Archivo Digital UPM: No conditions. Results ordered -Date Deposited. 2019-11-18T10:57:45ZEPrintshttp://oa.upm.es/style/images/logo-archivo-digital.pnghttp://oa.upm.es/2009-05-30Z2016-04-20T06:54:56Zhttp://oa.upm.es/id/eprint/1636This item is in the repository with the URL: http://oa.upm.es/id/eprint/16362009-05-30ZOn the dynamics of buoyant and heavy partióles in a periodic Stuart vortex flowIn 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.K.K. TioAmable Liñán MartínezJuan C. LasherasAlfonso Miguel Gañan Calvo2009-03-10Z2016-04-20T06:49:39Zhttp://oa.upm.es/id/eprint/1428This item is in the repository with the URL: http://oa.upm.es/id/eprint/14282009-03-10ZThe dynamics of bubbles in periodic vortex flowssTo analyze the dynamics of small, spherical, rigid bubbles in a certain class of turbulent shear flows dominated by large scale coherent vortical structures, we model the plane free shear layer with a periodic array of Stuart vortices. The equation of motion of the bubbles is then integrated numerically to obtain the Lagrangian description of the bubbles, the long-term dynamics of which depends on the free-stream Reynolds number, the Stokes number, the gravitational field, and the strength of the vortices. Depending on the values of these four parameters, it is found that either there exists a stable equilibrium point near the center of each vortex, where bubble accumulation occurs, or all bubbles escape from captivity by the vortices. In the limiting case of dominant viscous drag
forces, an Eulerian description of the "bubble flow field" is derived. Furthermore, the divergence of this flow field is negative in the neighborhood of a vortex center, where it achieves its minimum. This indicates that bubbles accumulation may indeed exist, and thus qualitatively confirms the more general numerical results obtained without the assumption of dominant viscous drag forces.K.K. TioJuan C. LasherasAlfonso Miguel Gañan CalvoAmable Liñán Martínez