in future studies. The effect of changing the rotor rotational speed on ηtt at different flow and loading coefficients has also been examined. The efficiency is found to increase linearly with increasing rotational speedsPDF Image | Mean-Line Design of a Supercritical CO2 Micro Axial Turbine
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