# Numerical Study of Endwall Modification with Micro-Scale Ribs in a Turbine Cascade
## 3 Results and Discussions
### Film Cooling Characteristic
Meanwhile, the vertical rib performs better in the axial direction in terms of cooling coverage. Vertical ribs with a 8 mm spacing exhibit  
Figure 6: \(\eta\) of horizontal ribs. better cooling coverage than that of vertical ribs with a 10 mm spacing, indicating that vertical ribs have a more obvious guiding effect on the coolant flow at a small spacing, resulting in better axial cooling coverage for each internal rib channel. Although most of the literature reports that the micro-rib could improve the cooling coverage, the cooling performance in the vicinity of the PS was not observed in this paper, unlike reports in the literature [19; 23]. It is speculated that the difference is caused by the rib height and layout of cooling units, which are different for these papers. In terms of the linear cascade, upstream leakage will not only cool the endwall surface, but also converge on the blade and produce a secondary cooling effectiveness on the SS, which is called phantom cooling. Figure 9 shows the phantom cooling effectiveness on the SS of the original and ribbed endwall. It can be concluded that the phantom cooling performance of the SS was sensitive to the rib types. The original endwall showed moderate cooling effectiveness, which concentrated in the middle \(x/C_{\mathrm{ax}}\) range of the SS under the influence of the secondary flow. The case of horizontal \(s=8\) mm showed a much higher \(\eta\) than that of the \(s=10\) mm case, for the reason that the coolant did not dissipate in the front few rows of the ribs. Although the \(\eta\) of the tilted \(s=8\) mm performed slightly higher than that of the tilted \(s=10\) mm, the distribution of \(\eta\) did not show much difference, which means that the phantom cooling was less sensitive to the rib spacing for tilted ribs. However, both the scope and the magnitude of \(\eta\) for the vertical ribs showed excellent performance compared  
Figure 8: \(\eta\) of vertical ribs. Figure 7: \(\eta\) of tilted ribs. with the above rib types. Actually, the \(\eta\) value of vertical ribs for both rib spacings could reach about 0.8 in some contour regions. The reason for the difference in \(\eta\) among these rib cases is because of the flow guiding effect of the ribs on the coolant, and whether the coolant dissipated before it reached the SS of the blade. For vertical ribs, a smaller rib spacing means that the interference for the secondary flow to the coolant was lowest, so the \(\eta\) of vertical \(s=8\) mm was best. For the tilted ribs, although the coolant could reach the middle region of the endwall passage, but the rib would guide the coolant to the opposite direction, the \(\eta\) of tilted ribs would not perform well regardless of the rib spacing. Finally, the \(\eta\) of horizontal ribs almost depended on the dissipation of the coolant under the influence of ribs, because the flow direction is vertical to the ribs, in which the interference is largest, producing strong interaction between the coolant and the mainstream. Figure 10 shows the \(\eta_{l}\) for the ribbed endwall. At the downstream direction of the slot outlet (0-0.1 x/C\({}_{\text{ax}}\)), the tilted rib and horizontal rib (10 mm) performed better in cooling effectiveness, while that of the horizontal rib (8 mm) was only approximately 0.58. Figure 9: Phantom cooling effectiveness on the SS of blade (LE: leading edge; TE: trailing edge). (**a**) Original; (**b**) Horizontal s = 8 mm; (**c**) Horizontal s = 10 mm; (**d**) Tilted s = 8 mm; (**e**) Tilted s = 10 mm; (**f**) Vertical \(s=8\) mm; (**g**) Vertical s = 10 mm. However, in the range of 0-0.4 \(x\)/\(C_{\rm ax}\), the values of \(\eta_{l}\) for each case showed a sharp decline, and the decline in vertical ribs was weakest. In the range of 0.8-1 \(x\)/\(C_{\rm ax}\), the \(\eta_{l}\) for each case almost coincided, indicating that the coolant on the endwall surface almost dissipated with no obvious cooling effectiveness in this region, which agreed with results shown in Figures 6-8.