D. Saha

Analytical study of nuclear-coupled density-wave instability in a natural circulation pressure tube type boiling water reactor

Abstract An analytical model has been developed to study the nuclear-coupled density-wave instability in the Indian advanced heavy water reactor (AHWR) which is a natural circulation pressure tube type boiling water reactor. The model considers a point kinetics model for the neutron dynamics and a lumped parameter model for the fuel thermal dynamics along with the conservation equations of mass, momentum and energy and equation of state for the coolant. In addition, to study the effect of neutron interactions between different parts of the core, the model considers a coupled multipoint kinetics equation in place of simple point kinetics equation. Linear stability theory was applied to reveal the instability of in-phase and out-of-phase modes in the boiling channels of the AHWR. The results indicate that the stability behavior of the reactor is greatly influenced by the void reactivity coefficient, fuel time constant, radial power distribution and channel inlet orificing. The delayed neutrons were found to have a strong influence on the Type I and Type II instabilities observed at low and high channel powers, respectively. Also, it was found that the coupled multipoint kinetics model and the modal point kinetics model predict the same threshold power for out-of-phase instability if the coupling coefficient in the former model is half the eigen value separation between the fundamental and the first harmonic mode in the latter model. Decay ratio maps were predicted considering various operating parameters of the reactor, which are useful for its design.

Effect of Loop Diameter on the Steady State and Stability Behaviour of Single-Phase and Two-Phase Natural Circulation Loops

In natural circulation loops, the driving force is usually low as it depends on the riser height which is generally of the order of a few meters. The heat transport capability of natural circulation loops (NCLs) is directly proportional to the flow rate it can generate. With low driving force, the straightforward way to enhance the flow is to reduce the frictional losses. A simple way to do this is to increase the loop diameter which can be easily adopted in pressure tube designs such as the AHWR and the natural circulation boilers employed in fossil-fuelled power plants. Further, the loop diameter also plays an important role on the stability behavior. An extensive experimental and theoretical investigation of the effect of loop diameter on the steady state and stability behavior of single- and two-phase natural circulation loops have been carried out and the results of this study are presented in this paper.

Linear and Nonlinear Stability Analysis of a Supercritical Natural Circulation Loop

Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water cooled reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN has been developed employing supercritical water properties to carry out the steady-state and linear stability analysis of a SCW natural circulation loop (SCWNCL). The conservation equations of mass, momentum, and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure, and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been benchmarked against published results. Then the code has been extensively used for studying the effect of diameter, heater inlet temperature, and pressure on steady-state and stability behavior of a SCWNCL. A separate computer code, NOLSTA, has been developed, which investigates stability characteristics of supercritical natural circulation loop using nonlinear analysis. The conservation equations of mass, momentum, and energy in transient form were solved numerically using finite volume method. The stable, unstable, and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behavior of loop, predicted using nonlinear analysis has been compared with that obtained from linear analysis. The results show that the stability maps obtained by the two methods agree qualitatively. The present paper describes the linear and nonlinear stability analysis models and the results obtained in detail.

Study on the stability behaviour of a natural circulation pressure tube type boiling water reactor

The stability behaviour of a natural circulation pressure tube type boiling water reactor (BWR) has been investigated analytically. The analytical model considers homogeneous two-phase flow, a point kinetics model for the neutron dynamics and a lumped heat transfer model for the fuel dynamics. The results indicate that both Type I and Type II density-wave instabilities can occur in the reactor in both in-phase and out-of-phase mode of oscillations in the boiling channels of the reactor. The delayed neutrons were found to have strong influence on the stability of Type I and Type II density-wave instabilities. Also, the stability of the reactor is found to increase with increase in negative void reactivity coefficient unlike that observed previously in vessel type BWRs. Decay ratio map was predicted considering the effects of channel power, channel inlet subcooling, feed water temperature and channel exit quality, which are useful for the design of the reactor.

Study on the flow-pattern-transition instability in a natural circulation heavy water moderated boiling light water cooled reactor

A mathematical model has been developed to study the flow pattern transition instability which may occur in a boiling two-phase system. The model considers flow pattern transition criteria for vertical upward and horizontal flow in pipes to identify the flow pattern transition and flow pattern specific pressure drop models. It also considers the drift flux model to estimate the void fraction in the two-phase region. The model has been applied to predict the flow pattern transition instability in a natural circulation heavy water moderated boiling light water cooled reactor. It is found that the instability characteristics is similar to that of the Ledinegg-type instability. However, the number of multiple steady states for a given operating power can be much larger in the flow pattern transition instability as compared to that of the Ledinegg-type instability. Stability maps were plotted and compared for both the flow pattern transition instability and that of the Ledinegg-type instability. The influence of various geometric and operating parameters on this instability were investigated.

Natural Circulation in Nuclear Reactor Systems

It gives us great pleasure to bring out this special issue on “Natural circulation in nuclear reactor systems” which assumes special significance in the context of present energy technology scenarios. Today nuclear energy produces about 15% of total world electricity. However, public concern about the safety of nuclear plants has resulted in sociopolitical constraints on its use in some countries. Now a worldwide renewed interest in nuclear energy is evident which is caused mainly by the following factors: (a) progressively dwindling world reserve of fossil fuel, (b) a deep-rooted concern about global warming, (c) increasing oil price, and (d) good performance of current plants. These factors are leading to rising expectations for nuclear energy for the future. For the sustenance of this renewed interest, besides fuel resource, a number of important issues are being addressed leading to the development of advanced reactor designs as well as fuel cycle technologies. The major issues, which these advanced reactors and fuel cycle concepts are addressing, include economic competitiveness, achieving very high level of safety, waste disposal, environmental effects and proliferation resistance. An important feature of several advanced reactors designs is the incorporation of passive safety systems. The IAEA conference on “The Safety of Nuclear Power: Strategy for the Future,” convened in 1991, recommended that for new plants “the use of passive safety features is a desirable method of achieving simplification and increasing the reliability of the performance of essential safety functions and should be used wherever appropriate.” Nuclear plant designers select active safety systems, passive safety systems, or combinations considering fulfilment of required safety functions with sufficient reliability, and the impact on plant operation and cost. A number of passive systems incorporated in advanced reactors employ natural circulation as the mode of energy removal underlining the importance of natural circulation in nuclear reactor design By definition, natural circulation is a process in which the fluid motion is driven by a density gradient and no external source of energy is required. However, the driving head for natural circulation is low and can be influenced by small changes in operating conditions. Sometimes the flow is not fully developed and can be multidimensional in nature. All these have led to the need of thoroughly understanding the phenomena involved to ensure reliability of natural circulation systems. This has necessitated dissemination of knowledge in this complex and important area. This special issue is a timely and very effective step in this direction. The papers in this issue cover most of the important aspects of natural circulation-modeling and code development, experimental investigations, development of performance evaluation tools, flow instabilities, safety analysis, and lastly reliability of natural circulation systems. This issue has been a modest effort to bring to the readers an update on a subject of importance to the reactor designers. We are sure that the readers of this issue will find the papers of immense value and get provoked to explore further in this area.

Steady-State Behavior of Natural Circulation Loops Operating With Supercritical Fluids for Open and Closed Loop Boundary Conditions

Supercritical water (SCW) exhibits excellent heat transfer characteristics and a high volumetric expansion coefficient (hence high mass flow rates in natural circulation systems) near the critical temperature. SCW is being considered as a coolant in some advanced nuclear reactor designs on account of its potential to offer high thermal efficiency, compact size, and elimination of steam generator, separator, and dryer, making it economically competitive. The elimination of phase change results in elimination of the critical heat flux phenomenon. Cooling a reactor at full power with natural instead of forced circulation is generally considered an enhancement of passive safety. In view of this, it is essential to study natural circulation behavior at supercritical conditions. Carbon dioxide can be considered to be a good simulant of water for natural circulation at supercritical conditions, since the density and viscosity variation of carbon dioxide follows a curve parallel to that of water at supercritical conditions. Hence, experiments were conducted in a closed supercritical pressure natural circulation loop (SPNCL) with supercritical carbon dioxide as working fluid. A nonlinear stability analysis code (NOLSTA) has been developed to carry out steady-state and stability analysis of open and closed loop natural circulation at supercritical conditions. The code has been validated for steady-state predictions with experimental data available in open literature and experiments conducted in SPNCL.

Experimental and analytical investigations on core flow distribution and pressure distribution in the outlet header of a PHWR

The Indian pressurised heavy water reactor (PHWR) comprises of a number of horizontal channels containing nuclear fuel bundles. The parallel channels are connected to headers at the inlet and outlet through feeder pipes. The flow distribution between the channels of the PHWR is an important aspect of the design of the core and primary heat transport system. A correct determination of the channel flow distribution is required to evaluate the thermal safety margin. The estimation of the design flow rate in the channels is based on the assumption that the pressure in each header is uniform. Moreover, in the reactor core only sixteen channels out of the 306 channels are provided with flow metering elements. An analytical model has been developed to enable a better prediction of the flow distribution between the different channels and the variation of pressure in the outlet header. The flow rates in the channels and the pressure distribution in the outlet header are predicted from the solution of two first order differential equations (pressure-flow equation set) involving the flow rate and the pressure difference across the headers. The outlet header is divided into four basic combining flow manifolds and an iterative procedure has been adopted to satisfy the flow and pressure conditions at each junction point between two successive manifolds by solving the pressure-flow equation set for each manifold. The model adopted for the analytical studies has been validated against experimental data. The experimental studies were carried out on a one-fourth scale model to determine the channel flow distribution in the reactor core and the pressure distribution in the outlet header at different flow rates, with (i) both the steam generating (SG) branches open and (ii) one of the steam generator branches closed. Air was used as the test fluid. The measured flow distribution in the test model has been compared with the theoretically obtained flow distribution. The pressure variations in the outlet header for different modes of pump operation are compared. The analytical results for the flow distribution are in excellent agreement with the experimental data. Analysis is also performed for the prototype reactor header using the validated model for different modes of pump operation. The analytically obtained results are compared with the plant data.

Linear and Non-Linear Stability Analysis of a Supercritical Natural Circulation Loop

Supercritical water has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN has been developed employing supercritical water properties to carry out the steady state and linear stability analysis of a SCW natural circulation loop. The conservation equations of mass, momentum and energy have been linearised by imposing small perturbation in flow rate, enthalpy, pressure and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been benchmarked against published results. Then the code has been extensively used for studying the effect of diameter, heater inlet temperature and pressure on steady state and stability behavior of a Supercritical Water Natural Circulation Loop (SCWNCL). A separate computer code NOLSTA has been developed which investigates stability characteristics of supercritical natural circulation loop using non-linear analysis. The conservation equations of mass, momentum and energy in transient form were solved numerically using finite volume method. The stable, unstable and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behavior of loop, predicted using non-linear analysis has been compared with that obtained from linear analysis. The results show that the stability maps obtained by the two methods agree qualitatively. The present paper describes the linear and nonlinear stability analysis models and the results obtained in detail.© 2009 ASME

Heat Transfer Studies on Lead-Bismuth Eutectic Flows in Circular Tubes

The use of accurate heat transfer model in liquid metal like Lead Bismuth Eutectic (LBE) flow is essential for the designing of the liquid metal cooled nuclear reactor systems. In the present study, the existing physical correlations for heat transfer in LBE flow through circular tube have been reviewed and assessed with the experimental results. In CFD analysis, PHOENICS-3.6 is used to carry out the evaluation of the various turbulence models in the tube geometry and to identify the difference between the numerical results and experimental ones in LBE flows. Based on the assessment of the existing correlations for heat transfer in LBE flow and the CFD results achieved, the best-suited correlation for turbulent Prandtl number is recommended in terms of Peclet number. This Prt can be incorporated in PHOENICS for LBE flow analysis.Copyright