Application of fourier transform analysis to determine transient condensation heat transfer coefficients in reactor containment experiments

The method of Fourier transform analysis is used to determine the instantaneous values of condensation heat transfer coefficient at a point within the containment vessel of a simple blowdown rig. The shape of the measured heat transfer transient appears to be similar to that of the energy outflow from the blowdown pressure vessel, and a heat transfer coefficient which varies in this way is shown to give close fit to the shape of containment pressure transient when used in a lumped parameter calculation.     

TACR热传输系统热工水力瞬态分析

钍燃料的利用对于缓解核燃料资源短缺具有重要意义,坎杜型反应堆(Canadian Deuterium Uranium,CANDU)在堆芯布置、中子利用效率及先进燃料循环方面具有较高的灵活性,使得其在CANDU反应堆中引入钍燃料循环更具现实意义。CANDU型反应堆中钍基燃料应用关键基础技术研究是加拿大与我国正在开展的合作课题,其中开发自主的CANDU堆堆芯热工水力设计和安全分析程序是钍基燃料应用必不可少的设计工作之一。本文针对CANDU型反应堆热传输系统结构特点,采用FORTRAN程序设计语言开发了适用于CANDU型反应堆热传输系统的热工水力瞬态分析程序CANTHAC(CANDU Thermal-Hydraulic Analysis Code)。利用CANTHAC对钍基先进CANDU堆(Thorium-based Advanced CANDU Reactor,TACR)进行了瞬态分析,计算工况包括满功率稳态、无保护蒸汽发生器(Steam Generator,SG)二次侧给水温度降低事故及完全失流事故。其中,满功率稳态计算结果与清华大学设计的钍基先进CANDU堆TACR设计值吻合较好,相对误差不超过2%,在可接受范围内;无保护SG二次侧给水温度降低事故及完全失流事故在计算条件下所得的燃料温度及系统压力等关键热工水力参数均在安全限值内,满足安全准则要求。程序为模块化编程,便于移植和改进,具有一定的通用性,为进一步研究工作奠定了基础。     

Application of the finite-element-synthesis model to multidimensional reactor transient problems without feedback

The finite-element-synthesis model has been employed to solve time-dependent multigroup diffusion equations with multiple delayed-neutron precursor groups. Feedback effects are not considered. Precursor equations are analytically integrated within a time step, assuming linear variation of fission rate during the time interval. A fully implicit scheme is used for the time integration of the mixing functions. A coarse-mesh rebalancing technique is found to considerably accelerate the convergence of the inhomogeneous source problem of each time step. Many 2-D and 3-D problems were analysed with the present calculational model. The results are in good agreement with those of other less approximate methods, except for the problems in which the reflector zone is perturbed. There is a considerable saving in computer time due to the synthesis approximation.     

Finite element solution to transient convective-conductive heat transfer problems

The paper discusses finite element approximations to problems in transient convective-conductive heat transfer in a fluid region. The governing equations are expressed in terms of the primitive variables; the flow is assumed to be laminar and the fluid incompressible within the Boussinesq approximation.The properties of the discrete advection-diffusion equation are analyzed with regard to the possible choices for mass representation (consistent or diagonal) and time integration procedure (explicit or implicit). In particular, the diagonal mass matrix and the explicit time integration method are shown to be a poor combination in terms of accuracy for meshes consisting of linear or multilinear finite elements. A simple remedy is suggested to improve the frequency response of such lumped-explicit schemes.Then, finite element formulations for the incompressible Navier-Stokes equations are considered. The various methods for incorporating the incompressibility constraint are briefly reviewed and those associated with explicit time integration of the momentum equations are discussed in detail. In particular, a method is presented for solving the pressure field, which does not require inter-element continuity of the pressure and does not exhibit a chequerboard splitting on square meshes. A numerical example is presented which illustrates the use of the proposed method for the explicit solution of time-dependent natural convection problems.     

Boundary element method in nonlinear transient heat transfer of reactor solids with convection and radiation on surfaces

This paper deals with the boundary (integral) element method for non-steady conduction problems of solids, subject to non-linear convective and radiation conditions on surfaces. Boundary integral equations for the mixed-type and non-linear boundary conditions, both for the case with constant and variable heat conductivity are derived, modelled by non-conforming boundary elements, while domain integrals are evaluated within triangular cells. A test case is included to illustrate the described procedure.     

中国铅基研究堆非能动余热排出系统可靠性分析

铅冷快堆是第四代核能系统推荐堆型之一,世界上多个铅冷快堆采用非能动余热排出系统。非能动系统中作为驱动的自然力与阻力在数量级上接近,由周边环境、材料参数的变化引起的波动不可忽略,因此需要研究非能动系统可靠性。改进了常用的响应面分析法,并应用于中国铅基研究堆反应堆容器空气冷却系统(Reactor Vessel Air Cooling System,RVACS)中。分析中使用流体计算软件Fluent模拟中国铅基研究堆RVACS系统的余热排出过程,研究了输入参数的不确定性对系统可靠性及反应堆安全产生的影响。在大量模拟数据的基础上结合神经网络法建立了输入参数不确定性和结果不确定性之间的映射关系,并以此分析RVACS非能动失效概率。分析结果表明在全厂断电的情况下,RVACS四组并联排热管中的两组也能够可靠地导出反应堆余热。     

Improving the NAA laboratory pneumatic transfer system for using Tehran research reactor

Neutron activation analysis (NAA) is a precise multi-elemental method which performs well for qualitative and quantitative analyses. This method has been applied to the laboratory of Radiation Applications Research School (RARS) at University of Tehran. The new pneumatic transfer system (Rabbit) has been designed and constructed for transferring samples, in particular short half-life samples, to Tehran Research Reactor (TRR) core for NAA. With this system samples were transferred and returned to/from the reactor as fast as possible in both automatic and manual modes. This system has two distinct paths for sending and receiving with transfer time of 30 s to the reactor core and 36 s from the irradiation position to the counting station in NAA laboratory which is about 700 m from the laboratory. Experiment and calculation have been carried out for calibration of the neutron flux and spectrum.     

A study of the sensitivity of loca heat transfer analysis for a water-cooled reactor system

Results are given of computer calculations, using the reactor thermal analysis code THETA1-B, to determine the significance and relative importance of various heat transfer regimes in predicting maximum fuel cladding temperature for the blowdown phase of a postulated loss-of-coolant accident (LOCA) in a pressurized water reactor system. The factors considered include the choice of heat transfer correlation for a particular heat transfer regime, the method of delineating the boundaries between regimes, and core inlet coolant flow conditions.For a hot-leg rupture, the maximum surface temperature is sensitive to a number of factors, including choices of critical heat flux correlation, flow boiling transition heat transfer correlation, and in particular, stable film flow boiling correlation. However, for a LOCA resulting from a double-ended rupture of an inlet feeder, these factors have only marginal effects on maximum cladding temperature. In this case the importance of heat transfer to dry steam coolant at low net flow rate conditions is demonstrated, indicating a need for further information.     

Two phase natural circulation and the heat transfer in the passive residual heat removal system of an integral type reactor

An investigation of the thermal hydraulic characteristics and the natural circulation performance in the passive residual heat removal system (PRHRS) for an integral type reactor have been carried out using the VISTA facility and the calculated results using the MARS code, which is a best estimate system analysis code have been compared with the experimental results. The VISTA facility consists of the primary, secondary, and the PRHRS circuits, to simulate the SMART design verification program. The experimental results show that the fluid is well stabilized in the PRHRS loop and the PRHRS heat exchanger accomplishes well its functions in removing the transferred heat from the primary side in the steam generator as long as the heat exchanger is submerged in the water in the emergency cooldown tank (ECT). The decay heat and the sensible heat can be sufficiently removed from the primary loop with the operation of the PRHRS. The MARS code predicts reasonably well the characteristics of the natural circulation in the PRHRS. From the calculation results, most of the heat transferred from the primary system is removed at the PRHRS heat exchanger by a condensation heat transfer.     

Three-dimensional transient thermal stresses of reactor graphite subjected to internal heat generation and asymmetric surface heating

The present paper is concerned with three-dimensional transient thermal stresses of graphite in a nuclear reactor. In analyzing this problem, reactor graphite may be approximated by a transversely isotropic finite circular cylinder subjected to internal heat generation and asymmetric heating on an end surface. Thermal stresses are analyzed by means of the transversely isotropic potential functions method proposed by Takeuti and Noda. Numerical calculations were carried out for a special type of heating conditions, and time variations of temperature and thermal stresses of graphite are shown in figures.     

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.     

Thermo-physical properties and transient heat transfer of concrete at elevated temperatures

The objective of this study is to produce our own experimental data of physical properties of domestic concrete used in Korean NPPs, and to study on the thermal behavior of concrete exposed to high temperature conditions. The compressive strength and chemical composition of the concrete used in the Yonggwang NPP units 3 and 4 were analyzed. The chemical composition of Korean concrete is similar to that of US basaltic concrete. The thermal properties of the concrete, such as density, conductivity, diffusivity, and specific heat were also measured with a wide temperature range of 20–1100 °C. Most thermo-physical properties of concrete decrease with an increase in temperature except for the specific heat, and particularly the conductivity and the diffusivity are a 50% lower at 900 °C as compared with the values at room temperature. The specific heat increases until 500 °C, decreases from 700 to 900 °C, and then increases again when temperature is above 900 °C. In this work, we also have performed CORCON analysis and MCCI experiments to simulate a transient thermal behavior of concrete exposed to high temperature conditions. The measured maximum downward heat flux to the concrete specimen was estimated to be about 2.1 MW m⁻² and the maximum erosion rate of the concrete to be 175 cm h⁻¹ with maximum erosion depth of about 2 cm. In the CORCON analysis, it is found that the concrete compositions have an important effect upon concrete erosion.     

Neutron transport in a reactor system with temperature feedback

When the effect of temperature feedback in a reactor system is considered the neutron transport equation for the neutron density is supplemented by a temperature equation which is a partial differential equation of parabolic type if heat conduction is taken into consideration. This consideration leads to a coupled system of nonlinear partial integro-differential equations. The aim of this paper is to present an iterative scheme for the determination of the solution of the nonlinear coupled system and to establish some qualitative property of the solution. The iterative scheme consists of two monotone sequences which converge monotonically from above and below, respectively, to a unique solution. The qualitative aspect includes the existence and uniqueness of a positive solution, upper and lower bounds of the solution and stability of a steady-state solution.     

Analysis of heat source distribution in internal circulating surface heat transfer molten salt reactor

The Molten Salt Reactor (MSR) is one of the Generation IV nuclear reactor concepts that were selected by the Generation IV International Forum in 2000. The concept is based on liquid fuel instead of solid fuel assemblies. Besides the advantages, there are several aspects of operation that can hinder the realization of this reactor concept. In this paper, the authors investigate the neutronics behaviour of a new sub-concept that offers solutions for many of the technical problems. The analysis was performed using the particle transport code MCNPX 2.7. The paper focuses on the short-term and steady state heat source distribution in the fuel salt and in the graphite moderator. Accordingly, neither burn-up effects nor reactivity transients are considered. The sensitivity of the effective multiplication factor on different geometrical and material parameters was studied. The results obtained indicate that the main region of heat deposition is in the internal and external channels of the graphite moderator. Only a few percent of the total heat power is released in the graphite moderator, where the gamma and neutron related heat deposition is on the same scale. The results also prove that the heat source distribution does not change drastically upon the actuation of the control rods.     

圆柱形带反射层反应堆的数值传热计算

在结构化和非结构化网格中,采用有限容积方法,数值计算带有反射层(反射层布置分为轴向、径向和复合双向三种情况)的圆柱形反应堆的物理和热特性。首先采用单组法数值求解堆芯和反射层中的热中子注量率密度,并同其精确解相比较,验证彼此的正确性;然后用类似法确定堆内两区中热中子产生的热功率分布规律,并进行数值传热计算。所有结果都与没有反射层的反应堆(裸堆)状况进行比较,并且得到具有参考价值的结果。     

Heat transfer in heat exchangers of sodium cooled fast reactor systems

The present paper describes the heat transfer in heat exchangers of sodium cooled fast reactors. Practical empirical correlations regarding heat transfer coefficients for intermediate heat exchangers (IHXs) and air coolers (ACs) were derived using test data obtained at the fast reactor ‘Monju’ and ‘Joyo’ and also at the 50 MW steam generator facility (50 MW SG). The correlation proposed by Seban and Shimazaki was applicable to estimate the heat transfer coefficients in both flows of IHX, i.e., primary and secondary flows, when the Péclet number was larger than 30. When the Péclet number for shell-side was small, the Nusselt number decreased as a function of the Péclet number. It was clarified that this characteristic was not caused by the heat conduction in flow direction. The heat conduction effect can be neglected even in the natural circulation conditions of the Monju plant. As for the heat transfer coefficient of AC provided in the secondary heat transport system of the fast breeder reactor, data in the above mentioned three facilities were evaluated. As a result, empirical correlations were derived for the average heat transfer coefficients of a large capacity finned air cooler made of stainless steel. These correlations could contribute to analyze the plant dynamics with better accuracy than before.