Degree of turbulence

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The degree of turbulence is a dimensionless quantity to describe the quality of an external flow . The influence of the turbulent external flow on flow tests , especially in the wind tunnel, was determined for the first time. The smaller the degree of turbulence, the better the wind tunnel; Low-turbulence wind tunnels have degrees of turbulence The degree of turbulence plays a role in the transferability of wind tunnel measurement results to one another, but also in the transfer of the values ​​of the model to the original within the framework of the similarity theory . ${\displaystyle T_{U}}$ ${\displaystyle T_{U}\leq 0{,}0005.}$

Definition of the degree of turbulence (here 3D view in the direction of flow ): ${\displaystyle u}$

${\displaystyle T_{U}={\frac {1}{U_{\infty }}}{\sqrt {{\frac {1}{3}}\left(\sigma _{u}^{2}+\sigma _{v}^{2}+\sigma _{w}^{2}\right)}}}$

With

• ${\displaystyle U_{\infty }}$: undisturbed flow velocity (outside of boundary layers )
• ${\displaystyle \sigma _{u}^{2}={\frac {1}{n-1}}\cdot \sum _{i=1}^{N}(u_{i}-{\overline {u}})^{2}:}$ mean square of the speed fluctuations in the x-direction
  • ${\displaystyle N}$: Number of measurements at different points in the flow field ${\displaystyle i}$
  • ${\displaystyle u_{i}:}$ Speed ​​in x-direction instead ${\displaystyle i}$
  • ${\displaystyle {\overline {u}}:}$ Speed ​​in x-direction, averaged over all measuring points ${\displaystyle i}$
• ${\displaystyle \sigma _{v}^{2}={1 \over {n-1}}\cdot \sum _{i=1}^{N}(v_{i}-{\overline {v}})^{2}}$
• ${\displaystyle \sigma _{w}^{2}={1 \over {n-1}}\cdot \sum _{i=1}^{N}(w_{i}-{\overline {w}})^{2}}$

With the degree of turbulence, one records the fact that turbulent flows in the three spatial axes x, y, z have different mean velocity fluctuations:

${\displaystyle \sigma _{u}^{2}\neq \sigma _{v}^{2}\neq \sigma _{w}^{2}}$

An attempt is made to equalize this by means of close-meshed grids and sieves and we speak of isotropic turbulence when the mean speed fluctuations are the same in all three directions:

${\displaystyle \sigma _{u}^{2}=\sigma _{v}^{2}=\sigma _{w}^{2}}$

See also

• Empirical standard deviation