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Turbulence intensity

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==Definition==
==Definition==
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The turbulence intensity is defined as:
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The turbulence intensity, also often refered to as turbulence level, is defined as:
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:<math>Tu \equiv \frac{u'}{U}</math>
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:<math>I \equiv \frac{u'}{U}</math>
Where <math>u'</math> is the root-mean-square of the turbulent velocity fluctuations and <math>U</math> is the mean velocity ([[Reynolds averaging|Reynolds averaged]]).
Where <math>u'</math> is the root-mean-square of the turbulent velocity fluctuations and <math>U</math> is the mean velocity ([[Reynolds averaging|Reynolds averaged]]).
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If the turbulent energy, <math>k</math>, is known <math>u'</math> can be computed as:
If the turbulent energy, <math>k</math>, is known <math>u'</math> can be computed as:
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:<math>u' = \sqrt{\frac{2}{3}\, k}</math>
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:<math>u' \equiv \sqrt{\frac{1}{3} \, ( u_x'^2 + u_y'^2 + u_z'^2 )} = \sqrt{\frac{2}{3}\, k}</math>
<math>U</math> can be computed from the three mean velocity components <math>U_x</math>, <math>U_y</math> and <math>U_z</math> as:
<math>U</math> can be computed from the three mean velocity components <math>U_x</math>, <math>U_y</math> and <math>U_z</math> as:
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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:
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#'''High-turbulence case''': High-speed flow inside complex geometries like heat-exchangers and flow inside rotating machinery (turbines and compressors). Typically Tu is between 5% and 20%
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#'''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%
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#'''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%
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#'''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%
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#'''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.
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#'''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===
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 +
For fully developed pipe flow the turbulence intensity at the core can be estimated as:
 +
 
 +
:<math>I = 0.16 \; Re_{d_h}^{-\frac{1}{8}}</math>
 +
 
 +
Where <math>Re_{d_h}</math> is the [[Reynolds number]] based on the pipe [[hydraulic diameter]] <math>d_h</math>.
 +
 
 +
The above equation is from the ANSYS Fluent User's Guide (Release 18.0, Eq. (6.62)); however, no reference is provided. Russo and Basse published a paper [1] where they derive turbulence intensity scaling laws based on CFD simulations and Princeton Superpipe measurements. The turbulence intensity over the pipe area is defined as an arithmetic mean (AM). The measurement-based scaling laws are:
 +
 
 +
:<math>I_{\rm Smooth~pipe~axis} = 0.0550 \; Re^{-0.0407}</math>
 +
:<math>I_{\rm Smooth~pipe~area,~AM} = 0.227 \; Re^{-0.100}</math>
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 +
Scaling of the area-averaged (AA) turbulence intensity has been calculated in [2]:
 +
 
 +
:<math>I_{\rm Smooth~pipe~area,~AA} = 0.317 \; Re^{-0.110}</math>
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 +
== References ==
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 +
{{reference-paper|author=[1] Russo, F. and Basse, N.T.|year=2016|title=Scaling of turbulence intensity for low-speed flow in smooth pipes|rest=Flow Meas. Instrum., vol. 52, pp. 101–114}}
 +
 
 +
{{reference-paper|author=[2] Basse, N.T.|year=2017|title=Turbulence intensity and the friction factor for smooth- and rough-wall pipe flow
 +
 
 +
|rest=Fluids, vol. 2, 30}}

Revision as of 08:18, 11 June 2017

Contents

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.

The above equation is from the ANSYS Fluent User's Guide (Release 18.0, Eq. (6.62)); however, no reference is provided. Russo and Basse published a paper [1] where they derive turbulence intensity scaling laws based on CFD simulations and Princeton Superpipe measurements. The turbulence intensity over the pipe area is defined as an arithmetic mean (AM). The measurement-based scaling laws are:

I_{\rm Smooth~pipe~axis} = 0.0550 \; Re^{-0.0407}
I_{\rm Smooth~pipe~area,~AM} = 0.227 \; Re^{-0.100}

Scaling of the area-averaged (AA) turbulence intensity has been calculated in [2]:

I_{\rm Smooth~pipe~area,~AA} = 0.317 \; Re^{-0.110}

References

[1] Russo, F. and Basse, N.T. (2016), "Scaling of turbulence intensity for low-speed flow in smooth pipes", Flow Meas. Instrum., vol. 52, pp. 101–114.

[2] Basse, N.T. (2017), "Turbulence intensity and the friction factor for smooth- and rough-wall pipe flow", Fluids, vol. 2, 30.

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