Turbulence length scale
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| - | The turbulence length scale, <math>l</math> , is a physical quantity describing the size of the large energy containing eddies in a turbulent flow. | + | The turbulence length-scale, <math>l</math> , is a physical quantity describing the size of the large energy containing eddies in a turbulent flow. |
| - | The turbulent | + | The turbulent length-scale is often used to estimate the turbulent properties on the inlets of a CFD simulation. Since the turbulent length-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 length-scale. The turbulent length-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 [[Standard k-epsilon model|k-epsilon model]] the turbulent | + | In the [[Standard k-epsilon model|k-epsilon model]] the turbulent length-scale can be computed as: |
:<math>l = C_\mu \, \frac{k^\frac{3}{2}}{\epsilon}</math> | :<math>l = C_\mu \, \frac{k^\frac{3}{2}}{\epsilon}</math> | ||
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<math>C_\mu</math> is a model constant which in the standard version of the k-epsilon model has a value of 0.09. | <math>C_\mu</math> is a model constant which in the standard version of the k-epsilon model has a value of 0.09. | ||
| - | ==Estimating the turbulent | + | ==Estimating the turbulent length-scale== |
| - | It is common to set the turbulent | + | It is common to set the turbulent length-scale to a certain percentage of a typical dimension of the problem. For example, at the inlet to a turbine stage a typical turbulent length-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 length-scale can be estimated from the [[hydraulic diameter]]. In fully developed pipe-flow the turbulent length-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) |
Revision as of 10:53, 24 March 2006
The turbulence length-scale, 
, is a physical quantity describing the size of the large energy containing eddies in a turbulent flow.
The turbulent length-scale is often used to estimate the turbulent properties on the inlets of a CFD simulation. Since the turbulent length-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 length-scale. The turbulent length-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 length-scale can be computed as:
is a model constant which in the standard version of the k-epsilon model has a value of 0.09.
Estimating the turbulent length-scale
It is common to set the turbulent length-scale to a certain percentage of a typical dimension of the problem. For example, at the inlet to a turbine stage a typical turbulent length-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 length-scale can be estimated from the hydraulic diameter. In fully developed pipe-flow the turbulent length-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)
