Title   name
KSIAM 2006 Annual Meeting
  Speaker   Sohn, Sung-Ik  
  Date 2006-11-25
  Place 건국대학교
  File  의 1 번째 Real Media 동영상입니다. 의 1 번째 강연자료입니다.
Abstract : Fluid mixing occurs frequently in basic science and engineering applications. When a heavyfluid is supported by a lighter fluid in a gravitational field, the interface between the fluids isunstable under small perturbations. This phenomenon is known as the Rayleigh-Taylor instability[1]. The Rayleigh-Taylor instability plays important roles in many fields ranging fromastrophysics to inertial confinement fusion. Since Rayleigh first considered this problem, it hasreceived attentions in a wide range of contexts, but many aspects of dynamics of the instabilityare still uncertain.Small perturbations at the interface grow into nonlinear structures in the form of bubbles andspikes. When the interface has random initial perturbations, different frequencies excite nonlinearinteractions and the flow eventually develops into a turbulent mixing. At the randomperturbations, bubbles of different radii propagate with different velocities and the leading bubblesgrow in size at the expense of their neighboring bubbles. This phenomenon is known as abubble interaction or bubble merger process [1,2].A central issue in the turbulent mixing by the RT instability is a scaling law for the growth ofmixing zone. It has been known that the bubble front in the RT mixing grows ash = ®Agt2; (1)and the coefficient ® is insensitive to the density ratio [1,2], where A = (½1 ¡ ½2)=(½1 + ½2) isthe Atwood number and g is a gravitation acceleration. Previous theoretical models for multiplebubble interactions to estimate the growth coefficient ®, are based on statistical or phenomenologicalequations, which usually include unknown parameters. A number of numerical simulationsalso have been performed to study the scaling law (1), but it is difficult to draw a unifiedconclusion from numerical simulations.In this talk, we present the mathematical model for the evolution of multiple bubbles in Rayleigh-Taylor mixing for the system of arbitrary density ratio [3]. The model is the extension of thepotential source-flow model for single-mode bubble [4]. We investigate dynamics of the evolutionof multiple bubbles for finite density contrast and demonstrate bubble interaction processfrom the model.We also discuss the prediction from the model for the scaling law (1) of bubblefronts, comparing with experimental and numerical results.