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Accelerated flows past a rigid sphere or a spherical bubble. I: Steady straining flow. (English) Zbl 0848.76063
This paper provides an improved knowledge on the forces acting on a sphere or a spherical bubble in accelerated flows at finite Reynolds number, Re. The full Navier-Stokes equations expressed in velocity-pressure variables are solved using a finite volume approach over the range \(0.1\leq \text{Re}\leq 300\). It is observed that the presence of strain has spectacular consequences in the case of rigid sphere, as it influences strongly the conditions under which separation occurs and the characteristics of the separated region. Another important feature of the straining flow is the existence of vortex stretching mechanism. This mechanism reduces the vorticity in the wake of the sphere in a converging flow, whereas the vorticity produced at the surface of the spheres tends to grow indefinitely as the sphere is transported downstream in a diverging flow. For a flow extending to infinity, it is shown that the Kelvin-Helmholtz instability may occur in the wake. Computations of the hydrodynamic force show that the effects of strain increase rapidly with an increase in Re. The total drag is significantly modified at high Reynolds numbers.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
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