Doctoral Dissertations

Date of Award

5-1996

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Chemical Engineering

Major Professor

Osman Basaran

Committee Members

Charles H. Byers, Charles P. Moore, Leonard J. Gray, Robert M. Counce, Jack S. Watson

Abstract

Fluid flow in and around and mass transfer to and from single drops that are either falling in a tube (the falling drop problem) or fluidized by an up- flowing ambient fluid in a tube (the fluidized drop problem) are analyzed both experimentally and theoretically. An experimental system has been developed to study the enhancement of mass transfer to and from a drop by forcing it to undergo oscillations by the application of a pulsed d.c. electric field. With millimeter-size drops immersed in organic solvents, mass transfer enhancement on the order of 35% has been achieved. Previous theories based on the concept of surface stretch are unable to account for the observed increases in mass trans- fer rates and coefficients. First, the change in drop surface area that occur in the experiments is too small to account for the observed enhancement in mass transfer. Moreover, these previous theories also assume that the fluid inside the drops is well mixed. The validity of this assumption has been tested by flow visualization studies which has revealed that the flow inside the drops is lami- nar and not turbulent. Such experimental observations, which agree with recent theories of drop oscillations, point to the need to develop a better understanding of the fluid mechanics in and around drops and the implications of the flow to transient conjugate mass transfer.

In this thesis, computational techniques based on the Galerkin/ finite element method (G/FEM) are used to solve both the fluid mechanics and mass transfer problems. The solution of the fluid mechanics part of the problem is expedited by using a highly efficient penalty formulation of the Navier-Stokes equations, which eliminates the need for explicitly solving for the pressure field.

The problem of the axisymmetric flow past a solid sphere in a tube is solved first to verify the correctness of the G/FEM algorithm and computer code developed for determining flow fields. Notwithstanding that this is a much studied and classical problem in fluid mechanics, two new correlations accounting for wall effects on drag for falling and fluidized solid spheres are presented that are valid over a range of Reynolds numbers and ratios of the radius of the tube to that of the sphere. The new computations and correlations evaluate the validity of correlations and approximations of others that have lurked around in the literature, often untested, for nearly a half century. Moreover, conditions are identified for which recirculating wakes form behind the spheres. It is shown that as the ratio of the tube radius to that of the sphere decreases, the Reynolds number for the onset of wake formation increases and the length of the wake decreases. Computations are also carried out that determine for the first time the effect of thin wire that has often been used in past experiments in measuring drag.

Attention is next turned to flow past a falling and fluidized fluid spheres in tubes. By way of example, the flow field inside and outside a fluid sphere that is falling in a tube undergoes remarkable transitions when the ratio of the viscosity of the drop to that of the ambient fluid, κ, varies over a narrow range. When κ is small enough, no wake forms behind the sphere. When lies between about 3 and 10, a wake that is wholly detached from the drop forms behind the sphere at a Reynolds number less than 100 and disappears as Reynolds number exceeds a certain amount. When κ ≥ 10, it is shown for the first time that detached wakes can attach to the drop when Reynolds number becomes sufficiently large. Additionally, two new correlations are developed and reported that account for the effects of a tube wall and finite fluid inertia on drag for fluidized and falling droplets. Moreover, in contrast to related correlations of others for fluid spheres that are placed in an infinite expanse of ambient fluid, the new correlations are valid over the entire range of Reynolds numbers considered.

A fully implicit, transient algorithm and a computer code are developed for calculating mass transfer to or from a fluid sphere in a tube using velocity fields from solutions to the aforementioned Navier-Stokes problems. In contrast to most existing models in the literature that rely on some sort of drastic simplification or another, rigorous results computed in this thesis indicate that significant differences in rates of mass transfer from one situation to another can be attributed to whether or not a recirculating eddy is present in the continuous phase at the downstream face of the drop. Such zones of fluid recirculation are of course due to fluid convection at finite Reynolds number and cannot be predicted by such ad hoc models as surface stretch or approximating the real flow field by creeping flow solutions which are often available in analytical form.

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