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.     

Scaling laws for single-phase natural circulation loops

The power-to-volume scaling laws used for the construction of scaled test facilities simulating the primary system of nuclear power plants result in loops of the same elevation (and length) with reduced diameters. The adequacy of these scaling laws for simulating single-phase natural circulation was tested in three rectangular loops, each having the same elevation but different loop diameters of 6 mm, 11 mm and 23.2 mm respectively. The experiments showed that the power-to-volume scaling principles adequately describe the steady state behaviour. The stability behaviour observed in the loop 23.2 mm in diameter, however, could not be reproduced in the smaller diameter loops. Subsequent theoretical investigation of the single-phase natural circulation phenomenon showed that the transient and stability behaviour can be simulated only if the diameter ratio D_p/D_m is also simulated. The theoretical investigation suggested the following scaling laws for single-phase natural circulation:

(Gr_m)_p=(Gr_m)_m

(St_m)_p=(St_m)_m

For simulating the steady state behaviour alone, it is sufficient to simulate the product Gr_m(D/L).     

Experimental observations on flow characteristics in an open two-phase natural circulation loop

The flow behavior in an open two-phase natural circulation loop was studied experimentally using Freon-113. The heat flux, inlet- and exit-restrictions, liquid charging level and inlet subcooling were taken as parameters. As a result, three basic circulation modes were observed with variation of the heat flux: periodic circulation (A), continuous circulation, and periodic circulation (B). Of these modes, only the continuous circulation mode was stable and the maximum circulation rate appeared with this mode. An increase in the inlet-restriction and/or decrease in the exit-restriction broadened the range of the continuous circulation mode and stabilized the system. When the liquid charging level was lowered or the inlet subcooling was decreased, the continuous circulation mode started at a lower heat flux and the system became stable. The results are summarized on instability maps in the plane of heat flux vs. inlet subcooling.     

Linear analysis of flow instabilities in an open two-phase natural circulation loop

This paper describes the instability maps for the excursive and the density wave instabilities which may occur in an open two-phase natural circulation loop. Criteria for the excursive and the density wave instability were obtained from the steady loopwise momentum equation and the characteristic equation, respectively. A simple, one-dimensional two-phase homogeneous equilibrium flow was assumed. Heat flux, inlet subcooling, inlet- and exit-line restrictions, condenser liquid level, loop height and the heater section length were taken as parameters. The results were summarized on the instability map in the plane of N_pch(Fr)^1/2 vs. N_sub. The stable region appears at the lower left part of the map, bounded by two boundaries; the excursive instability region appears at the upper right part of the map. From the map, it can be readily confirmed that the dynamic stability criterion automatically satisfies the excursive stability criterion. Effects of parameters on the stability of the system were also discussed in this paper. The upper boundary of the stable region was compared with the experimental results reported previously.     

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.     

Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop

The objective of this paper is to develop a nonlinear numerical model to investigate the stability and nonlinear dynamics of a nuclear-coupled two-phase natural circulation loop. Some stability maps, parametric effects and transient characteristics of this natural circulation loop have been studied. Results indicate that the system indeed has two instability regions, the type-I and type-II instabilities, as is well known for a natural circulation loop. Parameters may induce different effects on the system stability in type-I and type-II unstable regions. In particular, the void-reactivity feedback destabilizes the system in both regions of low and high operating powers. Moreover, by strengthening nuclear feedback effect, period-doubled bifurcation may prevail in the system at relatively high inlet subcoolings and eventually a chaotic attractor appears with a fractal dimension of 1.79 ± 0.01 and an embedding dimension of 5.     

Characteristics of two-phase natural circulation in freon-113 boiling loop

A freon-113 flow visualization loop for simulating the hot-leg U-bend natural circulation flow has been constructed and hot-leg two-phase flow behavior has been studied experimentally. From the present experiments, an understanding of the basic mechanisms of the two-phase natural circulation and flow termination were obtained. The power input, loop friction and the liquid level in the simulated steam generator played key roles in the overall flow behavior. Experimental results show that the flow behavior strongly depends on phase changes and coupling between hydrodynamic and heat transfer phenomena. Non-equilibrium phase-change phenomena such as flashing create unstable hydrodynamic conditions which lead to cyclic or oscillatory flow behaviors.     

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.     

Experimental study on two-phase natural circulation and flow termination in a loop

In order to study the two-phase natural circulation and flow termination during a small break loss of coolant accident in LWR, a hot leg U-bend simulation loop has been built based on the two-phase flow scaling criteria developed under this program. The nitrogen-water system has been used to isolate the key hydrodynamic phenomena from heat transfer problems. Various tests were carried out to establish the basic mechanism of the flow termination and reestablishment as well as to obtain essential information on scale effects of various parameters such as the loop frictional resistance, thermal center, U-bend curvature, and inlet geometry. It was found that the permanent termination of the natural circulation was related to the head balance between the hot and cold legs. The local flow condition at the inverted U-bend could produce intermittent flow, however was not related to the permanent flow termination. The void distribution in a hot leg, flow regime, and natural circulation rate have been measured in detail for various conditions. Significant effects of the inlet geometry on these were observed. Near the flow termination condition, large amplitude flow oscillations occurred. The occurrence of this type of flow instability is important for safety analyses, because it may lead to loop-to-loop oscillations or flow excursions in a prototype system which has a multi-loop configuration.     

Effect of steam quality on two-phase flow in a natural circulation loop

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Experimental observation of flow instability in a semi-closed two-phase natural circulation loop

In this experimental study, the flow instabilities within a semi-closed two-phase natural circulation loop were examined, with an emphasis placed on the role of the expansion-tank-line resistance. Six different modes of loopwise natural circulation were identified: the single-phase natural circulation, periodic two-phase natural circulation with a nonboiling period between the cycles, two-phase continuous circulation (stable circulation), and three other modes of the two-phase natural circulation characterized by different ranges of the cyclic period. The results were also shown in the instability map in the plane of the heat flux and the heater-inlet subcooling. When the frictional resistance at the expansion-tank line becomes larger, the circulation becomes stable, especially at the high heat-flux and high inlet-subcooling conditions, and, as a whole, the stable operation region becomes larger in the instability map. Similarly, the longer expansion-tank line stabilizes the system. However, unlike the analytical prediction, the excursive instability was not identified with the semi-closed loop due to the flow restriction at the expansion-tank line.     

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.     

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。     

Experimental study on two-phase flow instability of natural circulation under rolling motion condition

Two-phase flow instability of natural circulation under a rolling motion condition is experimentally studied. The experimental results show the rolling motion induces a fluid flow fluctuation. At the trough point of the flow fluctuation, rolling motion can cause the early occurrence of natural circulation two-phase flow instability, and this case is defined as trough-type flow oscillation. The system stability decreases with increasing rolling amplitude and effect of rolling frequency is nonlinear. The complex overlap effect of trough-type flow oscillation and density wave oscillation can enhance the system coolant fluctuation; this case is defined as complex flow oscillation. Complex flow oscillation may be divided into two types: regular and irregular complex flow oscillations. Irregular complex flow oscillation is a transition type from trough-type flow oscillation to regular complex flow oscillation. Under the same thermal hydraulic conditions, the marginal stability boundary (MSB) of regular complex flow oscillation is similar to that of density wave oscillation without rolling motion, and the influences of rolling parameters on the MSB are slight.     

An analytical investigation of role of expansion tank in semi-closed two-phase natural circulation loop

Role of the expansion tank in a semi-closed two-phase natural circulation loop was examined analytically with the emphasis placed on the flow instability. Loopwise steady circulation rate was obtained, and conditions for flow instability were examined by using the method of the linear stability analysis with perturbations. The homogeneous two-phase model was adopted for the analysis. As well as the pressure at the expansion tank, the length and the cross-sectional area of the tube connected to the expansion tank appeared to be the important parameters determining the flow instability. The system was predicted to be stable with the longer length and the smaller cross-sectional area of the expansion-tank line and also with the higher expansion-tank pressure.     

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.     

A new method to derive one set of scaling criteria for reactor natural circulation at single and two-phase conditions

Natural circulation is one of the most important thermal-hydraulic phenomena that makes the fluid flow along a closed loop without any external driving force. With this merit, it is adopted by the passive heat removal system to bring the residual heat out of the core at accidents, and by the primary system of some new conceptual reactors instead of pumps to drive the coolant in the loop at operation. To investigate the reactor natural circulation and verify system thermal-hydraulic codes, it is a way to construct an integrated effect test facility and perform experiments on it with the scaling criteria. With one-dimensional assumption, the natural circulation system was simplified as the heat source, heat sink and pipes, and described by two groups of equations independently for the single-phase and two-phase flow conditions. Based on these equations, a set of non-dimensional equations were derived and the criteria were obtained both applicable for single-phase and two-phase natural circulation. According to these criteria, the practical application was analyzed and discussed. In the paper, the property similarity was strongly suggested in most cases. Though equal height simulation was widely used in the past, the reduced height simulation is a good way to reproduce three-dimensional (3D) phenomena that are of concern in the investigation. The CHF simulation is not suggested. The mass of metal and its distribution is of concern instead of heat transfer at transient simulation.     

Study on the stability behaviour of two-phase natural circulation systems using a four-equation drift flux model

Theoretical investigations were carried out to study the influence of two-phase flow parameters such as friction factor multiplier, drift velocity and void distribution parameter on the stability of boiling two-phase natural circulation systems. The theoretical model considers a four-equation drift flux model which solves the linearised conservation equations of mass, momentum and energy applicable to boiling two-phase natural circulation systems. The model was applied to three boiling natural circulation loops wherein Type I and Type II instabilities were observed over a wide range of operating pressures. The two-phase friction loss was predicted using different friction factor multiplier models available in literature. It was found that these models influence the steady state and threshold powers for stability, especially the Type II instabilities in natural circulation significantly. Since the void fraction depends on the drift velocity and the void distribution parameter in two-phase flow, these parameters were varied and their effects on the natural circulation flow stability were investigated. It was found that an increase in either the drift velocity or the void distribution parameter reduces the unstable regions observed in the Type I or Type II flow instabilities in two-phase natural circulation systems.Further, investigations were carried out to study the effect of loop diameter on the Type I and Type II instabilities in natural circulation. This study is important to reveal the capability of the reduced diameter scaled facilities of the prototype systems to simulate natural circulation instabilities. The results indicate that with increase in the loop diameter, the threshold power of the Type I instability and the Type II instability increases. Moreover, the stability of natural circulation greatly enhances with increase in the diameter of the loop.