07-08-2012, 04:15 PM
Turbulence Models
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Introduction
Turbulent flows are characterized by fluctuating velocity fields
These fluctuations are too computationally expensive to simulate directly in practical engineering calculations.
Instead, the instantaneous (exact) governing equations can be time-averaged, resulting in a modified set of equations that are computationally less expensive to solve.
However, the modified equations contain additional unknown variables, and turbulence models are needed to determine these variables in terms of known quantities.
A turbulence model is a computational procedure to close the system of the mean flow equations.
Two-equations model employs two additional partial differential equations (PDE). One PDE for relating the turbulence length scale and one for relating the turbulence velocity scale.
The simplest ``complete models'' of turbulence are two-equation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined.
It is an unfortunate fact that no single turbulence model is universally accepted as being superior for all classes of problems
The choice of turbulence model will depend on considerations such as the physics encompassed in the flow, the established practice for a specific class of problem, the level of accuracy required, the available computational resources, and the amount of time available for the simulation.
The Standard Modelby Launder and Spalding
The standard k - ε model is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε).
Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations.
Limitations of model
Poor performance for flows with large extra strain (e.g. curved boundary layer, swirling flow).
The predictions are not good for three-dimensional flows.
The model needs modifications to include anisotropy, curvature and rotation effects, and turbulence amplifications through the shock wave.
The Standard ModelWilcox Model
The standard model is an empirical model based on model transport equations for the turbulence kinetic energy (k) and the specific dissipation rate ω
It incorporates modifications for low-Reynolds-number effects, compressibility, and shear flow spreading.
The Wilcox model predicts free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wall-bounded flows and free shear flows.