Power law fluid flow over spheroidal particles

Abstract

The equations of motion have been solved numerically for the incompressible power law fluid flow past spherical and spheroidal solid particles. The finite element technique has been employed to obtain the velocity and pressure fields prevailing around a particle. These have been further processed to evaluate the individual contributions of pressure and viscous forces to the total drag on spheres and spheroids (prolates and oblates). Streamline plots showing the nature of flow and the gradual development of the wake region are also presented. The computed drag results encompass wide ranges of physical and kinematic conditions given by 1 > n > 0.4,0.01 < Re < 100, and 0.2 < E < 5. Extensive comparisons are provided with previous theoretical and experimental results available in the literature.

Power‐Law Fluid Flow Over a Sphere: Average Shear Rate and Drag Coefficient

“…Evidently up to about Re n < ~ 5, the smaller the value of n, higher is the drag. At about Re n ~ 5, this dependence fl ips over and now the role of n is reversed, as also noted by Koziol and Glowacki (1988) and by Tripathi et al, (1994) (18) is D ~0.55 predicted by Equation (18) is D some 20% larger than the corresponding Newtonian value but is nowhere close to the value of 0.95. Finally, as can be seen in Figure 1, the drag coeffi cient appears to start leveling off at lower values of the Reynolds number (irrespective of the value of n) than that for Newtonian liquids.…”

“…where the best values of the three new constants, namely, β,b,k are evaluated with a non-linear regression sub-routine as ,b,k are evaluated with a non-linear regression sub-routine as ,b,k applied to the numerical results of Tripathi et al (1994) and Tripathi and Chhabra (1995) in the range Re n # 100 and 0.4 # n # 1.8 and these are found to be: { }…”

Forced convection heat transfer from a sphere to non‐Newtonian power law fluids

“…Although the boundary layer thickness changes with the power law index (n), the grid used in the present work is fine enough to resolve the boundary layer effects 34 for the entire range of parameters used. The grid used in the present work is much finer than that used in other previous studies (see, for example, Tripathi et al, 35 Tripathi and Chhabra, 36 and Graham and Jones 37 ). However, the degree of nonlinearity of the system of equations increases as the value of the power law index deviates increasingly from unity.…”

Momentum and heat transfer phenomena of spheroid particles at moderate Reynolds and Prandtl numbers

“…Most of these studies report drag coefficients of spheroid particles as a function of shape correction factor to the existing well known Stokes drag of spherical particles in the zero-Reynolds number regime. Similarly, few numerical results are also available on the flow phenomena of thin oblate particles (aspect ratio 0.05-0.2) at intermediate Reynolds numbers [13][14][15][16][17][18][19][20][21][22]. Wang et al [23] have experimentally studied the sedimentation characteristics of spherical and hemispherical particles with faces upward and downward while settling in a viscous fluid.…”