On the dynamics of buoyant and heavy partióles in a periodic Stuart vortex flow

Tio, K.K. and Liñán Martínez, Amable and Lasheras, Juan C. and Gañan Calvo, Alfonso Miguel (1993). On the dynamics of buoyant and heavy partióles in a periodic Stuart vortex flow. "Journal of Fluid Mechanics", v. 254 ; pp. 671-699. ISSN 0022-1120.

Description

Title: On the dynamics of buoyant and heavy partióles in a periodic Stuart vortex flow
Author/s:
  • Tio, K.K.
  • Liñán Martínez, Amable
  • Lasheras, Juan C.
  • Gañan Calvo, Alfonso Miguel
Item Type: Article
Título de Revista/Publicación: Journal of Fluid Mechanics
Date: 1993
ISSN: 0022-1120
Volume: 254
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Motopropulsión y Termofluidodinámica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper, we study the dynamics of small, spherical, rigid particles in a spatially periodic array of Stuart vórtices given by a steady-state solution to the two-dimensional incompressible Euler equation. In the limiting case of dominant viscous drag forces, the motion of the particles is studied analytically by using a perturbation scheme. This approach consists of the analysis of the leading-order term in the expansión of the 'particle path function' <P, which is equal to the stream function evaluated at the instantaneous particle position. It is shown that heavy particles which re-main suspended against gravity all move in a periodic asymptotic trajectory located above the vórtices, while buoyant particles may be trapped by the stable equilibrium points located within the vórtices. In addition, a linear map for <P is derived to describe the short-term evolution of particles moving near the boundary of a vortex. Next, the assumption of dominant viscous drag forces is relaxed, and linear stability analyses are carried out to investígate the equilibrium points of the five-parameter dynamical system governing the motion of the particles. The five parameters are the free-stream Reynolds number, the Stokes number, the fluid-to-particle mass density ratio, the distribution of vorticity in the flow, and a gravitational parameter. For heavy particles, the equilibrium points, when they exist, are found to be unstable. In the case of buoyant particles, a pair of stable and unstable equilibrium points exist simultaneously, and undergo a saddle-node bifurcation when a certain parameter of the dynamical system is varied. Finally, a computational study is also carried out by integrating the dynamical system numerically. It is found that the analytical and computational results are in agreement, provided the viscous drag forces are large. The computational study covers a more general regime in which the viscous drag forces are not necessarily dominant, and the effects of the various parametric inputs on the dynamics of buoyant particles are investigated.

More information

Item ID: 1636
DC Identifier: http://oa.upm.es/1636/
OAI Identifier: oai:oa.upm.es:1636
Deposited by: Biblioteca ETSI Aeronauticos
Deposited on: 30 May 2009
Last Modified: 20 Apr 2016 06:54
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