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By T. Urbanski

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85) Finally, the equation of motion of a sphere may be expressed by Newton’s second law in terms of all the instantaneous forces that act on the sphere. These forces are the hydrodynamic drag force on the sphere, FH (which is composed of two parts, the drag and lift) and the gravity/buoyancy force FB. The former may be written in terms of two dimensionless factors: the drag coefficient, CD and the lift coefficient, CL. , drag coefficient, lift coefficient, heat transfer coefficient, and mass transfer coefficient.

In this regime, the separation angle is a monotonically decreasing function of Rer, while the wake length and volume of the wake are monotonically increasing functions of Rer. 121) 3. Unsteady wake regime in laminar flow. The onset of instability for the wake occurs in the range 130 Ͻ Rer Ͻ 150 depending on the conditions of the study. At this Reynolds number, a weak longperiod oscillation appears at the tip of the wake and its amplitude increases with Rer. This is a laminar flow oscillation. Pockets of vorticity begin to be shed from the tip of the sphere and influence the flow field away from the sphere.

This unsteady wake regime has been observed in experiments in the range (130 to 150) Ͻ Rer Ͻ 270. 4. High subcritical range. This regime covers the range 270 Ͻ Rer Ͻ 3 ϫ 105. As the Reynolds number increases, vortices being are shed regularly from alternate sides of the sphere. 1 at Rer ϭ 400 to approximately 2 at Rer ϭ 6000. Above this value of Rer, separation occurs at a point that rotates around the sphere with frequency equal to the shedding frequency. Although this may suggest the presence of a helical or double-helical wake, it has been proved that this is not the case.

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