雷诺数关系式对膜状凝结湍流区传热计算的影响

膜状凝结现象广泛存在于核电站安全壳和稳压器中。关于膜状凝结液膜湍流区的传热模型,目前未明确辨析基于质量和能量关系的两种雷诺数关系式的差别。本文针对管外纯蒸汽自然对流膜状冷凝传热,定量地分析雷诺数关系式对膜状凝结液膜湍流区传热计算的影响。基于液膜湍流区修正项的一般性假设,推导了膜状凝结湍流区传热系数的表达式。同时,分别与雷诺数关系式Remass和Reenergy联立,求解得到不同雷诺数关系式之间以及对应的膜状凝结传热系数之间的关系。分析表明:受普朗特数Pr的影响,在膜状凝结液膜湍流区,雷诺数关系式Remass和Reenergy差别明显,并存在关于Pr的分界点。基于Remass和Reenergy得到的膜状凝结平均传热系数及其相对偏差是Re和Pr的非线性函数。当0.1Pr4.0且Re1 600时,基于Reenergy和Remass得到的膜状凝结平均传热系数相对偏差在-60%和+60%之间。通过实验和理论验证,在膜状凝结液膜湍流区基于Reenergy得到的膜状凝结传热系数更加准确。     

同轴交叉三扭带强化单相流体对流换热特性分析

核动力装置的非能动安全系统采用了大量的各类换热器。在自然循环条件下,换热器内的流动较弱,换热系数较低,处于层流状态。为了强化换热器的换热效果,提出了一种新型扭带——同轴交叉三扭带(CCTTT),并对换热管内插入不同扭率(2、3、4、∞)的CCTTT以强化水的换热效果进行了数值模拟研究。结果表明,在雷诺数Re=40～1200的范围内,CCTTT能有效强化换热器内流体的单相对流换热。随着扭率的减小,CCTTT的强化换热效果增强,评价准则数(PEC)增大。扭率为4.0的CCTTT的PEC是2.02,而扭率为2.0的CCTTT的PEC可达2.64。通过与其他工作介质比较发现,相同Re时,随着流动工质普朗特数的增大,CCTTT的PEC均增大。     

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.     

水平管内蒸汽冷凝局部换热特性实验研究

以水蒸气为工质,实验研究了水平管内纯蒸汽冷凝的局部换热特性。实验选取换热管内径为25 mm、换热管进口压力为0.15~0.4 MPa、局部蒸汽的Re=5756~92289,分析了蒸汽压力及流速、壁面过冷度对冷凝传热系数的影响,并将采用现有关系式计算的冷凝传热系数与实验结果进行了对比。结果表明：冷凝传热系数随壁面过冷度的增大而减小,随压力的升高和流速的增大而增大;采用现有关系式计算的冷凝传热系数与实验值的偏差较大,关系式有待进一步改进;在实验范围内,由拟合换热关系式计算所得冷凝传热系数与实验结果的相对偏差在15%左右。     

矩形窄缝通道内水稳态和瞬态流动换热特性实验

以去离子水为工质,在压力0.5～5.0 MPa的范围内,对矩形窄缝通道内水稳态及瞬态流动换热特性进行了实验研究。结果表明:矩形窄缝通道在水平和竖直放置以及稳态和瞬态条件下,水的流动换热特性呈现出基本相同的规律。层流向紊流过渡区域的雷诺数(Re)为900Re1300,比常规通道提前,单相摩擦阻力系数比常规通道大;采用Dittus-Boelter公式的形式拟合得到了新的换热实验关联式,其系数较Dittus-Boelter公式的系数约小11.3%。在稳态条件下,紊流区换热系数随质量流速的增加而增大,增大趋势比较明显;换热系数随热流密度的变化不明显;压力对单相强迫对流换热特性基本没有影响。     

骨架发热多孔介质内单相水流动传热实验研究

针对骨架发热多孔介质内单相水流动阻力和传热特性开展了实验研究,拟合获得骨架发热多孔介质内热态流动阻力和对流换热关系式。实验参数范围是:雷诺数Re取127～394,表面热流密度12～62 kW/m2。实验结果表明:在本文研究的孔隙有效雷诺数范围内,惯性项阻力系数Rf受流动参数影响;基于骨架发热条件下获得的阻力关系式具有较好的扩展性,可以较好地预测骨架不发热条件下多种几何结构的多孔介质通道内单相水、单相蒸汽流动阻力;随着表面热流密度增大,对流换热系数不断降低;在相同热流密度条件下,随着质量流速的增大,对流换热系数也会随之增大。     

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.     

Local heat transfer and hot-spot factors in wire-wrap tube bundle

Heat transfer coefficients and hot-spot factors have been determined from measured local temperatures and calculated local mass flux in seven adjacent tubes and associated subchannels of a 61 wire-wrap tube bundle characteristic of the blanket of a GCFR (Gas Cooled Fast Reactor). The bundle consisted of 2.11 cm OD stainless steel tubes on a triangular array with a pitch/diameter ratio of P/D = 1.05. The helical wire of 0.1067 cm in diameter was coiled on the tube with a respective initial orientation of 0–120–240°C and 30.48 cm helical pitch. The experiment used water at atmospheric pressure and temperature as coolant. The resulting dimensionless correlation for heat transfer is applicable to gases and all non-metal fluids in one phase flow when the fluid properties at subchannel bulk temperature are used. This correlation is based on local subchannel mass flux and is applicable to all wire-wrap configurations. Local subchannel mass fluxes were determined with a computer program COBRA IV and used to correlate the average Nusselt number for each subchannel in terms of local Reynolds number and fluid Prandtl number. The differences of up to 19% between that correlation and the one presented in earlier work are discussed in the text. The hot-spot factors on the convective heat transfer coefficient for tubes and subchannels are given as a function of Reynolds number based on a bundle average mass flux and a local subchannel hydraulic diameter. These factors are specific to the bundle configuration and are also dependent on the wire-wrap configuration.     

Analysis of the suction effect on the mass transfer when using the heat and mass transfer analogy

The transport phenomenon between a fluid in movement and a wall is strongly affected by the permeability of the wall. The application of a correction factor standing for the transpiration effect will be required whenever a heat transfer model is based either on the use of heat, mass or momentum analogies or on the use of empirical correlations for the computation of the heat transfer coefficient.The suction factor commonly used when solving as a function of either mass or molar fractions is called the Bird suction factor. The validity of this factor rests on the hypothesis of the film theory or Couette flow.This paper reviews the Bird suction factor in laminar regime, extending the analysis to turbulent flow conditions and finding thereby that Bird's equation can overestimate the suction factor under turbulent condensation conditions in the gas phase.Finally, an alternative formulation for the suction factor under turbulent condensation conditions has been proposed and compared with Bird's original formulation. In doing this, both data and models developed by other authors and the UW-Madison test facility database have been used.The results show the suitability of the alternative formulation when calculating the condensation rate in turbulent natural circulation scenarios, whereas Bird's formulation seems to be more appropriate for laminar regimes.     

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。     

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.     

The modeling and validation of the flow and heat transfer models of pulsating flow in channels in rolling motion

The flow and heat transfer models of laminar flow and turbulent flow in rolling motion are established theoretically and modified with CFD results and experimental data. The correlations of frictional resistance coefficient and Nusselt number in pipes in rolling motion are obtained. The effect of rolling motion on the flow and heat transfer is mainly affected by the Reynolds number, angular acceleration and channel diameter. As the channel diameter is small, the effect of rolling motion on the flow and heat transfer is weak. The modified correlations of frictional resistance coefficient and Nusselt number in rolling motion could predict the flow and heat transfer in pipes in rolling motion correctly. The average discrepancy between theoretical correlations and experimental data is about 15%.     

Single phase transport within bare rod arrays at laminar, transition and turbulent flow conditions

A theoretical analysis has been performed to study molecular and turbulent transport phenomena between subchannels of infinite bare rod arrays at laminar, transition and turbulent flow conditions. For this investigation, the theoretical approach of Ramm and Johannsen for predicting turbulent momentum and heat transfer in rod bundles has been extended to evaluate three-dimensional temperature fields. Results are presented enabling the prediction of the onset and growth of laminarization in typical subchannels of square and triangular rod arrays. These results are further applied to interpret the characteristic effects of variations in Reynolds number, Prandtl number or geometric spacing on integral exchange parameters as the thermal mixing flow rate and mixing length scale. These results are of particular significance relative to the explanation of recent data from tracer-type mixing experiments and also exhibit the importance of secondary flow effects on turbulent intersubchannel energy transport. In view of these findings, the physical relevance of current correlations derived from integral-type experiments to numerically predict exchange coefficients for use in lumped parameter subchannel analysis codes is discussed.     

Effect of interfacial wavy motion on film boiling heat transfer from isothermal downward-facing hemispheres

Film boiling heat transfer coefficients for a downward-facing hemispherical surface are measured from the quenching tests in Downward-Boiling Experiment Laminar Transition Apparatus (DELTA). Two test sections are made of copper to maintain low Biot numbers. The outer diameters of the hemispheres are 120 and 294 mm, respectively. The thickness of all the test sections is 30 mm. The effect of diameter on film boiling heat transfer is quantified utilizing results obtained from the test sections. The measured data are compared with the numerical predictions from laminar film boiling analysis. The measured heat transfer coefficients are found to be greater than those predicted by the conventional laminar flow theory on account of the interfacial wavy motion incurred by the Helmholtz instability. Incorporation of the wavy motion model considerably improves the agreement between the experimental and numerical results in terms of heat transfer coefficient. In addition, the film boiling was visualized using a digital camera.     

RELAP5-3D modeling of PWR steam generator condensation experiments at the Oregon State University APEX facility

This report describes modeling using RELAP5-3D of a series of six steam generator U-tube steam condensation (without non-condensable gas) tests conducted at the Oregon State University Advanced Plant Experiment Test Facility from 2005 through 2007. These tests were designed to evaluate steam condensation rates in a scaled pressurized water reactor steam generator at various primary and secondary side pressures and inlet steam mass flow rates. Comparisons between the experimental data and the RELAP5-3D model results are made to quantify the effectiveness of RELAP5-3D in handling steam condensation in U-tube steam generators. RELAP5-3D tends to over predict the condensation rate and heat transfer coefficient when compared against the experimental data when the code uses the laminar Nusselt correlation to determine the heat transfer coefficient. When RELAP5-3D results are used with the Shah correlation the comparison between the heat transfer coefficients is much improved.     

Film Boiling Heat Transfer around a Sphere in Forced Convection

Film boiling heat transfer around a sphere moving downward in a liquid, is analyzed in this study. The general solution obtained by the theory proposed, developed under certain reasonable assumptions, shows that the Nusselt number for predicting the boiling heat transfer coefficient depends on the Reynolds number, the Prandtl number, the liquid/vapor viscosity ratio, the kinematic viscosity of liquid, the absolute size of sphere, and on another dimensionless number C_p(π_d—π₁)Δi.

Results obtained numerically from the general solution are applied as examples to boiling heat transfer for water and sodium, from which it is possible to estimate the heat transfer coefficients for a sphere with boiling. The effect of radiative heat transfer is also examined.     

Discussion on heat transfer correlation in turbulent channel flow imposed wall-normal magnetic field

Heat transfer degradation in high Prandtl number fluid was evaluated via direct numerical simulation (DNS). Target flow fields were fully developed turbulent channel flows imposed a wall-normal magnetic field in the high and low Prandtl number conditions (Pr = 5.25 and 0.025, respectively). Values of the bulk Reynolds number (Re_b = 14,000) and the Hartmann number (Ha = 0-32) were set to be equivalent to those of the previous experimental study by Yokomine et al. The numerical results of the Nusselt number for the high Prandtl number fluid were in good agreement with the experimental results by Yokomine et al. However, the magneto-hydrodynamics (MHD) effect on the heat transfer degradation was considerably larger than the empirical correlation proposed by Blum, particularly in the large interaction parameter range. On the other hand, the DNS results for the low Prandtl number fluid were consistent with the empirical correlation proposed by Blum and the experimental results by Gardner and Lykoudis.Therefore, we proposed a new correlation of the MHD heat transfer in high Prandtl number fluid (Pr = 5.25), and suggested that the empirical correlation proposed by Blum could be recommended for low Prandtl number fluid in the large interaction parameter range.     

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.