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6 Proc IMechE Part A: J Power and Energy 0(0) Figure 6. Grid validation for the four-stage radial inflow turbine. where y is the distance to the nearest wall and v is the kinematic viscosity and 1 @k@! 10 CDk!1⁄4max 2 !@x @x ,10 ð13Þ !2 j j In the SST model, the proper transport behavior can be obtained by a formulation of the eddy- viscosity a1k vt 1⁄4 maxða1!; SF2Þ ð14Þ where vt 1⁄4 t=. F2 in equation (14) is a blending function similar to F1, which restricts the limiter to the wall boundary layer, as the underlying assumptions are not correct for free shear flows. S is an invariant measure of the strain rate. Figure 7. Geometry of the NASA radial turbine: (a) stator I; (b) rotor I.27 Table 2. Performance comparison for NASA radial turbine. Relative F2 1⁄4 tanhðarg2Þ pffiffiffi arg21⁄4max 2 k;500v 0!y y2! ! ð15Þ ð16Þ Mass flow (kg/s) Total-to-total efficiency (%) Output power (kW) Experiment CFD 2.71 2.70 88.50 90.88 424.30 435.52 error 0.36% þ2.70% þ2.64% The computational mesh for the numerical model is depicted in Figure 5. A structured grid is adopted for the stator and rotor domains. The grid is refined near the wall of the radial turbine and tip clearance of the blade to satisfy the requirements of the turbulence model. Generally, the minimum wall yþ is less than 1.0. Figure 6 shows the grid independence of the four radial turbines. It can be found that the total–total isentropic efficiency of stage 1 is almost unchanged as the grid element increases from 1.59 106 to 2.50 106. In order to save the computing resource, the 1.59 106 grid elements are adopted for the com- putations of stage 1, and grid elements of 1.27 106 are adopted for stage 2. For the radial inflow turbine with unshrouded rotor, more grid elements are adopted in the tip clearance region. It can be seen in Figure 6 that the total–total isentropic efficiency of stage 3 remains invariant as the grid element increases ents are adopted for stages 3, and elements are adopted for stage 4. Results and discussion 1.62 106 grid CFD: computational fluid dynamics. from 1.99 106 to 2.60 106, so 1.99 106 grid elem- Validation of the computational fluid dynamics model Up to now, experiemental data on the radial turbine operating in supercritical condition are limited, and the directly experiment validation of performance and flow structure in the supercritical radial turbine is difficult. In the present study, the National Aeronautics and Space Administration (NASA) com- pact inflow turbine is selected to validate the model for its similar operational principle and structural style, detailed geometric parameters and complete experimental data in the existing literatures.PDF Image | radial turbine supercritical compressed air energy storage
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