Fig.I-35 Hierarchy of basic
models of turbulence. The most important models in each
category are in the green colour boxes.
Such relations are collectively called

Models of turbulence

These are, of course, mathematical models, represented by a set of equations, not real physical objects. There is no ideal turbulence model. What is available is a hierarchy (Fig.I-35) of models of different complexity. More complex models make possible more precise solutions - at a price of more effort and more (computer) time. More comple models also require more extensive initial information (in particular information about values of various simulation constants), which is not always available. It is expedient to select always just as complex model as is needed for a particular problem. As a consequence, turbulence modelling requires knowledge at least of the basic properties of individual models and their ranges of suitable applicability.

Fig.I-36
Simple models assume that it is possible to characterise turbulence - as proposed already by Boussinesq - by the turbulent viscosity, a scalar quantity, Fig.I-36. The problem is that in contrast to molecular viscosity of laminar flows this turbulent or eddy viscosity is not a constant of a given fluid - but a property of a particular flow: in practice this
Fig.I-37
means that turbulent viscosity is a variable quantity with sometimes very complex spatial distributions in the flowfield. Were this distribution known in a solved problem, it would be possible to compute the turbulent flow with no more difficulty than in the laminar cases. Unfortunately, to compute this distribution in more complex flowfields may be a very difficult task.

Note that vortical fluctuating motions cause momentum transfer between fluid layers moving with different velocities - and similarly as the molecular momentum transport discussed in Fig.D-10, this appears as frictional, shear force between the layers. Fig.I-37 evaluates the magnitude of momentum transport caused by a typical turbulent eddy, of size , rotating with characteristic circumferential velocity . When the result is compared with the expression

Fig.I-38
for the turbulent shear stress

according to Fig.I-38, it becomes apparent that it is possible to evaluate the turbulent viscosity as the product of the two quantities, and . Basic models of turbulence differ in the way these quantities are evaluated, Fig.I-39.



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This is page Nr. I10 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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