Effects of Particle Diameter and Position on Hydrodynamics around a Confined Sphere

Abstract

The effect of confinement of a sphere within a tube on the hydrodynamics of Newtonian fluid flow around the solid surface is investigated. The ratio of particle diameter to tube diameter (blockage ratio), the ratio of sphere distance from the tube axis to the tube diameter (eccentricity), and the fluid flow rate were the parameters of this study. Computational fluid dynamics (CFD) simulations were carried out to obtain the flow field around the sphere from which the angle of boundary layer separations, as well as drag and lift coefficients, were obtained. The pressure distributions and friction factor along the sphere surface are also reported. To estimate the effect of confinement and eccentricity in position of the particle, with respect to the tube axis, the results are compared with the classical case involving the flow of an unbounded fluid over the sphere. The drag coefficient diminished when the particle was positioned eccentrically with respect to the tube axis at very low particle Reynolds number (Re p ). However, the drag coefficient increased with increasing eccentric positions at higher Re p . At eccentric particle positions, boundary layer separation occurred earlier from the upper hemisphere while, depending on the eccentricity, it was delayed or nonexistent in the lower hemisphere. The difference in pressure between the lower and upper hemisphere regions led to incursion of fluid into the upper hemispherical region. Correlations are proposed for the drag and lift coefficients in the range of 0.1e Re p e 500 for different possible eccentricities and blockage ratios. The results from this work will be of relevance in applications such as fluidization and aseptic food processing.

Natural Convection from a Heated Sphere in Bingham Plastic Fluids

“…First, the preceding numerical results − for the forced and free convection regimes approach the approximate boundary layer predictions of Acrivos and co-workers , and of others at large values of the Reynolds number or Grashof number. Second, these predictions are also consistent with the scant experimental results for spheres in power-law fluids. ,,, It is now possible to estimate the value of the mean Nusselt number for an unconfined sphere in power-law fluids over most ranges of conditions of practical interest, although this body of knowledge is nowhere as extensive as that in Newtonian fluids. , …”

“…Second, these predictions are also consistent with the scant experimental results for spheres in power-law fluids. 9,10, 17,18 It is now possible to estimate the value of the mean Nusselt number for an unconfined sphere in power-law fluids over most ranges of conditions of practical interest, although this body of knowledge is nowhere as extensive as that in Newtonian fluids. 19,20 On the other hand, many such fluids also possess the socalled yield stress.…”

Spheroids in Viscoplastic Fluids: Drag and Heat Transfer

“…On the other hand, in the forced convection regime, shear-thinning power-law viscosity promotes the rate of heat transfer with reference to that in Newtonian fluids . Both these trends are qualitatively similar to that for a sphere in power-law fluids. − …”

Numerical Predictions of Momentum and Heat Transfer Characteristics from a Heated Sphere in Yield-Stress Fluids

“…Thus, for instance, Dhole et al 9 were probably the first to report on the forced convection heat transfer from a heated unconfined sphere in power-law fluids. These results have been subsequently extended to a confined sphere 5,6,10,11 exposed to uniform and Poiseuille-type fully developed profiles in tube flow of power-law fluids. 10,11 The corresponding results in the free convection 12 and mixed-convection 13 regimes from an isothermal sphere in power-law fluids have been reported very recently.…”

“…In eq 4 and eq 5, |τ| and |γ| represent the magnitudes of the extra stress and the rate of deformation tensor, respectively. As noted earlier, the inherently discontinuous nature of the Bingham constitutive equation, eq (4) and eq (5), is not amenable to implementation in a numerical scheme for the solution of the field equations. Hence, to obviate this difficulty, a few regularization schemes have been proposed in the literature which effectively converts this discontinuity into a gradual transition between the fluid-like and solid like regions prevailing in the flow field.…”