Stability analysis of large-scale structures in highly confined turbulent wakes

Accurate characterization of wall confinement effects in turbulent wakes is crucial for proper de sign of wind tunnel experiments. Blockage effects may significantly alter vortex shedding frequencies, modify aerodynamic forces, and promote the formation of complex coherent structures [1]. Whereas unsteady Reynolds-averaged Navier-Stokes (RANS) simulations are generally adequate for the evalua tion of the aerodynamic forces in turbulent bluff-body wakes, this method is generally unreliable for the analysis of large-scale wake structures and the evaluation of the shedding frequency. In this work, we carry out global stability analyses to characterize coherent structures in confined turbulent wakes. The stability analyses rely on a matrix-free algorithm based on the direct integration of the linearized Navier-Stokes equations (LNSE) from a random initial condition. The LNSE are imple mented within an in-house solver embedded in OpenFOAM, to deal with the complex geometry under study. Physically meaningful stability modes are extracted from instantaneous LNSE velocity data using dynamic mode decomposition. The stability tool is applied to the analysis of the wake behind a thick plate in a wind tunnel of width W ([2], figure 1, left panel), at a Reynolds number Re = 32000 (based on the bulk velocity and trailing-edge thickness H). Uncertainties associated with the choice of the base flow are quantified using different steady/time-averaged solutions of the RANS equations (obtained by different turbulence models). In addition, quasi-laminar (ql) and frozen-viscosity approaches are both considered. The present SST results (figure 1, right panel) are in excellent agreement between the refer ence data in [2], which demonstrates the validity of the present stability tool. Finally, we determine the effect of the finite wind tunnel width on the shedding frequency by considering different H/W values. [1] R. Mondal and M.M.Alam. Blockage effect on wakes of various bluff bodies: A review of confined flow. Ocean Engineering, 286:115592, 2023. [2] M. Carini, C. Airiau, A. Debien, O. L´eon, and J. O. Pralits. Global stability and control of the confined turbulent flow past a thick flat plate. Physics of Fluids, 29(2):025103, 2017.