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Fig. 3 Parameters p04 T04 PR ðp04=p6Þ Fluid Operating point 1 Operating point 2 Operating point 3 Radial turbine rotor blade geometric parameters [13] Table 2 The initial conditions of the calculation while maintaining the same aerodynamic flows and performance by using the specific speed parameter (Ns) [14,30,31] xV_1=2 Ns 1⁄4 Dh3=4 (6) 0 To investigate this relationship and to explore the impact of scaling on turbine geometry and performance, a second turbine design with an output power of 200 kW, but with the same spe- cific speed (Ns), is analyzed. Due to the fixed cycle operating conditions, the power extracted per unit volume flowing through the turbine (Dh0) is constant. Hence, as net power is given by Wout 1⁄4 gts q V_ Dh0 (7) it can be shown that to maintain a constant specific speed, the fol- lowing relationship exists between output power and shaft speed: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x1 1⁄4 Wout2 gts1 Wout2 (8) x2 Wout1 gts2 Wout1 The approximation is permissible as turbine efficiency is roughly constant for fixed specific speeds [14,31] (This is also confirmed by the current study). Hence, to generate a geometri- cally and aerodynamically similar turbine to the one used for the 100 kW, 160 kRPM operating point, but providing an output power of 200 kW, a shaft speed of 113 kRPM must be selected. 3 Results and Discussion For each of the three operating points (100 kW, 160 kRPM; 200 kW, 113 kRPM; and 100 kW, 120 kRPM), TOPGEN creates a design map including a total of 1271 potential designs. On these graphs, for example, Fig. 5, the outcome of the feasibility checks is plotted as point markers and the geometric and nondimensional properties are plotted as contour lines. For clarity, the outline of the feasible design space has been marked by a bold line. Not only does this facilitate the selection of optimum designs but it also pro- vides an excellent overview of the feasible design space in relation to design input parameters (e.g., blade dimensions). This permits the appropriate selection of a turbine design that meets operating conditions (speed and power) and that is appropriately far from fea- sibility limits, allowing further optimization and adaptation. 3.1 Operating Point 1: 100 kW, 160 kRPM. The area of feasible designs is located in the central part of the map shown in Fig. 5. It can be seen that the top and the bottom boundaries of the feasible area are cropped by contours of relative inlet flow angle (b4). The left side of the feasible area is determined by the critical blade trailing edge frequency (xn), and the right limit is set by the blade height limit, (b4) set at 0.9 mm. All the turbine designs out- side of this polyhedron are discarded as unfeasible turbines. The observed trends for inlet absolute angle (a4) and relative angle (b4), which have a significant impact on the feasible design space, are actually constant in relation to flow and head coeffi- cient. This is due to the approach used for the inlet velocity trian- gle calculation. Inlet relative angle (b4) is calculated by rffiffiffiffiffiffiffiffiffiffi Design value Parameters 20 MPa w 560 C u 2.22 Zr CO2 Zs 100 kW, 160 kRPM 200 kW, 113 kRPM 100 kW, 120 kRPM Design value 0.70–1.1 0.10–0.40 9 11 Fig. 4 [29] Bearing selection criteria calculation for radial turbines and bearing loads. Investigating these allows the benefits or penal- ties associated with rotor speed (N) to be analyzed. Besides rotor speed (N), turbine output power (Wout) is another important parameter to consider. Different output powers natu- rally require smaller or larger turbines and correspondingly differ- ent geometries. Such geometry changes can affect the feasibility of designs as manufacturing, strength, or dynamic vibration issues arise. It has been shown that turbomachine designs can be scaled 081008-4 / Vol.139,AUGUST2017 b4 1⁄4 tan1 Ch4 U4 (9) using b4 1⁄4 tan Ch4 1⁄4wU4; 1 n Cm4 1 w (10) 1 Cm4 1⁄4nuU4 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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