Investigation on condensation in presence of a noncondensable gas for a wide range of Reynolds number

A theoretical model has been developed to study the local heat transfer coefficient of a condensing vapour in the presence of a noncondensable gas, where the gas/vapour mixture is flowing downward inside a vertical tube. The two-phase heat transfer is analysed using an annular flow pattern with a liquid film at the tube wall and a turbulent gas/vapour core. The gas/vapour core is modeled using the analogy between heat and mass transfer. The model incorporates Nusselt equation with McAdams modifier and Blangetti model for calculating the film heat transfer coefficient, Moody and Wallis correlations to account for film waviness effect on gas/vapour boundary layer. The suction effect due to condensation, developing flow and property variation of the gas phase is also considered. A comparative study of heat transfer coefficient and vapour mass flow rate has been made with various models to account for condensate film resistance and condensate film roughness. Results show that for very high Reynolds number, the condensation heat transfer coefficient is higher than the film heat transfer coefficient.     

A simple model for vertical annular and horizontal stratified two-phase flows with liquid entrainment and phase transitions: one-dimensional steady state conditions

A simple one-dimensional three-fluid model is presented for the simulation and analyses of vertical annular and stratified horizontal or inclined two-phase flows. The model has been verified for various experimental data: developing annular flow, momentum transfer in an annular flow, plane flow with a hydraulic jump, flooding in a horizontal pipe, and stratified flow with direct steam condensation. Emphasis has been laid upon several mass, momentum and energy interfacial transfer processes. New correlations are proposed for the droplet entrainment intensity in annular flow and for steam direct contact condensation on the liquid film in a stratified flow. The liquid entrainment in the annular flow is correlated with the liquid film thickness. Direct contact condensation is correlated with the turbulent convective heat transfer in the liquid film. It has been shown that the present model is able to predict all dominant processes in both types of flow.     

Simple heat transfer model for laminar film condensation in a vertical tube

A new physical model for estimating the liquid film thickness and condensation heat transfer coefficient in a vertical tube, considering the effects of gravity, liquid viscosity, and vapor flow in the core region, is proposed. In particular, for calculating the velocity profile in the liquid film, the liquid is assumed to be in Couette flow forced by the interfacial velocity at the liquid-vapor interface. The interfacial velocity is calculated using an empirical power-law velocity profile. The film thickness and heat transfer coefficient from the new model are compared with existing experimental data and the original Nusslet condensation theory. The new model describes the liquid film thinning effect due to the vapor shear flow and predicts the condensation heat transfer coefficient from experiments reasonably well.     

竖直管内蒸汽完全冷凝换热特性的理论研究

Nusselt模型是静止蒸汽在竖直平壁上层流膜状冷凝换热的理论模型。蒸汽在竖直管内冷凝时,受管内蒸汽流速的影响,冷凝界面存在剪切应力,导致直接采用Nusselt模型计算冷凝换热系数会引入较大偏差。以非能动余热排出换热器冷凝换热工况为研究背景,考虑界面剪切力的影响,对Nusselt冷凝换热模型进行修正。分别采用Nusselt模型和修正模型对竖直管内蒸汽完全冷凝时的换热特性进行分析并与实验结果比较。研究表明,蒸汽在竖直管内完全冷凝时界面剪切力会改变蒸汽和冷凝液膜的流动状态,其对冷凝换热的影响不能忽略。修正模型合理地考虑了冷凝界面剪切力的影响,计算结果与实验结果吻合较好。     

竖直管束外含空气蒸汽冷凝的实验研究

本文对竖直管束及单管的管外冷凝换热进行了实验研究,分析了管壁面过冷度、混合气体压力和不凝性气体含量对管束外冷凝传热性能的影响,对比了管束与单管的传热特性,给出了管束外冷凝传热系数的计算关联式。研究结果表明,管束的平均冷凝传热系数随过冷度的增大而减小,随混合气体压力的增大而增大,随不凝性气体质量分数的增加而减小。在混合气体高压力、低不凝性气体含量时管束的传热效果明显优于单管。关联式计算值与实验值误差范围小于±10%。     

CFD modelling of wall steam condensation by a two-phase flow approach

Condensation heat transfer in the presence of non-condensable gases is a relevant phenomenon in many industrial applications. The present work is focused on the condensation heat transfer that plays a dominant role in many accident scenarios postulated to occur in the containment of nuclear reactors. The aim of the study is to contribute to the understanding of the heat and mass transfer mechanisms involved in the problem. The modelling proposed in the paper assumes that liquid droplets form along the wall at nucleation sites. Vapor condensation on droplets makes them to grow. Once the droplet diameter reaches a critical value, gravitational forces compensate surface tension force and then droplets slide over the wall. Droplets can also join the surrounding droplets and form a film layer.As a consequence of the modelling adopted in the paper, the starting point is the balance of heat and mass transfer between droplets and the gas mixture surrounding the droplet. So, the flow in the simulation domain is modelled as a two-phase flow. This approach allows taking into account simultaneously heat and mass transfer on droplets in the core of the flow and condensation or evaporation phenomena at the wall.Two tests were performed to validate the condensation model against experimental data: the COPAIN experiment (CEA Grenoble) and the TOSQAN ISP47 experiment (IRSN Saclay). Calculated profiles compare favourably with experimental results particularly for the helium and steam volume fraction. Nevertheless the cross-comparison of the gas velocities profiles should be improved in plume-jet configuration. Hence more investigations are needed in turbulence modelling for accurate predictions of heat transfer in the whole containment.     

Effect of non-condensable gas and wavy interface on the condensation heat transfer in a nearly horizontal plate

An experimental study was conducted to investigate the effect of non-condensable gas and wavy water film on condensation heat transfer. The experiment was performed in a nearly horizontal (4.1°) square duct of 0.1 m height, 0.15 m width and 1.52 m length at atmospheric pressure. A water film in a steady thermal condition was injected to simulate the effect of a wavy interface on the condensation. The experimental data for the heat transfer coefficient and the interfacial structure of the wavy condensate were obtained along with the three parameters: air mass fraction, mixture velocity and film flow rate. When the interface is smooth, the heat transfer coefficients with or without non-condensable gas agree reasonably with the previous theories. The waviness of condensate film increases the heat transfer up to several tenths of a per cent.     

Forced convection condensation in the presence of noncondensable gas in a horizontal tube; experimental and theoretical study

To have a better understanding on forced convection condensation with noncondensable gas inside a horizontal tube, an experimental research and theoretical investigation were conducted under annular and wavy flow. The effects of noncondensable gas mass concentration, mixture gases velocity, pressure and inner wall sub-cooling on the condensation heat transfer have been analyzed. The results indicate that the local heat transfer coefficient increases with the increase of the mixture inlet velocity and pressure while decreases with the increase of the noncondensable mass fraction and wall sub-cooling. Based on the above conclusions, an empirical correlation for predicting the local heat transfer coefficient was proposed which showed a good agreement with the experimental data with an error of ±20%. Furthermore, a theoretical model using the heat and mass transfer (HMT) analogy method was developed including the suction effect. The heat transfer capacity for the film, gaseous boundary and convective heat transfer of the bulk gases were compared along the tube. Besides, the axial distribution of the bulk gases and liquid–gas interface temperatures inside the tube were analyzed. The present theoretical model fits better with the experimental data compared with Lee's and Caruso's models for stratified flow.     

Separate effects tests for condensation and evaporative heat transfer models

The computer program, under development at NAI for EPRI, is a general purpose thermal hydraulics computer program for design, licensing, safety and operating analysis of nuclear containments and other confinement buildings. The code solves a nine-equation model for three-dimensional multiphase flow with separate mass, momentum and energy equations for vapor, liquid and drop phases. The vapor phase can be a gas mixture of steam and non-condensing gases. The phase balance equations are coupled by mechanistic and empirical models for interface mass, energy and momentum transfer that cover the entire flow regime from bubbly flow to film-drop flow. A variety of heat transfer correlations are available to model the fluid coupling to active and passive solid conductors.This paper focuses on the application of to two separate effects tests: condensation heat transfer on a vertical flat plate with varying bulk velocity, steam concentration and temperature, and evaporative heat transfer from a hot pool to a dry (superheated) atmosphere. Comparisons with experimental data are included for both tests. Results show the validity of two condensation heat transfer correlations as incorporated into GOTHIC and the interfacial heat and mass transfer models for the range of the experimental test conditions. Comparisons are also made for lumped vs. multidimensional modeling for buoyancy-controlled flow with evaporative heat transfer.     

Separate effects tests for gothic condensation and evaporative heat transfer models

The gothic computer program, under development at NAI for EPRI, is a general purpose thermal hydraulics computer program for design, licensing, safety and operating analysis of nuclear containments and other confinement buildings. The code solves a nine-equation model for three-dimensional multiphase flow with separate mass, momentum and energy equations for vapor, liquid and drop phases. The vapor phase can be a gas mixture of steam and non-condensing gases. The phase balance equations are coupled by mechanistic and empirical models for interface mass, energy and momentum transfer that cover the entire flow regime from bubbly flow to film-drop flow. A variety of heat transfer correlations are available to model the fluid coupling to active and passive solid conductors.This paper focuses on the application of gothic to two separate effects tests: condensation heat transfer on a vertical flat plate with varying bulk velocity, steam concentration and temperature, and evaporative heat transfer from a hot pool to a dry (superheated) atmosphere. Comparisons with experimental data are included for both tests. Results show the validity of two condensation heat transfer correlations as incorporated into GOTHIC and the interfacial heat and mass transfer models for the range of the experimental test conditions. Comparisons are also made for lumped vs. multidimensional modeling for buoyancy-controlled flow with evaporative heat transfer.     

曲率对竖直向上环形狭窄通道内环状流特性的影响

基于三流体分离流模型,以液膜质量、动量和能量守恒方程为基础,结合汽芯动量方程,对双面加热垂直向上流动环形狭窄通道内环状流特性进行数值模拟。将计算结果与实验结果相比较,两者符合较好。通过数值模拟,分析了曲率对环状流特性的影响,得到了曲率对液膜厚度、液膜内温度、液膜内速度、临界热流密度等的影响曲线。曲率越大,内液膜越薄,而外液膜越厚。内管干涸时,临界热流密度随曲率的减小而增大;外管干涸时,则反之。     

竖直环形狭缝通道内环状流的预测模型

对竖直环形狭缝通道内环状流流动沸腾传热理论模型进行了分析，以液膜质量、动量和能量守恒方程为基础，结合汽芯动量方程建立了竖直环形狭缝通道内环状流的数学物理模型。对该模型进行数值求解，得出了液膜厚度、液膜内的速度分布和温度分布、内—外管的换热系数以及通道内压降值，并与实验值进行了比较。     

Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube

An experimental study was performed to investigate local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The data obtained from pure steam and steam/nitrogen mixture condensation experiments were compared to study the effects of noncondensable nitrogen gas on the annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm (about 1/2-in.). The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen gas mass fraction decreased. The results obtained using pure steam and a steam/nitrogen mixture with a low inlet nitrogen gas mass fraction were similar. Therefore, the effects of noncondensable gas on steam condensation were weak in small-diameter condenser tubes.A new correlation was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. The new correlation proposed herein is capable of predicting heat transfer rates for tube diameters between 1/2- and 2-in. because of the unique approach of accounting for the heat transfer enhancement via an interfacial shear stress factor.     

水平管内含空气蒸汽强制对流冷凝换热模型研究

为研究含空气蒸汽在水平管内强制对流冷凝换热特性,基于对传热传质过程的分析,建立了管内为环状流与波状流条件下的流动冷凝换热模型。从潜热、显热和液膜3个环节对整个换热过程进行建模,最终得到计算局部冷凝换热系数的理论关系式。模型预测结果与实验数据的对比表明,二者相对偏差在±20%以内,验证了该换热模型的准确性与适用性。通过进一步的研究发现：从换热管入口至出口,随着冷凝的进行,管内换热主要热阻由液膜热阻向气液界面的凝结热阻转变;主流气体对流换热过程基本可忽略。     

不凝性气体对高温锂热管传热特性的影响研究

热管作为一种具有高热导率的传热装置,工作核心在于其内部工作流体的蒸发和冷凝。若热管工作过程中气腔内存在不凝性气体,主流区中蒸气和不凝性气体在对流运动的作用下将一起移动到气-液分界面,不凝性气体的存在阻碍了工作流体在气-液交界面处的正常冷凝。本文基于热阻网络法添加了不凝性气体区域传热模型,研究了不凝性气体对高温锂热管稳态传热特性的影响。结果表明,热管达到稳态时不凝性气体的存在缩短了热管的有效传热长度,破坏了热管的等温性和良好的传热效率。此外随着不凝性气体体积份额的增大,不凝性气体区域温度降低幅度越大;随着热管蒸发段输入功率的增大,热管正常工作区域整体温度越高,相同质量的不凝性气体占据的体积份额越小,热管壁面温度出现明显温度梯度降低的位置随着功率升高而向下游移动。     

高压下含不凝性气体的冷凝换热模型研究

少量的不凝性气体会在很大程度上削弱蒸汽凝结的热传递,现有的含不凝性气体的冷凝换热模型大都建立在理想气体状态方程的基础上,但高压条件下气体受到压缩作用,基于理想气体建立的传热模型预测值与实际值偏差较大。为建立高压下含不凝性气体的冷凝预测方法,对一体化堆安全分析提供技术辅助手段,本研究基于实际气体方程,在扩散层理论的基础上引入液膜波动因子、抽吸因子、雾化因子等修正系数,建立了高压下含不凝性气体的冷凝换热模型。本文模型和Kim试验数据进行了对比分析,改进后的模型比基于理想气体的模型预测值偏差范围更小,相对偏差大部分到±25%以内,充分体现了高压条件下模型的适用价值。     

A model for the performance of a vertical tube condenser in the presence of noncondensable gases

Some proposed vertical tube condensers are designed to operate at high noncondensable fractions, which warrants a simple model to predict their performance. Models developed thus far are usually not self-contained as they require the specification of the wall temperature to predict the local condensation rate. The present model attempts to fill this gap by addressing the secondary side heat transfer as well. Starting with a momentum balance which includes the effect of interfacial shear stress, a Nusselt-type algebraic equation is derived for the film thickness as a function of flow and geometry parameters. The heat and mass transfer analogy relations are then invoked to deduce the condensation rate of steam onto the tube wall. Lastly, the heat transfer to the secondary side is modelled to include cooling by forced, free or mixed convection flows. The model is used for parametric simulations to determine the impact on the condenser performance of important factors such as the inlet gas fraction, the mixture inlet flowrate, the total pressure, and the molecular weight of the noncondensable gas. The model performed simulations of some experiments with pure steam and air-steam mixtures flowing down a vertical tube. The model predicts the data quite well. The model described also provides a basis under which the presence of aerosol particles in the gas stream could be analyzed.     

非凝性气体于竖直壁面处冷凝传热压力特性影响机理研究

非凝性气体于竖直壁面处冷凝传热的研究对一体化压水堆汽-气稳压器的瞬态调节以及紧凑型安全壳余热排出进程具有重要影响,当前对含有非凝性气体的蒸汽竖直壁面冷凝传热中压力的影响特性研究较少。基于传热传质比拟方法,采用适用于高压的改进扩散层模型对汽-气竖直壁面冷凝传热的压力影响进行研究。研究发现,基于传热传质比拟方法改进的扩散层模型与已有的实验结果基本一致,适用于较高压力汽-气竖直壁面冷凝传热系数的预测;总压的增加对存在非凝性气体的冷凝传热具有促进作用,这种促进作用随总压的增加逐渐减弱;在一定压力范围内(0.1~7.0 MPa),存在压力分界点pc,在压力影响分界点以下的低压力区域(0.1 MPa~pc)为压力影响敏感区,在压力影响分界点以上的高压力区(pc~7.0 MPa)为非敏感区。同时,本文还对非凝性气体的种类和含量对蒸汽在竖直壁面处冷凝传热过程的影响进行了分析,从气体扩散系数方面进一步分析了造成影响差异的原因。     

环形狭缝通道内环状流模型的数值分析

对环形狭缝通道内的环状流建立了分离流模型。应用质量、动量和能量守恒方程 ,加上相应的边界条件和使方程组封闭的经验关系式 ,对环形狭缝通道的内、外液膜厚度、液膜内的速度分布和温度分布 ,以及内、外管的换热系数进行了数值计算求解     

Characteristics of two-phase condensing flow by visualization using computed image processing

The mechanics of the condensing behavior of vapor bubbles in a subcooled bulk flow is complicated and influenced by both heat and mass transfer. To examine the characteristics of such thermal-nonequilibrium two-phase flow, experimental and analytical researches have been made. In the experiment, the movement of each vapor bubble in a flowing channel was recorded on video tapes and analyzed by an image processing system. As result, the distributions of void fraction along the test section were obtained. In the analysis, a simple analytical model was introduced to predict the distributions of void fraction and liquid subcooling temperature. By considering the rate of vapor condensation along the flow direction, the differential equation of energy balance between two phases was obtained. Integration of this equation yielded the void fraction and bulk liquid subcooling at any position. The condensation rate was estimated as a function of the local liquid subcooling, interfacial area and mass velocity. Finally, a close fit between calculated results and experimental data was obtained.