Numerical Investigation of the Separated Flow over a Smoothly Contoured Ramp

Large Eddy Simulation (LES) and Reynoldsaveraged Navier-Stokes (RANS) calculations have been used to predict the development, separation, reattachment and downstream recovery of the flow over a smoothly contoured ramp. The statistically two-dimensional upstream flow separates along the ramp surface and then reattaches downstream on a flat section. A canonical flatplate turbulent boundary layer at a momentum thickness Reynolds number 1100, and having a boundary layer thickness , is introduced four ramp lengths upstream of the onset of curvature. Subgrid-scale (SGS) stresses in the LES are closed using the dynamic eddy viscosity model of Germano et al. (1991). RANS calculations of the steady-state solution are performed using two leading models: Spalart-Allmaras (Spalart-Allmaras 1994) and (Durbin 1991). Mean flow predictions obtained using all the models agree well with the experimental measurements of Song et al. (2000). Boundary layer detachment occurs along the curved section ( ) with reattachment at roughly . The primary turbulent shear stress sharply increases in the separated region and LES predictions of the shear stress development are accurate. RANS estimations of the shear stress are below the data in the separated region, though reasonable further downstream. INTRODUCTION AND OBJECTIVES Separated boundary layers are a challenging subset of flows that may be generally classified as ‘non-equilibrium’. Non-equilibrium boundary current address: Center for Simulation of Advanced Rockets, University of Illinois, Urbana, Illinois 61801, USA layers are the norm, rather than the exception, in engineering applications. The importance of additional length scales to describing the flow and/or a significant imbalance between production and dissipation are two features which characterize these flows. An adverse pressure gradient boundary layer approaching separation develops an inflection point, the height of which is an additional important length scale. Turbulent stresses, for example, develop large peaks around the inflection point and boundary layer recovery following reattachment should be expected to be sensitive to this length scale. These and other features of separated flows substantially challenge predictive methods. The vast majority of engineering predictions are obtained from solutions of the Reynolds-averaged NavierStokes (RANS) equations. In flows not far from equilibrium, the boundary conditions that define large scale structures remain nearly unchanged and the leading RANS models are typically adequate. In separated flows, however, RANS models often yield mixed results (e.g., see Apsley and Leschziner 1999), providing one rationale for use of techniques such as Large Eddy Simulation (LES). In LES, the large, energy-containing scales of motion are resolved on the mesh and only the small, subgrid scales are modeled. LES predictions are less sensitive to modeling errors than their RANS counterparts. This feature should be an advantage in prediction of flows far from the calibration range of RANS models and in regimes with multiple perturbations (e.g., in pressure gradient, streamline curvature, roughness, etc.). Assessment of simulation techniques for predicting separated boundary layers is complicated by the fact that there is relatively strong coupling between the freestream and boundary layer. This in turn increases the sensitivity of the flow to parameters not directly connected to the turbulence model and may not allow one to easily isolate the cause of discrepancies between numerical simulation and experiment. Therefore, it is useful in any study directed towards refined evaluation of techniques and models that careful evaluation of a baseline case be established. One of the overall aims in this work is prediction of the effect of Reynolds number on separated boundary layers (see also Song and Eaton 2001 in this volume). In the present contribution the flow at moderate Reynolds number is predicted using LES and RANS in order to assess the accuracy of each technique as well as to investigate some of the underlying characteristics of the flow. The particular flow under consideration is the statistically twodimensional boundary layer which separates over a smoothly contoured ramp (Figure 1). The location of boundary layer detachment is not fixed by the geometry and the flow provides a reasonably welldefined platform for investigating the processes of reattachment and downstream recovery. Experimental measurements from Song et al. (2000) are used to evaluate the predictions.