Investigation on scaling law for reactor natural circulation under motion conditions

For some Pressurized Water Reactors (PWR) operated on automobiles, boats or deep sea vessels, natural circulation simulation is important for understanding their safety during severe accidents, or system characteristics when natural circulation is adopted instead of the primary pumps to drive coolant in their loops. Based on the scaling laws of natural circulation for stationary reactors, the scaling laws for moving conditions are derived in this paper by analyzing accelerations and their distribution in a moving reactor with rigid motion theory, and introducing these accelerations into the momentum equations representing a one-dimensional natural circulation model. With modified equations, a set of motion simulation criteria was obtained, and equal height simulation and unequal height simulation were studied. A reduced height simulation is helpful for ensuring that three-dimensional phenomenon are reproduced, but time scaling is needed in a motion simulation.     

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.     

Nonlinear analysis for a double-channel two-phase natural circulation loop under low-pressure conditions

On the basis of the homogeneous flow model and Galerkin nodal approximation method, this study adopts the methodology in [Nucl. Eng. Des. 192 (1999) 31] to develop a nonlinear numerical model for a double-channel two-phase natural circulation loop. The calculated steady-state results provide a reasonable agreement against the experimental data in the high power region but overestimate in the low power region under both equal-heating and unequal-heating conditions. Nonlinear dynamics and stability boundary of the double-channel boiling natural circulation loop are also analyzed. Two unstable regions, type-I and type-II instabilities, are found in this system. Complex channel-to-channel interactions coupling with loop dynamics may occur in the double-channel natural circulation loop. For the equal-heating system, out-of-phase oscillations may prevail under the operating conditions that the gravitational pressure drops are very highly dominant, such as low subcooling and low power conditions. However, in-phase oscillations may exist in the medium to high power regions, where two-phase frictions are relatively important. For the unequal-heating system, the heating power difference between two channels may drive the system more unstable both in type-I and type-II regions. The two unequal-heating channels exhibit in-phase oscillation mode, instead of out-of-phase in the equal-heating system, at low subcooling and low power conditions. In addition, parametric effects on the stability are also evaluated in this study.     

A generalized flow correlation for two-phase natural circulation loops

A generalized correlation has been proposed to estimate the steady-state flow in two-phase natural circulation loops. The steady-state governing equations for homogeneous equilibrium model, viz. continuity, momentum and energy equations have been solved to obtain the dimensionless flow rate as a function of a modified Grashof number and a geometric number. To establish the validity of this correlation, two-phase natural circulation flow rate data from five different loops have been tested with the proposed correlation and found to be in good agreement.     

Analytical evaluation of two-phase natural circulation flow characteristics under external reactor vessel cooling

This work proposes an analytical method of evaluating the effects of design and operating parameters on the low-pressure two-phase natural circulation flow through the annular shaped gap at the reactor vessel exterior surface heated by corium (molten core) relocated to the reactor vessel lower plenum after loss of coolant accidents. A natural circulation flow velocity equation derived from steady-state mass, momentum, and energy conservation equations for homogeneous two-phase flow is numerically solved for the core melting conditions of the APR1400 reactor. The solution is compared with existing experiments which measured natural circulation flow through the annular gap slice model. Two kinds of parameters are considered for this analytical method. One is the thermal–hydraulic conditions such as thermal power of corium, pressure and inlet subcooling. The others are those for the thermal insulation system design for the purpose of providing natural circulation flow path outside the reactor vessel: inlet flow area, annular gap clearance and system resistance. A computer program NCIRC is developed for the numerical solution of the implicit flow velocity equation.     

Fluid-to-fluid scaling for a gravity- and flashing-driven natural circulation loop

In certain natural-circulation reactor systems proposed recently, vapor generation takes place by flashing in an adiabatic riser above the core. A step-by-step facility design procedure was used to define suitable scaling criteria for a refrigerant-113 (R-113) experiment simulating the dynamics and stability of such a loop. The fact that vapor generation does not normally take place in the core allows additional flexibility in designing the model; almost perfect simulation can be achieved, mainly by reducing the height of the facility according to the liquid density ratio and scaling for similar void fraction distributions in the prototype and the model.     

一种适用于小型长寿命自然循环铅基快堆的冷却剂研究

以小型化、长寿命、自然循环为铅基快堆的设计目标,构建100 MWt铅基快堆堆芯模型并开展冷却剂选型研究,选取Pb同位素/混合物及Pb-Bi混合物,分析比较了采用不同冷却剂堆芯的物理特性与自然循环特性。结果表明：得益于²⁰⁸Pb在高能区小的非弹性散射截面与中低能区极小的中子俘获截面,加之Bi较小的中子俘获截面,采用²⁰⁸Pb-Bi冷却的铅基快堆堆芯在30满功率年运行周期内的燃耗反应性损失最小,增殖性能最佳,且具备负值较大的空泡系数、冷却剂温度系数和较大的有效缓发中子份额,可装载较低富集度或较少量燃料,有利于堆芯小型化、长寿命和固有安全性;²⁰⁸Pb-Bi相比Pb冷却的铅基快堆具备更强的自然循环能力、更弱的材料腐蚀、更宽的运行温度区间,有利于反应堆安全运行与维护。高²⁰⁸Pb丰度的铅可以从钍矿石及钍铀矿石中提取,极大降低了²⁰⁸Pb的分离提取难度。     

Steady-state performances and scaling analyses for an open flashing-driven natural circulation system

Simulating investigations are carried out to study the steady-state performances, the pressure resistance distributions and the scaling methods of the single-phase and flashing-induced two-phase flow in the open natural circulation system, which is designed for the passive containment cooling system. The results show that the steady-state mass flow rate changes with the heat transfer regularly both in the single-phase and flashing-induced two-phase flow under a certain inlet subcooling. From the sensitivity analysis, it can be found that the riser height only has impact on the single-phase flow but has little influence on the flashing-driven two-phase flow. Both increasing the diameters of the riser and downcomer can enhance the flow and heat transfer in sing-phase and two-phase flow when keeping the structure of the heat exchanger unchanged, but the influence degree for each flow type is different. The flow resistance distributions of the loops under different flow modes have been studied to provide the foundation for improving the heat transfer capacity by choosing the structural parameters reasonably. The pressure resistance distribution of the steady single-phase flow only relates to the geometrical, but the pressure resistance distribution of the two-phase flow relates both to the pipe diameters and to the external conditions. The acceleration pressure resistance in the riser section is the main resistance under the higher-quality two-phase conditions. Therefore, the influence of the riser diameter on the flashing-induced two-phase flow is far greater than that of downcomer diameter and the most effective method to improve the two-phase flow and heat transfer is to increase the diameter of the riser. Finally, the scaling analysis is performed for the penetration and economy considerations after selecting the optimal dimensions. The scaling of the cold and hot sections is considered separately to insure the driven force of the system unchanged, and different scaling criterions are given for the single-phase and flashing-induced two-phase flow according to the analyses of the pressure resistance distributions. The results show that the scaling criterion of the two-phase flow can deal with the scaling problem accurately both in the single-phase and two-phase flow. However, the scaling criterion of the single-phase flow only can solve the single-phase scaling problem, but it will overestimate the operating results in the scaling model.     

Development of natural circulation analysis methods for a sodium cooled fast reactor

A natural circulation evaluation methodology has been developed to insure safety of a sodium cooled fast reactor (SFR) of 1500 MWe adopting a natural circulation decay heat removal system (NC-DHRS). The methodology consists of a one-dimensional safety analysis which can be applied to safety evaluation for SFR licensing taking into account the temperature flattening effect due to buoyancy force in the core, and a three-dimensional fluid flow analysis which can evaluate thermal-hydraulics for local convection and thermal stratification in the primary system and DHRSs. The one-dimensional safety analysis method and the three-dimensional fluid flow analysis method have been validated using the test results of a water test apparatus and a sodium test loop for some typical transient events selected from the design basis events of the SFR. Finally, it has been confirmed that a good agreement between the test results and analysis results has been obtained, and reliability of each method has been demonstrated.     

Theoretical investigation on the steady-state natural circulation characteristics of a new type of pressurized water reactor

1 Introduction With respect to the inherent safety of nuclear re- actors, application of passive systems/components including natural circulation phenomena as the main mechanism is intended to simplify the safety-related systems and to improve their reliability, to reduce the effect of human errors and equipment failures, and to provide more time to enable the operators to prevent or mitigate serious accidents. Natural circulation is the main mode of heat removal for removing decay heat from t…     

两相自然循环流动不稳定性脉动周期的实验和理论研究

通过实验研究两相自然循环流动不稳定性脉动周期,建立理论模型,用理论分析法得到脉动周期的理论公式。用该公式计算的结果与实验值符合得很好。     

Transient behavior of natural circulation for boiling two-phase flow (flow after pump trip)

The idea of a flow diode has been proposed to improve the pump coastdown characteristics of the internal recirculation pumps adopted by the ABWR. In this paper, the transient behavior from forced to natural circulation was experimentally investigated by simulating a pump coastdown condition for the purpose of providing an available source of information that is necessary for designing the flow diode. The results of the study showed that the transient behavior after pump coastdown was influenced by the coastdown period, the trigger velocity and the initial driving force of natural circulation. The potential of each driving factor was governed by the delay time for boiling, which is a very important parameter in natural circulation of boiling two-phase flow. In consequence, a guide for the designing of a flow diode was proposed.     

The light water integral reactor with natural circulation of the coolant at supercritical pressure B-500 SKDI

Pressure increase in the primary circuit over the critical value gives a possibility to construct the B-500SKDI (500 MWe) lightwater integral reactor with natural circulation of the coolant in the vessel with a diameter less than 5 m. The given reactor has a high safety level, simple operability, its specific capital cost and fuel expenditure being lower as compared to a conventional PWR. The development of the B-500SKDI reactor is carried out taking into consideration verified technical decisions of current NPPs on the basis of Russian LWR technology.     

Numerical simulation and artificial neural network modeling of natural circulation boiling water reactor

Numerical simulation of natural circulation boiling water reactor is important in order to study its performance for different designs and under various off-design conditions. Numerical simulations can be performed by using thermal-hydraulic codes. Very fast numerical simulations, useful for extensive parametric studies and for solving design optimization problems, can be achieved by using an artificial neural network (ANN) model of the system. In the present work, numerical simulations of natural circulation boiling water reactor have been performed with RELAP5 code for different values of design parameters and operational conditions. Parametric trends observed have been discussed. The data obtained from these simulations have been used to train artificial neural networks, which in turn have been used for further parametric studies and design optimization. The ANN models showed error within ±5% for all the simulated data. Two most popular methods, multilayer perceptron (MLP) and radial basis function (RBF) networks, have been used for the training of ANN model. Sequential quadratic programming (SQP) has been used for optimization.     

A new integral method for solving the point reactor neutron kinetics equations

A numerical integral method that efficiently provides the solution of the point kinetics equations by using the better basis function (BBF) for the approximation of the neutron density in one time step integrations is described and investigated. The approach is based on an exact analytic integration of the neutron density equation, where the stiffness of the equations is overcome by the fully implicit formulation. The procedure is tested by using a variety of reactivity functions, including step reactivity insertion, ramp input and oscillatory reactivity changes. The solution of the better basis function method is compared to other analytical and numerical solutions of the point reactor kinetics equations. The results show that selecting a better basis function can improve the efficiency and accuracy of this integral method. The better basis function method can be used in real time forecasting for power reactors in order to prevent reactivity accidents.     

Analysis of flow induced valve operation and pressure wave propagation for single and two-phase flow conditions

The flow induced valve operation is calculated for single and two-phase flow conditions by the fluiddynamic computer code DYVRO and results are compared to experimental data. The analysis show that the operational behaviour of the valves is not only dependent on the condition of the induced flow, but also the pipe flow can cause a feedback as a result of the induced pressure waves. For the calculation of pressure wave propagation in pipes of which the operation of flow induced valves has a considerable influence it is therefore necessary to have a coupled analysis of the pressure wave propagation and the operational behaviour of the valves.The analyses of the fast transient transfer from steam to two-phase flow show a good agreement with experimental data. Hence even these very high loads on pipes resulting from such fluiddynamic transients can be calculated realistically.     

Systematic and exact scaling analysis of the single-phase natural circulation flow: The hydraulic similarity

For the study of the hydraulic similarity in a single-phase natural circulation loop, the integral momentum equation is non-dimensionalized with respect to the initial flow kinematic energy of reference section, without intuitively specifying any reference parameters. By this mean, a unique hydraulic time scale, characterizing the system hydraulic response, is identified along with two dimensionless physical numbers: the dimensionless flow resistance number and the dimensionless gravitational force number. From the integral momentum equation, the mass flow rate at steady state is also obtained. The identified dimensionless parameters are then applied to derive a set of scaling criteria for the design of a full-pressure reduced-size similar model for a PWR (Pressurized Water Reactor). For exact hydraulic similarity, it was found for the first time that the cross sectional area scaling ratio should be related to the axial length scaling ratio. In addition, it is also found out that the relative cross-sectional area ratio should be preserved in order to preserve the flow resistances. Moreover, the scaling ratio for the number of the U-tubes was found to be unity if exact hydraulic similarity is pursued for the whole system. Three sets of scaling criteria for the design of a full-pressure model for a PWR are summarized in a table for different application. The accuracy and applicability of this proposed scaling method is demonstrated by proposing a simple loop and a PWR-like system, by scaling down the systems to get two corresponding models with this proposed scaling methodology, and by comparing the model results with their corresponding prototype results. Furthermore, the method for the evaluation of both system-level and local hydraulic scaling distortions are addressed.