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Wang et al. 3 Figure 2. Scheme of the multistage radial inflow turbine system. Table 1. Parameters of radial inflow turbine. uniform total temperature, and flow angles are speci- fied at the inlet of the model. The average static pres- sure is specified at the outlet of the model. The inlet turbulence intensity is set to 5%. The rotation speed of the rotors is set based on the requirements of the operating conditions. The interface between rotating and stationary parts is the ‘‘stage interface’’. The ANSYS CFX solver is adopted to conduct steady-state 3D viscous compressible flow simula- tions, and k–! shear stress transport (SST) turbulence model is used because of its better ability to solve flow separations and adverse gradients in a typical turbo- machinery case. The mass, momentum, and energy conservation equations solved in the present study are written as follows25 ð2Þ Parameters Inlet total pressure, Pin (MPa) Rotational speed, n (r/min) Rotor inlet diameter, Din (mm) Rotor axial length, lAxial (mm) Stage 1 7.00 40,000 135 34 0.10 Stage 2 2.80 40,000 135 34 0.40 Stage 3 1.20 20,000 305 70 0.13 Stage 4 0.40 20,000 305 70 0.53 inlet to outlet of rotor. The detailed definition of is given in the following equation ðlout linÞ @þr U~ 1⁄40 @t ð1Þ outlet height; lAxial is the blade average arc length from inlet to outlet. As shown in Figure 3, it can be found that the rotor blades in stages 2 and 4 present higher value of . It means that these rotors have higher variation rate of blade height from inlet to outlet of rotor. Numerical method Three-dimensional model with single channel is adopted in the present study for each stage. Figure 4 shows the numerical model of the four radial turbines. Considering that collection chambers are adopted for the radial inflow turbines, uniform total pressure, 1⁄4l where lin is the blade inlet height; lout is the blade Axial @ ð U~ Þ þ r U~ U~ 1⁄4 r p þ r þ S~ M @t ð 3 Þ where the stress tensor, , is related to the strain rate by ~~T2~ 1⁄4 rUþ rU 3rU ð4Þ The total energy equation is described as follows @ðhtotÞ@pþr @t @t U~htot 1⁄4r ðlrTÞþr U~ þ U~ S~ M þ S~ E ð 5 ÞPDF Image | radial turbine supercritical compressed air energy storage
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