Bubble migration inside a liquid drop in a space laboratory

Commercial production of glasses for advanced applications often requires processing techniques substantially different from those in common use. In particular, containerless processing is desirable where melt temperatures are sufficiently high that the container wall reacts chemically with the melt and/or promotes crystallization. An ideal environment for containerless processing is provided by the NASA Space Shuttle program because in orbit, near free fall conditions prevail and little levitation is necessary. In such an environment, however, there are serious problems associated with convective mixing and buoyant fining (bubble removal) of glass melts. Alternate techniques for the promotion of mixing and for managing bubbles in space have been proposed by Subramanian and Cole and include thermocapillarity, rotation, oscillation, etc. This paper will describe these experiments and discuss two of a number of ongoing ground-based projects in support of the flight experiments.     

A Taylor drop rising in a liquid co-current flow

The present work presents a numerical study on the behavior of isolated liquid Taylor drops rising in vertical tubes with co-current heavier continuous phase. Numerical simulations were performed with a previously validated model, implementing Volume of Fluid method in an axisymmetric geometry. Detailed flow patterns and drop shapes are provided and discussed for several conditions. The balance between gravity effect and velocity of the continuous phase flow was found to have a great influence in the flow patterns observed. The increase of inertial effects, due to the increase of Eo number and the co-current velocity, leads to the occurrence of closed recirculations below the drops. Furthermore, the continuous phase stabilization distance below the drop is a function of the drop Reynolds number. Drop and continuous phase velocities relationship was studied. A viscosity ratio related term was appended to a pre-existing correlation. The flow in the absence of gravity was also studied. Results demonstrate that micro-scale flow is a lower limit to the cases studied in the present work and suggest that the viscosity ratio affects mainly the inertial part of the drop velocity.     

Advective flow in a rotating liquid film

This paper presents a new exact solution of the Navier–Stokes equations in the Boussinesq approximation that describes thermocapillary advective flow in a slowly rotating horizontal layer of incompressible fluid with free boundaries. Such flow occurs in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution at the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.     

Wave flow of a liquid film in a horizontal separator

The calculation of the motion of separated moisture in a linear horizontal separator is made on the basis of the analysis of the development of the waves in a flow of a thin layer of liquid along a vertical surface without allowance for the transverse flow of mass [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1985.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Crown behavior and bubble entrainment during a drop impact on a liquid film

Physical and mathematical models are established to simulate a single liquid drop impinging onto a liquid film using the coupled level set and volume of fluid method. The crown liquid sheet after impact is obtained, which coincides well with the experimental results in literatures. Influence of Weber number, Reynolds number and the dimensionless film thickness on the crown diameter and height is discussed quantitatively. Results indicate that the crown diameter is independent of the two non-dimensional numbers, while it can be increased by reducing the dimensionless film thickness. The crown height increases with the increasing of Weber number, but Reynolds number has small effect on it. Mechanism of the jet formation process is revealed by analyzing pressure distribution and velocity field in the liquid. It is found that both pressure difference in the neck region and velocity discontinuity can greatly affect the jet formation. Besides, the bubble entrainment phenomenon during a liquid drop impact on a liquid film is successfully captured with this numerical method. It is found that the increase in both impact Weber number and the drop diameter contributes to the emerging of bubble rings.     

The flow of a power-law liquid in a continuous-flow squeeze film

Consideration is given to the flow of an inelastic ‘power-law’ liquid in a continuous flow squeeze film. This simulates the flow in a conventional squeeze film by continuously injecting fluid into the narrow gap between two plates through the lower plate (Oliver et al. [6]). To zero order in the usual lubrication approximation the results are identical with those for the conventional squeeze film. To first order, useful corrections to the normal force due to the effects of inertia are obtained.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

激波诱导高速气流中液滴的初期变形

基于激波管平台和高速摄影方法对平面激波诱导高速气流中液滴的早期变形现象进行实验研究。研究发现在相近的We数或Re数下,实验参数的改变可导致液滴形态发展出现显著差异。这种差异主要体现在背风面的脊状环形突起、褶皱区以及后驻点区的凹凸形态。对刚性圆球外流的数值模拟显示,液滴变形早期形态与外流场结构和表面气动力分布之间存在鲜明的对应关系。最后采用简化理论推导出一组估测液滴早期变形的表达式。将数值模拟所得气动力数据代入计算发现:导致液滴变形的主要驱动力是液滴表面不均匀压力的挤压效应,而不是界面剪切摩擦所引起的切向流动堆积效应,前者高出后者约2个数量级;此外,采用压力作用理论计算所得液滴外形在主要变形特征和变形量级上均可与实验图像很好地吻合。     

Transport coefficients of an evaporating liquid drop in creeping flow

A theoretical analysis is made of the heat, mass and momentum transfer from an evaporative liquid sphere which is suddenly introduced into a parallel stream of fluid at a higher temperature. The velocity field around the liquid sphere is assumed to be steady and of the Hadamard-Rybczynski type. Numerical solutions of energy and the vapour mass continuity equations have been carried out using the alternate direction implicit scheme of finite difference method. Temporal histories of the average Nusselt and Sherwood numbers (Nu, Sh) alongwith the drag coefficient (C _D ) during the life time of an evaporating drop have been predicted in terms of the pertinent input parameters, namely, initial and instantaneous Peclet number (Pe _i ,Pe), Lewis number (Le), and the ratio of free stream to initial droplet temperature (T _a /T _i ). Variations of local Nusselt and Sherwood numbers withPe, in the region of steady state evaporation, have also been presented. Values ofNu for steady state droplet evaporation are found to be in fair agreement with the corresponding values evaluated from the empirical equation of Eisenklam [5].Es wurde eine theoretische Untersuchung der Wärme-, Massen- und Impulsübertragung eines verdampfenden kugelförmigen Fluidtropfens, welcher plötzlich in eine gleichgerichtete Fluidströmung höherer Temperatur eingeleitet wird, untersucht. Das Geschwindigkeitsprofil um den Fluidtropfen herum wurde als konstant und als ein Hadamard-Rybczynski-Profil angenommen. Unter Benutzung eines ADI-Schemas der Finiten-Differenzen-Methode wurden numerische Lösungen der Erhaltungsgleichungen für Energie und Dampfmasse gewonnen. Zeitliche Gesetzmäßigkeiten der durchschnittlichen Nusselt und Sherwood-Zahlen (Nu, Sh) und des Widerstandsbeiwertes (C _D ) bis zur vollständigen Verdampfung des Tropfens wurden in Abhängigkeit von den zugehörigen Eingabeparametern nämlich der Anfangs-und momentanen Peclet-Zahl (Pe _i ,Pe) der Lewis-Zahl und dem Verhältnis von freier Strömungstemperatur zur Eintrittstemperatur des Tropfens (T _a /T _i ) berechnet. Ebenso werden die lokalen Nusselt und Sherwood-Zahlen in Abhängigkeit von der Peclet-Zahl im Bereich der stationären Verdampfung dargestellt. Es wurde festgestellt, daß Werte der Nusselt-Zahl im Bereich der stationären Verdampfung von Tropfen in guter Übereinstimmung mit den entsprechenden berechneten Größen aus der empirischen Gleichung von Eisenklam liegen.     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Dynamics of a finite-width liquid film in a co-current microchannel gas flow

The velocity fields and the parameters of a finite-width liquid film moving along the bottom of a mini- and a microchannel under the action of a gas flow are calculated. The investigations are performed for different levels of gravity. It is found that the thin liquid film distorts the velocity field in the gaseous phase. In contrast to the minichannel flow, in the microchannel the film surface is not leveled with increase in the gravity force.