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.     

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%。     

Reflux condensation of flowing vapor and non-condensable gases counter-current to laminar liquid film in a vertical tube

An analytical model using the heat and mass transfer analogy approach was developed for local heat transfer in reflux condensation of flowing vapor and non-condensable gases counter-current to laminar liquid film in a vertical tube. The liquid film model was derived from the two-phase integral momentum equations for counter-current flow. The non-condensable gas effect was accounted for using the diffusion layer theory. The momentum, heat and mass transfer for the liquid and gas phases are coupled together by the shear stress, temperature and gas mass fraction at the two-phase interface, which together with the unknown vapor flow conditions at the outlet of the tube were solved iteratively. The model anticipates that vapor might not necessarily condense completely inside the tube. The root mean square of the theory's relative error is 30% compared with available experimental data. The model provides a mechanism for the safety analysis codes to evaluate reflux condensation in the presence of non-condensable gases.     

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.     

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.     

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.     

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。     

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.     

Condensation in the presence of noncondensable gases

An experimental investigation to examine the effects of surface orientation on the condensation of steam in the presence of noncondensable gas is reported. An air-steam mixture was directed into a rectangular flow-channel over a condensing aluminum surface that has a painted surface finish. The mixture flow was concurrent in all the tests with condensate flow. In this series of experiments, the orientation of the condensing surface was varied from 0–90° (plate surface was facing downwards at 0°), with a variable air-steam mass fraction of 0–0.87, and a mixture velocity of 1–3 m/s. The heat transfer coefficient was measured in addition to making visual observations of the condensation process. It was found that the heat transfer coefficient varied from 100 to 600 W/m² K with the mass fraction of 0.87-0.24 and the maximum heat transfer coefficient of 6200 W/m² K was measured with mass fraction of 0. By tilting the condensing surface from the horizontal to vertical position, the heat transfer coefficient decreased 15 to 25% depending on the mass fraction. With a higher vapor content the effect of the orientation was smaller. This dependence was attributed to the existence of interfacial structure (droplets and ridges) that promoted heat transfer at small inclination angles, when the angle was increased the interface became smoother and heat transfer rates decreased. Heat transfer rates were also observed to increase with flow velocity, vapor content and pressure. The results are compared with some previously published data and a proposed condensation model that showed reasonable agreement with the data trends.     

非能动余热排出换热器池沸腾换热性能研究

以浸没在高位水箱中的竖直管束为研究对象,对不同热负荷条件下竖直管束的池沸腾换热特性进行研究,通过对比中心管与周围旁管外壁面过热度、凝液量的变化,分析了中心管与旁管换热特性的差异。实验结果表明,换热管束的换热能力明显优于单管,在相同热流密度条件下,管束沸腾换热系数可达到单管的1.2～1.5倍。与旁管相比,低热负荷条件下,中心管的换热能力优于旁管;高热负荷条件下,中心管的换热能力则不及旁管,在热流密度大于200 kW/m²时,旁管的沸腾换热系数相对于中心管提高了近7%,且从实验数据的变化趋势来看,旁管较中心管的沸腾换热能力有随热流密度增加而逐渐增大的趋势。     

A study of the unsteady flow and heat transfer in the reflooding of water reactor cores

In the event of a loss-of-coolant accident in a water-cooled reactor, the primary consideration is terminating the clad temperature excursion caused by release of the stored and decay heat in the fuel. This requires that emergency coolant injection systems reflood the reactor core.For certain break positions, the pressure loss incurred by venting steam partially offsets the hydrostatic head available to drive flow through the core. Flow oscillations can also be set up due to the fluid inertia and vapour compressibility.The present paper reports the results of an extensive series of experiments performed on unstable reflooding, covering wall temperatures up to 1000°C and reflooding rates typical of reactor values. Measurements are reported of quenching rates, oscillation frequencies and pre-quench heat transfer.It is shown, except for a short initial period of violent oscillations, that the rewetting rate and pre-quench heat transfer, for a given mass flow rate, are relatively unaffected by the presence of oscillations. The average pre-quench heat transfer coefficient is shown to vary as (water mass flow rate)ⁿ where n = 0.5–0.7, consistent with available world data.Theory and experiments also show that there is a critical value of outlet loss coefficient, for a given power level, where no further advance of the quench front can occur, the back pressure completely offsetting the available driving head for core reflooding. This value is much greater than the outlet loss coefficient for typical reactor designs, thus ensuring core reflooding. The critical loss coefficient is suggested as the relevant parameter for scaling purposes.A new theoretical model for the oscillations is derived which is shown to predict the oscillation frequencies of all available data. It is also shown that the frequency and damping are only weakly dependent on: upper plenum flow area, size of vapour space, effective inertia of water oscillating and pressure, and are independent of the outlet loss coefficient.     

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。     

Prediction of Liquid Film Dryout in Two-Phase Annular-Mist Flow in a Uniformly Heated Narrow Tube Development of Analytical Method under BWR Conditions

A method was developed based on the conservation lows to predict critical heat flux (CHF) causing liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube under BWR conditions. The applicable range of the method is within the pressure of 3–9 MPa, mass flux of 500–2,000 kg/m²·s, heat flux of 0.33–2.0 MW/m² and boiling length-to-tube diameter ratio of 200–800.

The two-phase annular-mist flow was modeled with the three-fluid streams with liquid film, entrained droplets and gas flow. Governing equations of the method are mass continuity and energy conservation on the three-fluid streams. Constitutive equations on the mass transfer which consist of the entrainment fraction at equilibrium and the mass transfer coefficient were newly proposed in this study.

Confirmation of the present method were performed in comparison with the available film flow measurements and various CHF data from experiments in uniformly heated narrow tubes under high pressure steam- water conditions. In the heat flux range (q“<2MW/m²) practical for a BWR, agreement of the present method with CHF data was obtained as, (Averaged ratio)±(Standard deviation)=0.984±0.077, which was shown to be the same or better agreement than the widely-used CHF correlations.     

Effect of noncondensable gas in a vertical tube condenser

An experimental study is performed to investigate the effects of noncondensable (NC) gas in the steam condensing system. A vertical condenser tube is submerged in a water pool where the heat from the condenser tube is removed by boiling heat transfer. The design of the test section is based on the passive condenser system in an advanced boiling water nuclear power reactor. Data are obtained for various process parameters, such as inlet steam flow rate, noncondensable gas concentration, and system pressure. Degradation of the condensing performance with increasing noncondensable gas is investigated. The condensation heat transfer coefficient and heat transfer rate decrease with noncondensable gas. The condensation heat transfer rate is enhanced by increasing the inlet steam flow rate and the pressure. The condensation heat transfer coefficient increases with the inlet steam flow rate, however, decreases with the system pressure. For the condenser submerged in a water pool with saturated condition, the strong primary pressure dependency is observed.     

Research on the effect of Reynolds correlation in natural convection film condensation

Film condensation is a vital phenomenon in the nuclear engineering applications,such as the gas-steam pressurizer design,and heat removing on containment in the case of postulated accident.Reynolds number in film condensation can be calculated from either the mass relation or the energy relation,but few researches have distinguished the difference between them at present.This paper studies the effect of Reynolds correlation in the natural convection film condensation on the outer tube.The general forms of the heat transfer coefficient correlation of film condensation are developed in different flow regimes.By simultaneously solving a set of the heat transfer coefficient correlations with Remass and Reenergy,the general expressions for Remass and Reenergy and the relation between the corresponding heat transfer coefficients are obtained.In the laminar and wavefree flow regime,Remass and Reenergy are equivalent,while in the laminar and wavy flow regime,Remass is much smaller than Reenergy,and the deviation of the corresponding average heat transfer coefficients is about 30％ at the maximum.In the turbulent flow regime,the relation of Remass and Reenergy is greatly influenced by Prandtl number.The relative deviation of their average heat transfer coefficients is the nonlinear function of Reynolds number and Prandtl number.Compared with experimental results,the heat transfer coefficient calculated from Reenergy is more accurate.     

超临界CO2在螺旋管中的流动换热特性研究

超临界蒸发器应用到核电中，可大幅提高机组的热效率。超临界压力流体的热物性在准临界温度附近变化非常剧烈，会对其流动和换热产生很大的影响。研究超临界压力流体在螺旋管内的流动和换热规律，有利于对超临界螺旋管蒸发器的设计。本文采用RNG k-ε和SST k-ω模型对超临界CO₂在螺旋管中的流动换热情况进行了数值模拟，发现SST k-ω模型模拟结果与实验结果符合得更好。基于此模型，分析了不同进口质量流速及不同热流密度对管壁温和换热系数的影响，发现随着质量流速的减小、热流密度的增加，峰值向远离h_pc的一侧偏移。最后讨论并分析了周向壁温和换热系数的分布情况，发现壁温在φ＝315°处最高，需在实验操作或实际运行中加以监控，以保障螺旋管蒸发器的安全运行。     

Diffusion layer modeling for condensation in vertical tubes with noncondensable gases

Noncondensable gases significantly modify the mechanism of condensation for cocurrent downward flow in vertical tubes. Two-dimensional experimental measurements presented here show similarity between gas concentration distributions and the temperature distributions encountered in laminar and turbulent heat transfer. Thus the analogy between heat and mass transfer, coupled with a reasonable condensate film model, can provide predictions of the local condensation rate. This work presents a simple 9-step iterative calculation procedure for calculating the local heat flux. The empirical model, based on a modified Dittus-Boelter formulation and utilizing an effective condensation thermal conductivity, converges with 2 to 10 iterations at each axial location. Experimental results from several investigators are compared with the predictions of the model, with good agreement.     

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。     

Computational-experimental modeling of processes in the protective shell with a passive condenser present in the passive heat-removal system

The modeling of the operation of a passive condenser based on a numerical solution of three-dimensional equations of hydrodynamics is examined. Questions associated with correct modeling of turbulent transport under free-convection conditions are examined. A model taking account of the dynamics of a condensate film and the conditions of heat and mass transfer on its surface is proposed for surface condensation. The results are used to develop recommendations for closure relations used in point codes with whose help design validation of a passive system removing heat from beneath the protective shell is performed.