Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
22
1
1995
A Numerical Description of a Liquid-Vapor Interface Based on the Second Gradient Theory
1-14
Didier
Jamet
DER/SSTH/LMDL, Commissariat à l’Energie Atomique/Grenoble, 38054 Grenoble Cedex 9, France
Olivier
Lebaigue
DER/SSTH/LMDL, Commissariat à l’Energie Atomique/Grenoble, 38054 Grenoble Cedex 9, France
Jean-Marc
Delhaye
Clemson University, Department of Mechanical Engineering, USA
N.
Coutris
INPG/ENSPG and DER/SSTH/LMDL CEA/Grenoble, 38054 Grenoble Cedex 9, France
The direct numerical simulation of liquid-vapor two-phase flows can be a useful tool both to investigate complex physical problems and provide closure relations used in models based on averaged equations. Several numerical methods that can be applied to liquid-gas problems involving immiscible fluids are able to track interfaces that are likely to merge or separate. These methods are based on an artificial enlargement of the interface, which prevents numerical oscillations, and they actually use a mixing model for the fluid behavior within the interfacial zone thus created. The main advantage of these methods is that only one set of equations has to be solved to obtain the flow field in each phase and to track the interfaces naturally. Although adaptation of these methods to phase-change problems is difficult, artificial enlargement of the interface can still be maintained if an effort is made to model the fluid within the interfacial zone. The second gradient theory is particularly adequate for that purpose since it allows a single set of equations of motion and energy to be written for the whole system, i.e. the liquid and vapor phases as well as the interfacial zone. Unusual terms then naturally appear in these equations and correspond to the transformation of the surface tension into a volumetric property. This article shows that it is possible to increase artificially the thickness of the interface without changing the values of the surface tension or the heat of vaporization, provided that ad hoc thermodynamic closure relations are determined. An example of the application of the second gradient theory is given for an isothermal system near the critical point at which the liquid-vapor interface is physically macroscopic. A numerical investigation shows that the interfacial zone keeps its macroscopic thickness as well as a strong cohesion even when its thickness is perturbed.
Oscillatory Thermocapillary Convection in Circular Containers with CO2 Laser Heating
15-28
J. H.
Lee
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio
Yasuhiro
Kamotani
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio 44106
Simon
Ostrach
Case-Western Reserve University, Cleveland, OH
Results are reported of an experimental study of oscillatory thermocapillary convection in small cylindrical containers with CO2 laser heating. The effects of container dimensions and heating zone diameter on the conditions for onset of oscillations are investigated. The test fluid was 5 centistokes silicone oil (Prandtl number = 45−60). A numerical analysis supplements the experimental data. Buoyancy is not important in the current tests. It is shown that the oscillatory flow is similar to that found in earlier work in which the authors used a heating rod. It is also shown that the Marangoni number is not sufficient to specify the onset conditions. The correlation of the present data suggests an additional parameter that represents free surface deformation. The current results are consistent with the data obtained in a space experiment by the authors.
Simulation of Steam Explosion Premixing Phase Using Probabilistic Multiphase Flow Equations
29-40
Jure
Marn
University of Maribor, Slovenia
M.
Leskovar
"Jozef Stefan" Institute, Slovenia
Violent interactions of two adjacent fluids with different material properties have been investigated. The first stage of this interaction, called premixing, was of particular interest. The idea of probabilistic multiphase equations suggested by Molodtsof and Muzyka (1989) was utilized and compared to results of experiment MIXA06.
Modeling of Vertical Fine Suspension Flow I. Model Foundations and Particle Velocity Fluctuations
41-65
Yu. A.
Buyevich
CRSS, University of California, Santa Barbara, USA
This paper presents a heuristic model for the random fluctuating motion found in macroscopically uniform vertical flows of a quiescent suspension. Suspended particles are presumed to be large enough so that their thermal fluctuations are insignificant. At the same time, the particles are presumed to be sufficiently fine so that interparticle exchange by fluctuation energy and momentum is facilitated by hydrodynamic interactions using random fields of ambient fluid velocity and pressure. Particle fluctuations are viewed as the random motion of groups (clusters) composed of fully correlated particles; however, the groups themselves are assumed to be statistically independent. Forces that originate fluctuating motion are caused by the interaction between random fluctuations in suspension concentration and relative fluid flow. These forces are opposed by special friction forces that are caused by an excessive viscous dissipation of energy that accompanies the fluid and particle velocity fluctuations and that supposedly occur mainly within the boundary layers that separate particle groups as these groups move relative to each other. The theory developed in this paper yields expressions for spectral density tensors representing particle and fluid velocity fluctuations; these tensors afford an opportunity to calculate various correlation functions. Vertical and horizontal particle velocity variances and particle self-diffusion coefficients are found to be functions both of physical parameters and mean suspension concentration. They are also shown to agree with available experimental data.
Calculation of an Effective Slip in a Settling Suspension at a Vertical Wall
66-77
Francois
Feuillebois
LIMSI-CNRS, BP 133, F-91403 Orsay Cedex, France
J.
Blawzdziewicz
PMMH, ESPCI, 10 rue Vauquelin, 75231 Paris cedex 05, France
Geigenmuller and Mazur (1988) demonstrated theoretically that an intrinsic convection develops in a homogeneous suspension settling in a cylindrical container with vertical walls. In large containers, the influence of the walls on the macroscopic suspension motion is described by the effective wall slip velocity. It is shown that the slip velocity in a dilute suspension of spherical particles can be expressed in terms of the induced force monopole and stresslet on a particle sedimenting in the presence of a vertical plane wall. The slip velocity calculated for a dilute hard-sphere suspension is 4.395φυst, where φ is the particle volume fraction and υst is the Stokes settling velocity.