# Turbulence intensity

(Difference between revisions)
 Revision as of 22:15, 18 April 2006 (view source)Jola (Talk | contribs) (changed nomenclature)← Older edit Revision as of 22:16, 18 April 2006 (view source)Jola (Talk | contribs) Newer edit → Line 19: Line 19: When setting boundary conditions for a CFD simulation it is often necessary to estimate the  turbulence intensity on the inlets. To do this accurately it is good to have some form of measurements or previous experince to base the estimate on. Here are a few examples of common estimations of the incoming turbulence intensity: When setting boundary conditions for a CFD simulation it is often necessary to estimate the  turbulence intensity on the inlets. To do this accurately it is good to have some form of measurements or previous experince to base the estimate on. Here are a few examples of common estimations of the incoming turbulence intensity: - #'''High-turbulence case''': High-speed flow inside complex geometries like heat-exchangers and flow inside rotating machinery (turbines and compressors). Typically I is between 5% and 20% + #'''High-turbulence case''': High-speed flow inside complex geometries like heat-exchangers and flow inside rotating machinery (turbines and compressors). Typically the turbulence intensity is between 5% and 20% - #'''Medium-turbulence case''': Flow in not-so-complex devices like large pipes, ventilation flows etc. or low speed flows (low [[Reynolds number]]). Typically I is between 1% and 5% + #'''Medium-turbulence case''': Flow in not-so-complex devices like large pipes, ventilation flows etc. or low speed flows (low [[Reynolds number]]). Typically the turbulence intensity is between 1% and 5% - #'''Low-turbulence case''': Flow originating from a fluid that stands still, like external flow across cars, submarines and aircrafts. Very high-quality wind-tunnels can also reach really low turbulence levels. Typically I is very low, well below 1%. + #'''Low-turbulence case''': Flow originating from a fluid that stands still, like external flow across cars, submarines and aircrafts. Very high-quality wind-tunnels can also reach really low turbulence levels. Typically the turbulence intensity is very low, well below 1%. ===Fully developed pipe flow=== ===Fully developed pipe flow===

## Definition

The turbulence intensity is defined as:

$I \equiv \frac{u'}{U}$

Where $u'$ is the root-mean-square of the turbulent velocity fluctuations and $U$ is the mean velocity (Reynolds averaged).

If the turbulent energy, $k$, is known $u'$ can be computed as:

$u' \equiv \sqrt{\frac{1}{3} \, ( u_x'^2 + u_y'^2 + u_z'^2 )} = \sqrt{\frac{2}{3}\, k}$

$U$ can be computed from the three mean velocity components $U_x$, $U_y$ and $U_z$ as:

$U \equiv \sqrt{U_x^2 + U_y^2 + U_z^2}$

## Estimating the turbulence intensity

When setting boundary conditions for a CFD simulation it is often necessary to estimate the turbulence intensity on the inlets. To do this accurately it is good to have some form of measurements or previous experince to base the estimate on. Here are a few examples of common estimations of the incoming turbulence intensity:

1. High-turbulence case: High-speed flow inside complex geometries like heat-exchangers and flow inside rotating machinery (turbines and compressors). Typically the turbulence intensity is between 5% and 20%
2. Medium-turbulence case: Flow in not-so-complex devices like large pipes, ventilation flows etc. or low speed flows (low Reynolds number). Typically the turbulence intensity is between 1% and 5%
3. Low-turbulence case: Flow originating from a fluid that stands still, like external flow across cars, submarines and aircrafts. Very high-quality wind-tunnels can also reach really low turbulence levels. Typically the turbulence intensity is very low, well below 1%.

### Fully developed pipe flow

For fully developed pipe flow the turbulence intensity at the core can be estimated as:

$I = 0.16 \; Re_{d_h}^{-\frac{1}{8}}$

Where $Re_{d_h}$ is the Reynolds number based on the pipe hydraulic diameter $d_h$.