# Optimization Design of Lattice Structures in Internal Cooling Channel of Turbine Blade
## 4 Results and Analysis
### Validation of Mechanical and Heat Transfer Performances
#### 4.2.2 Validation of Heat Transfer Performance  
Nusselt number (_Nu_) was used to evaluate heat transfer performance of the XLS channel. Relevant numerical simulation was developed to obtain values of _Nu_ for both the initial model and the optimization models to verify accuracy of the mathematical optimization model as follows.  
As shown in Figure 2, the XLS model was established for numerical simulation. The grid of XLS was finished by ICEM CFD. The commercial software CFX18.0 was used for simulation, and a standard \(k\)-\(\epsilon\) model was used for turbulent model. The pressure based on simple algorithm was adopted, and the second-order upwind scheme was selected.  
The boundary conditions were as follows. The inlet was a mass flow inlet of \(7.67\times 10^{-3}\) Kg/s, the inlet \(Re\) was 10,000, the inlet air temperature was set at 300 K, the turbulent degree was 5%, and the heat flux \(q\) of the heated wall was constant at 3000 W/m\({}^{2}\). The data processing methods involved were as follows:  
The definition of \(Re\):  
\[Re=\frac{D_{h}u_{m}\rho}{\mu}=\frac{4\dot{m}}{\pi D_{h}\mu} \tag{34}\]  
The definition of average _Nu_:  
\[Nu=\frac{qH}{(T_{w}-T_{air})k_{f}} \tag{35}\]  
where \(d_{h}\) is the hydraulic diameter of the lattice channel, \(d_{h}=50.33\) mm; \(q\) is target heat flux; \(T_{W}\) is target surface temperature; \(T_{air}\) is inlet airflow temperature; \(H\) is height of channel; \(\lambda\) is air thermal conductivity; \(\mu\) is aerodynamic viscosity, and \(\dot{m}\) is mass flow rate.  
In order to verify the reliability of the model, the experimental data of XLS from [PERSON] et al. (2018) was selected. The \(Nu\) values under different turbulent models are shown in Figure 12. It can be seen that the values of the standard \(k\)-\(\epsilon\) turbulent model were very consistent with the experimental values, with an error of 9.6%. Therefore, the standard \(k\)-\(\epsilon\) was used in the subsequent numerical simulation.  
Simulation results for fluid flow and heat transfer of the XLS channel were obtained. Figure 13a-c reveal that the XLS had a great disturbing effect on the air flow in the channel, and the flow velocity in the rear along the flow direction was significantly reduced. For the initial model, because the diameter of the member was smaller than that of the optimal structure, the low velocity area formed behind the member was small. For the Op-I model and the Op-II model, due to the increase of member diameter, airflow disturbance in the channel was all strengthened. Figure 13d-f show that the distribution of \(Nu\) of the optimal  
Figure 12: Validation of model.  
model was more uniform than that of the initial model, and Figure 13g shows that the \(Nu\) of the initial model obtained by the numerical calculation was close to the calculated value obtained by the optimized fin method. Moreover, pressure drops under the condition of \(Re=10\),000 were 302.179 Pa, 294.323 Pa, and 302.558 Pa for the initial model, the model of Op-I, and the model of Op-II, respectively. The pressure drops of these three models were similar, and acceptable for the LS channel which had only five simple LS cores. Therefore, pressure drop was not considered as a main parameter in this study.  
Therefore, the mathematical optimization model was accurate and reasonable for the heat transfer performance.