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LARGE-EDDY SIMULATION OF A LAMINAR SEPARATION BUBBLE: THE SMAGORINSKY AND DYNAMIC MODELS

The principal objective of the present simulation is to find the ability of Large-eddy simulation (LES) to resolve the transition mechanism of a laminar separation bubble apart from making a comparative assessment of subgridscales (SGS) models. The Smagorinsky model modified by the low-Reynolds number correction of Voke (1996) and the dynamic model are used to account for the nonresolvable subgrid stresses. Two values of the Smagorinsky constant Cs have been tested. Results from the dynamic model are closer to the DNS data compared to those from the Smagorinsky model. The simulation shows that no significant growth of fluctuations is observed in the first 27 percent of bubble length. Three-dimensional motion and non-linear interactions leading to break down to turbulence occur in the second half of the mean bubble length. The simulation also illustrates that the transition process is characterized by break down of longitudinal streaks, which appear via vortex stretching mechanism. The near wall characteristics develop far downstream indicating a very slow relaxation towards an equilibrium turbulent boundary layer. INTRODUCTION When a flow at relatively low Reynolds Number encounters an adverse pressure gradient, it may separate from the solid surface. The boundary layer leaves the surface approximately in a tangential direction forming a wedge shaped separated region. The separated but still laminar flow is highly sensitive to the external disturbances, which cause the flow to undergo transition. The transition region is located at the outer boundary of the separated shear layer; the thickness of the shear layer grows rapidly and it may finally reattach to the solid surface as a turbulent layer. The point where the laminar boundary layer separates from the solid surface is known as the point of separation and the point where the turbulent boundary layer reattaches to the surface again is known as reattachment point. The volume occupied by the regions of separated laminar flow and the turbulent flow is known as laminar separation bubble. The structure of a time averaged laminar separation bubble, given by Horton (1968) is reproduced in Fig. 1. The existence of a laminar separation bubble was first recognized by Jones (1934). The work was further carried out by Gault (1957). The most notable advancement in the understanding of bubble structure and behaviour came with the work of Gaster (1968). He investigated a large number of bubbles produced on a flat surface. A numerical study of 2-D laminar separation bubble using N-S equations was done by Briley (1971). Pauley and co-workers (1990, 1993) first pointed out the unsteady nature of laminar separation. Pauley’s analyses were 2-D and the effects of small-scale turbulence were completely neglected. Alam and Sandham (2000) performed a direct numerical simulation (DNS) of the incompressible N-S equations to study flows where laminar boundary-layer separation is followed by turbulent reattachment. In a recent work of Sarkar and Voke (2006), the physical mechanism of transition of an inflectional boundary layer over the suction surface of a highly cambered low-pressure turbine blade under the influence of periodically passing wakes was studied in detail The appearance of a laminar separation bubble is very common in case of low Reynolds number flows on wings and blades. The performance of almost all aircraft is influenced by the appearance of the laminar separation bubble. A separation bubble is often formed on the suction surface of a LP turbine. The boundary layer development depends on the growth and breakdown of this bubble. The flow transition over the separation bubble is complex and has been investigated by several researchers. DNS carried out by Spalart and Strelets (1997) and Alam and Sandham (2000) explain the transition mechanism apart from the flow structures. However, despite the incredible computing power available today, the cost of DNS is prohibitive and LES may be an alternative. The present study is an effort to explore the viability of simulating the laminar separation bubble using LES. Simulations have been performed using the Smagorinsky model modified by the low-Reynolds number correction of Voke (1996) and the dynamic model. Two values of the Smagorinsky constant Cs have been tested. Results obtained from the simulations are compared to the available DNS data. Sixth International Symposium on Turbulence and Shear Flow Phenomena Seoul, Korea, 22-24 June 2009