Modeling condensation heat transfer on a horizontal finned tube in the presence of noncondensable gases

European designs for the next generation of nuclear reactors incorporate innovative passive systems in their containments to enhance heat removal by condensation under postulated accident conditions. These systems consist of several units of cross-flow finned tube bundles internally cooled with water. So far most of the studies that have been addressed to the issue of heat transfer onto finned surfaces under condensing conditions have involved refrigerants and pure vapor conditions. This study presents a model (HTCFIN) capable of predicting condensation of a cross-flow air–steam mixture onto a single horizontal finned tube. The comparison of HTCFIN predictions to the available databases shows its acceptable accuracy in a wide range of conditions and allows an interpretation of the influence of major variables acting on the scenario. As a consequence, HTCFIN model represents a step forward in the present theoretical capability to estimate heat transfer within containments of next generation of European reactors in the case of a hypothetical accident.     

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.     

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.     

Measurement of heat transfer coefficients for steam condensation on a vertical 21.5-mm-O.D. tube in the presence of air

ABSTRACT

Governing the rate of heat transport by condenser tubes in the passive containment cooling system (PCCS), the steam condensation over a vertical cylinder in the presence of air was investigated experimentally. The main objective of this study was to explore if the condensation heat transfer coefficient relies on the tube dimension, which has been a variable missed in most condensation models or has been embraced without experimental demonstration under phase change environments. The mean heat transfer coefficient was measured in the condensation test facility named JERICHO (JNU Experimental Rig for Investigation of Condensation Heat transfer On tube). The outer diameter of the condenser tube used in this study was set to 21.5 mm. The measured heat transfer coefficients were compared to those obtained from the 40-mm-O.D. tube, and a multiplier to correct the variation of the heat transfer coefficient with the tube diameter was proposed for its application to Lee correlation. The proposed correlation was further validated against another set of experimental data obtained from a separate test facility housing the 31.8-mm-O.D. tube.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 1: Correlations for two parallel horizontal cylinders based on experimental and theoretical results

Natural convection heat transfer coefficients on two parallel horizontal test cylinders in liquid sodium were obtained experimentally and theoretically for various setting angles, γ, between vertical direction and the plane including both of these cylinders’ axes, over the range of 0°–90°. Both test cylinders are 7.6 mm in diameter and 50 mm in heated length with the ratio of the distance between each cylinder axis to the cylinder diameter, S/D, of 2. Theoretical equations for laminar natural convection heat transfer from the two horizontal cylinders were numerically solved for the same conditions as the experimental ones. The average Nusselt numbers Nu on the cylinders obtained experimentally were compared with the corresponding theoretical values on the Nu versus modified Rayleigh number R_f [= Gr*Pr²/(4?+?9Pr^1/2?+ 10Pr)] graph. The experimental values of Nu for the upper cylinder are about 20% lower than those for the lower cylinder at γ = 0° for the range of R_f tested here. The value of Nu for the upper cylinder becomes higher and approaches that for the lower cylinder with the increase in γ over the range of 0°–90°: the values for each cylinder agree with each other at γ = 90°. The values of Nu for the lower cylinder at each γ are almost in agreement with those for a single cylinder. The theoretical values of Nu on two cylinders except those for R_f < 4 at γ = 0° are in agreement with the experimental data at each γ with the deviations less than 15%. Correlations for two cylinders were obtained as functions of S/D and γ based on the theoretical solutions. A combined correlation for multi-cylinders in a vertical array based on the correlations for two cylinders was developed. The values by the correlation agree with the theoretical solution for the multi-cylinders for R_f ranging from 4.7 to 63 within 10% difference.     

Theoretical modeling of condensation of steam outside different vertical geometries (tube, flat plates) in the presence of noncondensable gases like air and helium

Condensation of steam coming out from the coolant pipe during a loss of coolant accident (LOCA) plays a key role in removing heat from the primary containment of the advanced nuclear reactor (ANR). The presence of large mass fractions of air (W_air = 0.25-0.9) and a small mass fraction of helium (W_He = 0.017-0.083) reduces the overall heat transfer coefficient (HTC) substantially. The present work emphasizes on the issue that modeling the diffusion of water-vapor through the gas-liquid interface is the key to give good predictions in HTC. In this, condensation conductivity and effective diffusivity plays a key role. Therefore, modifications have been made in the derivation for calculation of condensation conductivity in the case of steam-air mixture and effective diffusivity (in the case of multicomponent mixture). The model validation has been done with the experimental data of Dehbi et al. [Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28] and Anderson et al. [Anderson, M.H., Herranz, L.E., Corradini, M.L., 1998. Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. 185, 153-172] and other analytical models available in the literature [Herranz, L.E., Anderson, M.H., Corradini, M.H., 1998a. The effect of light gases in noncondensable mixtures on condensation heat transfer. Nucl. Eng. Des. 183, 133-150; Herranz, L.E., Anderson, M.H., Corradini, M.L., 1998b. A diffusion layer model for steam condensation within the AP600 containment. Nucl. Eng. Des. 185, 153-172; Peterson, P.F., Schrock, Y.E., Kageyama, T., 1993. Diffusion layer theory for turbulent vapor condensation with noncondensable gases. J. Heat Transf., 115; Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28]. Since the validations of the results were found satisfactory, the datasets [Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28; Anderson, M.H., Herranz, L.E., Corradini, M.L., 1998. Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. 185, 153-172] have been compared with a wide range of subcooling and the operating pressures. An extensive comparison has been reported and the results predicted by the present model were found to be satisfactory.     

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.     

CFD analysis of flow and heat transfer of turbulent pulsating flow in a tube in rolling motion

The investigation of flow and heat transfer of turbulent pulsating flow is of vital importance to the nuclear reactor thermal hydraulic analysis in ocean environment. In this paper, the flow and heat transfer of turbulent pulsating flow is analyzed. The calculation results are firstly verified with experimental data. The agreement between them is satisfactory. The effect of spanwise and wall-normal additional forces is significant in small Reynolds number, and decreases with Reynolds number increasing. The rolling axis and rolling radius contribute slight to the flow and heat transfer. The effect of velocity oscillation period on the heat transfer is limited than that of Reynolds number and oscillating velocity Reynolds number. The traditional empirical correlations could not predict the flow and heat transfer of turbulent pulsating flow in rolling motion.     

Eigenvector solution of the linearized equations of thermal convection in a closed gas centrifuge part I — Problem formulation and solution by collocation

The recirculating continuum flows developed in a closed cylindrical centrifuge with a perfect, constant conductivity, constant viscosity gas, due to small equal and opposite arbitrary radial temperature perturbations applied to the end caps and with zero radial heat loss at the wall, can be expressed as a combination of an axially independent pure recirculating axial flow developed by a constant temperature gradient, and the set of radial eigenfunctions. A complete numerical solution has been developed, using the full set of finite radial eigenvectors associated with a set of radial finite difference approximations to the five governing linear differential equations and applying simple collocation for the boundary conditions. A numerical example gives the associated complete eigenvalue spectrum, and the axial velocity distributions resulting from a simple specified temperature distribution, calculated from the particular combination of eigenvector solutions and ‘gradient’ solution which satisfies in detail the boundary conditions.     

Experimental and theoretical study of the gas-water two phase flow through a conductance multiphase Venturi meter in vertical annular (wet gas) flow

Annular gas-liquid two phase flow widely occurs in nuclear industry. Various combinations of techniques have been employed in annular gas-liquid two phase flows to measure the flow parameters (e.g. liquid film thickness, gas volume fraction and the phase flow rates). One of the most useful techniques which has proven attractive for many multiphase flow applications is the electrical conductance technique. This paper presents an advanced conductance multiphase Venturi meter (CMVM) which is capable of measuring the gas volume fractions at the inlet and the throat of the Venturi. A new model was investigated to measure the gas flow rate. This model is based on the measurement of the gas volume fractions at the inlet and the throat of the Venturi meter using a conductance technique rather than relying on prior knowledge of the mass flow quality x. We measure conductance using two ring electrodes flush with the inner surface of the Venturi throat and two ring electrodes flush with the inner surface of the Venturi inlet. The basic operation of the electrical conductance technique in a multiphase flow is that the conductance of the mixture depends on the gas volume fraction in the water. An electronic circuit was built and calibrated to give a dc voltage output which is proportional to the conductance of the mixture which can then be related to the water film thickness in annular flow (and hence to the gas volume fraction). It was inferred from the experimental results that the minimum average percentage error of the predicted gas mass flow rates (i.e. −0.0428%) can be achieved at the optimum gas discharge coefficient of 0.932.     

Carbon deposition from a γ-irradiated CO2/CO/CH4/C2H6 gas mixture on the manganese oxides MnO, Mn3O4 and Mn2O3

The composition of oxides formed on steel surfaces within power reactors may influence heat transfer efficiency. Previous studies have indicated that carbon is deposited on spinal-type oxides containing manganese, iron, cobalt, nickel and chromium. In this investigation, characterised manganese oxides have been subjected to γ-irradiation under conditions similar to those experienced in reactors in an effort to understand the catalytic processes involved in deposit initiation and growth. Mn₃O₄ and Mn₂O₃, under the conditions present in the γ-cell, were reduced to MnO during the time of exposure. Relative carbon deposition rates were observed to follow the trend MnO>Mn₃O₄≈Mn₂O₃.