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.     

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.     

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

Ｅｆｆｅｃｔｏｆｓｔｅａｍｑｕａｌｉｔｙｏｎｔｗｏ－ｐｈａｓｅｆｌｏｗｉｎａｎａｔｕｒａｌｃｉｒｃｕｌａｔｉｏｎｌｏｏｐＪｉａＨａｉ－Ｊｕｎ（贾海军）；ＷｕＳｈａｏ－Ｒｏｎｇ（吴少融）；ＷａｎｇＮｉｎｇ（王宁）ａｎｄＹａｏＳｉ－Ｍｉｎ（姚思民）（Ｉｎ...     

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.     

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.     

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.     

Experimental investigation of natural circulation in a symmetrical loop under large scale rolling motion conditions

In ocean environment, the ship motion significantly affects the natural circulation behavior in ship-based integrated-type reactor. This paper theoretically and experimentally investigated natural circulation characteristics in symmetrical loops under rolling condition. Experiments were carried out on a test loop with a symmetrical configuration by simulating the structure of an accrual reactor. The theoretical results revealed that only angular acceleration contributes to the resultant force under zero power rolling condition. In a closed circuit with a uniform cross-section area, the angular acceleration force integral is proportional to the angular acceleration and the area enclosed by the circuit. The integral value varies over time and causes flow oscillations. However, the angular acceleration force does not influence the flow status in the shared part of the two symmetrical neighbor circuits due to force interactions. Rolling experiments with a zero power load confirmed these results. Full power experiments under rolling condition exhibited observable flow rate and temperature oscillations in each branch of the flow channel. The oscillations in the side flow channels had the same values for both the period and the phase with the variation of rolling angle. The angular acceleration force was the main cause of this. The oscillations in the middle channel had a period half the value of the rolling period. The periodical variation of the vertical component of gravity caused this. The horizontal component of gravity was out-phasing with angular acceleration. Therefore, it alleviated oscillation in the side channels. The experimental results showed that for the same rolling period, as the rolling angle increased, the average flow rate decreased and oscillation amplitudes increased. Also, as the power load increased, the oscillations in the middle channel increased and the oscillation in the side channel decreased.     

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.     

Non-dimensional analysis of static bifurcation in a natural circulation loop

The steady-state characteristics of a two-phase natural circulation loop were investigated based on the homogenous model. Transcendental equations of non-dimensional loop mass flow rate under various conditions were also derived. The static bifurcation diagram of a two-phase natural circulation described with non-dimensional variables Npch-m^＋ was obtained. In addition, various steady-state characteristics of a natural circulation loop were analyzed and discussed. These characteristics include the existence of multiple solutions under certain conditions, and the maximum mass flow rate. The authors also examined the effects of important parameters such as sub-cooling number, riser-to-heated-region length ratio, and riser-to-heated-region diameter ratio.     

硝酸盐自然循环回路系统特性分析

硝酸盐自然循环回路(Nitrate natural circulation loop,NNCL)是研究熔盐自然循环特性的重要实验平台,可为氟盐冷却高温堆的非能动余热排出系统设计和验证积累经验。通过修改RELAP5/MOD4.0程序,对NNCL进行了系统分析,分析了不同加热功率、空气流量和入口温度等情况下的系统特性。结果表明,加热功率和空气流量是影响NNCL系统平衡温度和质量流量的重要因素,对系统稳态时的温度和流量有很大影响;自然循环达到稳定时所需时间较长,不同工况下需要8-27 h的稳定时间;在空气设计流量下,为了防止硝酸盐因温度过高而变质或因温度过低而凝结,加热功率应保持在20-40 k W。     

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.     

Numerical analysis of supercritical flow instabilities in a natural circulation loop

Numerical studies have been carried out to investigate flow instabilities in a natural circulation loop with supercritical CO₂. For steady-state and dynamic analyses of the loop under supercritical conditions, a single-channel, one-dimensional model is developed. In this model, equations for the conservation of mass, momentum and energy are discretized using an implicit finite difference scheme. A computer code called flow instability analysis under supercritical operating conditions (FIASCO) is written in FORTRAN90 to simulate the dynamics of natural circulation loops with supercritical fluid. Stability boundaries are determined by simulating the loop's time evolution following a small perturbation under different operating conditions. Stability threshold results substantially deviate from the results reported by previous investigators, and contradict some of the reported findings. The disagreement in results is most likely due to the undesirable dissipative and dispersive effects produced from the large time steps used in previous studies, thereby leading to a larger stable region than those found using smaller time steps. Results presented in this paper suggest that the stability threshold of a natural circulation loop with supercritical fluid is not confined to the near-peak region of the (steady state) flow-power curve. Results obtained for the range of parameter values used in this investigation always predict the stability threshold to be in the positive slope region of the (steady state) flow-power curve. Parametric studies for different operating conditions reveal the similarity of stability characteristics of flow under supercritical conditions with those in two-phase flows.     

Examination of transient characteristics of two-phase natural circulation within a Freon-113 boiling/condensation loop

Transient characteristics of two-phase natural circulation within a Freon-113 loop with a large condenser have been examined mainly focused on the flashing phenomenon. General behavior was described and parametric studies were performed. The items observed were the period and duration of flashing, peak flow rate, amount of flow carryover per flashing, lowest-peak liquid level within the condenser, and the peak void distribution in the riser section. The parameters considered were the heater power input, valve friction at the heater inlet (simulating the loopwise friction), condenser cooling, degree of subcooling at the heater inlet, and the heat loss to the surroundings. As a whole, the heater power input, valve friction, and the rate of condenser cooling played important roles in flashing while the other effects being marginal. In general, the flow appeared to be more unstable with the larger condensing surface which causes the condensation-induced flashing.     

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.     

Effect of inlet geometry on hot-leg U-bend two-phase natural circulation in a loop with a large diameter pipe

In relation to nuclear reactor accident and safety studies, experiments on hot-leg U-bend two-phase natural circulation in a loop with a relatively large diameter pipe (10.2 cm ID) was performed for understanding the two-phase natural circulation and flow termination during a small break loss of coolant accident in LWR. The loop design was based on the scaling criteria developed under this program and a horizontal section was inserted between the gas injector and the hot leg in order to investigate the effect of the vapor phase inlet section on the flow regimes and flow interruption. The loop was operated either in a natural circulation mode or in a forced circulation mode using nitrogen gas and water. Various tests were carried out to establish the basic mechanism of the flow termination as well as to obtain essential information on scale effects of various parameters such as the loop frictional resistance, thermal center, and pipe diameter. The void distribution in a hot leg, flow regime and natural circulation rate were measured in detail for various conditions. The termination of the natural circulation occurred when there was insufficient hydrostatic head in the downcomer side. The superficial gas velocity at the flow termination could be predicted well by the simple model derived from a force balance between the frictional pressure drop along the loop and the hydrostatic head difference. The bubbly-to-slug flow transition was found to be dependent on axial locations. It turned out that the inlet geometry affected the flow regime at the inlet of the hot leg, namely the void distribution in the hot leg.     

Study of flow instabilities in double-channel natural circulation boiling systems

Natural circulation boiling systems consisting of parallel channels can undergo different types of oscillations (in-phase or out-of-phase) depending on the geometric parameters and operating conditions. Disturbances in one channel affect the flow in other channels, which triggers thermal–hydraulic oscillations. In the present work, the modes of oscillation under different operating conditions and channel-to-channel interaction during power fluctuations and on-power refueling in a double-channel natural circulation boiling system are investigated. The system is modeled using a lumped parameter mathematical model and RELAP5/MOD3.4. Parametric studies are carried out for an equal-power double-channel system, at different operating conditions, with both the models, and the results are compared. Instabilities, non-linear oscillations, and effects of recirculation loop dynamics and geometric parameters on the mode of oscillations, are studied using the lumped model. The two channels oscillate out-of-phase in Type-I region, but in Type-II region, both the modes of oscillation are observed under different conditions. Channel-to-channel interaction and on-power refueling studies are carried out using the RELAP model. At high powers, disturbances in one channel significantly affect the stability of the other channel. During on-power refueling, a near-stagnation condition or low-velocity reverse flow can occur, the possibility of reverse flow being higher at lower pressures.     

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.     

Stability analysis of a two-phase test loop

This paper presents an analytical model developed for investigating the stability characteristics of a low-pressure natural circulation test facility. The approach is to convert the two-phase flow system into a linear feedback system with respect to a steady-state operating point and linear theory is then applied to determine if the system would be stable around the operating point. The analysis results show that the stability of the system is sensitive to its inlet temperature and power level.