# Turbulence intensity

(Difference between revisions)
 Revision as of 15:26, 23 March 2006 (view source)Jola (Talk | contribs) (fixed a typo)← Older edit Latest revision as of 09:14, 3 January 2012 (view source)Peter (Talk | contribs) m (Reverted edits by Reverse22 (talk) to last revision by Peter) (13 intermediate revisions not shown) Line 1: Line 1: ==Definition== ==Definition== - The turbulence intensity is defined as: + The turbulence intensity, also often refered to as turbulence level, is defined as: - :$Tu \equiv \frac{u'}{U}$ + :$I \equiv \frac{u'}{U}$ Where $u'$ is the root-mean-square of the turbulent velocity fluctuations and $U$ is the mean velocity ([[Reynolds averaging|Reynolds averaged]]). Where $u'$ is the root-mean-square of the turbulent velocity fluctuations and $U$ is the mean velocity ([[Reynolds averaging|Reynolds averaged]]). Line 9: Line 9: If the turbulent energy, $k$, is known $u'$ can be computed as: If the turbulent energy, $k$, is known $u'$ can be computed as: - :$u' = \sqrt{\frac{2}{3}\, k}$ + :$u' \equiv \sqrt{\frac{1}{3} \, ( u_x'^2 + u_y'^2 + u_z'^2 )} = \sqrt{\frac{2}{3}\, k}$ $U$ can be computed from the three mean velocity components $U_x$, $U_y$ and $U_z$ as: $U$ can be computed from the three mean velocity components $U_x$, $U_y$ and $U_z$ as: Line 17: Line 17: ==Estimating the turbulence intensity== ==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 necessary 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-exchanges and the flow inside a turbine or compressor. Typically Tu 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 flow with low speed (low [[Reynolds number]]). Typically Tu 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 the flow across cars, submarines and aircrafts. Very high-quality wind-tunnels can also reach really low turbulence levels. Typically Tu is very low, well below 1%. In this case Tu is normally not used directly to set the inlet conditions for a CFD simulation. Instead a typical eddy viscosity ratio is estimated. + #'''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]] $d_h$.

## Definition

The turbulence intensity, also often refered to as turbulence level, 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 $d_h$.