# Turbulence length scale

(Difference between revisions)
 Revision as of 17:27, 6 May 2006 (view source)Jola (Talk | contribs)m (Turbulent length scale moved to Turbulence length scale)← Older edit Revision as of 12:35, 15 May 2008 (view source) (→Estimating the turbulent length scale)Newer edit → Line 9: Line 9: $C_\mu$ is a model constant which in the standard version of the k-epsilon model has a value of 0.09. $C_\mu$ is a model constant which in the standard version of the k-epsilon model has a value of 0.09. - ==Estimating the turbulent length scale== + ==Estimating the turbulence 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. + It is common to set the turbulence length scale to a certain percentage of a typical dimension of the problem. For example, at the inlet to a turbine stage a typical turbulence length scale could be say 5% of the channel height. In grid-generated turbulence the turbulence length scale is often set to something close to the size of the grid bars. ===Fully developed pipe flow=== ===Fully developed pipe flow=== - 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 diameter]] (in the case of a circular pipe the [[hydraulic diameter]] is the same as the diameter of the pipe). Hence: + In pipe flows the turbulence length scale can be estimated from the [[hydraulic diameter]]. In fully developed pipe flow the turbulence length scale is 7% of the [[hydraulic diameter]] (in the case of a circular pipe the [[hydraulic diameter]] is the same as the diameter of the pipe). Hence: :$l = 0.07 \; d_h$ :$l = 0.07 \; d_h$ Where $d_h$ is the [[hydraulic diameter]]. Where $d_h$ is the [[hydraulic diameter]]. + + ===Wall-bounded inlet flows=== + + The turbulence length scale can be estimated (approximately) from the inlet boundary layer thickness. Set $l$ to half the inlet boundary layer thickness.

## Revision as of 12:35, 15 May 2008

The turbulence length scale, $l$ , 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:

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

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

## Estimating the turbulence length scale

It is common to set the turbulence length scale to a certain percentage of a typical dimension of the problem. For example, at the inlet to a turbine stage a typical turbulence length scale could be say 5% of the channel height. In grid-generated turbulence the turbulence length scale is often set to something close to the size of the grid bars.

### Fully developed pipe flow

In pipe flows the turbulence length scale can be estimated from the hydraulic diameter. In fully developed pipe flow the turbulence length scale is 7% of the hydraulic diameter (in the case of a circular pipe the hydraulic diameter is the same as the diameter of the pipe). Hence:

$l = 0.07 \; d_h$

Where $d_h$ is the hydraulic diameter.

### Wall-bounded inlet flows

The turbulence length scale can be estimated (approximately) from the inlet boundary layer thickness. Set $l$ to half the inlet boundary layer thickness.