Tension superfical

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Engineering Turbulence Modelling and Experiments - 5 W. Rodi and N. Fueyo (Editors) © 2002 Elsevier Science Ltd. All rights reserved.

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EFFECTS OF THE SURFACE STRETCHING OR THE SURFACEDEFORMATION RATE ON THE BREAKUP OF A VISCOUS DROP IN SIMPLE SHEAR FLOW: NUMERICAL SIMULATION
M. Klein, A. Sadiki and J. Janicka TU-Darmstadt, Energie- und Kraftwerkstechnik, Petersenstr. 30,64287 Darmstadt, Germany e-Mail: kleinm@hrzpub.tu-darmstadt.de

ABSTRACT Using Direct Numerical Simulations (DNS) along with a Volume of Fluid (VOF) method, this work aims to investigate theeffects of the surface stretching or the surface deformation rate in the dynamics of the drop deformation and breakup in simple shear flow between parallel plates. The fluid is composed of twoimmiscible liquids of different densities and viscosities. To account for the surface deformation rate, the interfacial stress tensor is extended by involving a viscous part besides the wellknown inviscid term. First, results of a liquid jet ejected into a gas phase modulated by turbulence are shown. Then, the influences of the deformation rate and capillary number on the drop arepointed out. They compare qualitatively well with existing theoretical knowledge and previous experimental data.

KEYWORDS drop breakup, surface stretching, DNS, turbulence, interfacialviscosity

NOTATION fkh Pni f^'fh f-^m vi, ui p U F a Ss K. density of droplet, matrix fluid viscosity of droplet, matrix fluid velocity in axial (x) direction pressure mean velocities (of Hquid,gas) volume concentration function surface tension delta function on the surface mean curvature

/
Kg fJ'S

^n ^a

9aP

K/3
Ta,T^

n

unit tensor surface dilatational viscositysurface shear viscosity velocity normal to the interface tangential velocity on the interface interfacial metric tensor curvature tensor surface base vectors unit normal on the surface

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