## 3 Numerical Method and Parameter Definition  
In this paper, numerical calculations are conducted to obtain the internal flow structure, heat transfer and friction characteristics by discretely solving the continuity, momentum, and energy equations, which are performed in ANSYS CFX. The coolant is air and boundary conditions are as follows: Inlet velocity determined by \(Re\), and the inlet temperature of 290 K; outlet pressure of 1 atm; constant heat flux on the endwalls of main channel considering that the outside walls of turbine blade are exposed to the high temperature gas environment; adiabatic boundary for the other walls. And all walls are no slip boundaries. It is worth noting that, for the OC4 case, the mass flow outlet boundary condition was applied on the lateral slots exits, and the mass flowrate of six slots was half the total mass flowrate of coolant. Mesh is generated in ICEM platform, and the grid dependence study is conducted based on the dimple-protrusion case at the \(Re\) of 10,000 to obtain a moderate mesh number. Three grid schemes with the node number of 1283219, 2827536, and 5766132 are used, and heat transfer coefficient and pressure drop are obtained by numerical calculations, listed in Table 2. It can be found that the relative deviations of heat transfer coefficient and pressure drop between the grid scheme 2 and grid scheme 3 are 0.08% and 0.09%, respectively, which has met the accuracy requirement of heat transfer simulations. Therefore, the grid scheme 2 is adopted in this investigation. Figure 4 presents the mesh model of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Outlet Configuration** & **Surface Structure** & \(Re\) (10\({}^{4}\))** \\ \hline \multirow{4}{*}{Part I} & OC1 & & \\  & OC2 & & \\  & OC3 & smooth & 1/3/5/10 \\  & OC4 & & \\  & OC5 & & \\ \hline \multirow{2}{*}{Part II} & OC4 &
\begin{tabular}{c} dimple \\ protrusion \\ dimple-protrusion \\ \end{tabular} & 1/3/5/10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case settings of this investigation. Figure 3: Dimple/protrusion structure and arrangement in the trailing edge channels. dimple-protrusion channel. Evidently, the O-topology is applied in the dimple/protrusion area to improve the mesh quality, and the grid is densified near the channel walls for more accurate flow and heat transfer results in the boundary layer. This investigation is carried out within the \(Re\) range of 10,000-100,000, which is in the condition of completely turbulent flow, thus the turbulence models were validated and carefully selected. The experimental data in reference [15], which is close to the OC1 case, was extracted and compared with the numerical results by Standard \(k\)-\(\varepsilon\), RNG \(k\)-\(\varepsilon\), \(k\)-\(\omega\) and SST \(k\)-\(\omega\) models, shown in Figure 5. It can be found that the Nusselt number of the \(k\)-\(\omega\) model and the SST \(k\)-\(\omega\) model exhibits the similar variation as the experimental data, and the SST \(k\)-\(\omega\) model presents a smaller relative deviation, within 8.2%. Moreover, literatures [14; 22; 25] also demonstrate that the SST \(k\)-\(\omega\) model gives high simulation accuracy in the fluid flow and heat transfer of blade trailing edge. Accordingly, the SST \(k\)-\(\omega\) model is applied in this paper. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Grid Scheme** & **Node Number** & \(\mathbf{h\) (W-m\({}^{-2}\).K-\({}^{-1}\))} & **Error (\%)** & \(\mathbf{\Delta P/l\) (Pa-m\({}^{-1}\))} & **Error (\%)** \\ \hline
1 & 1283219 & 48.31 & 0.56 & 483.87 & 0.59 \\
2 & 2827536 & 48.58 & 0.08 & 486.73 & 0.09 \\
3 & 5766132 & 48.62 & / & 487.18 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Grid dependence study with dimple-protrusion case, \(Re\) = 10,000. Figure 4: Mesh model of dimple-protrusion channel. Figure 5: Comparisons between the numerical results of the OC1 case and experimental data in reference [15]. The parameters involved in this study are introduced as follows.