Further considerations of two-dimensional condensation drop profiles and departure sizes

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface, presented in an earlier work, is extended to include advancing contact angles to 180°. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a threedimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length in contact with the wall. A maximum value of this length exists which provides a real solution, and this is taken as the departure size of the drop. It is shown that the general departure shape for an advancing contact angle of 180° includes the cases for all advancing contact angles.     

Effect of surfactants on the growth and departure of bubbles from solid surfaces

Bubbles are an essential mass and energy transport mechanism found in many industrial systems. The size of a bubble and time required for it to form impacts the efficiency of many systems. It has been observed that a surfactant added to an ebullient flow field reduces the departure size of the bubble and the formation time. Experiments and numerical simulations have been conducted to capture bubble growth with and without surfactants in an isothermal system. The results indicate that necking occurs more rapidly with a surfactant present. Final calculations have shown that the tangential velocity causes an increase in total pressure on the neck of the bubble. This additional force causes the neck to collapse more rapidly.     

Secondary atomization of water and isooctane drops impinging on tilted heated surfaces

The present paper reports an experimental study aimed at characterizing the effects of heat transfer on the secondary atomization, which occurs during droplet impact on hot surfaces at conditions reproducing those occurring at fuel injection in internal combustion engines. The experiments consider single isooctane and water droplets impacting at different angles on a stainless steel surface with known roughness and encompass a range of Weber numbers from 240 to 600 and heat transfer regimes from the film-vaporization up to the Leidenfrost regime. The mechanisms of secondary breakup are inferred from the temporal evolution of the morphology of the impact imaged with a CCD camera, together with instantaneous measurements of droplet size and velocity. The combination of a technique for image processing with a phase Doppler instrument allows evaluating extended size distributions from 5.5 μm up to a few millimetres and to cover the full range of secondary droplet sizes observed at all heat transfer regimes and impaction angles. Temporal evolution of the size and velocity distributions are then determined. The experiments are reported at impact conditions at which disintegration does not occur at ambient temperature. So, any alteration observed in droplet impact behavior is thermally induced. The analysis is relevant for port fuel injection systems, where droplets injected to impact on the back surface of the valves, behave differently depending on fuel properties, particularly when the use of alcohols is considered, even as an additive to gasoline.     

Terminal velocities of clean and fully-contaminated drops in vertical pipes

Terminal velocities and shapes of drops rising through vertical pipes in clean and fully-contaminated systems are measured by using a high-speed video camera and an image processing method. Silicon oils and glycerol water solutions are used for the dispersed and continuous phases, respectively. Triton X-100 is used for surfactant. Clean and contaminated drops take either spherical, spheroidal or deformed spheroidal shapes when the diameter ratio λ is less than a critical value, λ_C, whereas they take bullet shapes for λ > λ_C (Taylor drops). The applicability of available drag and Froude number correlations is examined through comparisons with the measured data. Effects of surfactant on the shape and terminal velocity of a Taylor drop are also discussed based on the experimental data and interface tracking simulations. The conclusions obtained are as follows: (1) drag and Froude number correlations proposed so far give reasonable estimations of the terminal velocities of clean drops at any λ, (2) the terminal velocities of contaminated drops are well evaluated by making the viscosity ratio μ^* infinity in the drag correlation for clean drops in the viscous force dominant regime, (3) the effects of surfactant on the shape and terminal velocity of a Taylor drop become significant as the Eötvös number, Eo_D, decreases and μ^* increases, and (4) the reduction in surface tension due to the addition of surfactant would be the cause of the increase in the terminal velocity and elongation of a contaminated Taylor drop.     

A numerical study of droplet motion/departure on condensation of mixture vapor using lattice Boltzmann method

Droplet motion/departure, which is governed by external force acceleration coefficient, droplet radius and surface wettability on solid surfaces under external forces such as gravitational force, play a significant role in characterizing condensation heat transfer, especially when high fractional non-condensable gases (NCG) present. However, due to the challenge in visualizing the vapor/steam velocity field imposed by droplet motion/departure, the detailed mechanism of droplet motion/departure on condensing surfaces has not been completely investigated experimentally. In this study, droplet motion/departures on solid surfaces under external forces and their interactions with steam flow are simulated using two dimensional (2D) multiphase lattice Boltzmann method (LBM). Large external force acceleration coefficient, droplet radius and contact angle, lead to large droplet deformation and high motion/departure velocity, which significantly shortens the droplet residual time on the solid surface. Our simulation shows that steam vortices (lateral velocity) induced by droplet motion/departure can greatly disturb the vapor flow and would be intensified by increasing external force acceleration coefficient, droplet radius, and contact angle. In addition, the location of vortex center shifts in the ascending direction with increase of these factors. The average lateral velocities induced by droplet motion/departure at various conditions are obtained. The mass transfer resistance is substantially reduced owing to the droplet motion/departure, leading to an enhanced heat flux. The experimental results are compared to validate the influence of droplet motion/departure on condensation heat transfer performance, especially for steam–air mixture with the presence of high fractional NCG.     

Three-dimensional numerical simulation of sedimenting drops inside a vertical channel

Numerical simulation of sedimenting deformable drops inside a vertical channel has been performed at finite Reynolds numbers. The channel is confined by two vertical walls in x-direction and is periodic in y- and z-directions. Results are obtained using a finite difference/front-tracking method. The main dimensionless parameters are the Reynolds number, the Bond number and ratio of the length of channel to the diameter of drops. The effect of these parameters on lateral migration of drops is investigated. It is found that the wall repulsion is the main mechanism of the lateral migration of the drop, and drop migrates toward the channel axis. When the Reynolds number is relatively low, two different lateral migration regimes are observed: migration with monotonic approach and migration with damped oscillations. These regimes are affected by the dimensionless parameters. When the Bond number increases, the oscillations of drop around the centerline of channel are stronger and drop reaches the channel centerline in a larger period. Results of lateral migration of one drop are consistent with perturbation theory, and two-dimensional numerical simulations performed by Feng et al. (1994). The drag coefficient has also been calculated, and effect of various parameters has been discussed. Two drops interaction is similar to that observed by Feng et al. (1994) for two-dimensional circular cylinders. Results are consistent with experiments performed by Wu and Manasseh (1998). Simulations of four sedimenting drops show that depending on the relative size of drops, they either fall in two rows or they form a single horizontal layer and settle with a unique velocity.     

On the impact of viscous drops onto dry smooth surfaces

An experimental study of the impact of glycerol/water drops onto a dry glass surface at Reynolds and Weber numbers around the splashing/deposition threshold is presented. Some new observed phenomena that may shed further light on the mechanisms underlying air bubble entrainment and splashing for high-viscosity liquids are presented and discussed. The experiments were recorded with a high-speed camera using two complementary lighting setups that enhance the visualization of different features of the air entrainment phenomena: backlighting with a light diffuser and oblique lighting without diffuser. Besides the ring of micro-bubbles surrounding the central entrapped bubble and the cloud of bubbles entrained as a result of the interaction between a levitated thin film and the solid surface, which have been studied by other authors in previous works, a second ring of micro-bubbles that delimits the outer cloud of bubbles has been detected in our investigation. Attention is mainly focused on analyzing the dependency of the behavior of the two rings of micro-bubbles on the drop impact velocity, the ranges of the relevant dimensionless numbers in which the rings are formed and the existence, in certain impact conditions, of an abrupt increase in the size of the second ring, which substantially modifies the impact outcome.     

Stability of the evaporation and condensation surfaces in a porous medium

The stability of a phase transition interface which separates the soil regions saturated with water and humid air, respectively, is investigated. The humid air region contacting with the atmosphere is assumed to be located above the water-saturated region. Water flows through the porous medium in the lower region, while diffuse vapor transfer is implemented in the upper region. Two cases corresponding to water evaporation and vapor condensation are considered. In the first case water flows out from the porous aquifer, evaporates, and comes out into the atmosphere. In the second case, during condensation, the atmospheric moisture saturates soil. The problem is solved in the steady-state case. The investigation of linear stability carried out by means of the normal mode method shows that the evaporation surface can be unstable in both nonwettable and wettable soils in the presence of the capillary pressure gradient. Depending on the parameters, the condensation surface can be unstable also in the neutral medium.     

Heat transfer in condensation on a vertical tube in a granular bed

S. S. Kutateladze Institute of Heat Physics, Siberian Branch of the Russian Academy of Sciences. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 6, pp. 102–107, November–December, 1995.     

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.     

Analysis of the film condensation process of vapor on a vertical finely serrated surface

The process of film condensation of vapor on vertical finely serrated surfaces is investigated. The analysis shows that owing to the specific conditions under which the distribution of the condensed film along the cooling surface is in the main affected by surface tension, the effectiveness of such surfaces may be several times higher than that of plain tubes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 93–97, May–June, 1969.     

Experimental study on condensation heat transfer of steam on vertical titanium plates with different surface energies

Visual experiments were employed to investigate heat transfer characteristics of steam on vertical titanium plates with/without surface modifications for different surface energies. Stable dropwise condensation and filmwise condensation were achieved on two surface modification titanium plates, respectively. Dropwise and rivulet filmwise co-existing condensation form of steam was observed on unmodified titanium surfaces. With increase in the surface subcooling, the ratio of area (η) covered by drops decreased and departure diameter of droplets increased, resulting in a decrease in condensation heat transfer coefficient. Condensation heat transfer coefficient decreased sharply with the values of η decreasing when the fraction of the surface area covered by drops was greater than that covered by rivulets. Otherwise, the value of η had little effect on the heat transfer performance. Based on the experimental phenomena observed, the heat flux through the surface was proposed to express as the sum of the heat flux through the dropwise region and rivulet filmwise region. The heat flux through the whole surface was the weighted mean value of the two regions mentioned above. The model presented explains the gradual change of heat transfer coefficient for transition condensation with the ratio of area covered by drops. The simulation results agreed well with the present experimental data when the subcooling temperature is lower than 10 °C.     

Heat and mass transfer during condensation in a vertical channel under mixed convection

The problem of condensation by mixed convection in a vertical channel has been numerically analyzed for an air water system. The plates of the channel are subjected to uniform but different heat fluxes. The effects of ambient conditions on the condensation process are investigated. The results show particularly the existence of a particular temperature called inversion temperature for condensation. This temperature is defined as the temperature above it the condensation rate is higher for a lower vapor concentration. It was found that this temperature increases with the increase of the ambient pressure and decreases with the cooling heat flux.