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).     

Scaling single-state variable catastrophe functions: an application to two-phase natural circulation

In this paper I present transformation laws to scale physical processes governed by polynomial equations. Of particular importance is the class of polynomials which describe catastrophe functions. Many important, stability-related, thermal hydraulic phenomena are described by these catastrophe functions, including flooding, two-phase natural circulation, and critical heat flux. Catastrophe functions can be used to define the boundaries of stable system behavior. If a process evolves such that one of these boundaries are crossed, it will undergo a discontinuity which radically alters its evolution (i.e. morphogenesis). By scaling these catastrophe functions, processes exhibiting discontinuous behavior can be studied in scaled test models rather than experimenting with a full-scale, and typically very expensive, prototype. To illustrate their usefulness, the catastrophe function transformation laws are applied to the practical problem of scaling two-phase fluid natural circulation. In addition, the catastrophe manifold for two-phase fluid natural circulation is developed and evaluated to obtain a criterion for the onset of flow instability.     

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.     

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.     

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.     

Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality

Based on the one-dimension two-phase drift flow model, the numerical simulation of two-phase flow stability characteristic on the test loop (HRTL-5) for 5 MW heating reactor (developed by the Institute of Nuclear and New Energy Technology of Tsinghua University, Beijing) is performed with and without coupled point neutron kinetics. The density wave oscillation instability is analyzed in the system under low pressure at 1.5 MPa and low steam quality less than 10%. The effect of inlet subcooling and heating flux on the system instability is simulated under the system pressure P_sys = 1.5 MPa. The numerical results show that there exist two instability inlet subcooling boundaries at different heat flux. The numerical results show good agreement with the experimental results on HRTL-5 without consideration of point neutron kinetics. If coupled with point neutron kinetics, the system will exhibit little difference on instability boundaries from that without considering the nuclear characteristics. But the amplitude and the phase of the oscillation of the thermal hydraulic parameters of the system will be somehow affected in unstable zone if the system is coupled with point neutron kinetics.     

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.     

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.     

Scaling laws for contained explosions

Assessment of structural integrity under postulated accident conditions in fast reactors has been based, in the past, on results of scale model tests conducted with chemical explosives. Though emphasis has currently shifted to the development and use of elaborate computational models to determine structural response in the postulated accident, idealised scale model experiments still serve the useful purpose of providing by extrapolation estimates of pressure, impulse and deformation without much expense or loss of time. However, the choice of appropriate scaling laws is important in performing the extrapolation. The results of experiments carried out for the case of a charge of high explosives set off in open waterfilled cylindrical vessels are presented and compared with earlier work by others. Measured shock overpressures at the vessel wall are reported as also impulse values derived by determining the area under the pressure-time traces. Deviations from free-field scaling laws have been observed which are significant for wall pressures and less so for impulse received by the vessel wall.     

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.     

Main coolant pump resistance influence on single phase water reverse flow in the inverted U-tubes under natural circulation

Based on nuclear power plant(NPP) best-estimate transient analysis with RELAP5 / MOD3 code,the reactor point kinetics model in RELAP5 / MOD3 code is replaced by the two-group,3-D space and time dependent neutron kinetic model,and two-fluid model is replaced by drift flux model.A coupled three-dimensional physics and thermal-hydrodynamics model is used to develop its corresponding computing code,thus simulating natural circulation of single-phase flow for the PWR.In this paper,we report the forward and reverse flow distribution in the inverted U-tubes of the steam generator(SG) under some typical operating conditions in the natural circulation case, and analyze the influence of main coolant pump resistance on the forward and reverse flow distribution.The calculation results show that,the pressure drop between SG inlet and outlet plenum decreases,and the SG inlet and outlet mass flow decrease with an increased main coolant pump resistance,but net mass flux of reverse flow in inverted U-tubes,and the ratio of mass flow in all reverse flow tubes to that of main coolant pipeline increase, meanwhile,the secondary steam load is invariable in this process.     

Scaling laws for spherical pinch experiments

Spherical pinch experiments are characterized by a central discharge in a spherical vessel followed by an inductive discharge in the vessel's peripheral shell gas. An analysis is carried out of the evolution of the imploding shock waves produced by the shell explosion in order to find out if the central discharge can be contained and compressed by the converging shocks, so as to maintain its temperature for a time sufficiently long for breakeven. The analytical model adopted is essentially that of the recent paper of Ahlborn and Key (Plasma Phys. 23: 435, 1981). One finds that the converging shocks are indeed capable of containing and compressing the central plasma. In addition, if the central spark reaches the critical temperatureT _L = 2.58 keV by the deposition of an energy density of 1.86×10⁸ J·g^?1, the scaling law required in order to contain such a plasma for breakeven isρ ₀ R(E_s/M_s)^1/2 ? 1.96×10⁶, whereρ ₀ is the initial fill gas density,R is the radius of the spherical vessel, andE _s is the energy deposited in the peripheral shell massM _s . The general applicability of the model to other fusion devices based on the implosion principle is discussed.     

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 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.     

Scaling of two-phase flow transients using reduced pressure system and simulant fluid

Scaling criteria for a natural circulation loop under single-phase and two-phase flow conditions are derived. Based on these criteria, practical applications for designing a scaled-down model are considered. Particular emphasis is placed on scaling a test model at reduced pressure levels compared to a prototype and on fluid-to-fluid scaling. The large number of similarity groups which are to be matched between model and prototype makes the design of a scale model a challenging task. The present study demonstrates a new approach to this classical problem using two-phase flow scaling parameters. It indicates that a real time scaling is not a practical solution and a scaled-down model should have an accelerated (shortened) time scale. An important result is the proposed new scaling methodology for simulating pressure transients. It is obtained by considering the changes of the fluid property groups which appear within the two-phase similarity parameters and the single-phase to two-phase flow transition parameters.Sample calculations are performed for modeling two-phase flow transients of a high-pressure water system by a low-pressure water system or a Freon system. It is shown that modeling is possible for both cases for simulating pressure transients. However, simulation of phase change transitions is not possible by a reduced pressure water system without distortion in either power or time.     

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 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 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.