17-10-2012, 05:57 PM
Turbulence models in CFD
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INTRODUCTION
The abbreviation CFD stands for computational fluid dynamics. It represents a vast area of numerical analysis in the field of fluid’s flow phenomena. Headway in the field of CFD simulations is strongly dependent on the development of computer-related technologies and on the advancement of our understanding and solving ordinary and partial differential equations (ODE and PDE). However CFD is much more than “just” computer and numerical science. Since direct numerical solving of complex flows in real-like conditions requires an overwhelming amount of computational power success in solving such problems is very much dependent on the physical models applied. These can only be derived by having a comprehensive understanding of physical phenomena that are dominant in certain conditions. [1], [8]
Why turbulence?
Ideal turbulence model
Solving CFD problem usually consists of four main components: geometry and grid generation, setting-up a physical model, solving it and post-processing the computed data. The way geometry and grid are generated, the set problem is computed and the way acquired data is presented is very well known. Precise theory is available. Unfortunately, that is not true for setting-up a physical model for turbulence flows.
Complexity of the turbulence model
Complexity of different turbulence models may vary strongly depends on the details one wants to observe and investigate by carrying out such numerical simulations. Complexity is due to the nature of Navier-Stokes equation (N-S equation). N-S equation is inherently nonlinear, time-dependent, three-dimensional PDE.
Turbulence could be thought of as instability of laminar flow that occurs at high Reynolds numbers (Re). Such instabilities origin form interactions between non-linear inertial terms and viscous terms in N-S equation. These interactions are rotational, fully time-dependent and fully three-dimensional. Rotational and three-dimensional interactions are mutually connected via vortex stretching. Vortex stretching is not possible in two dimensional space. That is also why no satisfactory two-dimensional approximations for turbulent phenomena are available.
Classification of turbulent models
Nowadays turbulent flows may be computed using several different approaches. Either by solving the Reynolds-averaged Navier-Stokes equations with suitable models for turbulent quantities or by computing them directly. The main approaches are summarized below.