# Effects of Bulk Flow Pulsations on Film Cooling with Two Sister Holes
## 1 Introduction
However, when the main flow velocity is disturbed by flow interactions, shock waves, turbulence generated in the combustion chamber, or passing shock waves on the turbine blade, the disturbance patterns are more similar to sinusoidal waves than pulses [9]. In an experimental study, [PERSON] et al. [9] showed how sinusoidal mainstream pulsations influence film cooling. They reported that for a small \(L/D\) ratio, increasing the pulsation frequency from 0 to 32 Hz at the blowing ratio, \(M\) of 0.5 decreased the adiabatic film cooling effectiveness and increased the iso-energetic Stanton number ratio. [PERSON] et al. [15] reported the effect of vane passage vortex generation on film cooling by using a pressure-sensitive paint. The strength of the vortex was adjusted by changing the attack angle of the main flow to the delta wing. They found that a stronger vortex resulted in increased the mixing, leading to a decreasing \(\eta\). [PERSON] et al. [16] showed a fractal solution to study the Kozeny-Carman constant and permeability for fibrous porous media. They stated that if the particle diameter was increased, the absolute permeability was increased and if the tortuosity fractal dimension was increased, the Kozeny-Carman constant was increased, however, the dimensionless permeability was decreased. [PERSON] et al. [17] proposed that a fractal theory of porous media in order to quantify the porous media's effective electrolyte diffusivity. The analytical results showed a good match with the experimental data. In this study, an analysis was performed using a large-eddy simulation (LES). Although a LES incurs higher computational cost than Reynolds-averaged Navier-Stokes (RANS), the RANS approach cannot accurately predict complex flow interactions because it involves ensemble-averaging the turbulent fluctuations in the flow. By contrast, the LES approach resolves large-scale turbulent eddies, enabling accurate predictions of complex flows [2,18]. [PERSON] et al. [19] found that an LES model showed considerably more spreading of the coolant jet compared with RANS turbulence models and that the LES results were similar to real film cooling fields. [PERSON] et al. [20] found that at the low blowing ratios, the effectiveness of the film cooling decreased rapidly as the coolant travelled downstream, despite high film cooling effectiveness around the cooling hole. This can be attributed to the small mass flow rate of the coolant. Furthermore, low blowing ratios cause the detrimental ingestion of the hot mainstream gas into the hole [9; 21]. [PERSON] [22] reported that the overall film cooling effectiveness increases with the blowing ratio up to the blowing ratio of 0.6. He observed that when the blowing ratio exceeds 0.85, the overall effectiveness decreases because of the separation of the coolant jet from the wall. Therefore, in this study, the average blowing ratio was fixed at 0.5. A sinusoidal pulsation in the main flow causes the difference between the static pressures around the inlet and the exit of the hole to oscillate, which in turn makes the coolant jet oscillate. Therefore, in the current study, a sinusoidal waveform was simultaneously applied to the main flow inlet and the plenum inlet with the same frequency. By performing an LES, the current study investigated the effect of oscillating the main flow at various Strouhal numbers on film cooling with cylindrical triple holes on a flat plate. The numerical results were compared with the numerical and experimental results for a single cylindrical hole on a flat plate. As a baseline, the effect of the main flow pulsation on contours of film cooling effectiveness and dimensionless temperature was first investigated for single-hole and triple-hole systems. Next, the time-averaged effectiveness of the film cooling was compared between these two systems. Instantaneous contours of \(\eta\) on the wall were also investigated. Contours of the time-averaged velocity magnitude in the cooling hole were compared between the single-hole and triple-hole systems.