On various forms of the heat and mass transfer analogy: Discussion and application to condensation experiments

The paper is focused on some of the different forms of the analogy between heat and mass transfer, as they appear in available textbooks and literature on condensation and evaporation. The motivation for the work is the need to clearly point out the assumptions at the basis of each one of them and to quantify the related differences in the application to real experimental data. In fact, the analogy is very often cast in apparently very different forms, whose relation to each other must be carefully understood when a selection among them is performed for a given application.Basing on previous experience in the analysis of heat and mass transfer for passive cooling in light water nuclear reactors, the present work briefly summarises the theoretical bases of the selected forms of the analogy, comparing the related relationships. Then, an experimental activity related to condensation on a flat plate in the presence of noncondensable gases, aimed at providing data for nuclear reactor containment analysis, is presented and the obtained results are processed by the different forms of the analogy to assess the related quantitative differences, thus providing a clearer perspective about the results of their use in engineering applications.     

Turbulent mixed convection heat transfer experiments in a vertical cylinder using analogy concept

A series of the turbulent mixed convection heat transfer experiments in a vertical cylinder was carried out. In order to achieve high Grashof number easily, the analogy concept was adopted and the heat transfer system was simulated by a mass transfer system. With reasonable facility heights, large Grashof numbers could be achieved using a copper electroplating system. The tests in buoyancy-aided and opposed flow configurations, were performed for Reynolds numbers from 4000 to 10,000 with a constant Grashof number of 6.2 × 10⁹ and Prandtl number of about 2000. The test results reproduced the typical of the mixed convection heat transfer phenomena in a turbulent situation and agreed well with the study performed by Palratan et al. The analogy experimental method simulated the mixed convection heat transfer phenomena successfully and proved itself to be a useful tool for the draft estimation of the heat transfer rate in the highly buoyant systems such as the VHTR.     

Effect of chemical reaction, heat and mass transfer on nonlinear boundary layer past a porous shrinking sheet in the presence of suction

This work is concerned with the viscous flow due to a shrinking sheet in the presence of suction with variable stream conditions. The cases of two-dimensional and axisymmetric shrinking have been discussed. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Analysis of heat and mass transfer to determine heat loss and the rate of condensation of the MVSTs off-gas ducts

Reduction of the existing nuclear waste in the Melton Valley Storage Tanks (MVSTs) at the Oak Ridge National Laboratory (ORNL) is of utmost concern to the scientists at this facility. This paper provides proof that a combination of vault heating, sparged air heating, and prevention of condensation is the best alternative to achieve this goal. Therefore, in this study a general system of mathematical equations has been developed taking into account all of the parameters affecting evaporation and condensation. This evaporation process has been analyzed by the careful modeling of a bubble chain through the extremely viscous, radioactive liquid contained in the storage tanks. This paper discusses in detail the evaporation procedure using bubble formation, air velocity, and determining the rate at which this liquid waste can be removed from the MVSTs by evaporation under different conditions of the sparging air. An additional objective is to study the heating/cooling of the condensation process of the off-gas piping inside the vault. A laboratory scale model has also been assembled for this purpose at ORNL to verify the accuracy of the mathematical modeling. A comparison of the experimental findings with the mathematical modeling shows excellent agreement.     

Prediction of the obstacle effect on film-boiling heat transfer

A correlation has been developed to account for the effect of obstacles (simulating the spacing devices in bundles) on heat transfer in dispersed-flow film boiling. The correlation is expressed as a modification factor to the reference geometry without any obstacles. The basic form of the correlation is an exponential decay function that resembles the diminishing effect on turbulence enhancement. The coefficients and constants in the correlation have been optimized with heat-transfer data of low-pressure single-phase (air) flow and high-pressure steam-water flow at film-boiling conditions.An experiment has been set up to obtain validation data with a heated tube of 4.1 mm inside diameter. HFC-134a was used as the working fluid. Three types of obstacles with the same blockage-area ratio of 37.8% were tested. The results showed that the obstacles exhibited a strong enhancement effect on the film-boiling heat-transfer coefficient at locations downstream of the obstacles. A comparison between predictions of the correlation for the spacing-device effect and experimental data showed an underprediction of the heat-transfer rate at locations downstream of the obstacle. The underprediction is due mainly to the rewetting of the heated surface at the location of an obstacle, beyond which the developing film-boiling effect becomes dominant. The agreement between prediction and data is significantly improved after accounting for the critical heat flux (CHF) enhancement and developing film-boiling effects in the calculations.     

Thermophoresis and chemical reaction effects on non-Darcy mixed convective heat and mass transfer past a porous wedge with variable viscosity in the presence of suction or injection

The effects of variable viscosity, thermophoresis and non-Darcy mixed convection flow with heat and mass transfer over a porous wedge are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Favorable comparison with previously published work is performed. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the Runge Kutta Gill and shooting methods. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first-order chemical reaction the concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat and mass transfer are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Prediction of transpiration effects on heat and mass transfer by different turbulence models

The paper reports the results of a study related to transpirating flows, stimulated by the interest that these phenomena, occurring in the presence of simultaneous heat and mass transfer, have for nuclear reactor applications. The work includes a summary and the follow-up of previous experimental and numerical investigations on filmwise condensation and falling film evaporation and of a recent review of different forms of the heat and mass transfer analogy. The particular objective here pursued is to compare transpiration effects as predicted by different turbulence models with classical suction and blowing multipliers based on stagnant layer theories, in the attempt to clarify their quantitative implications on the predicted mass transfer rates.A commercial and an in-house CFD code have been adopted for evaluating the heat and mass transfer rates occurring over a flat plate exposed to an air-vapour stream, with uniform bulk steam mass fraction and temperature boundary conditions at the wall. This simple configuration was purposely selected since it is a simplified representation of the test section of an experimental facility presently in operation at the University of Pisa. This allows a direct comparison between the heat and mass transfer coefficients predicted by CFD models and classical correlations for Nusselt and Sherwood numbers.     

Modeling of heat and mass transfer in accelerator targets during postulated accidents

The modeling of thermal-chemical behavior of targets used in accelerator applications is an important part of safety analysis. Tungsten is considered as a target material to produce tritium in a linear proton accelerator. The prediction of the chemical reactivity of tungsten in a steam flow at high temperatures is the most important part of a safety analysis of target design. The oxidation and volatilization of tungsten in steam at high temperatures is a complex phenomenon that involves various mechanisms (depending on the temperature), steam pressure, and steam velocity. A simple diffusion model that considers chemical equilibrium at the reaction interface and effective diffusion thickness, including the boundary and oxide layers, is proposed for predicting the volatilization rate. The proposed simple model predicts the available data reasonably well. The proposed model is implemented into a computer program that is developed to predict the radiological releases during postulated loss-of-coolant accidents (LOCAs). The computer program models heat production, heat transfer, and oxidation reactions in the multiple radiation enclosures representing the accelerator target elements. It treats each element of the radiation enclosures as a lumped control volume, or heat structure. Each heat structure may generate or lose heat by conduction, convection, or radiation and is subject to mass loss as a result of oxidation, melting, and volatilization. Postulated beyond-design-basis LOCAs are simulated with this computer program for the accelerator-production-of-tritium target. Sample calculations demonstrate oxidation/volatilization model capabilities and sensitivity to the assumptions selected.     

Experiments on microgravity boiling heat transfer by using transparent heaters

To clarify the relation between the liquid–vapor behavior and the heat transfer characteristics in the boiling phenomena, the structures of transparent heaters were developed for both flow boiling and pool boiling experiments and were applied to the microgravity environment realized by the parabolic flight of aircraft. In the flow boiling experiment, a transparent heated tube makes the heating, the observation of liquid–vapor behavior and the measurement of heat transfer data simultaneously possible. The heat transfer coefficient in the annular flow regime at moderate quality has distinct dependence on gravity provided that the mass velocity is not so high, while no noticeable gravity effect is seen at high quality and in the bubbly flow regime. The measured gravity effect was directly related to the behavior of annular liquid film observed through the transparent tube wall. In the pool boiling experiment, a structure of transparent heating surface realizes both the observation of the macrolayer or microlayer behavior from underneath and the measurements of local surface temperatures and the layer thickness. It was clarified in the microgravity experiments that no vapor stem exists but tiny bubbles are observed in the macrolayer underneath a large coalesced bubble at high heat flux. The heat flux evaluated by the heat conduction across the layer assumes less than 30% of the total to be transferred. The evaporation of the microlayers underneath primary bubbles just after the generation dominates the heat transfer in the microgravity, not only in the isolated bubble region but also in the coalesced bubble region.     

EAST-NBI反向电子吸收板换热计算与分析

中性束注入是托卡马克主要的辅助加热手段。目前先进实验超导托卡马克中性束注入(Experimental Advanced Superconducting Tokamak-Neutral Beam Injection,EAST-NBI)装置采用的是正离子源,运行过程中离子源的部分部件有很大的热沉积,其中反向电子吸收板最为严重。经实验研究,当束功率为3.5 MW时,沉积在反向电子吸收板上的平均功率密度高达4.4 MW·m~(-2),有着较大的换热负担。为探究反向电子吸收板的极限运行时间,采用数值模拟的方法,对反向电子吸收板在不同束功率、冷却水水压等多种工况进行了计算。结果表明,电子吸收板随着束功率的增大,换热负担加重、换热效果变差,通过增压泵提高冷却水入口压力一定程度上可以提高换热能力,使其极限运行时间延长。对该课题的研究可以指导EAST-NBI的运行,以保证离子源安全、稳定工作,此外还为反向电子吸收板的进一步结构优化奠定理论基础,对发展长脉冲、高功率的离子源具有重要意义。     

Vapor heat transfer in post-CHF region including the effect of thermodynamic non-equilibrium

Vapor phase heat transfer in the post-CHF region is modelled using momentum-transfer analogy and allowing for thermodynamic non-equilibrium. The vapor heat transfer coefficient is determined by momentum-transfer analogy, using an appropriate two-phase friction factor. The degree of thermodynamic non-equilibrium, denoted by the ratio of actual quality to equilibrium quality, is correlated in terms of a dimensionless temperature difference which includes the superheated vapor temperature. This correlation is solved simultaneously with a heat balance equation to determine the actual quality and the vapor temperature. Post-CHF vapor heat flux, calculated by this method, is compared to experimental tube data from eight different sources at pressures up to 2830 psia and over a wide range of mass fluxes. Results indicate an average deviation of 14.9% between measured and predicted heat fluxes for 2854 data points.     

Numerical investigation of acceleration effect on heat transfer deterioration phenomenon in supercritical water

It is important to understand the heat transfer deterioration (HTD) phenomenon for specifying cladding temperature limits in the fuel assembly design of supercritical water-cooled reactor (SCWR). In this study, a numerical investigation of heat transfer in supercritical water flowing through vertical tube with high mass flux and high heat flux is performed by using six low-Reynolds number turbulence models. The capabilities of the addressed models in predicting the observed phenomena of experimental study are shortly analyzed. Mechanisms of the effect of flow structures and fluid properties on heat transfer deterioration phenomenon are also discussed. Numerical results have shown that the turbulence is significantly suppressed when the large-property-variation region spreads to the buffer layer near the wall region, resulting in heat transfer deterioration phenomenon. The property variations of dynamic viscosity and specific heat capacity in supercritical water can impair the deterioration in heat transfer, while the decrease of thermal conductivity contributes to the deterioration.     

Analyses on fluid flow and heat transfer inside Calandria vessel of CANDU-6 using CFD

In a CANada Deuterium Uranium (CANDU) reactor, fuel channel integrity depends on the coolability of the moderator as an ultimate heat sink under transient conditions such as a loss of coolant accident (LOCA) with a coincidence of a loss of emergency core cooling (LOECC), as well as a normal operating condition. This study presents the assessments of moderator thermal–hydraulic characteristics in the normal operating condition and one transient condition for CANDU-6 reactors, using a general purpose three-dimensional computational fluid dynamics code. This study consists of two steps. First, an optimized calculation scheme is obtained by many-sided comparisons of the predicted results with the related experimental data, and by evaluating the fluid flow and temperature distributions. Then, in the second step, with the optimized scheme, the analyses for real CANDU-6 of normal operating condition and transition condition have been performed. The present model has successfully predicted the experimental results and also reasonably assessed the thermal–hydraulic characteristics of the real CANDU-6 with 380 fuel channels. Flow regime map with major parameters representing the flow pattern inside Calandria vessel has also proposed to be used as operational and/or regulatory guidelines.     

Analysis of prompt supercritical process with heat transfer and temperature feedback

The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper.Considering the effect of heat transfer on temperature of the reactor,a new model is set up.For any initial power,the variations of output power and reactivity with time are obtained by numerical method.The effects of the big inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed.It was found that the effect of heat transfer on the output power and reactivity can be neglected under any initial power,and the output power obtained by the adiabatic model is basically in accordance with that by the model of this paper,and the analytical solution can be adopted.The results provide a theoretical base for safety analysis and operation management of a power reactor.