Binarization of the gray scale images of droplets during dropwise condensation on textured surfaces

Session: Image Analysis IIInternational audienceIn this research two methods for recognizing water droplets that are formed during dropwise condensation on the flat and pillared substrates are presented. The aim of these methods is to binarize the gray scale images of the droplets taken by a CCD camera in order to extract the information related to the droplets size and density

Modélisation et simulation de la croissance de gouttes d'eau sur substrat texturée lors de la condensation

The aim of this thesis is to develop a numerical simulation model to study the process of dropwise condensation on flat and textured substrates. The experimental part was carried out on the poly carbonate surfaces that were duplicated from a metallic mold textured using laser technology. The samples are monted on a home-made condensation set-up. The results of these experiments are gray scale images that had to be binarized in order to get the information related to droplets growth rate, density and spatial distribution. Then, three different models were developed during this thesis to describe droplets behavior:1. a classical method that considers droplets as spherical-caps growing on a flat substrate2. a method that considers elliptical droplets (contact angle = 90°) growing on the textured substrates,3. and a modified method that considers ellipsoidal-cap droplets (contact angle ≠90°) growing on the textured substrates.The results of these three methods are validated by comparison with experimental data on a flat surface, 6 different configurations of pillared surfaces, and 6 configurations of sinusoidal patterns. The spatial distribution of droplets on both flat and textured substrates are studied using Fry plot and Ripley’s K directional methods as well. Moreover, a method for studying the size distribution function of small droplets is proposed by modifying the method of Abu-Orabi for the unit surface. The results show acceptable accordance between the models proposed and respective experimental data. Also regarding spatial distribution, the initial small droplets are distributed completely randomly, while the coalescing drops forms in the direction of texturing patterns on the substrate.Le but de cette thèse est de développer un modèle de simulation numérique pour étudier le processus de condensation par gouttelette sur des substrats plats et texturés. La partie expérimentale a été réalisée sur des surfaces de polycarbonate qui ont été dupliquées à partir d'un moule métallique texturé en utilisant la technologie laser. Les échantillons sont montés sur une installation de condensation conçue dans le laboratoire. Les résultats de ces expériences sont des images en échelle de gris qui ont dû être binarisées afin d'obtenir les informations liées au taux de croissance des gouttelettes, à la densité et à la distribution spatiale. Ensuite, trois modèles différents ont été développés au cours de cette thèse pour décrire le comportement des gouttelettes:1. une méthode classique qui considère les gouttelettes comme des calottes sphériques se développant sur un substrat plat,2. une méthode qui considère les gouttelettes elliptiques (angle de contact = 90°) en croissance sur les substrats texturés,3. et une méthode modifiée qui considère les gouttelettes à coiffe ellipsoïdale (angle de contact ≠ 90°) en croissance sur les substrats texturés.Les résultats de ces trois méthodes sont validés par comparaison avec des données expérimentales sur une surface plane, 6 configurations différentes de surfaces à piliers et 6 configurations de motifs sinusoïdaux. La distribution spatiale des gouttelettes sur les substrats plats et texturés est étudiée à l'aide des méthodes Fry plot et K directionnel de Ripley. De plus, une méthode pour étudier la fonction de distribution de taille de petites gouttelettes est proposée en modifiant la méthode d'Abu-Orabi pour la surface unitaire.Les résultats montrent une concordance acceptable entre les modèles proposés et les données expérimentales respectives. Toujours en ce qui concerne la distribution spatiale, les petites gouttelettes initiales sont distribuées de manière complétement aléatoire, tandis que les gouttes coalescentes se forment dans le sens des motifs de texturation sur le substrat

Random and geometric model of droplets nucleation on textured surfaces

International audienceThe aim of this study is to simulate dropwise condensation in order to control the rate of droplets nucleation and growth. The process of dropwise condensation attracted lots of attention since about 80 years ago, when Schmidt et al. proved that its heat transfer coefficient is significantly higher than filmwise condensation. Dropwise condensation is preferred when higher rate of heat transfer is needed. The problem that we are dealing with is the formation of liquid droplets in car light shield which will cause the light reflection, in such cases it is preferred to achieve the filmwise regime. In this research we are going to develop a computer algorithm to simulate spatial distribution as well as growth rate of droplets at each time step. The results of the presented algorithm are validated by comparing with the experimental data and spatial distribution in Poisson point process

Mathematical model of dropwise condensation on textured surfaces

Catégorie: Communication par afficheNational audienceIntroduction: The aim of this project is to develop a geometric and mathematical model for simulating dropwise condensation in order to control the rate of droplets growth on a textured surface. Comparison between gray-scale images taken from droplets growing on pillared and flat surfaces shows considerable differences between these two processes. Most importantly, since the droplets can be easily canalized between the texture patterns, the shape of droplets usually changes from spherical to ellipsoidal specially in later stages. The novel model proposed here calculates the growth rate of ellipsoidal droplets during adsorption and coalescence steps on pillared substrates. The first step is to position the pillars as cylinders with the specified diameter and height. Then, the random ellipses with their densities issued from the experimental procedure are distributed on the 3-dimensional pillared substrate. Since on a textured surface the droplets can be located at different positions with respect to texturations, there will be a 3-D configuration of droplets that can coalesce in all the directions of X, Y , or Z. The results of this model can be validated by comparison with the results obtained from gray-scale images during the experimental process. In this regard a different image binarization method that enables to detect droplets from the pillars is applied to the gray scale images. The problem with recognizing droplets on the pillared substrates is that droplets are very similar to the pillars (both of them are circular with darker boundaries and brighter centers) or some droplets cover several pillars at the same time.Results and conclusion: The results of the simulation model is compared with real data from 6 different configurations of pillars and the mean error of the model is calculated equal to 2.28± 0.42%

Mathematical model of dropwise condensation on textured surfaces

Catégorie: Communication par afficheNational audienceIntroduction: The aim of this project is to develop a geometric and mathematical model for simulating dropwise condensation in order to control the rate of droplets growth on a textured surface. Comparison between gray-scale images taken from droplets growing on pillared and flat surfaces shows considerable differences between these two processes. Most importantly, since the droplets can be easily canalized between the texture patterns, the shape of droplets usually changes from spherical to ellipsoidal specially in later stages. The novel model proposed here calculates the growth rate of ellipsoidal droplets during adsorption and coalescence steps on pillared substrates. The first step is to position the pillars as cylinders with the specified diameter and height. Then, the random ellipses with their densities issued from the experimental procedure are distributed on the 3-dimensional pillared substrate. Since on a textured surface the droplets can be located at different positions with respect to texturations, there will be a 3-D configuration of droplets that can coalesce in all the directions of X, Y , or Z. The results of this model can be validated by comparison with the results obtained from gray-scale images during the experimental process. In this regard a different image binarization method that enables to detect droplets from the pillars is applied to the gray scale images. The problem with recognizing droplets on the pillared substrates is that droplets are very similar to the pillars (both of them are circular with darker boundaries and brighter centers) or some droplets cover several pillars at the same time.Results and conclusion: The results of the simulation model is compared with real data from 6 different configurations of pillars and the mean error of the model is calculated equal to 2.28± 0.42%

Differential and average approaches to Rose and Mei dropwise condensation models

International audienceTwo well-known models for drop-size distribution function during dropwise condensation -called Rose model and Mei model- were examined in two different aspects, average and differential point of view. It has been proved that these two models are able to describe the relation between droplets size and distribution function at each time step. The goal of this research is to investigate how these models can predict the relation between average distribution function (Nave) and average radius (rave) of droplets during a complete procedure of dropwise condensation and the relation between differential distribution function (dN/dr ) and drops radius (r) at each time step. The empirical parameters are drop size distribution exponent (n) and fractal dimension (df) in Rose model and Mei model respectively. At first these two parameters were calculated based on the experimental data and then the validity of these calculations for our computer simulation was investigated. It was concluded that Rose method fits the results of differential distribution function with exponent n between 0.33 and 0.35, and average distribution function with n of around 0.38. The Mei model also can describe both differential and average results of simulation and experiments with fractal dimension of 1.79df<1.99. Also it was observed that the value of both n and df vary with changing the ratio of radius of two following droplets generation (&#947) in our computer simulation

Spatial analysis of condensation of droplets on textured surfaces

Session 1: Caractérisation des objets et descripteurs morphologiques - Animateurs: A. Liné - J. DebayleNational audienc

Investigation spatial distribution of droplets and the percentage of surface coverage during dropwise condensation

International audienceThe aim of this research is to develop an algorithm to simulate droplets nucleation and growth during dropwise condensation in order to study the droplets spatial distribution. The proposed algorithm starts with droplets distributed based on the Poisson point process and investigates the spatial distribution of droplets using Ripley's L function method. Also, the effects of substrate temperature (Tw) and initial density (ND) on the percentage of area occupied by droplets (&934) are studied. Good agreement between model predictions and experimental data for the rate of growth and changes in droplets density (Nt ) as well as spatial distribution of droplets verifies the validity of the simulating model

Recognition the droplets in gray scale images of dropwise condensation on pillared surfaces

International audienceThis study deals with developing an image processing algorithm that is able to recognize spherical and ellipsoidal droplets growing on pillared surfaces during heterogonous dropwise condensation. The problem with recognizing droplets on the pillared substrates is that droplets are very similar to the pillars or they cover several pillars at the same time, so characterizing the pillars is very important. On the other hand the droplets are not always perfectly spherical or they are connected and form irregular shapes, in such cases the ability to recognizing and separating connected droplets is another challenging step. The method that is used here consists of three main parts: pillars characterization, droplets categorizing and droplets segmentation. The result of this algorithm will be binarized images that enable to extract the information related to the size and density of droplets needed for studying droplets evolution during time. Also a computer simulation method is proposed to generate ellipsoidal droplets on pillaredsubstrate. The results of this algorithm then are validated by comparing with results from experimental procedure

Spatial distribution modeling of droplets during water dropwise condensation on textured surfaces

International audienceThe aim of this study is to simulate water droplets spatial distribution on a flat glassy surface under atmospheric pressure. This process has a great importance in analyzing and manufacturing of condensers, heat exchangers and other steam operating devices. In the dropwise condensation there are two main mechanisms for droplet growth. When the droplets are smaller than the half of the mean distance between two drops, they grow by absorbing water molecules from the gas phase, and for droplets bigger than this amount the mechanism is the droplets coalescence which means joining of the neighboring drops to form a new bigger drop. In the current study, the process of dropwise condensation was modeled using a computer program considering both absorption and coalescence. Then the results of this model were compared to experimental results using Ripley function method