Solver Study: Turbulent Flow Models

Posted by : Unknown Thursday 26 December 2013

Turbulence

Turbulence or turbulent flow is a flow characterised by random and chaotic fluid flow with unexpected property changes.

Turbulence Models

A turbulence modelling is a computational procedure to close the system of mean flow equations. For most engineering applications it is unnecessary to resolve the details of turbulent fluctuations. Turbulence models allow the calculation of the mean flow without first calculating the full time-dependent flow field. we only need to know how turbulence affected the mean flow.

The classical turbulence models are based on the Reynolds Averaged Navier-Stokes equations (RANS) :

One equation model: Spalart-Allmaras

Two equation model: -> k-epsilon (Standard, RNG and realizable)
-> k-omega
Seven equation: Reynolds stress model (RSM)

Spalart-Allmaras one equation model:

This model solves a single conservation equation (PDE) for the turbulent viscosity. It contains both connective and diffusive transport terms as well as expressions for the productive dissipation of turbulent viscosity.

It was developed for the use in unstructured codes in the aerospace industry. It gives accurate results for attached wall-bounded flows and flows with mild separation and recirculation. however it gives improper results for massively separated flows, free shear flows and decaying turbulence.

Can be used for:

Drag prediction with mild turbulence
Wing parameter calculation for mild separation conditions

K epsilon 2 equation model:

The transport variable used in the equations is the turbulent kinetic energy. The second transported variable in this case is the turbulent dissipation (epsilon). The K-epsilon model has been shown to be useful for free-shear layer flows with relatively small pressure gradients. Similarly, for wall-bounded and internal flows, the model gives good results only in cases where mean pressure gradients are small; accuracy has been shown experimentally to be reduced for flows containing large adverse pressure gradients. It has 3 variations :

Standard k epsilon model: Good for simple simulations
Realisable k epsilon model : Improved performance for flows involving boundary layers under strong adverse pressure gradients or separation, rotation, re circulation and strong streamline curvature
RNG k epsilon model : It offers improved accuracy in rotating flows, favoured for indoor air simulations. better results for rotating flow and effect of swirl on turbulence

It is a really simple model to implement and leads to stable calculations that converge easily and gives reasonable predictions for many flows.

although it is not favored for rotating and swirling flows.

k omega 2 equation model

It is another 2 equation model similar to k epsilon model which solves 2 additional PDE's resulting in a faster converging solution. however it is not widely used because it might give errors(An assumption based on trial and error)

Reynolds stress seven equation model

RSM closes the Reynolds-Averaged Navier-Stokes equations by

solving additional transport equations for the six independent

Reynolds stresses. It is a good model for accurately predicting complex flows. Accounts for streamline curvature, swirl, rotation and high strain rates.

The rate of convergence is low but the results are accurate and it can handle complex flows well

Wall treatment in turbulent models

A wall treatment is the set of near-wall modelling assumptions for each turbulence model. The wall functions are a set of semi empirical functions used to satisfy the physics of the flow in the near wall region. Turbulence is affected in many ways by the presence of the wall through the non slip condition that must be satisfied at the wall. Four areas in the near wall region are defined, the laminar sub-layer, the blending region, the log law region and the outer region. Each region has a different effect on turbulence. In ansys Fluent they are of 4 types :

Standard wall functions : A wall treatment is the set of near-wall modelling assumptions for each turbulence model.
Non-equilibrium wall function : When the near-wall flows are subjected to severe pressure gradients, and when the flows are in strong non-equilibrium, which means that the turbulence production term and the dissipation term are not equals, the results given by the standard functions are not satisfactory enough and the non equilibrium wall function allows for better calculations.
Enhanced Wall Functions : The enhanced function in FLUENT are used to achieve near wall modelling approach having the accuracy of the standard two layer approach for fine meshes and at the same time not degrading the results for the wall function meshes. In order to do so the enhanced wall functions are combined with the two layer model.