Notes on Computational Fluid Dynamics: General Principles

Chapter 7 Reynolds-Averaged Turbulence Modelling

For CFD to be useful, it must calculate the flow, forces, heat transfer, etc. with sufficient accuracy. The accuracy of any calculation is always compromised by various approximations.

First, there are approximations from the numerical methods that are employed. Discretisation schemes, described in Chapter 3 , affect accuracy which can be improved by reducing the size of cells and time step, at the cost of increased solution times.

The algorithms and solvers, described in Chapter 5 , are a further source of numerical approximation. Linear solvers are generally iterative with tolerances that balance computational cost against accuracy of the solution. Algorithms may include loops with a fixed number of iterations that limits the overall solution convergence.

Boundary conditions, described in Chapter 4 , are applied as part of the configuration of the CFD simulation. Invariably there is some level of approximation in the way the conditions represent the problem of interest. The approximation is physical, not numerical, and includes everyday examples such as:

• setting a fixed value condition with a uniform value, e.g. on velocity at an inlet;
• applying a zero gradient condition, e.g. to pressure at a wall boundary;
• imposing the direction of inflow, e.g. with the inlet-outlet-velocity condition, Sec. 4.15 .

Beyond the numerical methods and boundary conditions, are the models that describe fluid dynamics. The governing equations and basic models in Chapter 2 are accurate for laminar flows with modest speeds and heat transfer. However, as the flow physics becomes more complex, the models become increasingly approximate.

It is clear from Chapter 6 that turbulence is highly complex, so turbulence modelling is often a major source of error in a CFD solution. It exemplifies the observation of statistician George Box that all models are wrong.¹ He advises that we should seek “an economical description of natural phenomena” and “simple but evocative models”.

It is with that advice we present some of the Reynolds-averaged turbulence models commonly used in CFD. The models take the form of transport equations for turbulence fields, typically turbulent kinetic energy and dissipation rate.

The models are accompanied by advice on specification of the inlet and initial conditions for the fields. Particular attention is given to the modelling of the flow within turbulent boundary layers at wall boundaries.

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