Experimental Thermal and Fluid Science 34 (2010) 879892Contents lists available at ScienceDirect

Experimental Thermal and Fluid Science

journal homepage: www.elsevier .com/locate /et fsExperimental investigations on flashing-induced instabilitiesin one and two-parallel channels: A comparative study

Christian P. Marcel *, M. Rohde, T.H.J.J. Van Der HagenDepartment of Physics of Nuclear Reactors, Delft University of Technology (TUDelft), Delft 2629 JB, The Netherlands

a r t i c l e i n f o a b s t r a c tArticle history:Received 2 September 2009Received in revised form 29 January 2010Accepted 4 February 2010

Keywords:Parallel channelsFlashing-induced instabilitiesNatural circulation0894-1777/$ - see front matter 2010 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2010.02.002

* Corresponding author. Present address: CentroBustillo km 9.5 (8400), S.C. de Bariloche, Ro Negro,445100x5384.

E-mail addresses: christian.marcel@cab.cnea.gov.a(C.P. Marcel).In this investigation, experiments conducted in a natural circulation test facility at low power and lowpressure conditions, in the one single and two-parallel channels configuration are presented and dis-cussed in detail. The novel manner of visualizing the results allowed characterizing the facility at anytime and position which helped to thoroughly understand the instability mechanisms. Different modeswere observed for each configuration. In the case of having two-parallel channels, four different behav-iors have been observed: stable flow circulation, periodic high subcooling oscillations, a-periodical oscil-lations and out-of-phase periodical oscillations. In addition, stability maps were constructed in order toclarify the region in which each mode is dominant. The results obtained from both the one and two-par-allel channels configurations are thus analyzed and compared. As a result, some similarities have beenobserved between the intermittent flow oscillations found in the single channel experiments and thehigh subcooling oscillations found in the two-parallel channels experiments. Moreover, similarities havealso been found between the sinusoidal flow oscillations existing in the single channel experiments andthe out-of-phase oscillations from the two-parallel channels experiments. The experiments presented inthis work can be used to benchmark numerical codes and modeling techniques developed to study thestart-up of natural circulation BWRs.

2010 Elsevier Inc. All rights reserved.1. Introduction

Natural circulation cooling is a key issue in the design of mod-ern nuclear power plants for simplicity, inherent safety, and main-tenance reduction features [21]. For this reason, new generationboiling water reactors (BWRs), which are optimized to be econom-ical and reliable, are cooled with natural circulation in order to im-prove their competitiveness. The prototypical natural circulationBWR (NCBWR) is the Economic Simplified Boiling Water Reactor(ESBWR) [4,22]. An item of concern of these reactors is the suscep-tibility to exhibit thermalhydraulic instabilities since the flowcannot be controlled externally as in forced circulation systems.

Safety concerns of nuclear reactors have attracted the attentionof many researchers on flow instabilities in natural circulationboiling loops. Experiments performed on the DANTON facility atstart-up conditions (i.e. low pressure-low power) have shown thatthe pressure increase caused by the steam produced in the reactorvessel is not sufficient to suppress completely the flow oscillationsll rights reserved.

Atmico Bariloche; Av. E.Argentina. Phone: +54 2944

r, chris.p.marcel@gmail.comand that without external pressurization, an instability region be-tween single-phase and two-phase operation has necessarily tobe crossed [23]. Unstable behavior at low power and low pressurehas also been encountered at specific conditions explored in anexperimental campaign at the Dutch natural circulation BWRDodewaard [26,27].

The tall adiabatic chimney, placed on top of the core to enhancethe flow circulation, makes flashing phenomenon (the sudden in-crease of vapor generation due to the reduction in hydrostatichead) likely to occur during the low pressure start-up phase ofNCBWRs. The feedback between vapor generation in the chimneyand buoyancy in the natural-circulation loop may give rise toself-sustained flow oscillations.

Flashing-induced flow oscillations were first pointed out by thepioneering work of Wissler and colleagues [25], who reportedabout flashing-induced instabilities in a natural circulationsteam/water loop in the 1950s. Since then, several experimentalstudies have addressed stability of natural circulation two-phaseflow systems at low pressure [1,12,13,14,23,15].

These flow oscillations make the operation of the reactor duringstart-up rather difficult and could cause strong mechanical vibra-tions of the reactors internal components. Well-defined start-upprocedures are therefore needed to cross the instability region dur-ing the transition from single-phase to two-phase flow conditions.

http://dx.doi.org/10.1016/j.expthermflusci.2010.02.002mailto:christian.marcel@cab.cnea.gov.armailto:chris.p.marcel@gmail.comhttp://www.sciencedirect.com/science/journal/08941777http://www.elsevier.com/locate/etfs

Nomenclature

A section flow areaCpl specific heat capacity at constant pressureD section diameterEkin kinetic energy per unit of volumeM inlet mass flow rateFdriv two-phase driving force per unit of areag acceleration due to gravityKin inlet friction coefficientL section lengthq applied powerQ time averaged coolant volumetric flow ratet cross correlation time delayuin coolant mean inlet velocityvgj drift velocityV volume of the section and

Greek lettersa void fractionDP inlet restriction pressure dropDTsub,in fluid subcooling at the channel inletDq density difference between liquid and vapor phases

ql coolant inlet densitys transfer function from void-fraction fluctuations to flow

rate time constantsChannel fluid transit time in the channelsbd boiling delay timesf period of geysering-induced oscillationssb,tt transit time of the bubbles passing through the chimney

Subscript0 relative to the steady state conditionC relative to the heated sectionCh relative to the chimney sectionChannel relative to the channelDC relative to the downcomerl relative to the liquid phasemodel referred to modelv relative to the vapor phase

Operatorsh i time average

880 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892Marcel et al. [17] performed a thoroughly description of themechanism of flashing-induced oscillations occurring in the CIR-CUS test facility with a single chimney configuration. The experi-ments were presented in a novel manner, allowing observing thedynamic evolution of important parameters which gave an excel-lent characterization of the phenomenology present in the system.

In natural circulation BWRs the chimney section is usually di-vided into subchannels to avoid cross flow and to better dividethe coolant flowing through the core. Flashing-induced instabilitiesoccurring in parallel channels may occur during the start-up phaseof a natural circulation BWR equipped with such adiabatic sec-tions. Such instabilities may be different from the more commonflashing-induced oscillations occurring when only one chimney ispresent. Experimental investigations on this field are still very lim-ited. Aritomi et al. [1,2] studied the low pressure stability of paral-lel channels with a chimney but in their experiments, thechimneys were too short compared to those from modern naturalcirculation BWRs, and therefore flashing played a secondary role.Fukuda and Kobori [11] observed two modes of oscillations in anatural-circulation loop with parallel heated channels. One wasthe U-tube oscillation characterized by channel flows oscillatingwith 180 phase difference, and the other was the in-phase modeoscillations in which the channel flow oscillated along with thewhole loop without any phase lag among them. Out-of-phase oscil-lations were also observed in the parallel channels of the CIRCUSfacility by Marcel et al. [16]. The mechanism of flashing-inducedinstabilities occurring in two-parallel channels, however, is notfully understood and therefore, more experimental investigationsare needed in order to clarify this issue. Such a topic is importantto assure a safe start-up process of novel natural circulation BWRs.2. Investigation tools

2.1. The CIRCUS facility in the single channel configuration

The CIRCUS facility [9] is a steam/water facility designed to per-form studies on two-phase flow dynamics relevant for the starting-up of natural circulation BWRs. CIRCUS is an axially fully scaled,radially lumped version of the Dodewaard reactor [26] . A simpli-fied scheme of the CIRCUS facility including technical details isgiven in Fig. 1. Further details regarding the CIRCUS facility (e.g.location of sensors, geometry, etc.) can be found in Appendix A.

CIRCUS can be operated in two different ways: the single chim-ney configuration and the two parallel chimneys configuration. Inthe first one, CIRCUS is equipped with a single tall adiabatic sectionrepresenting the reactor chimney which is placed on top of theheated section. The heated section simulates the reactor core andconsists of two heated channels with two bypasses. For this reasonthis section is also referred as the core section.

The steam produced in the heated section and in the chimney iscondensed in the heat exchangers and to some extent in the steamdome. A buffer vessel is used to damp temperature oscillations atthe downcomer inlet, ensuring a constant inlet subcooling. Twomagnetic flow-meters (maximum inaccuracy of 0.01 l/s) charac-terize the flow at the heated section inlet and chimney outlet. Sev-eral thermocouples (maximum inaccuracy of 0.5 C) are located atthe inlet and outlet of each heated channel, along the chimney sec-tions, in the heat exchanger and in the steam dome. Two PT100sensors are located at the inlet of the core section and in the steamdome for more accurate temperature measurements. Absolutepressure sensors are placed at the inlet of the core section, at thechimney outlet and in the steam dome. Differential pressure sen-sors are mounted across the steam dome, for measuring the waterlevel, and across the core inlet valve. Advanced measuring tech-niques are used for detailed high sampling rate void-fraction mea-surements, e.g. conductivity needle probes and capacitance-basedsensors. The channels in the facility are made of glass, allowing vi-sual inspection during the operation. To reduce the heat losses tothe surroundings, all the sections are covered with removable ther-mal isolation.

CIRCUS can be operated with a maximum electrical power perrod of 3 kW. By varying the inlet subcooling and the applied power,several configurations can be studied in the power-subcoolingplane. The core inlet valve allows changing the inlet restrictioncoefficient.2.2. The CIRCUS facility in the two-parallel channels configuration

In this configuration, the CIRCUS test facility is operated withtwo chimneys on top of the core section (see Fig. 1).

AIR

Pump

Bypass Channels

Pressure Vessel

Heat Exchanger Steam Dome

BufferVessel

T

T

T

T

T

T

T

T

T

T

In Out

P

P

P

P

F

F

P

T

P

Heated Channels

T

T

Chimney

Downcomer

Inlet friction

2 chimneys config.

Fig. 1. Schematic view of the CIRCUS facility and its sensors in the single chimney and the two-chimney configuration (not to scale).]

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 881Two parallel chimneys are installed above the four electricallyheated channels representing the core, from which two of theseare connected to each chimney. Channel 1 represents the set ofheated channels number 1 and 2 together with Chimney 1; Channel2 represents the set of heated Channels 3 and 4 together withChimney 2. In this configuration, the CIRCUS facility is equippedwith 16 void sensors for measuring the axial void-fraction profilein the chimneys. Moreover, 30 thermocouples allow measuringthe temperature in the loop. Reverse flow (counter-current flow)may occur in the channels during very strong oscillations. Specialhigh sensitive dp-sensors capable of measuring both negativeand positive pressure drops are therefore installed at the inlet ofeach heated channel and core bypass channels where the coolantis always in liquid phase for all conditions.

3. Experimental results

The following experiments are performed with the steam domeopen to the surroundings, thus the pressure at the top of the facil-ity is assumed to be always at 1 bar. In this way, any pressure feed-back occurring during oscillations is greatly reduced. Eachexperimental point is obtained by fixing the power applied in theTable 1Experimental conditions for the measurements obtained with CIRCUS facility in thesingle chimney configuration.

Magnitude Value

Power per rod 03000 WInlet temperature 5099 CPressure 1 barFlow circulation NaturalCore-bypass channels ClosedNumber of chimneys 1Inlet restriction coef. 5.6heating rods and varying the inlet temperature by changing thepower applied in the buffer vessel. By repeating this process at dif-ferent powers, the whole operational map can be covered. Theoperational conditions used for the experimental study performedin the CIRCUS facility are summarized in the following table (seeTable 1).

The value of the inlet friction coefficient is obtained experimen-tally by taking the channel flow area AC as a reference.

The inlet subcooling is defined in terms of the saturation tem-perature at the steam dome (100 C).

In this investigation, the same friction has been used for the sin-gle channel and the two-parallel channels configuration, whichcorresponds to Kin = 5.6.3.1. Single channel configuration

3.1.1. The stability mapsFig. 2 shows the stability map corresponding to the single chan-

nel configuration.0

5

10

15

20 Kin=5.6

Unstable

Stable

High subcooling SB Low subcooling SB Intermmittent osc. Sinusoidal osc.

Cor

e in

let s

ubco

olin

g [o C

Power per rod [kW]0.5 1.0 1.5 2.0 2.5

Fig. 2. Measured stability boundaries corresponding to the case with Kin = 5.6.

20 24 28 32 36 40 44 48 52 56

40

60

80

100

Kin= 5.6

period

= 1.5 C

hannel

period

= 2 Cha

nnel

Cha

nnel

osc

. per

iod,

f [

s]

Channel[s]

Increasing Tin

Fig. 3. Channel oscillation period vs. transit time for the case with Kin = 5.6.

882 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892The power-subcooling plane is useful to characterize the systemsince with these two parameters the working point of the facility isunivocally determined.

From the results it is observed that instability occurs within acertain range of inlet subcooling. This result is in agreement withfindings reported in literature (see [12,15,18]).

In order to clarify the origin of the instabilities the period ofexperimental oscillations is compared with typical periods ofDWOs. The fluid transit time in the channel is estimated as

sChannel VCh 12VC

Q; 1

where Q is the time averaged coolant volumetric flow rate, VCh thevolume of the chimney section and VC the total volume of the coresection. The factor 1/2 before VC appears since a perturbation of theinlet flow rate produces a perturbation of the enthalpy at the coreoutlet with an average phase lag corresponding to half of the transittime from the inlet to the outlet of this section. Since the transittime is a time-dependent variable in case of flow oscillations, it isevaluated on the basis of the mean flow rate.

Oscillatory cases obtained by applying 2 kW per rod have beenselected for this investigation. The relation between the oscillationperiod and the transit time for such experimental cases is shown inFig. 3.

The oscillation period from the experiments agrees well withthe estimated one from DWOs (being between one-and-a-half totwo times the coolant transit time through the channel) indicatingthe density wave character of the flashing-induced oscillations. Ithas to be recalled that numerical simulations performed by Maner-a [15] have shown that the strong effect of the energy accumulatedin the heat structures, namely the chimney walls and heated sec-tion tends to increase the incubation time and therefore the oscil-lation period. Heat losses have shown to cause the same effect.Such phenomena are obviously present in the results presentedhere. For small oscillation periods, which correspond to low subco-oling values, the period slightly deviates from these limits. In orderto understand this, a more detailed characterization of the experi-ments is needed. Such a study is presented in the following section.

3.1.2. From stable to unstableFrom experiments such as those presented in Fig. 2 it is ob-

served that by increasing the inlet temperature (while maintainingthe power constant) four different types of behavior are present[15]: (a) stable flow at high subcooling, (b) unstable intermittenttwo-phase flow, (c) unstable sinusoidal two-phase flow, and (d) sta-ble flow at low subcooling. These four behaviors have been exten-sively discussed in [17]. Part of that analysis is included here inorder to discus similarities and differences with the results ob-tained with the two-parallel channels configuration. The experi-ments selected here correspond to Kin = 5.6, a power of 2 kW perrod and different inlet subcoolings. It has to be noted that for thisconfiguration, the behavior with stable flow at low subcoolingcould not be reached.

To characterize the facility at any position and time, the tempo-ral evolution of the axial temperature profile in the channel to-gether with the void fraction axial profile in the chimney isincluded in special plots developed for that purpose. In these plotsthe color scale represents the value of the corresponding variablewhile the horizontal and vertical axes refer to the time and the ax-ial position, respectively. The temperature profile is obtained fromthe eight different places where the temperature is measured (seeFig. 1). The void fraction evolution is reconstructed from the sixvoid sensors placed in the chimney. A small scheme of the CIRCUSfacility is included to clarify the axial positions in the plots.

Time traces of the core inlet coolant flow are plotted togetherwith the power spectral decomposition (PSD).

3.1.3. High subcooling stable flow circulationFig. 4 presents the case measured with an inlet temperature of

86 C, where single-phase buoyancy plays a major role.It is seen that cold water enters the channel and is heated in the

core section. The coolant then travels through the chimney sectionwith no significant heat losses.

The temperature profile and the flow remain unchanged intime, only exhibiting small fluctuations which can be attributedto statistical fluctuations and turbulence. This is in accordancewith the PSD plot of the flow signal where no natural frequencyis seen. In this case, no significant amount of vapor is detected inthe chimney (see void fraction plot).

3.1.4. Intermittent oscillationsBy reducing the coolant inlet subcooling the high subcooling

stability boundary is crossed where intermittent oscillations arefound. Fig. 5 shows the case with an inlet temperature of 89.2 C.

In order to clarify the details of the dynamic process shown inthe plots, let us focus on what happens at 30 s. The coolant isheated in the core, driving the flow upwards due to single-phasenatural circulation (no vapor is identified in the chimney). At a cer-tain point flashing occurs in the chimney since the saturation tem-perature is reached by the hot coolant.

The vapor created by flashing enhances the flow circulation.Due to the flow increase, the coolant passes the heated section fas-ter and therefore is heated less. This liquid bulk is not hot enoughto vaporize in the chimney and flashing thus stops. As result of this,the driving mechanism is again single-phase buoyancy and theflow circulation decreases. This flow decrease causes the coolantto stay longer in the heated section and consequently the temper-ature at the chimney inlet starts to increase. Some vapor is conse-quently created by boiling at regions close to the core exit, causinga small second flow increase which disappears soon after enteringthe chimney. The hot front originated in the heated section travelsupwards starting the cycle again. Since from one flashing event tothe next one a certain time is needed (the so-called incubationtime) this behavior is named intermittent flashing.

As in the experiments with the single chimney configuration,the interaction with the structures (in particular in the chimneys)and the heat losses most probably influences the incubation timeof the system.

The PSD plot shows numerous frequencies after the main fre-quency indicating the presence of higher modes.

3.1.5. Sinusoidal oscillationsA further decrease in the inlet subcooling allows reaching the

unstable case with sinusoidal oscillations. The results of the mea-surements performed with an inlet temperature of 95.1 C are de-picted in Fig. 6.

Temperature plot

0 50 100 1500.0

0.1

0.2

0.3

0.4

Flow

[kg/

s]

Time [s]

Flow [kg/s]

0.0 0.1 0.21E-8

1E-6

1E-4

0.01

Flow

PSD

[Hz-

1 ]

Frequency [Hz]

Void fraction plot [-]

[oC]

Fig. 5. Unstable intermittent oscillations. This case is characterized by periodical oscillations occurring after a certain incubation time. The PSD plot shows clear frequencies.

0 50 100 1500.000

0.025

0.050

0.075

0.100

Flow

[kg/

s]

Time [s]

Flow [kg/s]

Void fraction plot

Temperature plot

0.0 0.1 0.2 0.3

1E-81E-61E-40.01

1

Flow

PSD

[Hz-1

]

Frequency [Hz]

[-]

[oC]

Fig. 4. Stable high subcooling flow circulation. Very low vapor values and a constant axial temperature profile in the chimney characterize this case. The flow signal is roughlyconstant only exhibiting some noise.

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 883Unlike the intermittent oscillations case, in the sinusoidal oscil-lations case during the flashing event vapor appears in the coresection first. The coolant flow shows a regular behavior with anon-existent incubation time (see the PSD plot).

It is seen that just before the steam is produced in the core, thetemperature profile shows a clear hot spot (see Fig. 6). It is ex-pected that the existing negative temperature gradient (Includingthe heat transfer with the structures) may diminish the vapor cre-ation. An extreme example of this effect is the geysering phenom-enon which can lead to sustainable oscillations. Since the geyseringmechanism is characterized by a much longer oscillation periodthan that of DWOs, having such temperature profile prior to theflashing event may tend to reduce the oscillation period. Thisagrees with the shorter oscillation periods found for the cases withlow subcooling values (see Fig. 3).3.1.6. Low subcooling stable flow circulationBy increasing the coolant temperature at the core inlet even fur-

ther, the low subcooling stable case is found (see, for exampleFig. 8 from [17]).

In this case, coolant in a two-phase state is permanently presentin the chimney. The temperature profile is characterized by a cleartemperature decrease in the flashing region. This decrease is due tothe decrease in the saturation enthalpy which corresponds to thehydrostatic pressure decrease.

3.1.7. Analysis of the dynamics of the flashing frontIn this section, the dynamics of the flashing front for the two

oscillatory cases is further investigated. The signals from thenon-intrusive, high frequency, capacitance-based void detectorsare used for this purpose.

884 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892The cases presented in Figs. 5 and 6 are used in this section. Thetime traces of the signals from the void fraction sensors placed inthe chimney are shown in Fig. 7a. To facilitate the comprehension,the sensor positions are numbered from bottom to top, being thelowest one number 1 and the top one number 6.

Fig. 8a shows that in the intermittent oscillations case the flash-ing front starts at the top of the chimney, at positions 6 and 5. This isdue to the fact the temperature profile is quite flat prior to the onsetVoid fraction plot

Temperature plot

[-]

[oC]

hot spot

Fig. 6. Sinusoidal oscillations case. This behavior is characterized by regular oscillationinside the heated section.

104 106 108 110 112 1140.0

0.2

0.4

0.6

0.8

1.0

Void

frac

tion

[-]

Time [s]

Pos 1 Pos 2 Pos 3 Pos 4 Pos 5 Pos 6

Intermittent two-phase osc.

0.

0.

0.

0.

0.

1.

Void

frac

tion

[-]

(a) (b)

Fig. 7. (a) Time evolution of the flashing front for the intermittent oscillation

0.0 0.5 1.0 1.5 2.00.000

0.005

0.010

0.015

0.020

0.025

0.030

2 driving force, (l-v) L g [kPa]

Kine

tic E

nerg

y,

l2 /2

[kPa

]

(a)

Fig. 8. (a) Relation between the driving force and the kinetic energy. (b) Crofflashing (see Fig. 5) and thereforeflashing is likely to occur at high-er positions where the hydrostatic pressure is lower. The flashingfront then reaches the lower regions in the chimney, at positions 4and 3. The flashing front then travels upwards leaving the chimney.

The flashing front evolution for the sinusoidal two-phase oscil-latory case is presented in Fig. 7b. As can be observed, in this casevapor appears at the lowest void sensor location first and thentravels upwards along the chimney.0 50 1000.0

0.1

0.2

0.3

0.4

Flow

[kg/

s]

Time [s]

Flow [kg/s]

0.0 0.1 0.21E-6

1E-4

0.01

1

100

Flow

PSD

[Hz-

1 ]

Frequency [Hz]

s with a practically non-existent incubation time. The flashing/boiling front starts

36 38 40 42 44 46 480

2

4

6

8

0Sinusoidal two-phase osc.

Time [s]

Pos 1 Pos 2 Pos 3 Pos 4 Pos 5 Pos 6

1

2

3

4

5

6

s and (b) flashing front time evolution for the sinusoidal oscillatory case.

0 5 10 15 20 25 30 35-0.6-0.4-0.20.00.20.40.60.81.01.2

Time [s]

CC

F [-]

CCF from void-to-flow Intermittent osc.

0.0 0.5 1.0 1.5 2.0 2.5 30.6

0.8

1.0

1.2

CC

F [-]

tdelay= 0.77s

Zoomed View

(b)

oss correlation between the void fraction and resulting flow response.

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 8853.1.8. Analysis of the inertia of the loopDuring the oscillations the buoyancy in the system is mainly

due to the two-phase driving force which, per unit of area, is de-fined as follows

Fdriv ql qva L g; 2

where a is the mean void fraction (obtained by integrating in spacethe temporal evolution of the axial void fraction in the channel) andL is the channel length. The use of fast response void fraction andpressure drop sensors assure that no dynamic effects are introducedby the measurement system (besides some delay which may beintroduced by the void transport).

The system response due to a change in the driving force can beaccounted by the kinetic energy per unit of volume, which is de-fined as

Ekin qlu2in=2; 3

where vin is the coolant velocity at the core inlet.Fig. 8a illustrates the response of the kinetic energy to changes

in the two-phase driving force, for intermittent oscillations mea-sured with Kin = 5.6 an inlet temperature of 88 C and a power in-put of 2 kW per rod.

The figure clearly shows that no linear relation exists betweenthe two plotted quantities. To clarify this issue, the cross correla-tion of the mean void fraction and the coolant velocity is calculatedand plotted in Fig. 8b.

A clear time delay of 0.77 s exists between these two signals.The time constant of the transfer function from void-fraction fluc-tuations to flow rate can be estimated from a first-order transferTable 2Experimental conditions corresponding to the measurements performed in theCIRCUS facility with parallel channels.

Magnitude Value

Power per rod 03000 WInlet temperature 7099 CPressure 1 barFlow circulation NaturalCore-bypass channels ClosedNumber of chimneys 2Inlet restriction coef. 5.6

0.5 1.0 1.5 2.00

5

10

15

20

25

II

I- Stable flow II- In-phase osc. III- A-periodical osc. IV- Out-of-phase osc. Stability Boundary

Subc

oolin

g [o C

]

Power per rod [kW]

I

Fig. 9. Stability map and typical time traces of the flow found when the inlet friction isdetail in Sections 3.2.33.2.6. The arrow indicates the points used in the investigation pfunction derived from a model based on the linearized version ofthe momentum balance (see [18] in which two driving mecha-nisms are considered: the single-phase and the two-phase naturalcirculation.

s M0

PiLiAi

2L ghaiChql;Ch qv ql;DC ql;Ch: 4

A time constant of smodel 0:91 s is found from themodel, whichis in the same range as the time delay from the cross correlation(tdelay = 0.77 s). The inertia term Rli/Ai is particularly important innatural circulation systems and therefore has to be taken intoaccount. In other words, the flow cannot be considered to instanta-neously adjust itself to changes in driving force and friction.

It can be concluded that the delay between the two-phase driv-ing force and the kinetic energy is caused by a combination of twoeffects: the inertial effects of the fluid plus some delay which maybe introduced by the void transport.3.2. Two-parallel channels configuration

As in the case with only one chimney, during the experimentswith the two-parallel channels configuration, the power appliedin the heating rods is fixed and the inlet temperature is varied bychanging the electrical power applied in the buffer vessel. Byrepeating this procedure with different powers, the full operationalmap can be covered. The operational conditions used in this studyare summarized in Table 2.3.2.1. The stability mapsIn the out-of-phase oscillation mode, the primary flow remains

constant, i.e. the total pressure drop in the parallel channels re-mains the same. Such oscillatory behavior, however, is never ob-served in our experiments. As soon as the system loses stability,the primary flow exhibited oscillations.

Fig. 9 shows the stability map found when Kin = 5.6 is set. Thestability map is divided into four regions, each one characterizinga different behavior for which typical time traces of the primaryflow are also included in the figure.

The first region I is mainly characterized by stable single-phaseflow. In the proximity of the stability boundary small bubbles werePrim

ary

flow

[kg/

s]

0.00.10.20.30.40.5 III- A-periodical osc.

0.00.10.20.30.40.5 II-In-phase osc.

0.00.10.20.30.40.5

IV- Out-of-phase osc.

0 50 100 150 200

0 50 100 150 200

0 50 100 150 200

0 50 100 150 200

0.00.10.2 I-Stable Flow

2.5

IV

III

Kin=8.65

Time [s]

set to a value equal to Kin = 5.6. The experiments marked with a h are analyzed inresented in Section 3.2.7.

886 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892observed at the chimney exit corresponding to low vapor qualityvalues.

The high subcooling oscillations are observed in region II. Thisregion exhibits regular oscillations in which the period and timeof occurrence of the cycles is the same for both the channel partialflows and the primary flow.

In region III, so-called a-periodical oscillations take place in thesystem.

In the last region IV regular oscillations, which are out-of-phaseregarding the partial flow in the channels, are found.

A more detailed description of the four behaviors is provided innext sections. It has to be remarked that no stable flashing region isobserved in this set of measurements.

3.2.2. Phenomenological description from regions IIVTo clarify the four behaviors introduced earlier, selected exper-

iments performed with a power input of 2 kW per rod are pre-sented in detail in this section. These cases are marked with hin Fig. 9.

The dynamics of the axial temperature profile and the void-frac-tion profile in the two channels is displayed by using the sametechnique used before. These profiles are obtained from the sixteendifferent positions where the temperature and the void fraction ismeasured (see Fig. 1). Finally, to easily correlate the dynamics ofthe flow changes with the void and the temperature fluctuationsin the channels, the partial flows are also superimposed on the ax-ial temperature plots.

The partial flows time traces are plotted to show the differencesbetween the cases. The primary flow signal power spectral decom-position (PSD) is also shown.

3.2.3. Region I high subcooling stable flow circulationA measurement performed with an inlet temperature of 80 C is

selected as example of the stable behavior of region I. Fig. 10 showsthis case where stable single-phase natural circulation occurs inthe facility.0 50 100 150 200 250 300-0.1

0.0

0.1

0.2

0.3

Time [s]

Flow

[kg/

s]

Partial Flow Ch 1 [l/s] Partial Flow Ch 2 [l/s] Primary Flow [l/s]

Fig. 10. Region I is characterized by identical axial temperature profiles in the channelThe temperature profile is similar in both channels. The partialflows only exhibit small fluctuations which can be attributed tostatistical fluctuations and turbulence. In this case no natural fre-quency is observed in the PSD of the primary flow signal.

From the figure it is observed how cold water entering into thechannels is heated in the core section. The coolant then travelsthrough the chimney section with no significant heat losses. Themain flow circulation driving mechanism is single-phase buoyancysince no significant void is detected.

This behavior is similar to the high subcooling stable flow circu-lation behavior reported in Section 3.1.3 obtained when having asingle chimney.

3.2.4. Region II unstable high subcooling flow circulationFig. 11 shows the typical behavior from region II. This particular

case is obtained by operating the facility with an inlet temperatureof 87 C.

Here, flashing occurs almost simultaneously in both chimneys(see the large peaks in the partial flow signals) since the conditionsfor flashing in both channels are fulfilled practically at the sametime. In this region the period and time of occurrence of the oscil-lations is the same for both partial flows and primary flow. Thecoupling between the channels cause that during the flashingevents the partial flows behave out-of-phase.

In order to clarify the process, let us focus on what happens at100 s. As can be seen in Fig. 11, (see plots with vapor), largeamounts of vapor are present in Channel 2 while Channel 1 stillcontains liquid water. Consequently, a strong increase in flow ap-pears in Channel 2 due to buoyancy. As a result, reversed flow oc-curs in Channel 1 due to the large inertia of the coolant in thedowncomer. This reversed flow forces hot coolant to re-enter thecore section and triggers the creation of large amounts of vaporin Channel 1. As a consequence, the partial flow in Channel 1strongly increases, thereby now reversing the flow in Channel 2.Hence, the water present in the core of Channel 2 is also heatedtwice (similar to Channel 1). The temperature in the lower part0.0 0.1 0.2 0.31E-8

1E-6

1E-4

0.01

1

Flow

PSD

[Hz-

1 ]

Frequency [Hz]

s and stable flows, similarly to the high subcooling stable cases from Section 3.1.3.

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 887of the chimney in Channel 2 is too low to create vapor now. Someflashing, however, occurs due to the presence of hot coolant at themiddle of the chimney in Channel 2. The partial flow in Channel 20 50 100 150 200 250

-0.4-0.20.00.20.40.60.8

Flow

[kg/

s]

Partial Flow Ch 1 [l/s] Partial Flow Ch 2 [l/s] Primary Flow [l/s]

Time [s]

-1

Fig. 11. Region II. The high subcooling oscillations are characterized by showing similar ttake place followed by a relative long incubation time.

Flow

PSD

[Hz-

1 ]

0 25 50 75 100 125 150

-0.4-0.20.00.20.40.60.8

Flow

[kg/

s]

Time [s]

Partial Flow Ch 1 [l/s] Partial Flow Ch 2 [l/s] Primary Flow [l/s]

Fig. 12. Region III. The a-periodical oscillations exhibit a very compincreases for a second time which causes (again) reversed flow inChannel 1. The coolant in Channel 1, however, is now too cold toflash again.0.0 0.1 0.2 0.31E-6

1E-4

0.01

1Fl

ow P

SD [H

z]

Frequency [Hz]

f-1=T~ 85 s

emperature axial profiles in both channels at any time. Large amplitude oscillations

0.0 0.1 0.2 0.31E-8

1E-6

1E-4

0.01

1

Frequency [Hz]

lex temperature and void fraction axial profile in the channels.

888 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892To summarize, the parallel channels show reversed flow andflashing in an alternating, but not sustainable way due to the rela-tively low power and low inlet temperature. Since the channels be-have more or less independently (whereas the mutual couplingonly triggers the flashing events synchronizing the channels) thisbehavior can be compared with the intermittent oscillations re-ported in Section 3.1.4 occurring in a system with a singlechimney.

From the analysis of the primary flow signal, two different timescales can be identified: the fast changes in flow (3 s), caused bythe very strong coupling between the channels during flashing, andthe long incubation time (85 s) needed to build up the conditionsthat will lead to the next flashing cycle in the channels. Numerousfrequencies appear in the PSD.

3.2.5. Region III unstable a-periodical oscillationsA further increase in the inlet temperature leads to the a-peri-

odical oscillations of region III. A typical case of this behavior isshown in Fig. 12, obtained with the inlet temperature set equalto 88.5 C.

In this case, the combination of power and inlet temperatureleads to very complex dynamics resulting in a-periodical oscilla-tions which are clearly visible in the axial void fraction and tem-perature plots. This behavior is hard to predict, contrasting withthe regular oscillations from regions II and IV.

In this region, since the periodicity is lost, a broad range ofamplitudes and frequencies is found in the PSD of the primary flowsignal which is characterized by the absence of clear peaks.

Despite the complex axial temperature profiles existing in thechannels, the correspondence between the presence of void andthe increase in flow can still be seen. This a-periodical region isstudied in depth in [7].

3.2.6. Region IV unstable out-of-phase oscillationsIncreasing the inlet temperature even more leads to region IV,

where so-called out-of-phase regular oscillations are found. The0 10 20 30 40 50 60

-0.4-0.20.00.20.40.60.8

Time [s]

Flow

[kg/

s]

Partial Flow Ch 1 [l/s] Partial Flow Ch 2 [l/s] Primary Flow [l/s]

-1

Fig. 13. Region IV. The out-of-phase oscillations are extremely regular, where reverexperiment depicted in Fig. 13 is obtained by setting the inlet tem-perature equal to 98.0 C.

To better explain the process taking place in this region, wewill focus on what happens at 39 s. The high core inlet temper-ature causes very hot coolant being present at the exit of theheated section of Channel 1 resulting in large amounts of vaporin the chimney (see void plot in Channel 1), while Channel 2 stillcontains liquid water. As a result of the vapor appearance in Chan-nel 1, buoyancy abruptly increases the partial flow in this channel.The large increase in the Channel 1 flow causes reversed flow tooccur in Channel 2, due to the large inertia of the coolant presentin the downcomer. This reversed flow forces hot coolant to re-en-ter the heated section of Channel 2, where it is heated for the sec-ond time.

The combination of high power and inlet temperature causesthe alternation of flashing events in both channels to be sustained,in contrast to the cases from region II. Due to the small inlet sub-cooling, the coolant that is heated twice starts to boil inside theheated sections. The noticeable gradient in the chimney axial tem-perature profile prior flashing causes condensation that suppressesthe vapor creation during the resulting oscillations (see the vapordecrease in the middle part of the flashing chimney).

The time evolution of the void-fraction profile shows a clearcorrelation in time between the vapor creation and the flow in-crease in the corresponding channel. It is also found that some va-por produced in one channel enters the other channel due toreversed flow.

The PSD of the primary flow signal exhibits a clear peak at theoscillation frequency and also higher harmonics.

3.2.7. Analysis of the instability mechanismSince two possible instability mechanisms are identified, flash-

ing and geysering, the periods of the unstable cases obtained whenapplying a power input of 2 kW per rod (indicated in Fig. 10 withan arrow) are compared with two characteristic parameters ofdensity wave oscillations (DWO) [3,28] and geysering oscillations0.0 0.1 0.2 0.31E-8

1E-6

1E-4

0.01

1

Flow

PSD

[Hz

]

Frequency [Hz]

APSD of the Primary Flow

se flow plays an important role creating hot spots which will flash afterwards.

15 20 25 30

20

40

60

80

100 Single channel osc. period Channel osc. period ( // Ch)

f =bd+

b,tt

IIIV

Boiling delay + bubble transit time, bd+ b,tt[s]

Cha

nnel

osc

. per

iod,

f [

s]

Fig. 15. Channel oscillation period vs. boiling delay time plus bubble transit time.

(b)

20 24 28 32 36 40 44 48 52 5620

40

60

80

100

f=1.5

Channel

IIIV

f=2 C

hannel

Cha

nnel

osc

. per

iod,

f [

s]

Channel[s]

Single channel osc. period Channel osc. period ( // Ch)

Inlet temperature [oC](a)

0.12 0.16 0.20 0.24 0.28 0.32

20

40

60

80

100

99

IVIII

93.5 94.5 96.588.5

Channel osc. period [s] Not periodic

Cha

nnel

osc

. per

iod,

f [s

]

Flow [kg/s]

82.5

II

Fig. 14. (a) Period of the oscillations vs. partial flow. The a-periodical region is marked with a shaded rectangle. (b) Channel oscillation period vs. characteristic transit time inthe channels for both, the single and parallel channels configuration.

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 889[1]: the traveling time through the channel and the boiling delaytime plus the bubble transit time.

Fig. 14a shows the relation between the oscillation period andthe flow where the inlet temperature is included in the upper axis.

It is found that the oscillation period monotonically decreaseswith the inlet temperature. The figure also reveals the long incuba-tion time from region II relative to the small oscillation period inregion IV.

Fig. 14b shows the relation between the channel oscillation per-iod and the transit time of the flow which is estimated by using Eq.(2).

The results for the single chimney configuration at equivalentconditions (in terms of the power per channel, inlet subcoolingand common inlet restriction) already discussed in Section 3.1.1are also included in the figure.

Fig. 14b clearly shows that the two regions with periodicaloscillations, i.e. regions II and IV, exhibit different slopes, suggest-ing the instability mechanism to be different. The smaller slope ofthe (roughly) straight line associated with region IV is due to thestrong effect of the reversed flow in the mechanism which pro-motes the appearance of vapor since a certain amount of hot cool-ant passes the heated section twice. The figure also shows that forall experiments, the parallel channels have a shorter oscillationperiod than that from the single chimney configuration. This differ-ence, however, is reduced for large values of transit times, whichconfirms that for high subcooling/low power conditions the chan-nels behave more independently, i.e. like in the single channel casefrom Section 3.1.4.

The existence of the geysering mechanism [20] which maycomplement flashing, is also investigated. Such a mechanism islikely to occur due to the heat transfer with the structures of thechimney section and core. The boiling delay time sbd is definedas the time required for the fluid with subcooling DTsub,in, to beheated up to the saturation temperature based on the pressure atthe channel inlet and is expressed by

sbd qlCplDTsubACLC

q; 5

where the liquid density ql, and the specific heat capacity at con-stant pressure Cpl,in, are computed at the temperature at the chan-nel inlet; Ac and Lc are the flow area and length of the heatedsection, respectively.

The non-heated chimney influences the geysering period sincethe effect of the transport of bubbles cannot be ignored [1]. It isfound an acceptable correlation for the measured data when theboiling delay time is added to the transit time of the bubbles pass-ing through the chimney sb,tt which can be calculated by the driftvelocity vgj, for slug flow in the following mannersb;tt LCh

vgj uin6

with

vgj 0:35gDqDCh

q

1=2; 7

g being the acceleration due to gravity, Dq the density differencebetween the liquid and vapor phases, and uin the mean inletvelocity.

In experiments performed with a chimney it is reported that theperiod of geysering-induced oscillations sf, is nearly equal to theboiling delay time sbd plus the bubble transit time sb,tt [1]. The per-iod of the oscillations sf are therefore plotted in Fig. 15 vs. sbd +sb,tt.

The regular oscillations from regions II and IV exhibit linearrelations with different slopes. In region II the slope is roughly sim-ilar to that in the case of single channel oscillations. Since the oscil-lation period is several times the boiling delay time, it can beconcluded that geysering plays a secondary role in this case. Incontrast, the slope of the linear profile of region IV is similar to thatfrom geysering instabilities. The magnitude of the periods, how-ever, is systematically underpredicted, suggesting that the instabil-ity mechanism cannot be attributed to geysering only. Thisdifference can be explained as follows. The boiling delay time as-sumes the flow is zero during the heating up process. The coolantflow, however, is not zero and therefore some enthalpy is trans-ported by the coolant, which is not used in the vaporization. As aresult the system needs more time to complete a cycle than thatpredicted by the geysering mechanism. For this reason, the periodof the oscillations in region IV is overestimated by DWO based esti-mations and underestimated by predictions based on geyseringoscillations.

890 C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 8798923.2.8. Experimental evidence of bifurcations and non-linear analysisIn this section, the experiments obtained at an input power

equal to 2 kW per rod are used. The inlet temperature is variedin small steps of 0.5 C. Each experiment is preceded by waiting1 h before measuring, to reduce as much as possible any long termdrift in the inlet subcooling. Then, each point is measured for 1 h inorder to get enough statistics for this analysis.

Fig. 16a is a contour plot that shows the PSD of the primary flowsignal for all measured cases. A Henning window is used. The colorrepresents the logarithmic value of the power level for the corre-sponding frequency component. Fig. 16b presents the PSD for threecases.

In the out-of-phase region IV, the spectrum shows the trend ofthe main frequency together with higher harmonics. By decreasingthe inlet temperature, a period-doubling occurs at around 96 C.The amplitude of the successive bifurcations becomes hard to beidentifiable in practice after the first period-doubling due to mea-surement noise.

An abrupt change in the frequency pattern is seen when reach-ing the a-periodical region III. Here, a broad band of frequenciesemerges around the main frequency. As predicted by the Feigen-baum scenario [10], this may be due to a cascade of period-dou-bling bifurcations which creates many possible oscillation modeswhich are impossible to discriminate from each other.

In region II, the PSD clearly shows higher harmonics. A furtherdecrease in the inlet temperature leads to the stable region I char-acterized by no peaks.

A non-linear characterization of experiments from region IIIbased on a Wavelet-Transform Modulus-Maxima (WTMM) formal-ism showed a multi-fractal structure in the dynamics of the mea-sured signal, thus revealing that the nature of the a-periodicalI II III IV (a)

Fig. 16. (a) Contour plot of the primary flow PSD. (b) PSD for three parti

Table 3Summary of the different behaviors found in the experiments obtained with the single ch

Single channel Parallel c

a Stable flow mainly driven by single-phase natural circulation. I Stableb Intermittent flow oscillations driven by flashing. Flat chimney axial

temperature profile prior to the flashing occurrence.II HighAlmost fl

c Sinusoidal flow oscillations driven by boiling plus flashing. Non-flatchimney axial temperature profile prior to the flashing occurrence.

III A-petemperatphenome

d Stable flow circulation induced by flashing. IV Out-chimneyimportan

Note: The cases are ordered according to their respective inlet temperature, with casesoscillations is deterministic chaos [7]. As explained before, thephysical mechanism driving these flow oscillations is mainly flash-ing combined with some geysering. Although the chaos is provento be deterministic, such a chaotic behavior of the flow oscillationsis difficult to be modelled, since there is sensitive dependence oninitial conditions. Therefore, when trying to model the behaviorof the facility for the transition region via a time-domain code,any inaccuracy in the determination of the initial conditions wouldlead to radically different responses of the facility. Any attempt tomodel such behaviors is further complicated by the strong asym-metrical response of each pair of heated channels/chimney.

3.3. Single channel behavior vs. two-parallel channels behavior

Table 3 shows the main features of the behaviors found for thetwo aforementioned configurations while the inlet temperature isincreased.

First, it should be noted that the physical phenomena causingthe dynamical behavior could be different for the single channeland the parallel channels configurations. A direct comparison be-tween the behaviors a and I, b and II, etc. as stated in Table 3 istherefore not always meaningful. Second, it has to be stressed thatthe configurations used in both sets of experiments make use ofthe same loop and therefore, although the number of channels isdoubled, the rest of the sections remains the same (this is differentfrom a situation where a chimney is divided into smaller sections).

From the experiments it is observed that the stable flow circu-lation behavior corresponding to very low quality values in thechimney (a and I) are similar for the two configurations. This sim-ilarity can be observed in the channel axial temperature profiles,the chimney void-fraction profiles and the stable mass flow rate1E-15

1E-13

1E-11

1E-9

1E-7 T =94 C

1E-15

1E-13

1E-11

1E-9

1E-7 T =89.4 C

0.0 0.1 0.2 0.3

0.0 0.1 0.2 0.3

0.0 0.1 0.2 0.3

1E-15

1E-13

1E-11

1E-9

1E-7 T =98 C

Frequency [Hz]

Flow

PSD

[Hz-

1 ]

(b)

cular cases. A bifurcation occurred from the first to the second plot.

annel and the parallel channel configuration.

hannels

flow mainly driven by single-phase natural circulation.subcooling flow oscillations driven by flashing and to some extent to boiling.at axial temperature profile in the chimneys prior to the flashing occurrence.riodical flow oscillations caused by flashing, boiling and geysering. Non-flat axialure profile in the chimneys. Reverse flow of great importance for thenon.of-phase flow oscillations driven by boiling, flashing and geysering. Non-flataxial temperature profile prior to the flashing occurrence. Reverse flow of greatce for the phenomenon.

with lower values first.

C.P. Marcel et al. / Experimental Thermal and Fluid Science 34 (2010) 879892 891(see Figs. 4 and 10). The very high subcooling natural circulationmechanism is efficient enough to cool the heated section. Appar-ently the cooling mechanism is able to suppress any perturbationwhich would lead to instabilities in the channel(s).

The intermittent oscillations occurring in the single channelconfiguration show analogies to the high subcooling oscillationsobserved in the parallel channels configuration). This is related tothe fact that flashing is the only instability generating mecha-nism present here. As can be seen from Figs. 5 and 11, the axialtemperature profiles are similar, except for the short time in whichreverse flow occurs for the case with parallel channels. The low-quality natural circulation mechanism is not efficient enough tosufficiently cool the heating rods and reach a steady-state situa-tion. In this case, flashing-induced instabilities and low-qualitynatural circulation are alternating phenomena.

The a-periodical flow oscillations involving flashing, boiling andgeysering effects show a high degree of complexity and are notfound in the single channel configuration. The strong coupling be-tween the channels together with the aforementioned effects cre-ates very complex, time-dependent, axial temperature profiles.

Some similarities exist between the sinusoidal oscillations ob-served in the single channel configuration and the out-of-phaseoscillations in the parallel channel case (IV), such as the axial tem-perature profile exhibiting the same trend (see Figs. 6 and 13). Thereverse flow from the latter case, however, is not present in the sin-gle channel configuration. Reverse flow shortens the flashing cyclesince part of the fluid is heated twice, as can be clearly seen inFig. 14b. The oscillation period of the partial flow in the parallelchannel configuration is therefore found to be smaller than thatfor the single channel configuration (see Fig. 14b).

The stable flow circulation induced by flashing observed in thesingle channel configuration has not been found in the parallelchannels cases reported here.4. Conclusions

Flashing-induced instabilities occurring in one and two-parallelchannels are investigated in detail. A novel representation of theresults allowed a thorough understanding of the instability mech-anism. As result of this investigation, the following is concluded.

The four different behaviors reported by previous authors areseen in the experiments obtained with the single chimney config-uration: stable flow at high subcooling; intermittent flow oscilla-tions; sinusoidal flow oscillations and stable flow at lowsubcooling.

The flashing front develops from the chimney top to bottomduring intermittent oscillations and from bottom to top in thesinusoidal oscillations.

The oscillation period found in the experiments agrees wellwith those from DWOs indicating the density wave character ofthe flashing-induced oscillations.

The delay between the two-phase driving force and the kineticenergy is affected by the inertia of the loop.

The instability mechanisms existing when having parallel chan-nels, have also been thoroughly investigated by using the CIRCUStest facility.

As a result of this study it is concluded that at least four differ-ent behaviors can be expected in a system of two identical heatedchannels equipped with parallel chimneys. These are:

stable flow circulation (corresponding to very low vapor qualityvalues);

periodic oscillations in which the primary flow is roughly in-phase with the partial flow in both channels and the main insta-bility mechanism is due to flashing. The two channels behavemore or less independently except for the clear synchronizationof the flashing events which can be attributed to the couplingbetween the channels;

a-periodical oscillations which are attributed to multi-fractaldeterministic chaos. Bifurcations have been observed in theexperiments which suggest that period-doubling is the routeto chaos followed by the system. This result has never beenreported before; and

out-of-phase periodical oscillations in which the primary flowexhibits a period which is half of the period of the partial flowsin the channels. Two main instability mechanisms seem to coex-ist in this case being flashing and geysering. The channel cou-pling creates reversed flow which causes hot spots in thechannels. This effect creates large gradients in the axial temper-ature profile that together with the interaction with the struc-tures, favors the occurrence of condensation effects.

In addition, some similarities have been observed between theintermittent flow oscillations found in the single chimney experi-ments and the high subcooling oscillations found in the two-paral-lel channels experiments. Moreover, similarities have also beenfound between the sinusoidal flow oscillations existing in the sin-gle chimney experiments and the out-of-phase oscillations fromthe two-parallel channels experiments.

The results from this investigation can be very useful to validatenumerical models which in turn can be used to investigate the sta-bility of natural circulation BWRs during start-up. From the exper-iments with a multiple chimney configuration, it can be concludedthat instabilities showing chaotic behavior might be of interest.Such a dynamical behavior may be difficult to predict by most ofthe time-modeling techniques, due to the sensitive dependenceon initial conditions and represents a challenge for the future.Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.expthermflusci.2010.02.002.References

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Experimental investigations on flashing-induced instabilities in one and two-parallel channels: A comparative studyIntroductionInvestigation toolsThe CIRCUS facility in the single channel configurationThe CIRCUS facility in the two-parallel channels configuration

Experimental resultsSingle channel configurationThe stability mapsFrom stable to unstableHigh subcooling stable flow circulationIntermittent oscillationsSinusoidal oscillationsLow subcooling stable flow circulationAnalysis of the dynamics of the flashing frontAnalysis of the inertia of the loop

Two-parallel channels configurationThe stability mapsPhenomenological description from regions IIVRegion I high subcooling stable flow circulationRegion II unstable high subcooling flow circulationRegion III unstable a-periodical oscillationsRegion IV unstable out-of-phase oscillationsAnalysis of the instability mechanismExperimental evidence of bifurcations and non-linear analysis

Single channel behavior vs. two-parallel channels behavior

ConclusionsSupplementary materialReferences