- Fig.I-35, is based upon number of solved differential equations. The simplest model is called algebraic, because it does not work with differential equations at all. It is suitable only for computing flows in which turbulence
is in equilibrium. It is not capable of taking into account spatial transport phenomena.
In many flows, there are regions in which turbulence predicted by the algebraic model is immediately seen to be predicted wrong: note that it predicts turbulent viscosity
proportional to local
transverse gradient of time-mean velocity. Basically, this is a plausible prediction since turbulence may develop and permanently exist only in flows with such a gradient. nevertheless, downstream of a grid there mey be a strong (though gradually decaying) turbulence even in absence of any gradient: turbulence is transported by advective mechanism. Note also that algebraic model predicts zero turbulence on a pipe axis (where there is zero transverse gradient of time-mean velocity), which is wrong: turbulence is transported there by diffusion effects.
It is possible to include these transport phenomena into account with the one-equation model, Fig.I-40.
Its weakness is that it is necessary to know in advance spatial distribution of turbulence length scale. The solved partial differential equation of the transport equation type generates, as its solution, information about velocity
scale of turbulent motions. Unfortunately, information about length scale distribution is known only in rather simple flows.
Whenever information about the length scale is not available, as is usual in all more complex flows, it is appropriate to use the two-equation model, Fig.I-41, first proposed by Kolmogorov, though presently used in the form which is based upon ideas of Chou (1945) and Rotta (1951).
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| Fig.I-41 |
This generates the spatial distribution of the length scale as the solution of the second transport equation (usually, however, indirectly).
Although the use of two-equation models is still no mean problem, it may be called the most promising model for engineering turbulent flow calculations for very near future.
It fails only in those situations, where turbulent vortices posses some preferential orientation in space.
 |
Andrei Kolmogorov
Born: 25 April 1903 in Tambov, Russia
Died: 20 Oct 1987 in Moscow, Russia
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Such an orientation requres more complex description of turbulence than is possibvle by the mere scalar quantity. It is then necessary to compute turbulence with the Reynolds stress model . It requires solving a partial differential equation of the trynsport type for each component of the Reynolds stress tensor.
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This is page Nr. I11 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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