Effects of Boundary Conditions on Thermal Response of a Cellulose Acetate Layer Using Hottel’s Zonal Method

Energy can transfer internally by radiation in addition to conduction in translucent polymers. Since radiant propagation is very rapid, it can provide energy within the layer more quickly than diffusion by heat conduction. Thus, the transient thermal response of a layer for combined radiative and conduction may be extremely different from that of conduction alone. In this paper, the behavior of a heat conducting, absorbing, and emitting layer of Cellulose Acetate layer is investigated during the transient interval when both conductive and radiative heat transfer are considered. Specifically, the effects of boundary conditions on the response of the layer are considered here. These boundary conditions include both conductive boundary conditions, such as convection coefficient and convective fluid temperature, and radiation boundary conditions, like radiation surrounding temperature and specular reflectivity. To this end, the governing differential equations including the equation of radiative heat transfer within the material coupled to the transient energy equation with radiative terms are presented. The solution procedure is based on nodal analysis and Hottel’s zonal method extended by the ray tracing method. The transient energy equation including the radiative internal energy source is solved using a time marching finite difference procedure with variable space and time increments.     

对蒸发曳力模型的修正

建立了一套研究高温小球落水的工程热物理基础实验装置。在此装置上进行了一系列实验,证实了蒸发曳力模型的可信性．同时也发现其局限性：对蒸发曳力模型进行了修正,增加考虑了辐射热在液体内部和汽液交界面的分布及对流换热对小球落水阻力的影响,扩大了蒸发曳力模型的适用性。     

Evaluation of Gap Heat Transfer between Boron Carbide Pellet and Cladding in Control Rod of FBR

Heat transfer across a gas gap between a boron carbide pellet and a cladding in FBR control rod has been experimentally investigated. The main purpose of this investigation is to present a calculational method for the gap heat transfer in order to improve accuracy of thermal design for the control rod with 0.5 mm gap width at a beginning of reactor operation.

Two types of tests have been carried out using simulated control rods. One is low temperature tests below 200°C. The test results indicated that the convective heat transfer has a negligible effect on the gap conductance when the Rayleigh number using the gap width as the characteristic length is below 0.1. The other is high temperature tests up to 600°C.

The results showed +10 to — 5% variations in the gap conductance data due to eccentricity between the pellet and the cladding. The prediction based on conduction and radiation heat transfers considering a thermal expansion and an eccentricity gave better results of gap conductance having a maximum difference of only 17% from the measured ones. Calculation in the radiation heat transfer used thermal emissivities. 0.85 for the boron carbide and 0.15 for the cladding, measured by infrared thermography.     

Transient Temperature Response of an Annular Flow with Step Change in Heat Generating Rod

An analysis is made on the transient temperature response of fluid and of heat generating rod in the case of annular flow. Special consideration is given to the effects of the rod heat capacity and radial thermal conduction in the rod during the transient.

The analysis is based on the following assumptions: (1) Initially the system has a uniform temperature distribution, and the rod undergoes a step change in heat generation; (2) the temperature of the fluid entering the annular space is kept constant; (3) the velocity distribution of fluid is uniform; (4) all physical properties remain unchanged during the transient; (5) axial thermal conduction in the rod is neglected in comparison with that in the radial direction; (6) axial thermal conduction in the fluid is neglected in comparison with axial thermal convection.

The present result is compared with values by quasi-static solution for various heat transfer parameters.     

Improvements of evaporation drag model

A special visible experiment facility has been designed and built, and an observable experiment is performed by pouring one or several high-temperature particles into a water pool in the facility. The experiment result has verified Yang‘s evaporation drag model, which holds that the non-symmetric profile of the local evaporation rate and the local density of vapor would bring about a resultant torce on the hot particle so as to resist its motion. However, in Yang‘s evaporation drag model, radiation heat transfer is taken as the only way to transfer heat from hot particle to the vapor-liquid interface, and all of the radiation energy is deposited on the vapor-liquid interface and contributed to the vaporization rate and mass balance of the vapor film. In improved model heat conduction and heat convection are taken into account. This paper presents calculations of the improved model, putting emphasis on the effect of hot particle‘s temperature on the radiation absorption behavior of water.     

Heat transfer from a partially uncovered reactor core

This paper documents a model which has been developed for predicting the temperature distribution along a “flow channel” of a pressurized water reactor during simulated, uncovered core conditions. In the model, heat conduction along the fuel element, convection from the surface to the coolant, radiation exchange between the clad surface and steam, and surface exchange between adjacent fuel rods are considered. Variations of the thermophysical properties of the fuel road and of the coolant with temperature are accounted for, but oxidation of Zircaloy is not modeled. Extensive sensitivity studies on the effects of heat generation in the core, steam velocity, pressure level, uncovered core height, presence of hydrogen gas in the coolant, power skew, clad emissivity, and convective heat transfer correlations have been examined. The results show that the importance of radiation in comparison with convection increases with an increase in the fuel rod temperature, pressure, and clad emissivity.     

高温液滴流辐射换热及蒸发特性

本文针对可应用于空间堆的矩形液滴辐射器（LDR）,研究其液滴流的辐射换热及蒸发特性。在传统的高温液滴流辐射换热模型的基础上,添加了液滴流蒸发模型,并将辐射换热模型与蒸发模型进行耦合,在该模型的基础上开发了高温液滴流辐射换热-蒸发特性分析程序LDFAC。将该程序的液滴层温度分布计算结果进行校核,其相对误差不超过1.9%。使用该程序对装载DC705硅油下不同光学厚度及长度的液滴层辐射换热蒸发特性进行了分析。结果表明：在液滴层的光学厚度较大的情况下,液滴层内部的温度分布非常不均匀,液滴层中心的温度没有显著降低,而液滴层接近外表面部分的温度下降较为明显;温度对LDR的系统寿命有着较大影响,温度每降低10 K,系统寿命可提高约450%,同时,液滴层光学厚度越大,系统寿命也越长。     

辐射屏数及密度对超导腔垂直测试杜瓦漏热的影响

超导腔垂直测试杜瓦为广口液氦容器,对绝热性能有较高要求,其内筒体采用高真空多层绝热,顶部盖板侧为多屏绝热。为减少杜瓦顶部盖板侧漏热,提出了变密度辐射屏方法,以盖板、辐射屏、液面和氦气为对象建立了导热、对流与辐射耦合换热的传热模型,并通过实验进行了验证。通过数值计算得到了辐射屏数对漏热的影响规律及最优辐射屏密度。结果表明：1） 实验测得的辐射屏温度与传热模型计算结果较为一致,平均相对偏差为8.37%,认为传热模型是合理的;2） 靠近液面处第1层辐射屏（屏1）与液面间氦气的格拉晓夫数Gr随屏1温度T₁的升高存在极大值（T₁=9.14 K,Gr=1.12×10¹⁴）,T₁超过35 K后Gr基本保持不变;3） 等间距分布时,辐射屏数大于11层后总漏热变化不明显,一定辐射屏数下,相邻两屏之间气体导热占主导地位,低温区域（靠近液面侧）至高温区域（靠近盖板侧）导热热流比重减小,辐射热流比重升高;4） 11层辐射屏数下,高温区域布置7层、低温区域布置4层的变密度辐射屏方式漏热最小,与等间距分布相比漏热可减少4%。     

纳米流体饱和池沸腾传热及CHF模型研究

纳米流体传热是一种新兴的换热方式,目前研究多集中在单相研究领域,而纳米流体沸腾传热特性的相关研究较少。本文采用热通量拆分方法,将壁面传热分为4种模型(微液层蒸发、气泡脱离前的瞬态导热、气泡脱离后的瞬态导热以及微对流换热),对这4种模型的传热量分别进行计算,结合壁面核化中心密度等参数,计算了壁面平均传热系数和CHF。结果表明,本文计算结果与国际上已发表的实验数据符合较好,充分验证了所建立模型的合理性。     

Development of a 2D conduction code for a finned fuel element analysis

The fuel element of KMRR (Korea Multi-purpose Research Reactor) has 8 longitudinal, rectangular fins to enhance the heat transfer performance. The existence of these fins makes it difficult to analyze the heat transfer phenomena within the fuel element using the conventional one-dimensional heat conduction model. As the uncertainty in the computation of the maximum sheath temperature significantly affects the core thermal margin, a computer code, called, TEMP2D, which is based on a two-dimensional heat conduction model has been developed to deal with the finned element and validated. This computer code TEMP2D has a fully implicit numerical scheme and can solve both the steady state and transient problems such as the changes in coolant thermal-hydraulic conditions and fuel pin power. The code accuracy, which proved to be an excellent one, was verified by comparing its results with those from two widely accepted computer codes, MARC and ADINA. The result of this code calculation has been used to compute the KMRR core thermal margin and to develop a correlation for the equivalent 1D heated diameter which can reproduce the maximum cladding temperature (or heat flux) at various steady states when used in the 1D heat conduction model.     

The stationary boiling front in liquid film cooling of a vertical heated rod

One process of transient rewetting has been experimentally characterized by the advance of a boiling front whose length is small with respect to the rod dimensions and whose rate of advance is nearly constant in time. With suitable coordinate transformations, the rewetting rate has been satisfactorily described by one (or two) dimensional heat conduction in the rod, coupled to the heat removal in the falling film by an average heat transfer coefficient and an assumed maximum temperature at the boiling front. To resolve present uncertainty in the choice of the coupling heat transfer coefficient and the maximum wetting front temperature, experiments were carried out in which detailed temperature profiles were obtained throughout all regions of a stationary boiling front on a vertical rod. Analysis of these experimental data show that for unconfined sputtering on a vertical rod, the maximum temperature at the boiling front is that associated with the point of DNB. This suggests that the boiling front may be modelled by assuming a nucleate boiling process. Based on this concept, one- and two-dimensional heat conduction effects are compared and a simplified one-dimensional model is illustrated and verified.     

多孔注入冷冻靶快速降温过程瞬态特性研究

高度均匀光滑的燃料冰层是惯性约束聚变冷冻靶成功点火的物质前提,其制备关键是在靶丸外建立均匀的球形温度场并进行精确控制。本文针对多孔注入冷冻靶系统,建立了三维仿真模型,数值研究了冷冻靶温度场稳态分布与瞬态降温特性,并分析了接触热阻、氦气压力等因素的影响。结果表明：冷臂温度恒定时,靶丸与充气管接触位置为低温区,激光入射口正对处为高温区,最大温差为003 mK;硅臂加热块功率突降后,靶丸表面最大温差在025 s内急剧上升至8788 mK,温度场均匀性显著恶化;与硅爪 套筒完美接触相比,低温胶层的存在可有效改善降温过程中温度场的恶化,但降温响应时间明显增加;1～10 kPa氦气压力范围内,快速降温过程中靶丸温度响应迅速,且最大温差峰值较小,有利于维持靶丸表面的温度均匀性。     

数值反应堆堆芯通道级三维热工水力程序CorTAF开发及初步验证

堆芯是核动力系统的核心部件,其完整性是反应堆安全运行的重要前提。传统核反应堆堆芯热工水力分析方法无法满足未来先进核动力系统的高精度模拟需求。本文依托开源CFD平台OpenFOAM,针对压水堆堆芯棒束结构特点建立了冷却剂流动换热模型、燃料棒导热模型和耦合换热模型,开发了一套基于有限体积法的压水堆全堆芯通道级热工水力特性分析程序CorTAF。选取GE3×3、Weiss和PNL2×6燃料组件流动换热实验开展模型验证,计算结果与实验数据基本符合,表明该程序适用于棒束燃料组件内冷却剂流动换热特性预测。本工作对压水堆堆芯安全分析工具开发具有参考和借鉴意义。     

密度锁内无扰动时稳态温度场分析

实验模拟了密度锁内无扰动时稳态温度场分布。结果发现,稳态温度分布曲线上存在一个温度分层结束点;它是导热层与恒温层的分界,只有当温度分层结束点在密度锁内才能有效地抑制传热。应用半无限大平板导热模型、一维等截面直肋稳态导热模型和Fluent流体计算软件对无扰动时稳态温度场分布进行了理论计算。结果表明,半无限大平板导热模型是计算密度锁内无扰动时稳态温度场分布和温度分层结束点位置的最佳方法。     

Forced convection heat transfer in rectangular ducts—general case of wall resistances and peripheral conduction for ventilation cooling of nuclear waste repositories

A numerical solution for laminar flow heat transfer between a flowing gas and its containing rectangular duct has been obtained for many different boundary conditions which may arise in nuclear waste repository ventilation corridors. The problem has been solved for the cases of insulation on no walls, one wall, two walls, and three walls with various finite resistances on the remaining walls. Simplifications are made to decouple the convective heat transfer problem from the far field conduction problem, but peripheral conduction is retained. Results have been obtained for several duct aspect ratios in the thermal entrance and in the fully developed regions, including the constant temperature cases. When one wall is insulated and the other three are at constant temperature, the maximum temperature occurs in the fluid rather than on the insulated wall. This maximum moves toward the insulated wall with increasing axial distance. Nusselt numbers for the same constant flux on all four walls with peripheral conduction lie in a narrow band bounded by zero and infinite peripheral conduction cases. A dimensionless wall conduction group of four can be considered infinite for the purpose of estimating fully developed Nusselt numbers to within an accuracy of 3%. A decrease in wall and bulk temperatures by finite wall conduction has been demonstrated for the case of a black body radiation boundary condition. Nusselt numbers for the case of constant temperature on the top and bottom walls and constant heat flux on the side walls exhibited unexpected behavior.     

兆瓦级空间气冷堆系统启停堆瞬态分析

本文针对兆瓦级高温气冷堆布雷顿循环系统,采用Fortran语言开发系统分析程序TASS,包括堆芯、透平-发电机-压气机、回热器、冷却器和热管式辐射散热器等模型。通过设计值与程序计算值对比对TASS进行验证,并利用TASS对系统启动、停堆瞬态工况进行数值模拟。结果显示,通过分两阶段、阶梯式引入正反应性和提高涡轮机械的转轴速度,堆芯流量和功率匹配良好,系统可在3.5 h内完成启动过程,达到反应堆功率3 406 kW、流量14.2 kg/s的稳态运行。系统停堆过程中,反应堆可依靠自身的非能动余热排出能力,确保芯块和包壳温度与熔点间存在较大安全裕量,实现安全停堆。     

Fuel rod model based on Non-Fourier heat conduction equation

In this paper we explore the applicability of a fuel rod mathematical model based on Non-Fourier transient heat conduction as constitutive law for the Light Water Reactors transient analysis (LWRs). In the classical theory of diffusion, Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The motivation for this research was to eliminate the paradox of an infinite thermal wave speed. The time-dependent heat sources were considered in the fuel rod heat transfer model. The close of the Main Steam Isolated Valves (MSIV) transient in a Boiling Water Reactor (BWR) was analyzed by different relaxation times. The results show that for long-times the heat fluxes on the clad surface under Non-Fourier approach can be important, while for short-times and from the engineering point of view the changes are very small. Some results from transient calculations are examined.     

环形通道内再淹没过程先驱冷却传热特性研究

骤冷前沿推进是失水事故后再淹没过程中堆芯冷却速率的重要标志,先驱冷却传热对骤冷前沿的推进起到关键作用,对先驱冷却传热特性的研究十分必要。本文通过数值求解二维非稳态导热方程获得先驱冷却传热系数,并基于环形通道内底部再淹没实验数据,分析先驱冷却传热系数受初始壁温、入口温度和入口质量流速等参数的影响规律。研究结果表明,初始壁温对先驱冷却传热系数的影响不显著,先驱冷却传热系数随入口质量流速的增加而明显增加,随与骤冷前沿距离的增加而减小,基于实验数据得到本参数范围内先驱冷却传热关系式。     

高温球床壁面区域有效导热系数模型优化

有效导热系数用来表征高温气冷球床堆堆芯综合传热能力,提高球床有效导热系数的预测精度对于高温气冷球床堆的热工设计和安全分析十分重要。为了优化球床壁面区域有效导热系数模型,本文针对无序石墨球床有效导热系数开展数值研究,分析了无序堆积球床主体区域、近壁面区域以及壁面区域有效导热系数的分布特性。结果表明：壁面区域有效导热系数相对于主体区域和近壁面区域显著降低,其平均降幅约为22%。因此引入了修正系数C_w对ZBS模型在壁面区域进行优化,对于球床主体区域及近壁面区域修正系数C_w=1,对于壁面区域,修正系数C_w=0.78。通过与前期无序球床实验数据和南非HTTU实验数据的对比,验证了优化后的ZBS模型能较好地预测球床壁面区域有效导热系数。