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Turbulence length scale

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The turbulence length scale, l , is a physical quantity describing the size of the large energy containing eddies in a turbulent flow.

The turbulent lenght-scale is often used to estimate the turbulent properties on the inlets of a CFD simulation. Since the turbulent lenght-scale is a quantity which is intuitively easy to relate to the physical size of the problem it is easy to guess a reasonable value of the turbulent lenght-scale. The turbulent lenght-scale should normally not be larger than the dimension of the problem, since that would mean that the turbulent eddies are larger than the problem size.

In the k-epsilon model the turbulent lenghts-scale can be computed as:

l = C_\mu \, \frac{k^\frac{3}{2}}{\epsilon}

C_\mu is a model constant which in the standard version of the k-epsilon model has a value of 0.09.

Estimating the turbulent lenght-scale

It is common to set the turbulent lenght-scale to a certain percentage of a typical dimension of the problem. For example, at the inlet to a turbine stage a typical turbulent lenght-scale could be say 5% of the channel height. In grid-generated turbulence the turbulent length-scale is often set to something close to the size of the grid bars. In pipe-flows the turbulent lenght-scale can be estimated from the hydraulic diameter. In fully developed pipe-flow the turbulent lenght-scale is 7% of the hydraulic diamater (in the case of a circular pipe the hydraulic diameter is the same as the diameter of the pipe)

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