7 - Simplified schemes

Summary

Rationale and organization

Models for the turbulent stresses and scalar fluxes have been in widespread use since the 1960s, incorporated within CFD codes of a wide range of types and capabilities. Over this period the vast majority of computations have been made using turbulence models simpler than second-moment closure. Quite clearly, such simpler models must deliver satisfactory predictions of some of the flows of interest – for otherwise they would be discarded. This chapter is devoted to such reduced models. The position adopted is that, of course, such simplification makes sense, provided it is made with an appreciation of what has been lost in the process.

This truism applies as much to the numerical solver as to the physical model of turbulence employed, for one would surely never use a three-dimensional, elliptic, compressible-flow solver if one's interests were simply in computing a range of axisymmetric, unseparating boundary layers in liquids. But, if we proceed in the reverse direction, while it is not usually possible to apply a simple numerical solver to flows well beyond the solver's capability, it is all too easy to assume that a turbulence model that functioned very satisfactorily in computing simple shear flows, will perform equally as well in computing complex strains or in the presence of strong external force fields. That is why it is seen as important that simple (or simpler) turbulence models should be arrived at by a rational simplification of the full second-moment closure (having regard for the particular features of the flow to be computed) rather than by adopting some constitutive equation as an article of faith.