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50 5. RESULTS Figure 5.13. Axial and secondary velocity components at the inlet. boundary divided by the axial bulk velocity. The strength of the Dean vortices is defined as the area averaged value of the secondary component divided by the axial component at the inlet. The strength of the secondary flow is obtained from LES-computations of the pulsatile flow in a four to one exhaust manifold. The evaluated data has been gathered for the last 4 of 20 revolutions of the turbine. This corresponds to 36 blade passages. This data have been used for the computing the time averages of the different parameters. In Figure 5.15 Table 4. Shaft power, available power at the inlet, isentropic efficiency, utility factor and pressure ratio. Case PSHAFT PINLET ηis κ PR (kW) (kW) 1 5.02 82.18 0.66 2 4.34 82.14 0.66 3 4.41 82.26 0.64 4 4.40 82.12 0.66 5 4.05 82.35 0.64 0.061 1.41 0.053 1.34 0.054 1.36 0.053 1.35 0.048 1.32 the time resolved shaft power for the different cases is shown. The shaft power fluctuates with a frequency that corresponds to the blade passage frequency. Fluctuations with lower frequencies are also present for all cases, depending on flow unsteadiness in the volute. In Table 4 the time averaged shaft power and two different ways of expressing the efficiency are given. For the time mean value of the shaft power, there are differences between the cases. The time mean shaft power for Case 5 is 19% lower than for Case 1, which is greater than the estimated numerical uncertainty. For Cases 2-4, the differences in the shaft power as compared to Cases 1 or 5 are of the same order as the numericalPDF Image | Numerical computations of the unsteady flow in a radial turbine
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