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52 5. RESULTS Figure 5.15. The time resolved shaft power for the different cases during 3 turbine wheel revolutions. where the velocity ui, density ρ and the enthalpy h is at the inlet boundary. Un is the normal velocity component. The utility factor can also be viewed as an efficiency parameter which reflects the ability of the turbine to extract power from the provided power. A result from the different perturbations at the inlet is that the axial inlet velocity component is different for the different cases, as seen Figure 5.13. This is so due to different absolute pressure at the inlet. Although Case 1 has the largest pressure ratio over the turbine it has the lowest absolute pressure at the inlet and the outlet, since the turbine extracts most energy from the gas for this case. The lowest pressure for Case 1 results in the highest perpendicular velocity at the inlet, and hence, the highest velocity in the volute. This results in the highest velocity into the turbine wheel, as seen Figure 5.16. For all the cases, a coherent structure is created at the inlet to the waste gate channel and it is convected downstream. For Cases 1-4 the vortex from the waste gate channel interacts with the wake downstream of the tongue. For Case 5 the vortex that is created at the inlet to waste gate channel does not interact with the wake downstream of tongue since it is convected downstream at the side of the tongue, as seen in Figure 5.17. In the volute, the strength of this vortex increases due to the radial pressure gradient. These two counter-rotating vortices, shown in Figure 5.18, are meandering in the cross- stream plane which create a non-uniform velocity distribution into the turbine wheel in space and time. The highly swirling motion at the inlet also feeds the wake behind the tongue. This effect can be seen in the energy spectra at a location just down- stream of the tongue. Case 3 has the highest fluctuating energy at a point downstream of the tongue, whereas Case 1 has there the lowest fluctuation energy.PDF Image | Numerical computations of the unsteady flow in a radial turbine
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