Bifurcation and hysteresis phenomena in the two-phase natural circulation system

The static bifurcation of the two-phase natural circulation (TPNC) system was studied theoretically and numerically. By the DERPAR algorithm the solution diagram was calculated, which shows that the static bifurcation occurs under some conditions in the TPNC systems. Also, it shows that, in a region of multiple solutions, the static instability may occur. It is defined as a region of thermal-siphon instability induced flow rate jumping. By means of the solution diagram, the stability margin can be determined in this region. Furthermore, the heat input at the peak of the solution diagram is defined as the maximum capacity Of heating load that can be used to judge the capacity of the TPNC of a given geometry topological structure. Meanwhile, it is interesting that the TPNC systems have the hysteresis phenomenon defined as thermal-siphon hysteresis. Some parametric effects related were also studied.

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

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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 DSSβ-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,andβ-andω-strain transformation methods were used to ana-lyze the single-phase natural circulation in the primary circuit.For comparison with the traditional method,simplified DSSβ-andω-strain methods were developed based on the standard scaling criterion.The strain parameters in these four methods were modified to form multiple groups of scaled-down cases.The transient process of the natural circulation was simulated using the Relap5 code,and the variation in the dynamic flow characteristics with the strain numbers was obtained using different scaling methods.The results show that both the simplified and standard DSS methods can simulate the dynamic characteristics of natural circulation in the primary circuit.The scaled-down cases in the simplified method exhibit the same geometric scaling and correspond to small core power ratios.By contrast,different scaled-down cases in the standard DSS method correspond to different geometric scaling criteria and require more power.The dynamic process of natural circula-tion can be simulated more accurately using the standard DSS method.

Flow characteristics of natural circulation in a lead–bismuth eutectic loop

Lead and lead-alloys are proposed in future advanced nuclear system as coolant and spallation target.To test the natural circulation and gas-lift and obtain thermal-hydraulics data for computational fluid dynamics(CFD) and system code validation, a lead–bismuth eutectic rectangular loop, the KYLIN-Ⅱ Thermal Hydraulic natural circulation test loop, has been designed and constructed by the FDS team. In this paper, theoretical analysis on natural circulation thermal-hydraulic performance is described and the steady-state natural circulation experiment is performed. The results indicated that the natural circulation capability depends on the loop resistance and the temperature and center height differences between the hot and cold legs. The theoretical analysis results agree well with,while the CFD deviate from, the experimental results.

Startup scheme optimization and flow instability of natural circulation lead-cooled fast reactor SNCLFR-100

Owing to the inherent instability of the natural circulation system,flow instability can easily occur during the operation of a natural circulation lead-cooled fast reactor,especially during the startup phase.A comprehensive startup scheme for SNCLFR-100,including primary and secondary circuits,is proposed in this paper.It references existing more mature startup schemes in various reactor types.It additionally considers the restriction conditions on the power increase in other schemes and the characteristics of lead-based coolant.On this basis,the multi-scale coupling code ATHLET-OpenFOAM was used to study the flow instability in the startup phase under different power-step amplitudes and power duration times.The results showed that obvious flow instability phenomena were found in the different startup schemes,such as the short-term backflow phenomenon of the core at the initial time of the startup.Moreover,an obvious increase in the flow rate and temperature to the peak value at the later stage of a continuous power rise was observed,as well as continuous oscillations before reaching a steady state.It was determined that the scheme with smaller power-step amplitude and a longer power duration time requires more time to start the reactor.Nevertheless,it will be more conducive to the safe and stable startup of the reactor.

Analysis of hot leg natural circulation under station blackout severe accident

Under severe accidents, natural circulation flows are important to influence the accident progression and result in a pressurized water reactor (PWR). In a station blackout accident with no recovery of steam generator (SG) auxiliary feedwater (TMLB' severe accident scenario), the hot leg countercurrent natural circulation flow is analyzed by using a severe-accident code, to better understand its potential impacts on the creep-rupture timing among the surge line, the hot leg, and SG tubes. The results show that the natural circulation may delay the failure time of the hot leg. The recirculation ratio and the hot mixing factor are also calculated and discussed.

Theoretical investigation on the steady-state natural circulation characteristics of a new type of pressurized water reactor

This article presents a theoretical investigation on the steady-state natural circulation characteristics of a new type of pressurized water reactor. Through numerically solving the one-dimensional steady-state single-phase conservative equations for the primary circuit and the steady-state two-phase drift-flux conservative equations for the secondary side of the steam generator, the natural circulation characteristics were studied. On the basis of the pre- liminary calculation analysis, it was found that natural circulation mass flow rate was proportional to the exponential function of the power and that the value of the exponent is related to the operating conditions of the secondary side of the steam generator. The higher the outlet pressure of the secondary side of the steam generator, the higher the pri- mary natural circulation mass flow rate. The larger height difference between the core center and the steam generator center is favorable for the heat removal capacity of the natural circulation.

CHARACTERISTIC DIFFERENCE METHODS FOR TWO-PHASE DISPLACEMENT IN NATURALLY FRACTURED RESERVOIRS

In this paper we shall give the characteristic difference methods for two phase displace meat problem in naturally fractured reservoirs.We shall prove the existence,uniqueness of the ap proximate solution and a priori discrete L2-error estimates.

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 processes were simulated using the Relap5 computational code.The results show that this DSS method can simulate the dynamic flow characteristics of scaled-down cases.The transient deviation of the temperature difference and mass flow rate of the scaled cases decrease with increases in the length ratio and dilation number.The distortion of the transient temperature difference is smaller than that of the mass flow;however,the overall deviation is within a reasonable range.

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.

Thermal-hydraulic stability of a natural circulation system with nuclear feedback

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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 vari-ables Npch-m + was obtained. In addition, various steady-state characteristics of a natural circulation loop were ana-lyzed 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.

Analysis on natural circulation capacity of the CARR

The investigation on natural circulation (NC) characteristics of the China Advanced Research Reac- tor(CARR) is very valuable for practical engineering application and also a key subject for the CARR. In this study, a computer code was developed to calculate the NC capacity of the CARR under different pool water temperatures. Ef- fects of the pool water temperature on NC characteristics were analyzed. The results show that with increasing pool water temperature, the NC flow rate increases while the NC capacity decreases. Based on the computation results and theoretical deduction, a correlation was proposed on predicting the relationship between the NC mass flow and the core power under different conditions. The correlation prediction agrees well with the computational result within ±10% for the maximal deviation. This work is instructive for the actual operation of the CARR.

Mechanism of ONB based on nonequilibrium thermodynamics of natural circulation in narrow channels

Based on the experiment of onset of nucleate boiling(ONB)in natural circulation and the nonequilibrium thermodynamics dissipative theory,the mechanism of ONB in narrow rectangle channels of natural circulation is proposed.It points out that the onset of nucleate boiling is influenced by the degree of superheat and the special conditions of narrow channels.Under the conditions of both density difference in natural circulation and narrow rectangle channels,the prediction model of ONB in natural circulation of narrow channels based on fluctuating is established.The experimental results show that the present model can be used to predict the heat flux of ONB in narrow rectangle channels.Features of ONB in natural circulation narrow rectangle channels are as follows:heating power is the incentive of the happen of ONB;the higher the heating power is,the higher the degree of superheat is,and the earlier the ONB will appear.With the pressurizing,the appearance of ONB will be delayed.The higher the degree of supercooling is,the later the ONB appears.The ONB will happen easier when there are noncondensable gases and roughness in the channels.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

“Eternal Motion” as a “Form of Movement of a Special Nature” and the Main Condition for the Creation of the Universe

The article hypothesizes that DE and DM (UCM) are a “Form of Motion of a Special Nature”, where “Form of Motion” means “Eternal Motion” as the power of dynamics of different levels and varying degrees of self-sufficiency, and by “Special Nature”, gravitational and two other properties of matter, “tied” to the “Eternal Movement” and completely dependent on it. Carriers of key properties of a “Special Nature” have been established: “0”-DE particles and “3”-DM particles (UDM). The unity of their inherent “motionally-gravitational” properties and the peculiarity of the relationship between “motion” and “gravity” are revealed: the higher the intensity of “Eternal Motion”, the stronger the gravitational properties of matter are manifested (and vice versa). The relationship of “time” with the “vibration frequency” and the “mass” of photons with the “degree of bonding and deformation properties of the field” is shown. The maximum level of gravity has been determined, which allows Nature to successfully create the Universe: such a landmark is the proximity to the property of the Primary Source—the “pure graviton” of the OSP space, the most powerful “motionally-gravitational” particle of the Universe. The reasons for the emergence of such an identity of the gravitational properties of particles with the indicators of a “pure graviton” are established: for “0”-DE particles, this is the acquisition of the function of “freedom of movement”;for “3”-DM particles (UDM), the creation of a special structure—a “double field” (“Main” and “Small”). The presence in the “double field” of specific “tools” for the creation of the worlds of the Universe—gravitational “waves” gives rise to impulses (shocks) of varying intensity and shape. A list of functions performed by “waves” in the “Main” and “Small” fields has been compiled. The specific conditions for the formation of “UDM Streams”, their transformation into a “Vortex” and, under the influence of a powerful Initial Impulse (push), sending them to the “place” of the creation of galaxies, are shown. It is suggested that there is a “Cycle of Matter in Nature” in the closed structure of our Universe due to the “work” of “waves” and the functioning of special “factories” in the form of exotic space objects—Black holes.

The Effect of Circulation Fan on Energy Consumption in Nature Convective Refrigerator-Freezer

The effect of the circulation fan installed in fresh food compartment on energy consumption of natural convective refrigerator/freezers (RFs) was experimentally studied. Five different RF models with different cycles were tested. The experimental results showed that the energy consumption of the single-loop cycle RF increased by 2.4%~3.8%, that of the bypass two-circuit cycle RF decreased by 1.0%, and that of the two-circuit cycle RF with its evaporators in parallel when the geometry parameters of refrigeration system and the refrigerant charge were not changed after the circulation fan was installed decreased by 3.3%. When the optimization on the refrigerant charge and the evaporator was carried out, the energy consumption of the single-loop cycle RF , the bypass two-circuit cycle RF and the two-circuit cycle RF with its evaporators in parallel, decreased by 1.0%~6.4%, 3.25% and 3.26% respectively. The present conclusions will provide a guideline to the optimum design for the RF with the circulation fan.

Numerical simulation of dense particle-gas two-phase flow using the minimal potential energy principle

A simulation method of dense particle-gas two-phase flow has been developed. The binding force is introduced to present the impact of particle clustering and its expression is deduced according to the principle of minimal potential energy. The cluster collision, break-up and coalescence models are proposed based on the assumption that the particle cluster are treated as one discrete phase. These models are used to numerically study the two-phase flow field in a circulating fluidized bed （CFB）. Detailed results of the cluster structure, cluster size, particle volume fraction, gas velocity, and particle velocity are obtained. The correlation between the simulation results and experimental data justifies that these models and algorithm are reasonable, and can be used to efficiently study the dense particle-gas two-phase flow.

Calculating densities and viscosities of natural gas with a high content of C_(2+) to predict two-phase liquid-gas flow pattern

The paper is devoted to the two-phase flow simulation.The gas-condensate mixture flow in a horizontal pipe under high pressure is considered.The influence of the equation of state(EOS)choice for mixture properties modelling on the flow regime calculation results is studied for gas with high content of methane homologues.An analytical overview of the methods to predict the flow pattern is provided.Based on this analysis,two techniques are selected.For these techniques,values of density and viscosity for each phase are required.Density calculation for the gas phase is performed with Van der Waals based EOS.The propriate EOS is selected based on studies of calculation errors for test mixtures.Calculation of liquid phase density is done by means of Patela-Teja and Guo-Du equations,two different models are considered for viscosity estimation.The flow patterns of gas-condensate mixture in a range of temperatures and pressures are calculated and verified via probability map.The results of study allow to recommend the Brusilovsky EOS for calculation of densities for similar gas mixtures and make more rigorous flow regime evaluation.The probability map shows that for the chosen composition and parameters of media the flow pattern is mostly transitional between segregated and annular independent from EOS.