# Efficiency of Pulsating Base Bleeding to Control Trailing Edge Flow Configurations
## 2 Computational Set-Up  
The geometry considered in this work is the same studied by [PERSON] et al. [19] that we reproduce here for clarity.  
A simplified trailing edge flow is achieved through a zero-cambered airfoil of 160 mm chord (\(c\)), with an aspect ratio value of 8 (defined as \(c/D\), \(D=0.020\) m being the trailing edge thickness). Boundary layer separation at the leading edge has been avoided using a smooth Haack Series [20] nose shape. The mass flow employed on the base bleed is first discharged in a stagnation plenum inside the airfoil, which is connected to the base region by a thinner passage covering a third of its width (\(b=0.3D\)). The model is confined between two parallel walls separated by 230 mm, and the inlet and outlet boundaries are placed at enough distance to avoid any interference of the boundary conditions. Subsonic conditions are imposed to recover a Mach and Reynolds number of \(\mathrm{M}=0.34\) and \(\mathrm{Re}_{\mathrm{c}}=1.53\times 10^{6}\), respectively. As no thermal aspects are covered in this analysis, a total temperature of 257 K is set at the free stream and a static temperature of 250 K is imposed on the base bleed flow.  
Without any flow actuation, pairs of vortices would detach from the trailing edge with an associated frequency related to the incoming flow velocity and the trailing edge thickness, under a characteristic Strouhal number of \(\mathrm{St}=0.287\). These vortices separate in an alternating manner from upper and lower sides, producing an oscillating behavior of the wake and the base region (Figure 1).  
Flow calculations in this work are computed with the Finite Volume DLR-TAU Code [21] (TAU). Based on a three-dimensional finite volume scheme approach, TAU is a state-of-the-art compressible flow solver used on the aerospace industry to accurately calculate flow solutions from the low subsonic to the hypersonic flow regime. On time-dependent solutions, such as TAU, employ a dual time-stepping scheme coupled with a multigrid acceleration. Due to its performance in compressible flow, turbulent fluxes are modeled with the [PERSON]'s 2003 Shear Stress Transport version of the \(k\)-\(\omega\) closure model [22]. The flow is considered to be fully turbulent from the leading edge, according to the suggestions of the high-pressure turbine community. The spatial discretization of the domain is done using a non-structured quadrilateral mesh (Figure 2), with localized refinements on the areas of interest, keeping \(y+\) values below unity so the boundary layer is fully resolved. Both mesh sensitivity and influence of the inlet turbulence intensity were evaluated in previous works [19], ensuring spatial discretization independence on the results and discarding sensitive results to changes in the turbulent inlet conditions. Furthermore, convergence of the periodic unsteady flowfield was ensured following the recommendations established by [PERSON] and [PERSON] [23].  
Figure 2: Detail of the grid spatial discretization used on the numerical analysis. General view (**a**) and trailing edge mesh details (**b**). Image partially reproduced from [PERSON] et al. [19]. Copyright © 2021, published by Elsevier Masson SAS. All rights reserved.