# Numerical Study of Endwall Modification with Micro-Scale Ribs in a Turbine Cascade
## 3 Results and Discussions
### Heat Transfer Characteristic
It is worth noting that the high-\(h\) region was distributed at each outlet of the rib channel, which proved the combination effect of the rib-like vortex and PV. The \(h\) of the vertical case is shown in Figure 14. Along the axial direction, the first high-\(h\) region was shown at the inlet of endwall, which was also the beginning position for the ribs. The mainstream impacted the rib and thus formed the vortex, like the horseshoe formed in the front of the LE. Similar to the tilted case, the vertical rib was axially straight to the LE. Thus, the stagnation line, caused by the horseshoe vortex, was present in both LEs of the two blades. It is worth noting that the high-\(h\) region, caused by the PV, was not as obvious as the other rib cases, which indicated that the PV was weakened by the vertical rib and, thus, it is beneficial for the cooling design for this rib layout. In addition, another high-\(h\) region appeared near the throat of the SS, which was dominated by the rib-like vortex instead of the corner vortex. Figure 12: \(h\) of the original case and horizontal rib case. (**a**) Original; (**b**) Horizontal s = 8 mm; (**c**) Horizontal s = 10 mm. The intensity of the rib-like vortex was a combination of the local mainstream, secondary flow, and rib geometry. In this paper, the rib geometry consists of two factors: rib spacing and rib type (exactly the layout orientation, which is relative to the local direction of the mainstream). The influence brought by the rib would spread in the downstream direction of the cascade, which would lead to the aerodynamic loss at the outlet of the cascade. The total pressure loss coefficient (\(C_{\text{pt}}\)) is defined as Equation (7). \[C_{\text{pt}}=\frac{P_{t,m}-P_{t,local}}{P_{t,m}-P_{s,out}} \tag{7}\]  
Figure 15 shows the \(C_{\text{pt}}\) at the position of \(x/C_{\text{ax}}=1\) for the original endwall and ribbed endwall. The PV of the upper endwall and lower endwall could be reflected in the contour whether for the original endwall or the ribbed endwall. The difference between them was mainly reflected here. Generally, the \(C_{\text{pt}}\) of the ribbed endwall increased for the magnitude and range in the position of the PV for the lower endwall. For the horizontal rib case, the PV was lifted. This is because the disturbance of the mainstream, which was caused by the rib, was more serious as the rib orientation was nearly parallel to the mainstream. Figure 14: \(h\) of the vertical case. (**a**) Vertical s = 8 mm; (**b**) Vertical s = 10 mm. Figure 13: \(h\) of the tilted case. (**a**) Tilted s = 8 mm; (**b**) Tilted s = 10 mm. To present the quantized aerodynamic loss, the laterally averaged \(C_{\text{pt}}\) is shown in Figure 16. In general, the original endwall exhibited better aerodynamic characteristics compared to the others. For the horizontal case, the major aerodynamic loss focused on the position around 0.3-0.6 z/H, which was larger than those of the other ribbed cases. This was mainly caused by the combination effect of the upper PV and lower PV, which was lifted by the rib-to-mainstream disturbance. For the tilted case, the major aerodynamic loss focused on the position around 0.2-0.3 z/H, which indicated that the intensity of PV was enhanced by the tilted rib. For the vertical cases, the aerodynamic loss performed better than other ribbed cases, despite the little difference between the vertical and tilted cases. To present the comprehensive performance of endwall modification with the micro-scale rib, the area-average of \(\eta\) and \(h\) with the original endwall and ribbed endwall are shown in Figure 12.0 The increments and decrements in the ribbed endwall are highlighted with better and worse performance, respectively, compared with the base case (original endwall).