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3-D Inviscid Analysis of Radial Turbine Flow

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3-D Inviscid Analysis of Radial Turbine Flow ( 3-d-inviscid-analysis-radial-turbine-flow )

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would be higher than the experimental mass flow rate. But, the rate,estimated by the DENTON code (0.2352 kg/s for the blunt leading-edge case and 0.239 kg/s for the rounded leading-edge case) is very close to the experimental value of 0.2372 kg/s due to the total pressure losses discussed earlier. The case with the reduced rotor inlet flow angle has an increased mass flow rate of 0.2646 kg/s because itproduces less total pressure losses. Velocities Figure 11 shows quasi-secondary velocity vectors on cross-channel sur­ faces. The primary flow direction.is chosen arbitrarily to be the streamwise grid direction in determining the secondary flow vectors. The velocity vectors shown inthe figure are the projections of these secondary velocity vectors on the cross-channel surfaces constructed for the computation. Computed results indicate that the average magnitude of the quasi-secondary flow vectors on the cross-channel surfaces isabout 17 percent of the average meridional velocity in the blade region. A fraction of the average meridional velocity is indi­ cated in the figure to show the relative strength of secondary flow in the rotor flow passage. As shown in the figure, the secondary flow in the first half of the blade passage is mostly in the direction from the suction surface tothepressuresurface. But,inthemiddleofthepassageatJ=39where the flow passage begins to turn in the tangential direction in addition to the continuous turn in the meridional plane, a weak single passage vortex is devel­ oped and its strength is increased for the remaining blade passage. The evol­ ution of the passage vortex is attributable to the highly three-dimensional rotor passage and rotation of the blade. Velocity components projected on the meridional surfaces are presented in figure12. Itcanbeobservedfromthefigurethatfluidenteringtheblade region on the suction surface migrates towards the shroud, while that entering on the pressure surface migrates towards the hub. Similar results are reported by Bosman and Highton (ref. 12). For comparison, figure 13(a).shows the meri­ dional streamlines predicted by a quasi-three-dimensional analysis (ref. 14), figure 13(b) shows the streamlines on the suction surface predicted by the DENTON code, and figure 13(c) shows the streamlines on the pressure surface predicted by the DENTON code. The large deviations inflow angle between the fully three-dimensional and quasi-three-dimensional analyses are evident, especially in the exducer region. Velocity vectors are plotted on blade-to-blade surfaces in figure 14. Streamlines predicted on the hub and tip surfaces are shown in figure 15. It can be observed that fluid entering the blade at midpitch on the hub migrates towards to the pressure surface in the first half of the blade passage, but, in the latter half of the passage, it remigrates back toward the suction sur­ face. Fluid entering the blade at'midpitch on the shroud section migrates toward the pressure surface throughout the entire blade passage. This result qualitatively agrees with the result of Bosman and Highton (ref. 12). A contour plot of the relative critical velocity ratio on a midspan blade to blade surface ispresented infigure 16. The critical velocity ratio is the ratio of fluid velocity to critical velocity, which is equal to the velocity of sound at the critical condition. It shows a rapid change in the critical velocity ratio around the leading edge on the suction side. region of sonic flow appears on the suction side leading edge with a peak .7 A small

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