The boundary layer formation over a circular cylinder when it is submerged in unidirectional flow is a well-established phenomenon. However, I am looking for the phenomena and characteristics of the boundary layer formation over the cylinder when placed in circulating fluid flow.
The drag, moment coefficient and critical Reynolds number are dependent on the ratio of the circumferential to free-stream velocity. The physical reason for this dependency is due to processes in the boundary layer where the fluid due to the no-slip condition co-rotates in the immediate vicinity of the wall and is therefore subject to the influence of strong “centrifugal forces.” As a result, the processes of separation and transition from laminar to turbulent flow are affected by these forces and therefore drag too.
The boundary layer on a rotating body of revolution in an axial flow consists of the axial component of velocity and the circumferential component due to the no-slip condition at the body surface. The result is a skewed boundary layer.
The thickness of the boundary layer increases as a function of the rotation parameter, Lambda_m, calculated by: (omega*r)/ u_z,inf,
where omega is the angular velocity of the cylinder, r is the radius of the cylinder, and u_z,inf is the free-stream axial velocity.
Kira Haller Thank you very much for your answer. Will you please share any reference of your answer you have stated. Moreover, my scenario is different as in my case the cylindrical is not rotating, and the surrounding fluid is rotated by using a magnetic stirrer. I want is there any formula for the boundary layer formation over the cylinder when it is steady but the surrounding fluid is rotating at constant angular speed.
If you any literature support for your answer feel free to share with me.
I believe it would still be the same. Laminar boundary-layer flows occur when a moving viscous fluid comes in contact with a solid surface and a layer of rotational fluid, the boundary layer, forms in response to the action of viscosity and the no-slip boundary condition on the surface.
My reference is: Pijush K. Kundu, Ira M. Cohen, David R. Dowling,
Chapter 10 - Boundary Layers and Related Topics,
Editor(s): Pijush K. Kundu, Ira M. Cohen, David R. Dowling,
Fluid Mechanics (Sixth Edition),
Academic Press,
2016,
ISBN 9780124059351,
https://doi.org/10.1016/B978-0-12-405935-1.00010-1.
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