# Thermal Fatigue Life Prediction of Thermal Barrier Coat on Nozzle Guide Vane via Master-Slave Model
## 4 Thermal Cycle Analysis and Life Prediction of NGV.  
### Temperature Field Analysis  
In general, the temperature curve of the thermal shock test is a series of trapezoidal waves, thus it is difficult to simulate the heat transfer process considering the time-varying momentum and temperature. As the heat transfer rate of gas is much larger than that of metals [18], the heating process of hot gas was neglected in the numerical simulation. With respect to the simulation study, a typical gas cycle profile is shown in Figure 9.  
According to the heating cycle, the inlet temperatures of the heating stage and cooling stage were 1310 K and 300 K, respectively. Based on the steady state conjugate heat transfer simulation, the heat transfer boundary conditions were obtained. The convection heat transfer coefficient is:  
\[h=\frac{q}{T_{\rm sp}-T_{\rm aw}} \tag{13}\]  
Figure 8: Thermal fatigue test and simulated data [14,37].  
Figure 7: Simulation results of the top coat (TC) layer in ceramic metal tube. (**a**) Maximum von-Mises stress in TC layer; (**b**) Strain contour of 2 \(\upmu\)m.  
Figure 9: Typical gas cycle profile of the thermal fatigue test [38].  
where \(q\) is the wall heat flux; \(T_{\text{aw}}\) is the wall temperature; and \(T_{\text{sp}}\) is the mean temperature at the inlet.  
Through different combinations of wall temperature and mean temperature as listed in Table 6, the convection heat transfer coefficients of different domains and stages were calculated. The convective heat transfer coefficient of the heating and cooling stages are shown in Figure 10.  
As revealed in Figure 10, the high-speed heat transfer regions were located on the leading edge, trailing edge, and the center of the inner surface of the master model, respectively. The convection heat transfer coefficient at the leading edge was larger because the leading edge was directed against the flow direction of the hot gas, and the kinetic energy and internal energy were directly converted to surface temperature. At the trailing edge, the high-temperature gas flowed along the surfaces of both the suction side (SS) and pressure side (PS), then mixed to form a strong turbulence intensity. The increase in the turbulent energy increased the heat transfer rate. In addition, the convective heat transfer coefficient of the heating stage was larger than that of the cooling stage due to the high gas speed in a high-temperature environment.  
Based on the acquired convective heat transfer coefficient of the heating and cooling stages, the master model was applied to the thermo-elastic coupling calculation of the NGV for 168 s under the thermal cycle, where the heat fluxes at the upper and lower surface were 10,000 w/m\({}^{2}\), referring to the solid rim [39]. The variation trend of the surface temperature field is shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Domain** & **Fatigue Test Cycle** & \(T_{\text{aw}}\) & \(T_{\text{sp}}\) \\ \hline \multirow{2}{*}{Hot gas} & Heating stage & 300 K & 1310 K \\  & Cooling stage & 1000 K & 300 K \\ \multirow{2}{*}{Cooling air} & Heating stage & 300 K & 500 K \\  & Cooling stage & 1000 K & 500 K \\ \hline \hline \end{tabular}
\end{table}
Table 6: Temperature parameters.  
Figure 11: _Cont._  
Figure 10: Convection heat transfer coefficient of the heating and cooling stages. (**a**) Heating stage; (**b**) Cooling stage.  
As shown in Figure 11, the surfaces of the leading edge and trailing edge were heated first, and then reached the maximum temperature quickly. The two areas corresponded to regions A and B in the master model in Figure 4a. In the heat transfer process in Figure 11b, the surface temperature of the NGV rose rapidly toward a stable value after 15 s.