A dynamic model for the Lagrangianaveraged NavierStokesα equations
Abstract
A dynamic procedure for the Lagrangianaveraged NavierStokesα (LANSα) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a selfconsistent way from the data contained in the simulation itself. In order to derive this model, the incompressible NavierStokes equations are Helmholtz filtered at the grid and test filter levels. A Germanotype identity is derived by comparing the filtered subgridscale stress terms with those given in the LANSα equations. Assuming constant α in homogenous directions of the flow and averaging in these directions result in a nonlinear equation for the parameter α, which determines the variation of α in the nonhomogeneous directions or in time. Consequently, the parameter α is calculated during the simulation instead of a predefined value. The dynamic model is initially tested in forced and decaying isotropic turbulent flows where α is constant in space but it is allowed to vary in time. It is observed that by using the dynamic LANSα procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kineticenergy decay are captured more accurately as compared with the LANSα simulations using a fixed α. In order to evaluate the applicability of the dynamic LANSα model in anisotropic turbulence, a priori test of a turbulent channel flow is performed. It is found that the parameter α changes in the wall normal direction. Near a solid wall, the length scale α is seen to depend on the distance from the wall with a vanishing value at the wall. On the other hand, away from the wall, where the turbulence is more isotropic, α approaches an almost constant value. Furthermore, the behavior of the subgridscale stresses in the nearwall region is captured accurately by the dynamic LANSα model. The dynamic LANSα model has the potential to extend the applicability of the LANSα equations to more complicated anisotropic flows.
 Publication:

Physics of Fluids
 Pub Date:
 July 2005
 DOI:
 10.1063/1.1965166
 arXiv:
 arXiv:physics/0408113
 Bibcode:
 2005PhFl...17g5106Z
 Keywords:

 47.27.Gs;
 47.27.Eq;
 47.10.+g;
 47.11.+j;
 47.60.+i;
 Isotropic turbulence;
 homogeneous turbulence;
 Flows in ducts channels nozzles and conduits;
 Physics  Fluid Dynamics
 EPrint:
 17 pages, 17 figures