Wu number

The Wu number (${\displaystyle Wu}$) is a nondimensional quantity in fluid mechanics describing the effects of rotating axisymmetric bodies on wall-bounded sheer flows. The parameter is named after the Chinese scientist Yongxiang Wu during his work on boundary layer instabilities.

Definition

The Wu number is defined as.[1]

${\displaystyle Wu={\frac {\omega D}{2u_{k}}}}$,

where ${\displaystyle \omega }$ is the circular frequency, ${\displaystyle D}$ the diameter of the axisymmetric body (like for instance a cylinder) and ${\displaystyle u_{k}}$ the local flow velocity at the top of the body. It is therefore the ratio of the velocities of the body edge and the surrounding flow.

Applications

Rotating bodies on boundary layers are a means of active flow control on wings, empennage or stabilizers on airplanes. For large Wu numbers (${\displaystyle Wu\gg 1}$), the instability mechanisms are governed by the rotation of the body. For small Wu numbers (${\displaystyle Wu\ll 1}$) the stability-related effects of the body itself may outweigh its rotatory effects[2]

See also

• Strouhal number
• Reynolds number

References

1. Max, Nüßle (2017). "Experimentelle Untersuchung zu Instabiliätsmechanismen hinter einer rotierenden Einzelrauigkeit in laminaren Grenzschichten". Bachelor thesis.
2. Wu, Yongxiang (2018). Proposed Contribution. "Stability of Rotating Cylindrical Roughness Element in Boundary Layer". New Results in Numerical and Experimental Fluid Mechanics. Contribution to the STAB Symposium 2018 in Dortmund, Germany. XII.