Encyclopaedia Index

2.1 Principles of selection

(a) The NOKFOS principle

NOKFOS is an acronym which stands for "NObody Knows FOr Sure" ; and it focusses attention upon a principle which must be borne in mind by all who seek answers to the question: "Which turbulence model should I use"?

Turbulence models have been seriously studied for little more than fifty years; and not until the last three decades have:

been sufficient to make scientific progress perceptible.
Moreover, much of the recent progress has been negative in tendency, leading to new doubts, where confidence had too soon prevailed.

(b) Experimental validation

That model should be chosen, for a particular application, which has been shown to generate the most correct predictions, by comparison with reliable experimental data FOR SIMILAR SITUATIONS.

It is practicable to follow this rule only for very well-researched applications, for example steady, uniform-property, two-dimensional boundary layers on smooth walls.

The greater the departure from the conditions of the experiments, whether through time-dependence, property variations, three-dimensionality, or roughness, the less certainly reliable become the predictions of the tested model.

Thereafter, re-circulation, swirl and other body-force effects, combustion and the presence of more than one phase, all lower the credence that should be placed in turbulence-model prediction.

When the flow is a complex one, for example that in a combustion chamber, even tests for the precise geometry in question cannot fully validate a model: there are too many independent variables.

(c) Physical plausibility

Often therefore the question to be asked is: which of the available models is the most plausible on physical grounds?

For example, for swirling turbulent flows those models should be preferred which allow for the "flinging outwards" of fast-moving or denser eddies and the centripetal tendency of the others.

Similarly, a model which allows a "probability density function" to be deduced from a plausible physical hypothesis should be preferred to one which simply presumes the shape of the function.

In 1967 a model was invented which differed from Prandtl's energy model of 1945 only in replacing the gradient-type energy- diffusion term by one proportional to the local shear stress.

Comparisons with data, at the first Stanford "Turbulence Olympiad", led some observers to favour the model highly. However, the model was always physically implausible; and it is now never used.

(d) The accuracy required

Even where experimental validation and physical plausibility may be thought to concur, some attention should be given to the question of the level of accuracy required.

For example, a Reynolds-Stress Model might be considered on the above grounds for computing the turbulent boundary layer on a turbine blade.

However, since the superiority of the model has been proven only for steady flows, whereas the flows in turbines are inherently unsteady (because of stator-rotor interactions), the expense and difficulty of using the Reynolds-Stress Model may not be worth incurring.

High accuracy in only one part of a system of calculations need not be sought in all circumstances.

(e) Practicability

The more complex (and perhaps therefore physically realistic) the model, the finer must be the computational grid, and the greater the expense.

For example, a grid which is fine enough for a prescribed-effective- viscosity model may not be fine enough for a k-epsilon model; for the latter requires squares of velocity gradients to be accurately computed.

Further, some models require knowledge of the distance from the wall; and this may be expensive to compute when many variously- shaped objects are immersed in the fluid.

Therefore, in the circumstances arising in engineering, the choice must usually be made of the most practicable model rather than of that favoured by researchers.

What is written below concerning LVEL illustrates this principle.