Two-parameter dynamical scaling analysis of single-phase natural circulation in a simple rectangular loop based on dilation transformation

Scaling analysis is widely used to design scaled-down experimental facilities through which the prototype phenomena can be effectively evaluated. As a new method, dynamic system scaling(DSS) must be verified as a rational and applicable method.A DSS method based on dilation transformation was evaluated using single-phase natural circulation in a simple rectangular loop. The scaled-down cases were constructed based on two parameters—length ratio and dilation number—and the corresponding transient...     

Investigations on single-phase natural circulation loop dynamics. Part 3: Role of expansion tank

Expansion tank is an important component of all single-phase natural circulation loops. The tank serves the twin purposes of venting the air out during the loop filling and accommodation of the swells and shrinkages of the loop fluid during the transient. In the present study, experimental investigations have been carried out in a rectangular single-phase natural circulation loop to bring out the role of expansion tank in loop dynamics. The results on loop stability and transient behavior are discussed. The experimental investigations show that there is significant amount of heat exchange between the main loop fluid and the expansion tank fluid. First, the results of experimental studies are presented. The different flow regimes observed in these experimental investigations are discussed. Next, a model is presented for taking into account the heat exchange between the main loop fluid and the expansion tank fluid. Finally, the model is applied to simulate the dynamic behavior of different single-phase natural circulation loops. The investigations carried out in this study have helped in resolving the issue of hysteresis observed in these loops.     

Investigations on the role of mixed convection and wall friction factor in single-phase natural circulation loop dynamics

The objective of the present paper is to present a 1-D model for simulating the startup from rest of water cooled single-phase natural circulation loops having horizontal heaters. The starting point of analysis is the inability of the 1-D codes to account for natural convection in the heater. Present 1-D models are unable to account for axial diffusion in the fluid caused by natural convection. Start-up from rest and many other characteristics cannot be simulated using classical 1-D models because of the inherent tendency of the predicted dynamics to be attracted by zero flow condition. The paper presents an elegant approach for taking into account both natural and forced convection. The enhancement of fluid motion and thermal mixing by natural convection is an important consideration in the design of nuclear reactors. Hence, the model developed is of direct relevance to nuclear reactor thermal hydraulics. The model developed for natural convection has been validated against the CFD simulations. The model developed has been incorporated in a classical 1-D model developed by the authors previously. The application of model to a rectangular single-phase natural circulation loop show that the model can predict the loop behavior from start-up with fidelity. The model reproduces most of the characteristics like unidirectional oscillation, bidirectional oscillations and chaotic switching reasonably well. Finally, model has been used to investigate the phenomenon of hysteresis observed in experimental loop. The paper also brings out the role of constitutive laws for wall friction in predicting the loop dynamics.     

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 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).     

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.     

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.     

硝酸盐自然循环试验回路实验研究

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,实验数据可用于开发或验证自然循环系统热工水力分析程序。在NNCL上进行了硝酸盐自然循环流动特性的实验研究,对熔盐温度在310°C、340°C、370°C,以及空冷塔风门开度在0%、25%、50%、75%、100%的工况条件下,观测回路的瞬态和稳态特性。实验结果表明:熔盐-熔盐换热器(DRACS Heat Exchanger,DHX)进出口温差和硝酸盐流量对熔盐池温度响应过程很慢,且幅度较小,至少需要20 h;对风速响应较快,并出现骤升现象,能在几分钟内到达新的值。基于实验数据,验证了:NNCL系统硝酸盐自然循环流量与DHX换热功率的m次方成正比,NNCL系统阻力与流量的(1-m)/m次方成正比,且NNCL系统的m值在0.47～0.49之间。     

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.     

Analysis of the unstable behaviour of a single-phase natural circulation loop with one-dimensional and computational fluid-dynamic models

This paper discusses the results obtained using one-dimensional and three-dimensional computational fluid-dynamic codes for the prediction of the dynamic behaviour observed in experiments carried out in a single-phase natural circulation apparatus. The loop is made of glass and is equipped with vertical and horizontal heaters and coolers that can be separately operated, thus obtaining different working configurations.     

Flow characteristic of single-phase natural circulation under ocean motions

Natural circulation is widely used in nuclear reactor systems as the passive safety system. With the development of the floating nuclear power plant (FNPP), researchers should pay more attention to flow and heat transfer characteristics for the natural circulation under ocean conditions for the safety of FNPP. In this paper, the flow characteristics in a single-phase natural circulation system were investigated and the effects of heaving, rolling and coupled motions were analyzed. The oscillation amplitude of flow rate increases with the increase of period in a certain range and maximum acceleration under heaving motions. With the increase of oscillation intensity (higher frequency and larger maximum rolling angle), the oscillation amplitude increases and the average flow rate decreases under rolling motions. Moreover, the lateral displacement of rolling center changes the oscillation period and induces larger amplitude oscillations. The flow characteristic becomes more complex when the system is subjected to coupled motions. The oscillation period is the least common multiple of two motions’ periods. The oscillation induced by coupled motions makes the system more unstable than that induced by an individual motion. The potential superposition effect exists under coupled motions and needs to be addressed for the operation safety.     

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.     

Theoretical and experimental study on single-phase natural circulation under inclined conditions

The natural circulation reactor is widely used in marine environments where thermo-hydraulic performance is heavily affected by the heaving, pitching, and inclining of a ship. This paper theoretically and experimentally investigated steady-state single-phase natural circulation under inclined conditions. Results showed that energy transported by natural circulation was proportional to 1.5 times the power of the temperature difference between the hot leg and the cold leg. Furthermore, a parameter, k, was presented that revealed the comprehensive influence of working fluid properties, resistance characteristics, gravity fields, and loop configurations. k was treated as the criterion for the circulation ability of a loop and it also acted as the basis for evaluating and optimizing different designs. Analysis under the guidance of k was confirmed by a series of experiments performed on a symmetrical two-circuit loop. Both theoretical and experimental results showed that the inclination restrained overall circulation due to the decrease in average altitude difference between the steam generators and the electric heater. The disparity in branch circulations increased with the increase in the inclined angle. A loop design consisting of a large altitude difference and a small width was preferable to confine the influence of inclination. However, if the loop width was too small, it caused a severe reduction in the circulation ability for large angle inclinations.     

Natural circulation studies in a lead bismuth eutectic loop

Lead Bismuth Eutectic (LBE) is increasingly getting more attraction as the coolant for advanced reactor systems. It is also the primary coolant of the Compact High Temperature Reactor (CHTR), being designed at BARC. A loop has been set up for thermal hydraulics, instrument development and material related studies relevant to CHTR. Steady state natural circulation experimental studies were carried out for different power levels. Transient studies for start-up of natural circulation in the loop, loss of heat sink and step power change have also been carried out. An 1D code named LeBENC has been developed at BARC to simulate the natural circulation characteristics in closed loops. The salient features of the code include ability to handle non-uniform diameter components, axial thermal conduction in fluid and heat losses from the piping to the environment. This paper deals with the experimental studies carried out in the loop. Detailed validation of the LeBENC code with the experimental data is also discussed in the paper.     

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.     

Dynamic scaling characteristics of single-phase natural circulation based on different strain transformations

To understand the dynamical system scaling (DSS) analysis theory, the applicability of DSS β-andω-strain transformation methods for the scaling analysis of complex loops was explored. A simplified model consisting of two loops was established based on the primary and secondary sides of a nuclear reactor, and β-andω-strain transformation methods were used to analyze the single-phase natural circulation in the primary circuit. For comparison with the traditional method, simplified DSSβ-andω-strain...     

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.