Heat and mass transfer of an individual vapor bubble in translational flow of an unbounded liquid volume

The condensational collapse of a spherical vapor bubble moving translationally through an unbounded incompressible liquid is investigated. The bubble moves at a varying velocity. The problem is solved within the framework of the axisymmetric formulation. The numerical investigation shows that the variability of the bubble rise velocity significantly affects the condensational collapse process. This effect is particularly prominent in the final stage, i.e., in the stage of thermal collapse. The results obtained agree well with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 109–115, May–June, 1994.     

Unsteady mass transfer to a droplet (bubble) in a three-dimensional shear flow

An exact analytic solution of the problem of unsteady convective mass transfer to a spherical droplet (bubble) from an arbitrary three-dimensional linear deformational shear flow, whose undisturbed velocity field is given by a symmetric shear tensor, is obtained in the diffusion boundary layer approximation. The dependence of the mean Sherwood number on time and the Péclet number is determined. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–119, November–December, 1986. The authors are grateful to Yu. S. Ryazantsev and L. A. Chudov for their interest and useful comments.     

The effect of cocurrent and countercurrent gas shear on entrance region mass transfer in turbulent falling liquid films

Predictions of average film thickness and mass transfer coefficients in the entrance region of gas absorption with high cocurrent and countercurrent gas flow in a turbulent falling film are presented. The model used is a modified van Driest eddy diffusivity in the inner wall region and an interface damping eddy diffusivity in the outher region of the film modified to include the effect of interfacial shear. The calculations show that the entrance length for mass transfer decreases with increasing film Reynolds number and interfacial shear for cocurrent flow. Also the model predicts a decrease in mass transfer coefficient with an increase in Schmidt number in accordance with experimental data. On the other hand, for counterflow and at a fixedRe, an increase in upward gas shear increases the film thickness and eventually leads to rising film flow. The entrance length for mass transfer decreases with increasing Reynolds number but slightly increases with countercurrent interfacial shear. The calculations show that, in practice, the entrance region for mass transfer for gas absorption with shear-thinned film can be neglected for cocurrent shear but often cannot be neglected for countercurrent shear with a shear-thickened film.Es werden Berechnungen für die mittlere Film-dicke und die Stoffübertragungs-Koeffizienten in der Eintrittsregion der Gasabsorption mit starkem Gleich- und Gegenstrom von Gas in einem turbulent fließenden Film aufgestellt. Das benutzte Modell ist ein modifizierter van Driest-Wirbel-Diffuser für die Innenwand und ein gedämpfter Grenzflächen-Wirbel-Diffuser in der Außenregion des Filmes, der so modifiziert ist, daß die Effekte der Grenzschichtschubspannungen berücksichtigt werden. Die Berechnungen zeigen, daß die Eintrittslänge für die Stoffübertragung mit zunehmender Grenzflächenschubspannung für Gleichstrom abnimmt. Das Modell sagt ebenso ein Sinken des Stoffübertragungs-Koeffizienten mit einer Zunahme der Schmidt-Zahl in Übereinstimmung mit den experimentellen Daten voraus. Auf der anderen Seite führt im Falle von Gegenstrom und einer konstanten Reynolds-Zahl ein Ansteigen der Gasschubspannung zu einem Anwachsen der Filmdicke und eventuell zu wachsender Filmströmung. Die Eintrittslänge für die Stoffübertragung sinkt mit zunehmender Reynolds-Zahl, steigt aber langsam bei Grenzflächenschubspannungen in Gegenstromrichtung. Die Berechnungen zeigen, daß in der Praxis die Eintrittsregion für die Stoffübertragung bei der Gasabsorption mit verdünntem Film für Gleichstromschubspannung vernachlässigt werden kann, bei Gegenstromschubspannung mit verdicktem Film diese jedoch meist berücksichtigt werden muß.     

Investigation of surfactant effect on the bubble shape and mass transfer in a milli-channel using high-resolution microfocus X-ray imaging

In this paper we present an experimental study on the influence of surface active agents (surfactants) on Taylor bubble flow in a vertical millimeter-size channel. Moreover we give a short review on the subject and previous investigations. We investigated the shape and dissolution rate of individual elongated carbon dioxide Taylor bubbles, which were hydraulically fixed in a downward flow of water. Bubble shape and dissolution rate was determined from microfocus X-ray radiographs. From the shrinking rate we calculated the liquid side mass transfer coefficient.The results show that the presence of surfactants causes a change of the bubble shape and leads to a slight increase of the liquid film thickness around the bubble and as a result the elongation of contaminated bubbles. In addition, the comparison of clean and contaminated bubbles indicate that presence of surfactant has a more significant impact on the dissolution rate of small bubbles. Furthermore, applying different concentrations of surfactant reveals that in our case, where surface coverage ratio of surfactant on the bubbles is high, increase of contamination does not have a noticeable influence on the mass transfer coefficient of bubbles.     

On the effect of wall oscillations on mass (heat) transfer in channel flow

Summary A mechanism is investigated which might lead to enhancement of the rate of mass (or heat) transfer in channel flow at relatively low Reynolds numbers. One of the possible areas of application of this mechanism concerns blood oxigenators. Enhancement of the transfer rate is sought by oscillating the channel walls. The mass transfer analysis given in this paper shows that, for large Peclet numbers and small amplitudes of the wall oscillations, the effect of the steady streaming can be exploited in order to increase mass transfer from the wall only for a range of moderate values of non dimensional frequency α close to 1.

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Sommario Si analizza un meccanismo che può rivelarsi idoneo ad attivare lo scambio di massa (o calore) in dispositivi di scambio operanti in condizioni di deflusso laminare. In particolare una verosimile e significativa area di applicazione di tale meccanismo è quella degli ossigenatori a membrana utilizzati nella circolazione extracorporea. Nel caso qui esaminato il procedimento di possibile attivazione dello scambio di massa consiste nel far vibrare ad opportune frequenze le pareti che delimitano i meati di cui è costituito l'ossigenatore. L'analisi mostra che per grandi valori del numero di Peclet e piccole ampiezze di oscillazione delle pareti, lo scambio di massa è incentivato solo per valori del parametro adimensionale di frequenza α (numero di Womersley) prossimi ad 1.

     

The effect of the vasomotion on the mass transfer in microcirculation

Detailed structure of the attracting set of the piecewise linear Henon mapping(x, y)→(1- a|x|+by,x)with a=8/5 and b=9/25 is described in this paper using the method of dual line mapping. Let A and B denote the fixed saddles in the first quadrant, and in the third quadrant, respectively. It is claimed that(1)the attracting set is the closure of the unstable manifold of saddle B, which includes the unstable manifold of A as its subset, and(2)the basin of attraction is the closure of the stable manifold of A, bounded by the stable manifold of B, which is in the limiting set of the stable manifold of A.Relations of the manifolds of the periodic saddles with the manifolds of the fixed point are given. Symbolic dynamics notations are adopted which renders possible the study of the dynamical behavior of every piece of the manifolds and of every homoclinic or heteroclinic point.     

Theoretical study of the effect of liquid desiccant mass flow rate on the performance of a cross flow parallel-plate liquid desiccant-air dehumidifier

A computer simulation using MATLAB is investigated to predict the distribution of air stream parameters (humidity ratio and temperature) as well as desiccant parameters (temperature and concentration) inside the parallel plate absorber. The present absorber consists of fourteen parallel plates with a surface area per unit volume ratio of 80 m²/m³. Calcium chloride as a liquid desiccant flows through the top of the plates to the bottom while the air flows through the gap between the plates making it a cross flow configuration. The model results show the effect of desiccant mass flow rate on the performance of the dehumidifier (moisture removal and dehumidifier effectiveness). Performance comparisons between present cross-flow dehumidifier and another experimental cross-flow dehumidifier in the literature are carried out. The simulation is expected to help in optimizing of a cross flow dehumidifier.     

Interfacial mass transfer around a vapor bubble during nucleate boiling

Interfacial mass transfer from vapor bubbles affects markedly the heat transfer efficiency of nucleate boiling. The position of the interfacial zone that exhibits zero net mass flux, namely, the zero-flux zone, represents an essential parameter in detailed modeling works on nucleate boiling. Assuming a linear temperature profile in the superheated liquid adjacent to the heating wall, our previous work (Li et al. [10]) demonstrated the zero-flux angle as a function of wall superheat, solid-liquid- vapor contact angle, and bubble growth rate. To make a more realistic framework, we refined in this paper the proposed mass flux model by taking into account the role of thermocapillary flow that is induced by the temperature gradient around the vapor bubble, and that of non-condensable gas presented in the boiling liquid. The Hertz-Kundsen-Schrage equation describes the interfacial mass flux distribution along the vapor bubble surface. Owing to the flattened temperature distribution produced by thermocapillary flow, which significantly reduces the interfacial area to evaporation, the zero-flux zone shifts to the bubble base with most of the cap regime to condense vapor at the interface and to produce the thermal jet. This occurrence also weakens the dependence of bubble growth rate and of the contact angle on the location of zero-flux zone, and yields early occurrence of the non-condensation limit at which the entire bubble surface is subjected to evaporation. Sensitivity analysis demonstrated the significance of process parameters on the evaluation of zero-flux angle using the HKS equation.     

Slip effect on the magnetohydrodynamics channel flow in the presence of the across mass transfer phenomenon

This paper deals with the slip effect on the across mass transfer (AMT) phenomenon in a three-dimensional flow of a hydromagnetic viscous fluid in a channel with a stretching lower wall. Both walls of the channel are considered to be porous so that the AMT phenomenon can be established. The governing equations are solved analytically. The accuracy of the series solution is proved by comparing the results with a numerical solution. The slip condition is observed to be helpful in reducing the viscous drag on the stretching sheet.     

The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK ₀ of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK ₀ is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases. The Project is supported by the National Natural Science Foundation of China.     

The effect of orifices on the liquid distribution in annular two-phase flow

The effect of using orifices to disrupt the water film in air-water annular two-phase flow has been studied experimentally in a vertical tube by measuring the wall film flowrate at various distances upstream and downstream of several different sizes of orifice. The orifices cause a temporary reduction in the downstream water film flowrate, which returns to its equilibrium value further downstream. The experimental results have been used, together with those of other investigators, to compare the effects of orifices to those of swirl tapes, and further to compare the processes of entrainment and deposition within annular two-phase flow.     

气泡夹带对壁面油膜流动特性的影响

油-气润滑系统工作过程中,润滑油膜受微油滴冲击和压缩空气扰动影响易形成气泡夹带现象,气泡夹带行为将对壁面润滑油膜层的形成及流动过程产生重要影响。基于VOF数值模拟方法,对含气泡油膜沿倾斜壁面的流动行为进行研究,考察了气泡的存在对油膜形态和流动速度的影响规律,以及气泡破裂阶段空腔邻域内流体压力变化特性。研究表明,油膜夹带气泡的形变和迁移诱发气泡周围微流场的速度扰动现象,导致气液界面处产生非均匀速度梯度分布,进而引发油膜表面的形态波动。气泡发生破裂时,油膜空穴部位发生明显的正负压力波动现象,气泡附近壁面将承受一定的交变载荷作用。     

The effect of free stream turbulence on the momentum,heat and mass transfer during flow around a sphere

On the basis of our own experimental investigations of the effect of the fluid stream turbulence on the mean heat transfer, a possibility of significant (up to about 60 per cent) intensification of the process was shown. In the second part of this work, the authors attempted to analyze phenomena which result in heat layer. The significant role of three-dimensional disturbances of the Goertler type in the process of formation of “pseudo-laminar” boundary layer, was emphasized.     

Momentum and heat transfer in two-phase bubble flow—I. Theory

A theory is proposed which describes the transfer process of momentum and heat in a two-phase bubble flow in channels. The eddy diffusivity to express the turbulent structure of the liquid phase is subdivided into the two components, one for the inherent wall turbulence independent of bubble agitation and the other for the additional turbulence caused by bubbles. On the basis of the theory, the velocity profile and the frictional pressure gradient for a given flow can be predicted when its void fraction profile is known. Furthermore, when a uniform heat flux is added to the system, its temperature distribution and heat transfer coefficient can be determined. A method for the numerical calculation of these parameters is also presented.     

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T _Wx and surface injectionv _Wx(–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

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Der Effekt des Oberflächenstoffaustausches bei auftriebsinduzierter Strömung in einem variablen porösen Medium, das an eine vertikale, beheizte Platte angrenzt

Zusammenfassung Es wird der Effekt des Oberflächenstoffaustausches in auftriebsinduzierter Strömung in einem variablen porösen Medium, das an eine vertikale, beheizte Platte angrenzt, für große Reynoldszahlen untersucht. Ähnliche Lösungen werden im Rahmen der Grenzschicht-Theorie, durch Variation des Potenzansatzes der Oberflächentemperatur,T _Wx , und der Oberflächengeschwindigkeit,v _Wx(–1/2), erreicht. Die Analyse vereinigt sowohl den Ausdruck, der Porösität und Permeabilität verbindet, als auch den Ausdruck, der Porösität und Wärmeleitfähigkeit miteinander verbindet. Der Einfluß der Temperaturverteilung auf Strömung und Wärmeübergangskennzahlen wird ebenfalls im Detail analysiert. Als Ergebnis der vorliegenden Untersuchung ergibt sich die Tatsache, daß variable Porösität Wärmeübertragungsrate und Betrag der Geschwindigkeit in Wandnähe steigert. Die bestimmenden Gleichungen, sowohl für das Darcysche Strömungsmodell als auch für das Forchheimersche Strömungsmodell, werden mit Hilfe eines implizierten Differenzenschemas gelöst. Die Berechnung wird für die beiden Fälle, isotherme Oberfläche und undurchlässige vertikale Platte, angewandt. Der Einfluß der Terme für die Trägheitskräfte im Forchheimerschen Modell senkt Wärmeübergangs- und Durchgangsrate, wogegen die Wärmeübergangsrate durch den Einfluß der Temperaturverteilung erhöht wird.

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Nomenclature a constant defined by Eq. (12) - A constant defined by Eq. (12) - B constant defined by Eq. (3) - b _s/_f ratio of thermal conductivities - C constant defined by Eq. (1) - C _P specific heat of the convective fluid - d particle diameter - f dimensionless function defined by Eq. (14) - f _w lateral mass flux parameter - g acceleration due to gravity - k ₀ mean permeability of the mediumk ₀= ₀ ³ d ²/150 (1– ₀)² k ₀=1.75d/(1– ₀) 150 (Inertia parameter) - L length of the source or sink - m mass transfer - n constant defined in Eq. (12) - k (y) permeability of the porous medium - k (y) interial coefficient in the Ergun expression - Gr modified Grashof numberGr=(g k ₀ k ₀ (T _w–))/ ² - R _a Rayleigh number (g k ₀ x T _w–)/ - R _ad modified Rayleigh number (g k ₀ d|T _w–|)/ - N _u Nusselt number - s x/d - Q overall heat transfer rate - T temperature - T _w surface temperature - T ambient fluid temperature - u velocity in vertical direction - v velocity in horizontal direction - x vertical coordinate - y horizontal coordinate Greek symbols ₀ mean thermal diffusivity _f/ C_p - coefficient of thermal expansion - constant defined in Eq. (4) - ratio of particle to bed diameter - _e effective thermal conductivity - f thermal conductivity of fluid - _s thermal conductivity of solid - dimensionless similarity variable in Eq. (13) - value of at the edge of the boundary layer - constant defined in Eq. (1) - _e effective molecular thermal diffusivity - (y) porosity of the medium - ₀ mean porosity of the medium - viscosity of the fluid - ₀ density of the convective fluid - stream function - w condition at the wall - condition at infinity