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# I. Motion of a sphere in the presence of a plane interface. II. Modeling of non-isothermal turbulent flows

## Citation

Lee, Seong Hee (1980) I. Motion of a sphere in the presence of a plane interface. II. Modeling of non-isothermal turbulent flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7k89-yq91. https://resolver.caltech.edu/CaltechETD:etd-10102006-105459

## Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Part I:

The motion of a sphere in the presence of a fluid/fluid interface is studied. First, a solution is derived for a point force near a plane interface. Then the solution is extended to include the higher-order terms which are required to describe the motion of a solid sphere. Singularities of higher orders at the center of the sphere are obtained by using the method of reflections. This method yields asymptotic solutions for the general motion of a sphere in the presence of an interface.

A general solution for Stokes' equation in bipolar coordinates is also derived, and then applied to the arbitrary motion of a sphere in the presence of a plane fluid/fluid interface. The drag force and hydrodynamic torque on the sphere are then calculated for four specific motions of the sphere; namely, translation perpendicular and parallel to the interface and rotation about an axis which is perpendicular and parallel, respectively, to the interface. These numerically exact solutions are compared with the previous approximate solutions. The latter can be generalized to a variety of particle shapes, and it is thus important to assess their accuracy for this case of spherical particles where an exact solution can be obtained.

Part II:

The second-order, mean Reynolds stress turbulence closure approximation is extended to non-isothermal turbulent flows with negligible buoyancy. We apply the method of invariant modeling [Lumley and Khajeh-Nouri (1974)] to systematically model the various higher order moments in the governing equations. This approach yields a general form for each unknown correlation in the transport equations of [...] and [...] each containing many terms with parameters that must be determined from experimental data. For practical application, it is necessary to reduce the number of terms. In the present work, the most important terms are filtered from the general model for each unknown moment and their parameters are evaluated based on experimental data. A semi-analytical method is used to derive models for the triple correlations of fluctuating velocity and temperature in a nonisothermal turbulent flow based upon the exact equations which govern their transport and production processes. In this study, these governing equations are transformed to a set of coupled linear algebraic equations for [...], [...], [...], and [...] by assuming: (1) a quasi-Gaussian structure for the fourth-order moments, (2) slow variations of the mean flow in the streamwise direction, (3) negligible convection of the triple correlations, and (4) certain simple models for the remaining higher-order correlations. A model for the triple correlations can thus be obtained by solving the set of linear algebraic equations.

Item Type: Thesis (Dissertation (Ph.D.)) California Institute of Technology Chemistry and Chemical Engineering Chemical Engineering Public (worldwide access) Leal, L. Gary Unknown, Unknown 20 December 1979 CaltechETD:etd-10102006-105459 https://resolver.caltech.edu/CaltechETD:etd-10102006-105459 10.7907/7k89-yq91 No commercial reproduction, distribution, display or performance rights in this work are provided. 4014 CaltechTHESIS Imported from ETD-db 20 Oct 2006 16 Apr 2021 22:13

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