Lift forces on a single rigid sphere in laminar flow

2 Lift forces on a single rigid sphere in laminar flow 

Rigid spheres sometimes experience a lift force perpendicular to the direction of the flow or motion. For many years it was believed that only two mechanisms could cause such a lift. The first one described is the so-called Magnus force which is caused by forced rotation of a sphere in a uniform flow field. This force may also be caused by forced rotation of a sphere in a quiescent fluid. The second mechanism is the Saffman lift. This causes a particle in a shear flow to move across the flow field. This force is not caused by forced rotation of the particle, as particles that are not forced to rotate also experience this lift (i.e., these particles may also rotate, but then by an angular velocity induced by the flow field itself). 

A rotating sphere in uniform flow will experience a lift which causes the particle to drift across the flow direction. This is called the Magnus effect (or force). The physics of this phenomenon are complex. 

The rotation of a rigid sphere will cause the surrounding fluid to be entrained. When the sphere is placed in a uniform flow, this results in higher fluid velocity on one side of the particle, and lower velocity on the other side. 

This gives an asymmetrical pressure distribution around the sphere. Originally this was thought to cause lift on the particle that move the particle towards the region of higher local velocity [22], see Fig 5.3. 

2 Lift Forces on a Single Rigid Sphere in Laminar Flow 

Maccoll [80] studied the aerodynamics of a spinning sphere, and observed a negative Magnus effect when the ratio of the equatorial speed of the rotating sphere to the flow speed, Wequa/n, was less than 0.5. 

Krahn [65] explained how the rotation of the sphere would cause the transition from laminar to turbulent boundary layers at different rotational velocities at the two sides of a sphere. The direction of the asymmetrical wake was explained based on the separation points for laminar and turbulent boundary layers. Krahn studied the flow around a cylinder. For a non-rotating cylinder the laminar boundary layer separates at 82° from the forward stagnation point, while the turbulent boundary layer separates at about 130°. Due to the rotation the laminar separation point will move further back, while the turbulent separation point will move forward. For some value of Wequa/w between 0 and 1 the laminar and turbulent separation points will be at equal distance from the stagnation point. The pressure on the turbulent side will be smaller than on the laminar side causing a negative Magnus force. 

Swanson [120] reviewed the investigations of the Magnus force, and presented experimental drag and lift coefficients for an infinite, rotating cylinder at different Reynolds numbers and velocity ratios. For velocity ratios less than 0.55, and Reynolds numbers between 12.8 x 10 and 50.1 x 10 the cylinder would experience negative lift. 

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