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100–200 kW range. Through visualization of the design space (Figs. 5, 7, and 9), it was possible to identify the geometry con- straints and operational constraints that limit the feasible design space. For the operational range considered, these are relative flow angle at the rotor inlet (b4), stator exit angle (a4), rotor blade height at the inlet (b4), and resonance of the rotor blade trailing edge (xn). These highlight the strong impact of stator geometry and rotational speed, which define the inlet velocity triangle as the dominating aspects that influence radial turbine design. The risk of trailing edge excitations is considered to be a less significant factor as the compact and complex 3D shapes allow a wide range of optimization approaches to shift resonant frequencies. One option to overcome these limitations is the use of rotor blades with forward sweep at the inlet. The sweep angle offsets the rela- tive flow angle, thereby allowing designs with a higher head coef- ficient. Similarly, complex blade geometries with increased trailing edge stiffness are being considered. Selecting the three operating points, 100 kW, 160 kRPM; 200 kW, 113 kRPM; and 100 kW, 120 kRPM, allowed the effect of scaling on performance to be investigated. Considering the con- stant specific speed (Ns) scaling from 100 kW to 200 kW (designs A and B1) showed that near identical performance is achieved. However, the actual design B1 is not realizable due to failing a fea- sibility constraint. The replacement design for 200 kW (design B2) has a more benign geometry, but is more than 2% less efficient. As the rotors are almost identical in size (see Fig. 11), these losses arise predominantly in the rotor passage which has a lower aspect ratio. Considering the two 100 kW operating points with rotor speeds of 160 and 120 kRPM, the trend is that the slower speed design requires more aggressive angles at the stator and rotor outlet, which are close to the practical limits. However, this design offers the best performance, primarily due to reduced exit energy, pas- sage, and incident losses, which outweigh increased windage that arises from the larger rotor. This occurs as the slower rotor speed results in reduced flow velocities within the rotor passage, which has a number of positive effects. Even more significant perform- ance advantages are expected for a low-speed variant of the 200 kW turbine, but studying this was outside the scope of the current work. In the absence of bespoke loss models for sCO2, the current work uses models that have been established for conventional working fluids and calibrated using empirical data. Considering the physical mechanisms they try to recreate, it can be concluded that due to the empirical nature not all physical phenomena lead- ing to losses are correctly recreated. Particularly, the impact of secondary flow structures in the rotor passages which are affected by the increased density of sCO2 will not be included correctly. However, it is expected that this affects all the designs equally, meaning that trends between the designs will persist, however, that absolute efficiencies may shift. 5 Conclusion This study uses TOPGEN a quasi-1D mean-line design code to perform a design space exploration for small sCO2 radial inflow turbines (100–200 kW power range). Compared to other mean- line tools, TOPGEN includes the effects of blade thickness, which has a significant impact on flow areas at this scale. Furthermore, TOPGEN produces comprehensive maps of the flow and head coeffi- cient state space to show a range of feasible designs. Using these maps, the effect of flow parameters, rotor geometry, and opera- tional parameters on turbine design and performance are high- lighted. Equally, they allow the selection of optimal geometries under consideration of the feasibility limits, performance, and other constraints. By selecting designs away from the feasibility limits, it is ensured that the final design can be further optimized, for example, during the detailed design phase, without encounter- ing limitations. Three operating points 100 kW, 160 kRPM; 200 kW, 113 kRPM; and 100 kW, 120 kRPM were analyzed to explore scaling 081008-10 / Vol.139,AUGUST2017 effects and how these affect the range of feasible designs. The comparison showed that for this power and speed range, geometry parameters at the rotor inlet (stator exit angle, blade height, and relative flow angle) and the natural frequency of the rotor blade trailing edge are the major limiters. Using these conditions, it was also confirmed that constant specific speed scaling results in geo- metrically similar turbines with near identical losses. However, for current design range, the resulting turbine was not realizable due to failing other constraints. Overall, three feasible turbine designs for the three operating points were identified, having total-to-static efficiencies between 78% and 82%. Using the most suitable loss models, an analysis of the loss break-down shows that key loss contributors in order of magnitude are passage loss, tip clearance loss, exit energy loss, incident loss, windage loss, and trailing edge loss. The turbine with the highest efficiency achieved this predominantly due to lower relative velocities within the rotor, suggesting this as a pre- ferred design direction to maximize performance. Through this work, new insight toward the design of small- scale radial inflow turbines operating with supercritical CO2 has been generated. This has been achieved through the development of an enhanced mean-line design tool and analysis of the design space to highlight both the existence of feasible designs and design trends that lead to more efficient turbines at this scale. Acknowledgment This research was performed as part of the Australian Solar Thermal Research Initiative (ASTRI), a project supported by the Australian Government, through the Australian Renewable Energy Agency (ARENA). Jianhui Qi would like to thank China Scholarship Council (CSC) for their financial support. The authors also thank the former members of the Geothermal Centre that has granted access to various codes. Nomenclature A 1⁄4 axial clearance ratio (%) b 1⁄4 rotor blade height (mm) C 1⁄4 rotor flow absolute velocity (m s1) Cr 1⁄4 rotor chord (m) Dh 1⁄4 rotor passage hydraulic diameter (mm) fr 1⁄4 rotor excitation frequency (Hz) ft 1⁄4 the fanning friction factor gc 1⁄4 the force–mass conversion constant h 1⁄4 enthalpy (kJ kg1) Lh 1⁄4 rotor passage hydraulic length (mm) M 1⁄4 rotor flow Mach number Mr 1⁄4 windage torque (kg m2 s1) m_ 1⁄4 mass flow rate (kg s1) N 1⁄4 turbine rotational speed (kRPM) Ns 1⁄4 specific speed p 1⁄4 turbine working flow pressure (MPa) r 1⁄4 rotor radius (mm) R 1⁄4 radial clearance ratio (%) Rer 1⁄4 rotor Reynolds number, Rer 1⁄4 ðq4 W4 Cr=lÞ t, tt 1⁄4 rotor blade thickness, trailing edge thickness (mm) T 1⁄4 flow temperature (C) U 1⁄4 turbine blade tip speed (m s1) V_ 1⁄4 volume flow rate (m3 s1) vi 1⁄4 iteration residuals W 1⁄4 rotor flow relative velocity (m s1) Wout 1⁄4 turbine output power (kW) Zr, Zs 1⁄4 rotor blade, stator number a 1⁄4 rotor inlet absolute flow angle (deg) b 1⁄4 rotor inlet relative flow angle (deg) e 1⁄4 clearance (mm) gts 1⁄4 total-to-static efficiency (%) l 1⁄4 dynamic viscosity (kg m1 s1) 1⁄4 Poisson ratio TransactionsoftheASME Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotuei/936123/ on 04/05/2017 Terms of Use: http://www.asme.org/a bPDF Image | S CO2 Radial Turbine Design as a Function of Turbine Size
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