Development of a Nonlinear Model for Subgrid Scale Turbulence and it's Applications
AdvisorWarsi, Z. U. A.
The present work addresses the fundamental question involving the modeling of subgrid-scale turbulence as a function of resolved field. A new-nonlinear model has been developed from the constitutive equation of subgrid stresses extending the Reynolds stress model proposed by Warsi. The time scale is expressed in terms of subgrid scale kinetic energy as opposed to strain rate tensor. Effort has been made to identify the terms appearing in the modeled subgrid stresses with "Reynolds term", "Leonard's term" and "cross term". The physical nature of these terms can be best understood from the triadic interactions in wave number space. Understanding these three terms leads to decouple the complex nature of the subgrid stresses. Modeling of these terms separately helps to capture the physics of the problem accurately. The turbulent field is assumed to be isotropic and Kolmogrov's hypothesis is used. The model coefficients are expressed as universal constants for Gaussian filter so as to satisfy the dissipation criteria in inertial subrange. Further dissipation term is assumed to be isotropic and equilibrium condition is used. Although the definition of the subgrid stress terms becomes less clear and separate for smooth filter, an attempt has been made to compare the stress terms with the exact definition obtained for sharp cut-off filter. An estimate of the backscatter of energy can be obtained from the Eddy-Damped Quasi Normal Markovian (EDQNM) theory. The model coefficients thus obtained are tested with results of plain homogeneous shear layer. The model results have been compared with the mixed-nonlinear model and Smagorinsky model. A priori test shows that new-nonlinear model has a good correlation with Smagorinsky model, which in turn has good correlation with experimental results, and has the behavior of the mixed-nonlinear model. The above model has been used for solving two-dimensional flow over backward facing step as a test case. The numerical model solves the vertically hydrostatic boundary layer equation. The top boundary is assumed to be a free surface. Terrain following coordinate system has been used. Because of the non-negativity of the subgrid scale dissipation term i.e. backscatter of energy, the nature of the solution is stochastic. The deterministic solution is obtained by clipping the dissipation term. The results are compared with the experimental data of Kim et al. Good agreement with the experimental data is obtained for the velocity profile and SGS kinetic energy. The reattachment point obtained is at 5.2h (h is the step height), which is less compared to 6h as suggested by other authors. This discrepancy may be due to the assumptions involved in the equations, which is being solved. The model is further extended for the diffusion of scalar variables and to include the buoyancy effect. It is implemented to explore the hydrostatic flow over three dimensional elliptical mountain ridges, where Boussinesq approximation is used for variable density. The flow characteristics have been studied for the various aspect ratios of the mountain and Froude?s number (Nh/U) based on Brunt-Vaisala frequency (N). The phenomenon of upstream blocking and Lee-vortices generation has been studied.