A Theoretical Approach to Dropwise Condensation Using Population Balance Concept

Author(s):  
S. Vemuri ◽  
K. J. Kim ◽  
B. D. Wood ◽  
T. W. Bell

A model using the population balance concept is used to derive a theoretical formula to predict the drop-size distribution of small drops which grow mainly by direct condensation. All the important resistances to heat transfer such as the heat conduction through the drop, vapor-liquid interface are considered in developing this model. By knowing the contact angle of the drop made with the condensing surface and the maximum drop radius the sweeping effect of large falling drops could be calculated which is also incorporated into the model. This is combined with the well known size distribution for large drops proposed by Le Fevre and Rose (1966) which grow mainly by coalescence and with the growth rate of single drops to compute the heat flux during the process of dropwise condensation. The data obtained from this theoretical model is compared to that of the data obtained from our experimentation. There has been a satisfactory agreement between our experimental data and the present theoretical model.

Author(s):  
Sunwoo Kim ◽  
Kwang J. Kim ◽  
John M. Kennedy ◽  
Jiong Liu ◽  
Ganesh Skandan

The effect of the drop-contact angle on dropwise condensation heat transfer of saturated steam on a single horizontal copper tube with the superhydrophobic coating was investigated theoretically. The theoretical model is established by combining heat transfer through a single droplet with a well-known drop size distribution theory. The analysis of single droplet heat transfer incorporates resistances due to vapor-liquid interface, drop curvature, conduction through the drop, and conduction through the superhydrophobic coating layer. Each resistance is expressed as a function of the contact angle. The total resistance for a drop with a fixed radius increases as the contact angle increases. A population balance model is used to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from the empirical equation proposed by Le Fevre and Rose (1966). The results indicate that the contact angle has a strong correlation with the maximum drop radius, which plays a pivotal role in determining drop size distribution. A high contact angle leads to a significant reduction in the radius of the largest drop that is about to fall down due to gravity and sweep away drops in its path. Thus, there are more areas on the condensing surface for small drops, allowing for greater heat transfer. Also, it is shown that surface wettability affects the performance of dropwise condensation heat transfer and our theoretical model successfully predicts this phenomenon.


1975 ◽  
Vol 97 (1) ◽  
pp. 72-78 ◽  
Author(s):  
Hiroaki Tanaka

The so-called steady dropwise condensation consists of the transient dropwise condensation occurring repeatedly from place to place on the tracks of departing drops. By taking statistical and geometrical conditions into account, the author derives fundamental equations describing the process of this transient dropwise condensation. By solving these equations, the existence of a universal drop-size distribution is predicted. Further, by introducing a model for the cycle of drop departure, a general expression for the heat-transfer coefficient under the so-called steady dropwise condensation is obtained.


2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Sunwoo Kim ◽  
Kwang J. Kim

A mathematical model is developed to represent and predict the dropwise condensation phenomenon on nonwetting surfaces having hydrophobic or superhydrophobic (contact angle greater than 150 deg) features. The model is established by synthesizing the heat transfer through a single droplet with the drop size distribution. The single droplet heat transfer is analyzed as a combination of the vapor-liquid interfacial resistance, the resistance due to the conduction through the drop itself, the resistance from the coating layer, and the resistance due to the curvature of the drop. A population balance model is adapted to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from a well-known empirical equation. The evidence obtained suggests that both the single droplet heat transfer and drop distribution are significantly affected by the contact angle. More specifically, the model results indicate that a high drop-contact angle leads to enhancing condensation heat transfer. Intense hydrophobicity, which produces high contact angles, causes a reduction in the size of drops on the verge of falling due to gravity, thus allowing space for more small drops. The simulation results are compared with experimental data, which were previously reported.


2012 ◽  
Vol 190-191 ◽  
pp. 1355-1360
Author(s):  
Shen Hua Hu ◽  
Xiang Rong Ma ◽  
Fan Wu

An experiment for Marangoni condensation of ethanol-water mixtures was carried out and the departing radius and drop size distribution on vertical surface was presented. An amended formula was obtained after considering the effect of ethanol mass concentration, vapor velocity and condensing temperature difference based on Le Fevre’s formula concerning departing radius of pure water, The calculations were in good agreement with experimental result, had a maximum error less than 23%. Owing to the significant effect on drop size contribution, vapor velocity was introduced into Rose’s formula, and the correctional result compared well with the experimental data.


Author(s):  
Jae Young Choi ◽  
Yong Hoon Jeong ◽  
Noriyuki Watanabe

The passive safety features of nuclear power plant against station blackout (SBO) and intact containment integrity are the main key issues after Fukushima accident. As a corresponding safety system, passive containment cooling system (PCCS) received attention as one of the candidate systems applying to advanced light water reactors. Next generation of light water reactor, AP-1000 and ESBWR have suggested their own PCCS design. However, PCCS have difficulty in its heat exchanger volume due to low heat transfer coefficient of condensation under the presence of non-condensable gas condition. Several attempts had been studied worldwide to enhance the heat transfer coefficient of PCCS and this paper focused on dropwise condensation, which has much higher heat transfer coefficient than those found with filmwise condensation. Historically, surface coating or applying organic promoter on the cooling surface were typically used to induce dropwise condensation, but those method had disadvantage of their duration time. In general, surface coating and organic promoter were considered to have few years and few days of their duration, respectively. Therefore, an aim of our experiment was to determine whether SUS316 without any surface treatment is able to utilize dropwise condensation for PCCS heat exchanger. Following studies were compared to the filmwise condensation on SUS316 with same condition and also the experiment results reported by other researchers. The overall results determined how much the heat transfer coefficient was enhanced. To analyze the behavior of dropwise condensation, visualized images of cooling surface with droplets were graphically processed. All experiments were conducted on 13mm diameter of vertical-oriented flat surface with 6mm thickness. Air concentration (non-condensable concentration) was estimated by the partial pressure ratio of steam and air. Subcooled temperature, the difference between steam saturated temperature and surface temperature, was tested from 1 to 30 degree Celsius. High-speed camera visualized the condensate on the cooling surface with several magnification and frame speed. All measurement was measured after the whole system reached to equilibrium state and sustained it more than 30 minutes. Each data was recorded for 60 seconds and time-averaged its measurement. Experiment results indicated that SUS316 surface without any surface treatment could sustain dropwise condensation phase over 12 hours of experiment under low subcooled temperature below approximately 20 degree Celsius. Also, dropwise condensation had around 3 to 4 times enhanced heat transfer coefficients than those of filmwise condensation. The result of dropwise condensation with pure steam condition was well proportional to the power of subcooled temperature. Otherwise, the result with non-condensable gas showed heat transfer coefficient, shaded in high uncertainty of systematic error, seems to be decreased in low subcooled temperature under 5 degree Celsius. Higher sensitivity of non-condensable concentration upon heat transfer coefficient was observed on dropwise condensation more than filmwise condensation. The variation of drop-size distribution with the periodic time passage after surface sweeping was observed and patterns of drop-size distribution were repeated after the surface sweeping regardless of experimental conditions. The study provides feasibility and benefit of the utilization of dropwise condensation to PCCS heat exchanger if the system has designed to be operated within low subcooled temperature.


1988 ◽  
Vol 110 (4a) ◽  
pp. 961-967 ◽  
Author(s):  
J. Orozco ◽  
R. Stellman ◽  
M. Gutjahr

This paper analyses both theoretically and experimentally the problem of film boiling from a body embedded in a liquid-saturated porous medium. Two body geometries are investigated thoroughly: a horizontal cylinder and a sphere. The theoretical model relies on the Brinkman-extended flow model to describe the flow field inside the thin vapor layer occupying the neighborhood near the heated surface. The theoretical model also includes an improved formulation of the effective conductivity in the vicinity of the heater as a function of the vapor layer thickness and the geometry of the porous medium material. Solutions are obtained for the vapor layer thickness and the local Nusselt number as a function of angular position. Numerical solutions are also obtained for the overall heat transfer rates from the surface to the fluid for a given vapor superheat. Experimental data for a 12.70 mm stainless steel cylindrical heater embedded in a 3-mm glass particle porous medium were obtained under steady—state operation. The experimental data obtained are compared with the theoretical analysis. The comparison shows that there is a good agreement between theory and experiments. The theoretical model is also compared with the experimental data obtained by other investigators for a spherical geometry. Excellent results are obtained in such comparison.


Sign in / Sign up

Export Citation Format

Share Document