# Large Eddy Simulation of Film Cooling with Bulk Flow Pulsation: Comparative Study of LES and RANS
## 4 Results and Discussion
### Film Cooling Effectiveness  
Figure 2b illustrates that several RANS models overpredicted the centerline effectiveness in the steady state, and results of the realizable k-\(\epsilon\) model differed the least from the experimental data. Even the Reynolds stress model, which solves more equations to reflect the anisotropy of turbulence, more severely overpredicted the centerline effectiveness than the realizable k-\(\epsilon\) model after \(x/D=5\). The results of the k-\(\omega\) model differed the most from the experimental results among the compared turbulence models. Based on these results, the realizable k-\(\epsilon\) model was adopted for the unsteady RANS, in which pulsation was applied to the main flow.  
It has been reported that the film cooling efficiency generally decreases when there is pulsation in the bulk flow. In particular, it has been reported that the film cooling efficiency decreases by about half when the pulsation frequency and blowing ratio are 32 Hz and 0.5, respectively [12; 15; 26], as observed in this study as well. As illustrated in Figure 3, both LES and URANS reproduced the decrease in film cooling efficiency upon the application of pulsation, although the RANS realizable k-\(\epsilon\) model overpredicted the centerline effectiveness. According to the figure, the RANS model overpredicted the centerline effectiveness by approximately 57% for 0 Hz and by approximately 105% for 32 Hz, whereas the centerline effectiveness obtained in LES differed by only about 5% relative to the experimental data.  
When the 32 Hz pulsation is applied, the amplitude of the pressure difference between P\({}_{1}\) and P\({}_{2}\) increased because of large phase shifts between them [12]. Then, the amplitude of the coolant velocity oscillation increased, and more jet lift-off was generated periodically, resulting in less effective film cooling. At 32 Hz, the computed cooling effectiveness of the centerline film was more accurate than that at 0 Hz because the jet lift-off effect was considerably stronger than the other vortex effects, such as horseshoe vortex or CRVP, which are detrimental to the film cooling effectiveness. Moreover, LES yielded a good prediction of jet lift-off. As shown in Figure 3, as the main flow passed downstream,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Grid**} & **Number of Cells in the** & **Number of Cells in the** & **Number of Cells in the** & **Number of Cells in the Main** & **Total Number of Cells (Million)** \\  & **x Direction** & **y Direction** & **z Direction** & **Block (Million)** & **Cells (Million)** \\ \hline First & 240 & 50 & 32 & 0.40 & 1.02 \\ Second & 248 & 60 & 48 & 0.73 & 1.35 \\ Third & 284 & 80 & 50 & 1.15 & 1.77 \\ Fourth & 302 & 94 & 56 & 1.60 & 2.22 \\ Fifth & 308 & 110 & 64 & 2.18 & 2.80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Specifications of mesh arrangements in crossflow block for mesh sensitivity test.  
Figure 3: Time-averaged centerline effectiveness at 0 and 32 Hz.  
the centerline effectiveness decreased, regardless of the frequency, because of the generation of the turbulence and mixing between the main flow and the jet.