A general one-dimensional model for conduction-controlled rewetting of a surface

A computer-oriented analytical method for predicting the rewetting rate of a hot dry wall is proposed. The wall, which is modeled as a thin flat plate with internal heat generation, receives a variable heat flux from one side while it is cooled from the other side. The model accounts for the large variations of the heat transfer coefficient near the wet front and for the temperature dependence of the thermal and physical properties of the wall. The one-dimensional heat-conduction equation is solved by dividing the quenching zone into small segments of arbitrary temperature increment and constant properties and heat transfer coefficient. A trial-and-error method is developed to predict the velocity of the wet front, the length of the quenching zone and the temperature profile. The one-dimensional models of other authors can be obtained as particular cases of the present model.     

Quench front propagation during bottom reflooding of a heated annular channel

A time-dependent two-dimensional conduction model of quenching, via bottom reflood, of hot, dry cylindrical tube of finite length in an annulus is presented. The method of finite integral transform is used in the solution. Multiregion heat transfer is considered at the heater surface, and no a priori assumption is made in regard to the quench front velocity. A possible mode of variation of the quench temperature with coolant inlet velocity is proposed. Predictions of the quench front velocity are compared with a few experimental data for Zircaloy-2 tube available in the literature.     

Transient heat conduction problems in inhomogeneous media discretized by means of boundary-volume element

An integral equation formulation is presented for the transient heat conduction problems in inhomogeneous media. The material constants are assumed to be prescribed as arbitrary, continuous and differentiable functions of position vector. The governing integral equations are derived from the weighted residual statement of the problems in which the fundamental solution to the corresponding heat conduction problems in homogeneous media is used as the weight function. The whole domain of interest is discretized into a series of boundary-volume-time elements, and then a set of linear simultaneous equations are obtained. Their solutions yield the temperature in the whole domain as well as the heat flux on the boundary.     

竖直圆管内超临界压力氟利昂传热试验研究

深入研究超临界压力下流体特殊的对流传热特性,对超临界水冷反应堆的堆芯设计至关重要。在上海交通大学SMOTH氟利昂回路上开展了压力4.3~4.7 MPa、质量流速600~2 500kg/(m2·s)、热流密度20~180kW/m2参数下的圆管内超临界上升流传热试验。远离拟临界温度区间内换热系数和Dittus-Boelter公式计算值很接近,热流密度越大,近拟临界区换热系数越小,小质量流速大热流密度下,发生显著传热恶化。加速效应无量纲数和浮升力无量纲数对传热特性显示了强烈的相关性。提出了氟利昂工质传热试验的传热恶化起始点关系式。Bishop关系式计算换热系数和试验值之间标准差很小,但整体略偏大;Jackson关系式计算值和试验值之间平均偏差很小,但标准差偏大。     

窄缝通道内过冷沸腾区域汽泡脱离频率研究

采用高速摄像仪对矩形窄缝通道内垂直上升流过冷流动沸腾区域汽泡脱离频率进行可视化实验研究。结果表明,汽泡脱离频率随质量流速的增大而减小,随入口过冷度的增大而减小,随热流密度的增大而增大。将实验数据与文献中汽泡脱离频率计算模型进行比较,发现基于池式沸腾和饱和流动沸腾开发的计算模型不能准确预测过冷沸腾区域汽泡脱离频率。本文以无量纲参数的形式,分别用液相雷诺数、过冷雅各布数和核态沸腾热流密度表示质量流速、主流过冷度和热流密度对汽泡脱离频率的影响,获得矩形窄缝通道内过冷沸腾区域汽泡脱离频率预测关系式,关系式的平均预测误差为±17.1%。     

Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (fp) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain fp. The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the fp of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the fp increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on fp. The increase of Reynolds number and Jakob number causes the increase of fp, and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors.     

Quenching of hot oxidizing surfaces

A one-dimensional time-dependent rewetting model is developed and assessed to describe the interrelated processes of conduction, convective cooling and exothermic steam–metal reactions at the vapor zirconium-cladding interface during quenching of degraded fuel rods. Upstream of the quench front a constant heat transfer coefficient is assumed whereas a heat flux profile of general spatial shape may be prescribed downstream. The quenching velocity history and the temperature profile are computed analytically via a Green's function approach. Numerical results of the present model compare favorably with published experimental data.     

A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model

This paper presents a numerical solution of one-dimensional transient two-phase flow in a vertical channel using the Drift Flux Model (DFM). The DFM treats the two phases as a mixture, but allows slippage between the gas and the liquid phase. The DFM was used for the calculation of velocity and fraction of each phase, combined with the most relevant closure relationships models for condensation, wall evaporation, and phasic velocities. The solution of the three conservation equations for the mixture and a continuity equation for the gas phases is obtained by a semi-implicit numerical method. A finite volume method is used to discretize the governing equations on a staggered grid in the computational domain. Satisfactory agreement is shown between predicted void fraction, RELAP5 code and available experimental data under both transient and steady state conditions. Numerical solution was also obtained for a wide two-phase flow conditions: system pressure, surface heat flux, mass flow rate and inlet sub-cooling to check the model ability to predict void fraction accurately. It is concluded, therefore, that the DFM is able to predict void fraction in subcooled flow boiling with sufficient accuracy. For pressures lower than 30 bars, the DFM overestimated the void fraction in comparison with the experimental data by about 15%. The model requires less computational power to simulate than other approaches and has no limitations on the nodalization process for numerical stability. It is therefore expected that development of presented model will be useful for the assessment of experimental data, as well as performing pre-test numerical experimentation.     

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.     

窄矩形通道污垢沉积数值仿真

为研究窄矩形通道内CaSO4溶液由于析晶沉积产生的污垢及对换热的影响,本研究基于合理的污垢沉积、污垢剥蚀与污垢热阻模型,利用FLUENT软件结合用户自定义函数（UDF）对一定热流密度、入口流速、入口温度和流体浓度的流体进行了析晶沉积模拟计算。研究结果表明了此工质的污垢产生情况和对换热的影响,同时得到热流密度、入口流速和流体浓度3种影响因素对污垢沉积的影响：污垢热阻随热流密度增大而增大,随入口流速增大而减小,随流体浓度增大而增大。本研究可用于模拟板状燃料元件窄矩形通道由于析晶导致的污垢沉积过程。     

Initiation of Melting and Evaporating of Materials under Plasma Disruption

Abstract

In a tokamak reactor, a pulsed high heat flux, whose heat flux should result in up to 2x10⁵MW/m², would be injected to the plasma facing components (PFCs) due to a plasma disruption. By this heat load the PFCs are melted, evaporated and cracked. In this study melting and evaporation behavior was investigated through performing the experiment with use of an electron beam to simulate heat loads due to plasma disruptions and the numerical and approximate analyses.

Experimental and analytical results show that the evaporated mass increases abruptly at a curtain heat flux and time, and that the thickness of melting layer has the maximum at a curtain heat flux. From dimensionless expressions of such results the simple dimensionless correlations between the relevant values were obtained to estimate the significant characteristics such as evaporation thresholds and maximum melting layer thickness. Applying them to evaluation of the thermal resistance of materials against various heat loads due to a plasma disruption confirms that against the milder heat load, the materials whose initiation of melting and evaporation occurs late, such as tungsten, are suitable for armor materials and against the severer heat load, the materials that have a large of latent heat evaporation, such as graphite, are suitable for armor materials.     

Parametric study on rewetting velocities obtained with a two-dimensional heat conduction code

A comprehensive parametric study has been performed to quantify the effect of different variables on the rewetting velocity in a light water reactor following a loss-of-coolant accident. To this purpose, a numerical solution of the general two-dimensional (axial and radial) heat conduction equation in cylindrical geometry has been obtained. The method used is the alternating-direction implicit procedure developed by Peaceman and Rachford. The model accounts for decay heat generation in the fuel, coolant subcooling, different wall temperatures and different heat transfer coefficients across the gap and at the clad surface. The two-dimensional model can be reduced to a one-dimensional model by setting the heat conduction in either the radial or axial direction to zero. Results with the new model agree with previous models and with experimental data.The variables studied were: axial and/or radial heat conduction, clad temperature, quench temperature, coolant temperature, temperature for the onset of nucleate boiling, heat transfer coefficients, stored and decay heats, clad material and clad thickness. The critical thickness (clad thickness for which the calculated rewetting velocity remains constant) was also determined and found to be larger than the clad thickness of light water reactor fuel pins under usual reflood conditions. According to these calculations, the stored and decay heats affect the rewetting velocity significantly.     

Discussion of similarity principles for fluid-to-fluid scaling of heat transfer behaviour at supercritical pressures

In this paper, a rationale for comparing heat transfer behaviour of different fluids at supercritical pressures is discussed. The study is performed as an extension to heat transfer of a previous proposal of dimensionless groups suitable for assessing stability in heated channels with supercritical fluids. The additional difficulty to be overcome with respect to the case of stability of channels with imposed heat flux is related to the role played in the present case by thermo-physical properties, whose trends as a function of dimensionless enthalpy are different for different fluids, sharing anyway a general similarity across the pseudo-critical threshold.The proposed considerations are discussed with the aid of results obtained by computational fluid-dynamic codes, contributing to clarify the extent at which the reported considerations can be considered promising for developing a coherent similarity theory for heat transfer to fluids at supercritical pressures.     

Heat transfer effects on flow past an impulsively started semi-infinite vertical plate with uniform heat flux

An implicit finite-difference technique is employed to derive a solution to the flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with uniform heat flux. Transient and steady-state velocity and temperature profiles, the local and average skin-friction and the Nusselt number are shown graphically. The velocity profiles at small values of time t are shown to agree with theoretical solution of the flow past an impulsively started infinite vertical plate with uniform heat flux. The effect of different parameters Pr (the Prandtl number) and Gr (the Grashof number) are studied. It is found that the number of time steps to reach steady-state depends strongly on Grashof number.     

An Analytical Model for Displacement Velocity of Liquid Film on a Hot Vertical Surface

The downward progress of the advancing front of a liquid film streaming down a heated vertical surface, as it would occur in emergency core cooling, is much slower than in the case of ordinary streaming down along a heated surface already wetted with the liquid. A two-dimensional heat conduction model is developed for evaluating this velocity of the liquid front, which takes account of the heat removal by ordinary flow boiling mechanism.

In the analysis, the maximum heat flux and the calefaction temperature are taken up as parameters in addition to the initial dry heated wall temperature, the flow rate and the velocity of downward progress of the liquid front. The temperature profile is calculated for various combinations of these parameters. Two criteria are proposed for choosing the most suitable combination of the parameters. One is to reject solutions that represent an oscillating wall temperature distribution, and the second criterion requires that the length of the zone of violent boiling immediately following the liquid front should not be longer than about 1 mm, this value being determined from comparisons made between experiment and calculation.

Application of the above two criteria resulted in reasonable values obtained for the calefaction temperature and the maximum heat flux, and the velocity of the liquid front derived therefrom showed good agreement with experiment.     

Author index to volume 79

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

Scaling laws for thermal-hydraulic system under single phase and two-phase natural circulation

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

An analytical method of evaluating the effect of rod displacement on circumferential temperature and heat flux distributions in turbulent flow through unbaffled rod bundles

An analytical method of evaluating the circumferential variations of temperature and heat flux fields inside and around a displaced fuel rod in triangular rod bundles in turbulent flow is presented with illustrative examples. The analysis consists mainly of the derivation of the simultaneous solutions of a set of heat conduction equations for fuel, cladding and coolant under the assumption of fully developed flow and heat transfer conditions. The local coolant velocity distribution, which is necessary for deriving the temperature field in coolant, is determined by solving the Navier-Stokes equation and the turbulent mixing of coolant is taken into consideration. The results show how the circumferential variations in the temperature and heat flux fields on the outer surface of the cladding increase the lower the ratio and the larger the fuel rod displacement due to thermal conduction and peripheral coolant flow velocity distribution.     

HFE-7100工质稳态临界沸腾传热实验研究

池沸腾临界热通量是沸腾相变传热的重要参数,决定了相变换热器件的推广应用。表面粗糙度和饱和压力对沸腾传热边界层分布、表面铺展润湿及工质动力学特性具有重要影响,进而对临界热通量作用显著。本文对HFE-7100工质在4种不同粗糙度的铜基表面（0.019、0.205、0.311和0.587 μm）条件及在不同饱和压力（0.07、0.10、0.15及0.20 MPa）工况下的池沸腾稳态临界状态下的传热及可视化实验进行了研究。对表面粗糙度及饱和压力对稳态临界沸腾的影响机制进行了分析,并考察了临界热通量预测模型对临界热通量的预测准确性。可视化研究表明,临界状态下的沸腾气液两相工质由小气泡、大气泡、气柱及蘑菇状气团组成,而在过渡状态下,沸腾表面会形成非平滑气膜,并不断分离出气泡。同时传热数据表明,表面粗糙度及饱和压力的增加能使表面临界热通量得到提升。相比而言,Bailey等建立的临界热通量预测模型能相对准确地预测HFE-7100工质沸腾临界热通量数据。为进一步提升预测准确度,建立了临界热通量无因次参数K预测经验关联式,其预测值与本实验及文献实验数据吻合较好。     

Heat conduction analyses on rewetting front propagation during transients beyond anticipated operational occurrences for BWRs

Our previous study investigated the rewetting behavior of dryout fuel surface during transients beyond anticipated operational occurrences for BWRs, which indicated the rewetting velocity was significantly affected by the precursory cooling defined as cooling immediately before rewetting. This study further investigated the previous experiments by conducting additional experimental and numerical heat conduction analyses to characterize the precursory cooling. For the characterization, the precursory cooling was first defined quantitatively based on evaluated heat transfer rates; the rewetting velocity was investigated as a function of the cladding temperature immediately before the onset of the precursory cooling. The results indicated that the propagation velocity appeared to be limited by the maximum heat transfer rate near the rewetting front. This limitation was consistent with results of the heat conduction analysis using heat transfer models for the precursory cooling expressed as a function of distance from the rewetting front, the maximum wetting temperature, and the heat transfer coefficients in the wetted region. This paper also discusses uncertainties in the evaluation of transient heat flux from the measured surface temperature, and technical issues requiring further investigation.