INERTIAL INTERACTIONS OF PARTICLES AND BOUNDARIES IN VISCOUS FLOWS.
Item
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Title
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INERTIAL INTERACTIONS OF PARTICLES AND BOUNDARIES IN VISCOUS FLOWS.
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Identifier
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AAI8614687
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identifier
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8614687
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Creator
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LAWRENCE, CHRISTOPHER JOHN.
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Contributor
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Sheldon Weinbaum
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Date
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1986
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Chemical
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Abstract
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The first part of the dissertation examines the behavior of the time-dependent Stokes equations for flow around a nonspherical body. A new result is derived for the force on a body in oscillatory axisymmetric motion in terms of the far-field behaviour of the stream function. This general result is then applied to the unsteady motion of a spheroidal body in unbounded flow. Asymptotic solutions are presented for small or large frequency and for a perturbed sphere. The exact stream-function is found as a sum of Legendre and spheroidal wave functions and the complex force on the body is determined. Since the exact solution is complicated, an analytic approximation is proposed based on the asymptotic solutions for the force. The force contains four terms: the quasi-steady Stokes drag, the generalized Basset force, the added-mass force and a fourth term which has not previously been described. For a body in arbitrary motion the new force term transforms to a memory integral of all previous accelerations with a memory function which is less singular then the t('- 1/2) of the Basset force.;The second part of the research relates to the solution of the full Navier-Stokes equations in the region beneath a flat-bottomed body which falls towards a parallel plane surface. The radial dependence of the stream-function separates and the flow is governed by three dimensionless parameters--a Reynolds number, an inertia parameter (beta) and a forcing parameter (gamma). When the body approaches from "far away", a time-dependent Reynolds number is defined which decreases to zero as the motion progresses; the results for all Reynolds numbers are described by a single solution curve for each value of (beta). When (beta) = 0, the large Re boundary layer solutions are new exact time-dependent similarity solutions of the full Navier-Stokes equations. When the body is dropped from rest, an integral momentum equation is used to describe the development of the boundary layers. The time-dependent gap height and radial velocity profiles are presented and the results are discussed in terms of the draining time, or the position of arrest when there is no applied force.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Engineering
