AIAA - 2002 - 0426 Combining the Baldwin Lomax and Smagorinsky Turbulence Models to Calculate Flows with Separation Regions

The present paper proposes a combination of the Baldwin Lomax and Smagorinsky turbulence models in order to compensate the de ciencies each one of these simple models exhibits. The proposed combination, named BLS, uses the turbulent viscosity of the Baldwin Lomax in the vicinity of walls, and a blend of Baldwin Lomax and Smagorinsky viscosity from the end of the inner layer (Baldwin Lomax) into the core ow region. Results obtained for a sphere, a cylinder and a cube indicate that the proposed model yields acceptable results, and represents an attractive alternative when transient simulations with wall e ects can not be performed with either RANS or LES. Introduction Over the last half century, a wide range of turbulence models has been developed to solve the closure problem of the Reynolds Averaged Navier-Stokes equations (RANS). However, it is di cult to nd an individual model that can be used reliably over the complete range of turbulent ow cases. These models can be classi ed according to their complexity as: algebraic models or zero equation models (i.e. based on Prandtl's mixing length hypothesis) one equation models, two equation models (i.e. based on the equation for the turbulence kinetic energy) and Reynolds-stress models. An extensive review of these models has been made by Wilcox [1, 2]. Another approach to solve the NavierStokes equations is via so-called Large Eddy Simulation (LES), which assumes that once the inertial scales of the ow have been captured by a su ciently ne grid, the even shorter (sub-grid) wavelengths can be modeled. This inherently transient approach has been reviewed in detail by Mason [3]. RANS are obtained using a time averaging process, and hence, in principle, are only suitable for stationary problems. However, RANS can be extended to transient problems if the period of the mean (stationary) solution is several orders of magnitude larger than the turbulent uctuations of the ow. If this condition is not met, RANS cannot be applied for transient problems (a typical example being atmospheric ows). LES, on the other hand, is a space averaging process and therefore applicable to transient ows for resolving part of the turbulent scales. The limitation is due to the grid size: scales smaller than the grid-size have to be modeled. Many variations exist on closure models for the unresolved scales, from variations of the classic Smagorinsky hS2 [4, 5] to Monotonically Integrated LES (MILES) c Copyright by the authors. Published by the AIAA with permission.