Two-phase Natural Circulation Loop Research Articles

06/02337 Modeling of solar passive techniques for roof cooling in arid regions: Jain, D. et al. Building and Environment, 2006, 41, (3), 277–287.

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.

Steady-state performance of a two-phase natural circulation loop

Using both HEM and TEDFM the steady-state behaviour of a rectangular uniform cross section two-phase closed NCL has been studied through one-dimensional approach. Uniform heat flux for heating as well as cooling has been considered along with the constant physical properties, uniform pressure inside the loop and water-steam as the working fluid. For the given operating range and loop geometry, the circulation velocity lies in the turbulent regime. The flow rate monotonically increases with the loop height. However, with heat flux it initially increases, reaches maximum and then falls. This implies that the surface heat flux should match the loop geometry and other operating parameters to produce the maximum flow rate. It has also been observed that the cooling and heating lengths and the temperature of the liquid at the entry of the heating section have to be selected optimally to generate the maximum mass flow rate.

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.

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

Abstract 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 N pch-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.

05/02348 Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop

05/02348 Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop

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.

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.

An assessment of pressure drop and void fraction correlations with data from two-phase natural circulation loops

Void fraction and pressure drop correlations play an important role in predicting the performance of natural circulation loops. Hence an assessment of the commonly used and often cited correlations for pressure drop and void fraction has been carried out with data from natural circulation loops. This assessment considered 33 void fraction correlations and 14 pressure drop correlations. The void fraction correlations were initially tested against the various limiting conditions. Only 14 correlations were found to satisfy at least two limiting conditions (i.e., at x = 0; α = 0 and at x = 1; α = 1) and were assessed against the data. This assessment showed that the Chexal et al. (1996) correlation is better than all the others considered. The assessment of pressure drop correlations were carried out with the Chexal et al. (1996) correlation for void fraction and Saha-Zuber model for the onset of subcooled boiling. This assessment showed that most correlations give predictions close to each other.

00/01342 Investigation of neutronic potential of a moderated (D-T) fusion driven hybrid reactor fueled with thorium to breed fissile fuel for LWRs

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 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.

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.

Analysis of two-phase flow characteristics in a natural circulation loop using the drift-flux model taking flow pattern change and subcooled boiling into consideration

This study investigated the steady-state characteristics of a two-phase natural circulation loop based on the drift flux model, taking flow pattern change and subcooled boiling into consideration. Transcendental equations of non-dimensional loop mass flow rate under various conditions were also derived. The model proposed herein was verified by comparing our results with experimental data found in literature. In addition, various steady-state characteristics of a natural circulation loop were analyzed and discussed; these characteristics include the one-third-power dependence of the single phase mass flow rate on heating power, the incipient power of two-phase flow, the maximum mass flow rate, and the existence of multiple solutions under certain conditions. This study also examined the effects of changing important parameters.

Two-phase flow instability experiment in a natural circulation loop using the Taguchi method

The thermal–hydraulic instability of a two-phase natural circulation loop, which is a complex multivariable system with high nonlinearity, was investigated experimentally based on the Taguchi method. Excellent results were obtained and a broad picture of the trends produced by the various parameters that affect instability is presented. This study concluded that, within the experimental range, the inlet temperature, heating power and the presence of the unheated bypass channel are the three most dominant factors affecting the loop instability. The Taguchi method is found to be very efficient and there is a great deal of saving in the experimental work. The 20 runs of experiment based on the Taguchi method suggests that the stability of the present two-phase natural circulation loop (TPNCL) would be improved under the following conditions: decreased inlet temperature, decreased thermal load, disconnected unheated bypass channel, installing the compressible volume with a higher water level in the downstream two-phase flow region, disconnected upstream compressible volume, increased single-phase flow restrictions, and decreased two-phase flow restrictions. Although the same trends bear the standard method of stabilizing a boiling channel, the restriction factors in the present experimental investigation are found to be ineffective in dampening the thermal–hydraulic instability.

Analysis of chaotic instabilities in boiling systems

An analytic model for the investigation of non-linear dynamics in boiling systems has been developed. This model is comprised of a nodal formulation that uses one-dimensional homogeneous equilibrium assumptions for diabatic two-phase flow, a lumped parameter approach for heated wall dynamics, and point neutron kinetics for the consideration of nuclear feedback in a boiling water reactor (BWR) loop. This model indicates that a boiling channel coupled with a riser may experience chaotic oscillations. In contrast, a boiling channel without a riser that is subjected to a constant pressure drop (i.e. a parallel channel) may undergo a supercritical bifurcation (i.e. may experience a limit cycle), but chaos was not found. Flow instabilities in a two-phase natural circulation loop have been verified using the model presented in this paper. The predictions of the effects of the channel inlet resistance, outlet resistance and liquid level in the downcomer agree with the data of Kyung and Lee. Finally, an analysis of nuclear-coupled density-wave instabilities in a simplified BWR (SBWR) was performed. Significantly, even for low pressure conditions, a simplified SBWR appears to be stable during start-up and normal operations; however, a limit cycle may occur for abnormal operating conditions.

Periodic flow excursion in an open two-phase natural circulation loop

Flow excursion instability in an open two-phase natural circulation loop was studied both experimentally and analytically. At high inlet subcooling, stable mode (continuous circulation) does not exist; instead, three different circulation modes such as periodic circulation (A), multimode circulation, and periodic circulation (B) appear at different heat flux conditions. The multimode circulation is represented by the combination of periodic circulations A and B and it is termed here as “periodic flow excursion”. The decrease in the inlet restriction and/or the increase in the exit restriction broadened the region of the flow excursion, and these aspects were summarized on the instability map of the heat flux vs. inlet subcooling. In addition, with the one-dimensional two-phase homogeneous equilibrium assumption, the region of flow excursion was obtained analytically, which fairly agrees with the experimental results.

Chaotic oscillations in a low pressure two-phase natural circulation loop under low power and high inlet subcooling conditions

The oscillation characteristics of a low pressure two-phase natural circulation loop have been investigated experimentally in this study. Experimental results indicate that the characteristics of the thermal hydraulic oscillations can be periodic, with 2–5 fundamental frequencies, or chaotic, depending on the heating power and inlet subcooling. The number of fundamental frequencies of oscillation increases if the inlet subcooling is increased at a given heating power or the heating power is decreased at a given inlet subcooling; chaotic oscillations appear if the inlet subcooling is further increased and/or the heating power is further decreased. A map of the oscillation characteristics is thus established. The change in oscillation characteristics is evident from the time evolution and power spectrum of a thermal hydraulic parameter and the phase portraits of two thermal hydraulic parameters. These results reveal that a strange attractor exists in a low pressure two-phase natural circulation loop with low power and very high inlet subcooling.

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.

Thermal and Stability Analysis of a Two-Phase Natural Circulation Loop

Natural circulation is an important passive heat-removal mechanism in both existing and next-generation light water reactors. Thermal and stability analyses are performed for a two-phase natural ci...

Bifurcation phenomena in two-phase natural circulation

Multiple steady-state solutions have been found theoretically for a two-phase natural circulation loop. This bifurcation phenomenon is attributed to the nonmonotonic behavior of the buoyancy and friction forces, and the discontinuities due to transitions between two-phase flow patterns. The paper outlines a general and consistent modeling method to describe two-phase natural circulation at steady state. The solution of the one-dimensional governing conservation equations is performed by a combination of analytical and numerical stages. The method is implicit, to treat the highly nonlinear problem by multinested iteration loops. Results are presented and discussed for the multiple solutions of the flow rate, temperature, quality and void distributions and two-phase elevations. Pressure effects are also studied. A comparison with available data shows that the theoretical model simulates the important characteristics of two-phase thermosyphons.

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.