Computations of Turbulent Flow over a Backstep

Abstract

*† Numerical simulations of a turbulent flow over a backward facing step are performed. The governing equations are solved by the finite volume code Cobalt. Fast two-dimensional Reynolds-Averaged and more computationally intensive three-dimensional Detached-Eddy Simulations are carried out, with Menter’s Shear Stress Transport turbulence model. Mean flow quantities such as pressure, velocity and skin friction coefficients are accurately predicted by both techniques. Pressure fluctuations can only be captured by the threedimensional computation. The dominant frequency is in good agreement with existing experimental data, and power spectral analysis is consistent with empirical relations found in the literature. I. Introduction ALL pressure fluctuations beneath a turbulent boundary layer are associated with noise generation and can lead to structural vibrations. It is desirable to understand the nature of pressure fluctuations to limit their impact in several engineering applications such as commercial airplanes and turbines. Turbulent boundary layer measurement has been the subject of numerous investigations, and precious information can be obtained from experiments [1-7], which can be used to validate available semi-empirical models. W With the advent of Computational Fluid Dynamics, numerical tools have been developed to study and understand a wide range of turbulent flow fields. There are mainly three approaches for the computation of turbulent flows. The Direct Numerical Simulation (DNS) approach is an “exact method” in the sense that the original governing equations are solved without any modifications, or filtering process. The second approach for turbulent flow computation is the Large Eddy Simulation (LES) [8]. Large scales are numerically computed, whereas the small scales are modeled by simple eddy viscosity models, known as Sub Grid Scale models (SGS). Algebraic models are sufficient, because the imperfections of these simple models should not greatly affect the solution. The two methods described above are very costly in terms of computational time and storage requirement. A more affordable method consists in averaging the Navier-Stokes equations in time, resulting in the Reynolds Averaged Navier-Stokes (RANS) equations. A turbulence model is required to close the system. Several different turbulence models exist, ranging from simple algebraic models to more sophisticated multi-equation models [9-13]. A hybrid method has been recently developed to take advantage of existing techniques. The Detached Eddy Simulation (DES) combines the RANS approach in regions of thin boundary layer where no separation occur, because this does not constitute a real challenge for RANS and switches to LES in region of massive separation [14]. This method allows a reduction of the prohibitive cost of LES method and therefore, the solution of a turbulent flow field can be obtained within a reasonable computational time.