Lift and drag on rigid spheres in turbulent flows

3 Lift and Drag on Rigid Spheres in Turbulent Flows 

Spheres in turbulent flows have not been extensively studied, partly due to the difficulties in measuring. 

Taneda [124] studied the flow past a sphere at particle Reynolds numbers between lO and 10, and found that the wake is not axisymmetric and that it rotates slowly and randomly about the sfleam-wise axis. The sphere is thus subject to a random side force. 

This new approach is described by Lee and Wiesler [77] and developed into a model that explains the transversal movement of particles as a result of the turbulent diffusion. The basis of their modeling is a particular form of the Maxey-Riley equation [85]  

They required that the turbulence should be locally isotropic and steady, that the particle Reynolds number should be small, that the particles concentration was small, and that the particle diameter should be much smaller than the length scale of the energy containing eddies for the diffusion controlled range of the model. The model 

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