Threedimensional mass transfer from nearendwall surfaces

The contour and surface plots of mass transfer Sherwood number on the pressure surface are shown in fig. 4.6 and fig. 4.7, respectively, for different mainstream Reynolds numbers and turbulence intensities. Prom these plots we can observe that the unsteady Taylor-Gortler vortices induce uneven mass transfer rates on the pressure surface away from the endwall for the low mainstream turbulence level (Tu=0.2%) cases with various Reynolds numbers. The higher mass transfer rates near the pressure surface-endwall junction can be attributed to the pressure side corner vortices(lpC and Vplc), of which the leading edge corner vortex generates a small semi-circular high mass transfer zone (Sp/C < 0.25) near the junction of the leading edge and the endwall. This high mass transfer zone increases in size at higher Reynolds number. For the high mainstream turbulence intensity (Tu=12.0%) case, the Taylor-Gortler vortices seem to disappear on the surface and the effects of corner vortices near the endwall are limited to the region very close to the endwall.

In fig. 4.8 and fig. 4.9, local Sh and Sh/ReJx are plotted along the span starting from the endwall at different curvilinear locations along the pressure surface, for different Reynolds numbers and turbulence intensities respectively. In fig. 4.8, higher mass transfer rates are obtained at higher mainstream Reynolds numbers and the mass transfer rates descends quickly close to the leading edge (Sp/C < 0.04). Further downstream the effect of Reynolds number is not obvious. We can also observe that the effect of corner vortices starts from Sp/C = 0.04, where a maximum mass transfer rate occurs at the endwall (Z/C = 0.0) and a minimum mass transfer rate appears at about Z/C = 0.05. Upstream of Sp/C = 0.04, the trend is reversed, with minimum mass transfer at the endwall, perhaps due to the stagnant flow at the leading edge and the endwall junction. The Taylor-Gortler vortices induced unsmoothness away from the endwall can also be clearly seen. At the high turbulence level of 12%, the effects of both corner vortices and Taylor-Gortler vortices are not apparent. For the normalized Sh numbers in fig. 4.9, we can find that the curves for the low turbulence intensity cases collapse to almost one near the endwall. Higher mainstream turbulence intensity increases the mass transfer rates up to 100% from the lower turbulence cases downstream of Sp/C > 0.09.

For the suction surface, fig. 4.10 and fig. 4.11 shows the contour and surface plot of Sherwood numbers for different mainstream Reynolds numbers and turbulence intensities, respectively. The effect of secondary flows on the mass transfer near the endwall can be identified from the similar large triangular region of high mass transfer in all cases. This triangular region remains almost the same for all low turbulence cases with Tu = 0.2% but becomes smaller for the high mainstream turbulence case. A mass transfer peak around Ss/C = 0.4 — 0.5 at the junction of the suction surface and the endwall is perhaps induced by the interaction between the suction leg of the horseshoe vortex (Vsh) and the suction surface when the horseshoe vortex turns around the blade and lifts off from the endwall. It is also clear that the transition to turbulence becomes earlier as the mainstream turbulence intensity and Reynolds number increases.

The local Sh and Sh/ReJx are plotted against the Z/C at different locations of Ss/C in fig. 4.12 and fig. 4.13 for different cases, respectively. The mass transfer rates also decrease steadily from the leading edge, and for Ss/C < 0.09, the effect of mainstream Reynolds number is more evident in fig. 4.12. As mentioned earlier, the sharp peak at Ss/C = 0.41 and Ss/C = 0.50 at the endwall is caused by the the suction leg of horseshoe vortex (Vsh), whose effect near the endwall starts from Ss/C = 0.09. Upstream of Ss/C = 0.09, the mass transfer has a minimum at the endwall, perhaps due to the stagnant flow near the leading edge. Downstream of Ss/C = 0.61, we can observe a second peak in the triangular zone of high mass transfer, this peak is probably caused by the passage vortex (Vp) separating from the suction surface. After Ss/C = 0.94, the second mass transfer peak becomes flat and a third one appear at Ss/C = 1.15, which probably shows the effects of the complex vortices including the suction leg of the horseshoe vortex (Fsc) and the wall vortex (Vwip). Also downstream of Ss/C = 0.94, mass transfer for the high turbulence case is much higher than those of low turbulence cases outside the triangular region due the earlier transition. In fig. 4.13, the normalized Sh for different Reynolds numbers collapse to one, except for the case with highest Reynolds number, which may have errors in measurement at Ss/C = 0.94 and Ss/C = 1.07. The effect of high mainstream turbulence level is only obvious close to the leading edge and downstream of Ss/C = 0.94 after transition.

The overall three-dimensional effects on mass transfer on the pressure surface and the suction surface are plotted in fig. 4.14 and fig. 4.15. We can see that from the figures the three-dimensional effect is not very obvious on the pressure surface for both low and high mainstream turbulence intensities, except around Sp/C = 0.2. On the suction surface, the three- dimensional effect are very strong, resulting in higher mass transfer rate from Ss/C = 0.5 up to transition for both low and high mainstream turbulence intensity cases. However, after the turbulent transition, the mass transfer rate goes down in the three-dimensional region for both cases.

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