Heat transfer of dilute spray impinging on hot surface (simple model focusing on rebound motion and sensible heat of droplets)

In the present paper, focusing on the effects of the rebound motion and sensible heat of droplets on spray-cooling heat transfer in the high temperature region, a simple model was developed to predict the heat flux distribution of a dilute spray impinging on a hot surface. In the model, the local heat flux was regarded as the sum of the heat flux components by droplets, induced air flow, and radiation. To estimate the heat flux component by droplets, it was assumed that the heat flux upon droplet impact is proportional to the sensible heat which heats up the droplet to the saturation temperature and the proportional factor C is constant. In addition, to take account of the contribution of the heat flux upon impact of rebounded droplets, it was assumed that the flight distance of droplets during rebound motion is distributed uniformly from 0 to L_max (maximum flight distance) . The values of C and L_max determined by experimental data of local heat flux indicate that the assumptions employed in the present model is valid at least as the first order approximation.     

Numerical analysis of meniscus dynamics in monolayer-wick dropwise condensation

The effect of hydrophobic monolayer sintered-particle wick on the growth and departure of droplets in dropwise condensation over a vertical surface is analyzed numerically using the minimum meniscus surface energy principle and the direct simulation of the meniscus and heat transfer through the partially liquid-filled pores. The condensate fills the pores, increases the capillary pressure, and joins with the menisci from adjacent pores, leading to a droplet formation. The droplet growth is supported by liquid supply from the adjacent pores until the critical droplet departure volume is reached. The heat transfer rate is controlled by the average meniscus thickness, and the droplet surface coverage. Based on these and the plain–surface limit (for very small and very large particle diameter d_p), a threshold band of d_p is predicted below which the dropwise condensation rate is slightly enhanced compared to the plain, hydrophobic surface. The analysis explains the existing experimental results (and new augmented experimental results) and the challenges in further enhancing the dropwise condensation with surface microstructures.     

A numerical study on growth mechanism of dropwise condensation

Based on the intrinsic growth rate (R ～ T^1/3) of single droplet, processes of nucleation, growth, renucleation and sweeping of droplet are simulated in this paper. The influences of number of initial droplets on average radius, surface coverage and number of droplets on substrate are investigated. The simulation results show that the apparent growth rate of droplets is strongly dependent on the number of initial droplets. In addition, statistical fractal characteristic of droplet size distribution is found to be consistent with experimental measurements, and the drop size distribution is also found to be consistent qualitatively with that from experimental observations. The validity of the present simulations is thus verified. The present work may provide a great help in well understanding of the growth mechanism of dropwise condensation.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.     

Dynamic properties of vibrated drops on a superhydrophobic patterned surface

With the development of micro- and nano-technology, superhydrophobic surfaces with higher apparent contact angle and lower sliding angle have considerable technological potential for various applications such as dewetting and dropwise condensation. In this work, the square-shaped pillars rough surfaces were prepared with the polydimethyl-siloxane substrate using photolithography techniques. The dynamic properties of the droplets were studied on the superhydrophobic patterned surface. By adjusting the frequency and the amplitude of the vertical displacement, we observe droplets bounding from the superhydrophobic surface at a certain frequency and amplitude. For a certain size of droplet, the results show that the vibration amplitude which induces a droplet to bounce off from the superhydrophobic surface at the resonant frequency is remarkably smaller than the detaching amplitudes of neighboring frequencies. In order to verify the analysis, the eigenfrequency of the other size of droplet was compared with its resonant frequency. The experimental results were in accordance with the theoretical analysis. Therefore, a novel method is provided to remove the condensation droplets from the solid surface in order to improve the heat transfer performance.     

Condensation on a spray of water drops: a cell model study-II. Transport quantities

The formulation for a unit cylinder cell model that was used to analyze the hydrodynamics and heat transfer associated with steam condensation on a spray of equal sized water droplets was presented in part I of this study. In this part II, we report the results and discussions for the condensation induced interfacial velocities, surface shear stress, Nusselt number and the Sherwood number. The heat transport in both phases and the species transport in the continuous phase have been treated as transient processes. The interactions between neighboring drops have been examined. Numerically obtained transport results have been compared with an experimental study. Results for a representative spray show that the use of correlations developed for an isolated drop to predict condensation spray behavior may be inaccurate, although isolated drop studies continue to merit investigations.     

Heat convection within evaporating droplets in strong aerodynamic interactions

The temperature field within evaporating ethanol droplets is investigated, relying on the two-color laser induced fluorescence (LIF) measurement technique and on a Direct Numerical Simulation (DNS). The configuration studied corresponds to a monodisperse droplet stream in a diffusion flame sustained by the droplet vapor. An experimental probe volume, small compared to the droplet size, is used to characterize the temperature field within the droplets, whereas DNS takes into account key aspects of the droplet heating and evaporation such as the non-uniform and transient stress, and the mass and heat transfer coefficients at the droplet surface. These investigations reveal that the frictional stresses are strongly reduced due to the small spacing between the droplets. They also show that the Marangoni effect has a significant influence on the internal motion and hence on the internal temperature field.     

Dropwise Condensation Enhancement Using a Wettability Gradient

ABSTRACT

This paper deals with the modeling of dropwise condensation process on a wettability gradient surface. The proposed heat transfer model explicitly takes into account the mechanical nonequilibrium on the periphery of the droplet due to the surface-energy gradient and the contact-angle hysteresis. The model aims to predict the dynamic behavior of a droplet placed on a wettability gradient surface regarding the temperature difference between the wall and the saturated vapor. A comprehensive analysis of all the contributing thermal resistances is proposed. The influences of contact angle, temperature difference, and other representative parameters on a single droplet on a horizontal surface are also discussed. The results indicate that a wettability gradient can cause a reduction of the mean size of the droplets on the condensing surface and thus enhance significantly the heat transfer rate.     

Interactions between molten metal droplets impinging on a solid surface

We photographed molten tin droplets (2.2 mm diameter) landing off-center on a circular splat formed by the impact and solidification of another, identical drop. Final splat shapes were sensitive to the spacing between droplet centers, which was varied from 1.0 to 5.0 mm. We used a three-dimensional model of spreading and solidification to simulate interactions between droplets. The model applied a fixed-grid Eulerian control volume method to solve the fluid dynamics and energy conservation equations. A volume-of-fluid algorithm was used to track free surface deformation. Predictions of droplet shapes during impact from the model agreed well with photographs. By following temperature variations at different points on the surface of the first splat we could identify locations where remelting occurred and the splats fused together. Splat shapes observed in experiments with large tin droplets qualitatively resembled those obtained by plasma-spraying nickel powders on a steel surface.     

Droplet Regulation and Dropwise Condensation Heat Transfer Enhancement on Hydrophobic-Superhydrophobic Hybrid Surfaces

ABSTRACT

Efficient Dropwise condensation on nanostructured superhydrophobic surfaces (SHS) has received extensive attention. However, good heat performance only occurs in two conditions: the presence of non-condensable gas, or low surface subcooling. For industrial pure steam condensation, large droplets tend to be pinned on the surfaces due to the large contact angle hysteresis (CAH) and impede heat transfer process. In this study, the SHSs and hydrophobic surface (HS) were integrated in spaced band pattern with different width and CAH. It was observed that the condensed droplets experience a fast horizontal shifting from hydrophobic zones to superhydrophobic zones driven by adhesive force. In this way, the departure path of droplets were altered and the refreshing frequencies are increased for both SHS and HS regions. The heat transfer coefficients for some 1 mm × 1 mm hybrid surfaces were found to be elevated by about 25% at subcooling of 6K compared to the weighted mean value of individual HSs and SHSs. For surfaces with short dividing distance (about 0.5 mm × 0.5 mm), the bridging effects between droplets in SHS regions were also observed, which is undesirable for heat transfer. These work indicates that strong adhesive force of SHSs can function as a promoter of droplet condensation for hybrid surfaces with proper choice of dividing width.     

Numerical investigation on wet steam non-equilibrium condensation flow in turbine cascade

Based on the two-phase wet steam flow with spontaneous condensation,experimental verification and flow analysis on nozzle and 2D cascade are carried out.The 3D Reynolds-Averaged gas-liquid two-phase flow control equation solver is explored with k ε k p turbulence model.Furthermore,3D flow numerical simulation on the last stage stator of the steam turbine is carried out.The results show that a sudden pressure rise on blade suction surface is mainly caused by the droplet growth in condensation flow.The more backward the condensation position is in cascade passage,the less the sudden pressure rise from condensation is,and the larger the nucleation rate is,the maximum under-cooling and the number of droplets per unit volume are.Interaction of condensation wave and shock wave has imposed greater influence on the parameters of the blade cascade outlet.     

Transient characteristics of initial droplet size distribution and effect of pressure on evolution of transient condensation on low thermal conductivity surface

The droplet size distribution evolution in the initial dropwise condensation process from formation of primary droplets to fully developed stage has been investigated by utilizing high speed camera and microscope. Focus was put on the transient characteristics of droplet size distribution in this duration, it has been revealed that the primary droplets just formed on the condensing surface satisfied Lognormal distribution, with coalescing among them (without departing from condensing surface), bimodal size distribution formed, finally the classical exponential size distribution showed on the condensing surface when the condensation became steady state. At the same time, the effect of steam pressure on the evolution of transient dropwise condensation on low thermal conductivity surface has been analyzed. All the investigations included in the present paper are for the first droplets cycle of dropwise condensation.     

液滴撞击低温超疏水表面运动状态的数值模拟研究

本文针对液滴撞击固体表面后出现的反弹和黏附两种运动状态,通过引入基于连续温度函数的能量方程,建立了用于计算液滴运动、传热和相变过程的数值模型,并与实验结果对比,验证了数值模型的准确性。进而模拟了具有不同韦伯数We和奥内佐格数Oh的液滴撞击低温超疏水表面的运动、传热和相变过程。结果表明：液滴撞击后的运动状态主要取决于奥内佐格数Oh,临界范围是0.022-0.026,而基本不受韦伯数We的影响。当液滴撞击后的运动状态为反弹时,韦伯数We越大的液滴,最大铺展直径越大。而当韦伯数相同时,随着奥内佐格数Oh的增大,液滴与表面的接触时间越大。     

Combustion characteristics of fuel droplets with addition of nano and micron-sized aluminum particles

The burning characteristics of fuel droplets containing nano and micron-sized aluminum particles were investigated. Particle size, surfactant concentration, and the type of base fluid were varied. In general, nanosuspensions can last much longer than micron suspensions, and ethanol-based fuels were found to achieve much better suspension than n-decane-based fuels. Five distinctive stages (preheating and ignition, classical combustion, microexplosion, surfactant flame, and aluminum droplet flame) were identified for an n-decane/nano-Al droplet, while only the first three stages occurred for an n-decane/micron-Al droplet. For the same solid loading rate and surfactant concentration, the disruption and microexplosion behavior of the micron suspension occurred later with much stronger intensity. The intense droplet fragmentation was accompanied by shell rupture, which caused a massive explosion of particles, and most of them were burned during this event. On the contrary, for the nanosuspension, combustion of the large agglomerate at the later stage requires a longer time and is less complete because of formation of an oxide shell on the surface. This difference is mainly due to the different structure and characteristics of particle agglomerates formed during the early stage, which is a spherical, porous, and more-uniformly distributed aggregate for the nanosuspension, but it is a densely packed and impermeable shell for the micron suspension. A theoretical analysis was then conducted to understand the effect of particle size on particle collision mechanism and aggregation rate. The results show that for nanosuspensions, particle collision and aggregation are dominated by the random Brownian motion. For micron suspensions, however, they are dominated by fluid motion such as droplet surface regression, droplet expansion resulting from bubble formation, and internal circulation. And the Brownian motion is the least important. This theoretical analysis explains the different characteristics of the particle agglomerates, which are responsible for the different microexplosion behaviors that were observed in the experiments.     

On the sliding and profile of a liquid droplet on a rotating disk

This theoretical and experimental study was conducted to investigate the critical condition at which a liquid droplet starts to move on a rotating disk. The critical rotational speed ω was theoretically calculated based on the force balance between the surface tension and the centrifugal force, where ω was experimentally measured for each combination between three kinds of test plates and test liquids. The movements of droplets were judged from the careful observation of infinitesimal motion of the three‐phase contact line. The calculated rotational speeds agreed well with measured ones for arbitrary contact angle when the droplets were set on the plate. The three‐dimensional surface profiles of droplets were calculated from the approximate Laplace equation in which the contact line was assumed as the combination of two ellipses with different ratio of measure to minor axis. The measured profiles on the rotating disk were approximated well by the method proposed in this study. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20276     

Advances in droplet array combustion theory and modeling

A review of research on the subject of the vaporization and burning of fuel droplets configured in a prescribed array is presented, including both classical works and research over the past decade or two. Droplet arrays and groups and the relation to sprays are discussed. The classical works are reviewed. Recent research on transient burning and vaporization of finite arrays with Stefan convection but without forced convection is presented, including extensions to non-unitary Lewis number and multi-component, liquid fuels. Recent results on transient, convective burning of droplets in arrays are also examined. In particular, transient convective burning of infinite (single-layer periodic and double-layer periodic) and finite droplet arrays are discussed; attention is given to the effects of droplet deceleration due to aerodynamic drag, diameter decrease due to vaporization, internal liquid circulation, and arrays with moving droplets in tandem and staggered configurations. Flame structure is examined as a function of spacing between neighboring droplets and Damköhler number: individual droplet flames versus group flames and wake flames versus envelope flames. Based on existing knowledge of laminar droplet array and spray combustion theory, experimental evidence, and turbulent studies for non-vaporizing and non-reacting two-phase flows, comments are made on the needs and implications for the study of turbulent spray and array combustion.     

Dropwise condensation from flowing air–steam mixtures: Diffusion resistance assessed by controlled drainage

In this study, the initial phase of drop growth, when diffusion is not limiting, is artificially made more important. An apparatus with controlled removal of condensate droplets from the condenser plates is designed and applied. The dropwise condensation process is frequently interrupted upon which nucleation restarts upon each sweep. Condensate growth and surface temperatures are assessed by simultaneous video and infrared recordings. Cold wakes downstream of big drops on the condenser plate were observed. A single controlled droplet removal action enables a ‘reset’ of the condenser surface. This allowed measurement of droplet growth histories. It is found that droplet growth follows a power law of D ∝ t^β, with β increasing with increasing ω_vap,in. Direct contact condensation on drops at condenser plate dominates drop growth. The main finding is that the total heat transfer resistance decreases with increasing droplet removal frequency, while two measures for mass transfer simultaneously increase. Increasing diffusion limitation is one explanation for the observed decreasing mass transfer rate with time. After initial fast growth of drops, the slight increase in interfacial temperature observed offers another explanation.     

Transient convective burning of interactive fuel droplets in double-layer arrays

The transient convective burning of n-octane droplets interacting within double-layer arrays in a hot gas flow perpendicular to the layers is studied numerically, with considerations of droplet surface regression, deceleration and relative movement due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Each layer in the double-layer array is a periodic droplet array aligned orthogonal to the free stream direction. The droplets in different layers are arranged either in tandem or staggered. Several different flame structures are found for the double-layer arrays. The transient behaviors of the droplets in both upstream and downstream layers are studied and compared, for various initial relative stream velocity and initial transverse droplet spacing. The average surface temperature and vaporization rate for the front (or upstream) droplets and back (or downstream) droplets are influenced by the flame structure. The front droplets in a double-layer array behave similarly to the droplets in a single-layer array for the streamwise droplet spacing considered in this study. The back droplets approach the front droplets because they generally have lower drag.     

Evaporation of an oil‐in‐water type emulsion droplet on a hot surface

Evaporation characteristics of an Oil‐in‐Water (O/W) emulsion droplet were examined experimentally. The evaporation time per unit of initial surface area of a droplet τ^* was used to estimate the evaporation characteristics of droplets with different diameters and to compare a water droplet and an emulsion droplet. Results show that τ^* of an O/W emulsion droplet is shorter than a water droplet in the Leidenfrost film boiling regime. The four evaporation modes of O/W type emulsion droplets were observed. These depended on the mixing ratio of water and oil, G_S, and hot surface temperature, T_W. Increasing G_S increases the emulsion droplet's Leidenfrost temperature when the droplet is used as a die‐cast releasing agent. Microexplosions were observed during Leidenfrost film boiling when T_W was greater than 250^°C. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 527–537, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20081     

Condensation of steam in silicon microchannels

A visualization study was performed on condensation of steam in microchannels etched in a 〈100〉 silicon wafer that was bonded by a thin Pyrex glass plate from the top. The microchannels had a trapezoidal cross section with a hydraulic diameter of 75 μm. Saturated steam flowed through these parallel microchannels, whose walls were cooled by natural convection of air at room temperature. The absolute pressure of saturated steam at the inlet ranged from 127.5 kPa to 225.5 kPa, and the outlet was at atmospheric pressure at approximately 101.3 kPa with the outlet temperature of the condensate ranging from 42.8 °C to 90 °C. Stable droplet condensation was observed near the inlet of the microchannel. When the condensation process progressed along the microchannels, droplets accumulated on the wall. As the vapor core entrained and pushed the droplets, it became an intermittent flow of vapor and condensate at downstream of the microchannels. The traditional annual flow, wavy flow and dispersed flow observed during condensation in macrochannels were not observed in the microchannels. Based on a modified classical droplet condensation theory, it is predicted that the droplet condensation heat flux increases as the diameter of the microchannel is decreased. It is also predicted that the droplet condensation heat flux of saturated steam at 225.5 kPa can reach as high as 1200 W/cm² at ΔT=10 °C in a microchannel having a hydraulic diameter of 75 μm.