Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

An investigation of falling liquid films on a vertical heated/cooled plate

The temperature field and flow patterns of a liquid film flowing over a vertical uniformly heated surface have been experimentally investigated. Our experiments show that this film flow is sensitive to the heating conditions. When the film is cooled by the substrate, its surface area increases, and when it is heated its surface area decreases. The analysis attributed the changing properties of the flow to lateral Marangoni effect, i.e. to surface tension gradient transverse to the flow. The influence of the viscosity variations on the non-isothermal liquid film flow was also considered and compared with that of the surface tension variations. It was shown that the contraction or extension of the films was mainly caused by the lateral surface tension gradient that might be determined by the viscosity variations.     

Wave formation on vertical falling liquid films

The method of integral relations is used to derive a nonlinear “two-wave” structure equation for long waves on the surface of vertical falling liquid films. This equation is valid in a wide range of Reynolds numbers and reduces to the known equations for high and low Re. Theoretical data for the fastest growing waves are compared with the experimental results on velocities, wave numbers and growth rates of the waves in the inception region. The validity of theoretical assumptions is also confirmed by the direct measurements of the instantaneous velocity profiles in a wave liquid film.     

Heat transfer to non-newtonian laminar falling liquid films with smooth wave free gas—liquid interface

The present paper investigates analytically the problem of heat transfer to a non-Newtonian laminar falling liquid film flowing along an inclined wall for the thermally developing and thermally developed regions. In the developing region of the temperature profile, the Nusselt number decreases monotonically until the thermal boundary layer touches the interface. But immediately after this point, the liquid film thickness decreases as well as the temperature difference in the film. The influence of parameters such as α (i.e. Fr/Re_mod ratio), γ (i.e. modified form of ?μ), modified Prandtl number and the flow behaviour index “n’ on heat transfer results is also presented.     

等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明,模型方程在小到中等Reynolds数下都适用,并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加,展向不稳定性增长率则随着Marangoni数增加而增加,随着Reynolds数增加而减小,流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明,在等热流密度加热条件下,液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构,液膜与气体的换热也因溪流状结构的出现而加强;在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强,液膜会提前破裂;在随机扰动的基础上引入占优势地位的流向最不稳定扰动时,液膜的换热会增强,但不会提前破裂;在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时,换热会加强且液膜会提前破裂。     

The effect of liquid viscosity on mixing in falling films

The effect of liquid viscosity on mixing in falling liquid films has been investigated using a Macropore as a means of simulating conditions in a packed column.-Mass transfer coefficients and transfer unit heights have been calculated for the absorption of stagnant carbon dioxide at atmospheric pressure and 25° C into aqueous glycerol for a range of liquid rates and glycerol concentrations, and the values compared with those from Penetration theory correlations.-Deviations from expected behaviour have been observed, notably that the exponent on the overall mass transfer coefficient with respect to film Reynolds number is significantly greater than the value of one-third predicted from the Higbie model.-It has been shown that mixing at the discontinuities is more than 75% complete for pure water but that this mixing factor decreases with increasing viscosity.     

Phenomena of a liquid drop falling to a liquid surface

Two kinds of phenomenon have been observed when a liquid drop falls to a surface of the same liquid. The first, which can nearly always be observed, involves splash and some degree of penetration and cleavage and the conditions for this occurrence are identified. The experimental observations are compared with previous computational results. The second kind of colliding phenomena can be observed only by chance in an ordinary falling drop experiment and appears to be random. It includes the two phenomena investigated in this paper: the floating drop and the rolling drop.     

Selection of solitary waves in vertically falling liquid films

Two-dimensional solitary waves at the surface of a film flow down a vertical plane are considered. When the system is subjected to inlet white noise, solitary waves are formed after an inception region and interact with each other. Using open-domain simulations of reduced equation models, we investigate numerically their late time process dynamics. Close to the instability threshold, the waves synchronize themselves into bound states. For higher values of the Reynolds number, the separation distance between the waves increases and the synchronization process at work is weaker. Performing statistics, we show that the mean characteristics of the waves correspond to the minimal value of the mean film thickness along the traveling-wave branch of solutions. In this regime, synchronization occurs through the waves tails which is associated with a change of scaling of the waves features. A similar behavior is observed performing simulations in periodic domains: the selected waves maximize the mean flow rate.     

Three-dimensional surface characteristics of a falling liquid film

Optical methods are described for examining the three-dimensional character of waves on a falling liquid film. This involved monitoring the motion of the local film surface normal through the use of laser beam refraction. The wavy motion was found to be primarily of a two-dimensional nature only for Re (equal to 4Q/v) less than 1500.

Surface characteristics were examined for Reynolds numbers from 217 to 4030 and for different distances along the direction of flow.     

Interaction between liquid droplets and heated surface

In this paper, experimental methods and investigation results of interaction between droplets of different liquids and a heated surface are presented. Wetted area, contact time period and transition boundary from wetted to non-wetted interaction regimes are experimentally evaluated. A simple connection of the wetted area value and contact time period with the heat removal efficiency is shown.     

Evaporation and explosion of liquid drops on a heated surface

The literature pertinent to various aspects of drop evaporation on a heated surface is reviewed. Both the laser shadowgraphic and direct photographic methods are employed to study thermal stability and flow structures in evaporating drops in all heating regimes. It is revealed that four flow regions exist in stable and unstable type drops at low liquid-film type vaporization regime. As the surface temperature is raised, the flow regions reduce to two. In the nucleate-boiling type vaporization regime, the interfacial flow structure changes due to a reduction in the Marangoni number as well as the dielectric constant of the liquid. An evidence of bubble growth in the drops is disclosed. The micro explosion of drops is found to occur in the transition-boiling type heating range. No drop explosion takes place in the spheriodal vaporization regime except when the drop rolls on to a microscratch on the heating surface. It is concluded that the mechanisms for triggering drop explosion include the spontaneous nucleation and growth phenomena and the destabilization of film boiling.     

Entropy generation in a liquid film falling along an inclined porous heated plate

In this paper, the second law analysis of a laminar falling viscous incompressible liquid film along an inclined porous heated plate is investigated. The upper surface of the liquid film is considered free and adiabatic. Based on some simplifying assumptions, analytical solutions for the fluid velocity and temperature are constructed. The expressions for the entropy generation rate and irreversibility ratio are obtained and the results are presented graphically and discussed quantitatively for several values of suction Reynolds number (Re) and group parameter (BrΩ⁻¹).     

Investigations of the Marangoni effect on the regular structures in heated wavy liquid films

Formation and development of quasi-regular metastable structures within laminar-wavy falling films were studied. These structures emerge within the residual layer between large waves and could be one reason for the break up of the falling film. The temperature field of the film surface was visualised using IR-thermography. The film thickness was obtained from point measurements with the chromatic confocal imaging method and converted into a film thickness field, based on a quasi-steady assumption and IR thermography images. The thermo-capillary nature (Marangoni effect) of the regular structures was proven experimentally.     

Evolution of metastable quasi-regular structures in heated wavy liquid films

Formation and development of quasi-regular, metastable structures within laminar wavy falling films were studied using IR-thermography. These structures emerge within the residual layer between large waves. It is shown that the typical size of regular structures does not depend on the liquid flow rate and is in the order of magnitude of the critical length of the Rayleigh–Taylor instability. Also a model of thermal-capillary breakdown on the basis of a simplified force balance between the surface tension and the tangential stress as well as the energy balance in the residual layer is presented. Model predictions and experimental data are in good agreement.     

Rate of evaporation from the free surface of a heated liquid

A method and an experimental setup are developed for determining the intensity of evaporation from the free surface of water. During the measurement, the ambient air velocity and the water temperature can be varied. The mass and temperature of water, as well as the temperature, pressure, and humidity of the ambient air are measured as functions of time. The evaporation rates are calculated from the measured and recorded data in the cases of natural and forced convection.     

Wave frequency of falling liquid films and the effect on reflux condensation in vertical tubes

Visual investigations of effective wave frequency, structure and formation of isothermal and fully developed falling liquid films inside vertical tubes are presented without and with countercurrent flow of vapour. These are supplemented by novel transmissivity measurements leading to considerable improvement of the established wave shape and liquid film structure classifications. In addition, reflux condensation heat transfer data evaluated for the limiting case of zero shear stress are represented in terms of the wave factor. These are correlated with Reynolds and Kapitza numbers and they are interrelated with the observed wave characteristics.     

Experimental study of the stochastic nature of wave phenomena on the surface of a liquid film

An experimental study was made of wave phenomena on the surface of a liquid film freely flowing down the walls of a vertical channel in the range of Reynolds numbers for film flow (Re=Γ/η= 50–2500, where Γ is the mass spray density and η is the dynamic viscosity) at various distances from the entrance. The working fluid (water) was fed into the operating section at a temperature of 15–30 °C. The dependence of typical wave parameters on mode parameters was obtained.     

A numerical study of the non-absorbable effects on the falling liquid film absorption

A numerical study for the simultaneous heat and mass transfer in a falling liquid film absorption process with the presence of non-absorbable gases is presented. Water vapor mixed with air as the non-absorbables being absorbed into a falling smooth aqueous lithium chloride film flow was chosen as the model problem for the study. The finite difference numerical calculation was proceeded by marching downward from the top end, owing to the parabolic type energy and concentration equations for both liquid and gas phases. The results indicate that the local non-absorbable gas concentration is much higher at the gas-liquid interface than that in the ambient, hence the local vapor pressure is lowered there such that the absorption driving potential of the vapor pressure difference is reduced. The resulting reduction of the absorption rate due to the presence of the non-absorbables suggests that its effect must be carefully considered in the application of absorption heat pump design. The present study can provide some useful information for this purpose.

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Numerische Studie über die Einwirkung von nicht absorbierbaren Stoffen auf die fallende Flüssigkeitsfilmabsorption

Zusammenfassung Hier wurde eine numerische Studie der Wärmeund Stoffübertragung in einem Absorptionsprozeß eines fallenden Flüssigkeitsfilms in Anwesenheit von nicht absorbierbaren Gasen dargestellt. Ein Wasserdampf-Luft-Gemisch, das in Anwesenheit von nicht absorbierbaren Gasen von einer fallenden glatten flüssigen Lithium-Chlorid-Filmströmung absorbiert wird, wurde als das Modellproblem für diese Studie gewählt. Die numerische Berechnung mit dem Finite Differenzenverfahren wurde schrittweise vom obersten Ende nach unten durchgeführt. Die Berechnung bezieht sich auf den parabolischen Typ der Energie- und Konzentrationsgleichungen für die Flüssigkeits- und Gasphasen. Die Ergebnisse weisen darauf hin, daß die lokale nicht absorbierbare Gaskonzentration bei der Gasflüssigkeitsphase sehr viel höher ist als in der Umgebung. Weiter ist der lokale Dampfdruck so erniedrigt worden, daß sich das Absorptionsbewegungspotential des Dampfdruckunterschiedes reduziert. Die resultierende Reduzierung der Absorptionsrate, die auf die Anwesenheit der nicht absorbierbaren Stoffe zurückzuführen ist, verlangt eine sorgfältige Einbeziehung ihere Einflüsse auf die Gestaltung der Absorptionswärmepumpen. Diese Arbeit kann einige nützliche Informationen für diesen Zweck geben.

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Nomenclature C absorbent concentration in weight fraction of salt - C _a nonabsorbables concentration in molar fraction - C _a at inlet and infinity - C _in C at film inlet - c _p specific heat of liquid - c _{p g} specific heat of gas - D species diffusivity for LiCl-H₂O - D _g species diffusivity for air-water vapor - g gravity - h _o film thickness - H _a heat of absorption - k thermal conductivity of liquid - k _g thermal conductivity of gas - L transformation constant - water vapor mass absorption rate - P _v water vapor pressure - Re film Reynolds number=V ₀ h ₀/ - T film temperature - T _in film temperature at inlet - T _g gas temperature - T _w wall temperature - T gas temperature at inlet and infinity - u velocity inx-direction - U =1.5V ₀ - V ₀ mean film velocity=g h ₀ ² /3µ - x coordinate parallel to the wall - y coordinate normal to the wall in the film region - y _g coordinate normal to the wall in the gas region - transformedy _g Greek letters dynamic viscosity - liquid density - _g gas density