# Numerical Study of Endwall Modification with Micro-Scale Ribs in a Turbine Cascade
## 1 Introduction  
For modern gas turbines, the cascade faces increasing thermal loads. These thermal loads are affected by many factors: cascade geometry, mainstream conditions, and so on. To prevent the harm from thermal loads, film cooling was used to protect the turbine cascade. In addition, due to the installation of the blade, there is an upstream slot and a slashface on the endwall surface. The coolant will flow out of these gaps and cool the endwall. Early research carried out by [PERSON] et al. [1] indicated that it was feasible for a numerical calculation to simulate the flow in turbine cascades with the correct turbulence model and numerical setup. [PERSON] and [PERSON] [2] studied the leakage from a combustor-turbine gap and presented a pattern of cooling effectiveness (\(\eta\)). [PERSON] et al. [3] thought that the cross-flow led the coolant to the suction side (SS). [PERSON] and [PERSON] [4] measured the heat transfer of the endwall with the modification of the leading edge (LE) and the endwall. [PERSON] et al. [5] experimentally studied film and impingement cooling on the endwall. Their results showed that film cooling was affected by the passage vortex (PV), thus improving the cooling performance of the endwall, close to the SS. [PERSON] et al. [6] carried out experimental and numerical research on an endwall with a first-stage blade in a turbine cascade. They found that the heat transfer of the endwall corresponded to the distribution of secondary flows. [PERSON] et al. [7] carried out a numerical study on the upstream interrupted slot and found that the blowing ratio and the distance between the LE of the blade and the slot-affected \(\eta\). Phantom cooling research has increased in recent years. An experimental investigation was carried out by [PERSON] et al. [8], and they found that the coolant from blades could cool the endwall surface using a proper compound angle. Similarly, [PERSON] et al. [9] carried out a numerical investigation on the phantom cooling of an endwall with the coolant from the LE of a blade. In addition, [PERSON] et al. [10] experimentally studied the effect of the coolant from the endwall on the phantom cooling of the blades, and the results showed the cooling coverage on the SS roots. [PERSON] et al. [11] carried out a sensitivity analysis on a non-axisymmetric endwall and analyzed which position most affected the aerodynamic characteristics for passage. [PERSON] et al. [12] numerically studied the effects of a cooling jet in a special position to counter the horseshoe vortex of an LE leg. [PERSON] et al. [13] carried out experimental research on a contour endwall with upstream holes. The results showed that the negative effect of the PV on cooling could be inhibited when the mass flow ratio (_MFR_) of the upstream coolant was more than 0.75%. [PERSON] et al. [14] carried out an investigation of film holes and the mid-passage gap (MPG) on a turbine endwall, using experimental and numerical methods. They found that the leakage from the MPG demonstrated little impact on the coolant from upstream film holes. [PERSON] et al. [15] also studied film cooling patterns with upstream leakage and found that it benefited the film cooling from the film holes. [PERSON] et al. [16] numerically studied lobe-shaped holes using a large eddy simulation (LES) to track the flow field of film cooling. [PERSON] et al. [17] used the response surface method to analyze the cooling characteristics of a stream-cooled blade. There are complex secondary flows in the cascade that affect aerodynamic, cooling, and heat transfer characteristics. In recent years, a novel endwall modification, the micro-scale rib, was proposed to improve the flow in the cascade. [PERSON] et al. [18] considered incidence effects on an endwall with micro-scale ribs. The results showed that the ribs effectively weakened the intensity of the horseshoe vortex and PV and thus enhanced the cooling performance. [PERSON] et al. [19] numerically studied small-scale structures, which are the ribs, on the endwall.