Magnus effect

While the lift on a stationary cylinder in an air stream is zero [Fig. 6.8 (a)], that for a rotating cylinder [Fig. 6.8 (6)] is not zero. Air is dragged along with the rotating cylinder. This circulation, when combined with the translational flow, causes the velocity on the top side of the cylinder to be higher than that on the bottom side. As a consequence of the Bernoulli equation [Eq. (5.15)], the pressure on the bottom side of the cylinder will be higher than that on the top side, giving rise to an upward lift (L). 

For a cylinder of diameter (d) and axial length (f) (projected area perpendicular to V=Ap = id), rotating at Arps V = ndN) in air of density (p), the lift force (Z) will be as follows before dimensional analysis  

After dimensional analysis, takingp, V, and p as the dimensionally independent set  

It is found experimentally that with other variables held constant, L is approximately proportional to VqIVand  

The lift associated with a rotating cylinder in a translating air stream is called the Magnus effect and it is this effect that causes a slice or hook in golf, a cut ball to move off to the side in tennis or ping pong, or a curve ball in baseball. 

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Magnus Force (Magnus Effect). A sideways thrust acting on a spinning projectile in flight because of the component of the air current acting perpendicular to the axis of the yawing projectile... 

Use could be made of aerodynamic effects such as Bernouille or Magnus effects to generate quite high forces. Water could also be used as a source of variable mass, filling containers which can change the balance of various hinged parts of a sculpture. 

General Principles There are two main types of mass flowmeters (1) the so-called true mass flowmeter, which responds directly to mass flow rate, and (2) the inferential mass flowmeter, which commonly measures volume flow rate and fluid density separately. A variety of types of true mass flowmeters have been developed, including the following (a) the Magnus-effect mass flowmeter, (b) the axial-flow, transverse-momentum mass flowmeter, (c) the radial-flow, transverse-momentum mass flowmeter, (d) the gyroscopic transverse-momentum mass flowmeter, and (e) the thermal mass flowmeter. Type b is the basis for several commercial mass flowmeters, one version of which is briefly described here. 

Fig. 10,8 Schematic diagram showing Magnus effect on rotating sphere.

Saltation of solids occurs in the turbulent boundary layer where the wall effects on the particle motion must be accounted for. Such effects include the lift due to the imposed mean shear (Saffman lift, see 3.2.3) and particle rotation (Magnus effect, see 3.2.4), as well as an increase in drag force (Faxen effect). In pneumatic conveying, the motion of a particle in the boundary layer is primarily affected by the shear-induced lift. In addition, the added mass effect and Basset force can be neglected for most cases where the particle... 

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. 

Maccoll [95] 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, Ve ua/v, was less than 0.5. 

Swanson WM (1961) The Magnus effect A summary of investigations to date. Transactions of the ASME Journal of Basic Engineering, pp. 461-470... 

Taneda S (1957) Negative Magnus effect. Reports of Research Institute for Applied Mathematics 5(29) 123-128, Printed in Fukuoka Taneda S (1978) Visual observations of the flow past a sphere at Reynolds numbers between 10 and 10 . J Fluid Mech 85 187-192... 

Epstein [1988] has drawn attention to two hydrodynamic effects that he terms "neglected" and are not generally taken into account in models. They include the Magnus effect and the induced fluid drainage force. 

The Magnus effect is the force imposed on a rotating object in a shear flow. When a fluid and a solid particle are flowing downwards across a surface, due to the density difference the particle will be travelling at a higher velocity than the fluid in the vicinity of the particle, the result is a force directed towards the wall. For the corresponding upflow the particle would be directed away from the wall. 

Epstein [1988] concludes that for gases the Magnus effect and the fluid drainage force are likely to be small, but for liquids they could assume importance. The empirical sticking probability is a way of taking these unrecognised influences into account. 

The residence time and, therefore, the reaction behavior of particles depend on the transport conditions of particles in the laminar flo v, if homogeneous fluids are applied. The non-linear velocity gradients inside microchannels cause unsymme-trical shear forces. As a result, particles are not only brought to rotation, but are also transported to the central region of the microchannel (Magnus effect). Therefore, the fluid transport behavior leads to an enhancement of particle concentration in the center of microchannels and to a lo vering of their concentration near the valls. 

Figure 16.3. Configurations for studying the lift force exerted on a particle in a fluid flow in an infinite medium, (a) Magnus effect in a uniform flow the particle is rotated about a fixed axis, (b) The particle moves in the direction of a fluidflow with constant shear. Two sub-cases are considered (i) the particle is prevented from rotating w = 0) ...

The first case (Figure 16.3(a)) is that of the very classic Magnus effect for a high-Reynolds-number flow. If a rotation with angular velocity co about the Oy axis... 

Takemura F, Magnaudet JJM (2003) The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate leynolds number. J Fluid Mech 495 235-253 Taneda S (1957) Negative magnus effect. Rep Res Inst Appl Math 5(29) 123-128 (Printed in Fukuoka)... 

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