Chapter 3
Moltenª²Pool Sloshing Motion
3ª±1Introduction

As introduced in Chapter 1,in the transition phase during CDA of SFR,the reactor core melts and a largeª²scale molten fuel pool containing sufficient amount of fuel with the potential to exceed the prompt criticality by fuel compaction are formed and confined in the neutronic active core region as a result of channel blockage due to core material freezing in the subassembly blanket structures (Figure 1ª²9)£Û1ª²4£Ý. According to various calculations from SIMMERª²¢ò code,the moltenª²pool sloshing motion,a specific pattern of compacted fluid motion in the largeª²scale molten fuel pool,was revealed£Û5ª²8£Ý. In the molten pool,a local excursion of neutronic power or pressure buildup might drive the liquid fuel away from core center towards the peripheries,and then the fuel is impelled back to the pool center by the gravity,leading to the energetic nuclear power excursion resulted from the probable fuel compaction involved in such centralized inward sloshing motion£Û3ª²4£¬8£Ý. As a result,the moltenª²pool sloshing motion is of great essence to reasonably assess the energetic potential of the moltenª²fuel pool and enhance analyses of SFR severe accidents.


For the reason that a part of a liquid coolant might be entrapped into the moltenª²fuel pool during the pool enlargement,
the local Fuelª²Coolant Interaction (FCI) is considered as one of the various inducing factors that may result in the pressure generation and subsequent sloshing motion£Û1ª²3£Ý. In the past years,to ascertain the characteristics of pressure generation from local FCIs in the pool,several series of simulated experiments were carried out using a 
Pressurization Characteristics in Meltª²Coolant Interaction (PMCI) facility developed at the Sun Yatª²sen University (SYSU)£Û9ª²10£Ý. Based on the detailed analyses performed,much of knowledge and experimental database such as the effect of various experimental parameters (eª±g. melt temperature,water subcooling and the liquid volume delivered into the pool) along with the interaction mode (melt injection or water injection) on local FCIs have been accumulated£Û9£Ý,thereby greatly stimulating the acceleration of researches on the sloshing motion following the local FCI.


Actually,considering the significance of moltenª²pool sloshing motion in evaluating the progression of reactor severe accidents (especially for the energetic recriticality issues),over the past decades a few pioneering investigations were conducted in narrower 
2D or larger 3ª²dimensional (3D) cylindrical water pools£Û3£¬8£¬11ª²21£Ý. For instance,in the analysis of CDA energetics for Clinch River Breeder Reactor,with the fast reactor safety analysis code SIMMERª²¢ò,inª²slosh motion or centralized sloshing motion in a moltenª²fuel pool was observed by Theofanous and Bell (1986) under perfectly symmetrical conditions in both geometry and power distribution£Û8£Ý. To provide validation data for safety analysis codes,Maschek et al. (1992) conducted several laboratoryª²level damª²break and fluidª²step experiments by releasing liquid water from a smaller inner cylindrical column to a larger outer transparent container£Û3,11£Ý. In their study,the effects of different experimental parameters (such as the diameter of the inner water column as well as the depths of water in the inner water column and the outer container) on the sloshing motion were detailly investigated. Based on their damª²break experiments,Yamano et al. (2012) used SIMMERª²¢ô code,an advanced 3D fast reactor safety analysis code,to perform some numerical calculations at the Japan Atomic Energy Agency (JAEA) and it was demonstrated that the SIMMERª²¢ô code can reasonably simulate the experimental results (especially for the compaction velocity) under both symmetric and asymmetric conditions£Û13£Ý.  Furthermore,the applicability of the 
Finite Volume Particle (FVP)  method and Smoothed Particle Hydrodynamics  (SPH)  method was validated for the simulation of the damª²break experiments by Guo et al. (2010,2012),Vorobyev (2012) and Jo et al. (2019)£Û14ª²17£Ý.


Nevertheless,it should be highlighted that although some important nature of the sloshing motion (eª±g. piling up of molten fuel at pool peripheries and the gravityª²impelled inward sloshing) can be captured by the damª²break experiments conducted by Maschek et al. (1992),it is believed that their experimental conditions are still quite far from the actual scenario in a CDA in which the outward sloshing is induced by a rapid vapor generation and expansion around the pool center (Figure 1ª²9). Following the above studies,the overlaying (augmenting or mitigating) effect of different hydraulic disturbances concerning the integrated value of lateral momentums for the whole sloshing system was investigated by Morita et al. (2014) at Kyushu University by injecting nitrogen gas into a narrow 2D sloshing water pool at different moments during sloshing motion£Û18£Ý. What¬ðs more,simulations under centralized moltenª²fuelª²fragment falling condition was performed by Tatewaki et al. (2015) at Kyushu University and the mitigation effect concerning the integrated value of absolute momentums for the whole sloshing system was studied£Û19£Ý.



Figure 3ª²1Research program on pool sloshing motion at SYSU£Û25£Ý


Recently,for the purpose of understanding the mechanisms of the sloshing motion triggered by a local FCI,a systematic research program on the pool sloshing motion,which includes several series of experimental,modeling and numerical studies,has been initiated at SYSU in China£Û20ª²25£Ý. Figure 3ª²1 shows the technology roadmap of this 3ª²step research program. In Step 1,the investigations were performed for understanding the mechanisms and performing modeling studies for pool sloshing motion in a pure water pool within 2D conditions. In these investigations,the effects of experimental parameters (including injected nitrogen gas pressure,initial water depth,gasª²injection duration along with the nozzle size) on the sloshing characteristics (eª±g. maximum elevation of water level at the pool center and peripheries) were analyzed£Û20£Ý.



While in Step 2,for the research program at SYSU,further 2D sloshing investigations are conducted under various complicated conditions. Due to the coª²existence of molten structure (iª±e. stainless steel) and molten fuel in the pool,it is easily speculated that a scenario of liquid stratification might be encountered for the actual moltenª²fuel pool formed in a reactor accident. Aiming to provide some insight for understanding such a scenario,a series of experimental and modeling investigations under gasª²injection condition with stratified liquids were performed and a preliminary empirical model has been established to predict the sloshing motion under both pure singleª²liquidª²phase and stratifiedª²liquidª²pool conditions£Û21£Ý. Furthermore,it was noticed that during an actual reactor accident,in light of the insufficient melting of solidª²fuel pellets and structural materials,a multiphase system,composed of a mixture of molten fuel,molten structure,solid fuel pellets,refrozen fuel,steel particles,control particles,fission gas,fuel vapor and other materials,will possibly form in the moltenª²fuel pool£Û26ª²28£Ý. As a result,during an actual reactor accident a certain volume of solid particles would likely be accumulated on the bottom of the molten pool. 
To clarify the effect of such solid particles on the sloshing motion,a series of experiments with solid particles in different scenarios (eª±g. singleª²size spherical particles,singleª²size nonª²spherical particles and mixedª²size particles) in a narrow 2D liquid pool were also conducted at SYSU. It was found that due to different mechanisms of interactions between different phases (iª±e. solid particles,liquidª²and gasª²injected),three kinds of flow regimes (namely the bubbleª²impulsionª²dominant regime,the transitional regime and the bedª²inertiaª²dominant regime) could be identified£Û22ª²24£Ý. Owing to plenty of experimental database,to predict the regime transition underlying the sloshing process,an empirical model and a regime map were proposed from experiments using singleª²size spherical particles and then were extended to improve their applicability for more complicatedª²particle conditions (iª±e. singleª²size nonª²spherical particle and mixedª²size spherical particle conditions)£Û23ª²25£Ý. Otherwise,motivated to further improve the understandings on sloshing motion,investigations under more realistic conditions (eª±g. rodª²structure condition,highª²density liquid condition) have been also planned simultaneously. Finally,in Step 3,not only the above 2D experimental results will be validated at largerª²scale 3D¬ðs,but also predictive models that may be directly applicable for reactor safety analyses will be developed and numerical simulations using CFD codes will also be performed under various conditions.


In this chapter,the past efforts on moltenª²pool sloshing motion are summarized and discussed with the aim to clarify sloshing mechanisms in the CDA of SFR more deeply and provide a systematic view of the research activities. Investigations on moltenª²pool sloshing motion in a pure liquid pool are described in Section 3ª±2. While in Section 3ª±3,investigations on moltenª²pool sloshing motion in a liquid pool with solid phase are introduced in detail. Finally,a summary of researches on sloshing motion are given in Section 3ª±4.


3ª±2Sloshing Motion in a Pure Liquid Pool


To generally understand the characteristics and mechanisms of the sloshing motion,several series of investigations in a pure liquid pool,consisting of experimental studies,modeling analyses and numerical simulations,were performed£Û3£¬11ª²21£Ý. Various conditions,including damª²break,fluidª²step,centralized moltenª²fuelª²fragment falling and gasª²injection,were considered for better simulating the sloshing motion in the postulated CDAs of SFR.

3ª±2ª±1Symmetric damª²break conditions
1. Experiments under symmetric damª²break conditions

A series of pioneering sloshing experiments was performed by Maschek et al. (1992) under symmetric damª²break condition£Û11£Ý. The basic experimental apparatus comprised two Plexiglas cylindrical containers for initiating a liquid sloshing process of converging water waves (Figure 3ª²2). 


Figure 3ª²2Schematic view of the basic apparatus for damª²break experiments£Û11£Ý


The inner diameter of the outer container (Dv) was 44 cm and different inner containers (Dc=11 cm and 19 cm) were used to produce different experimental conditions. Figure 3ª²3 illustrates the sloshing motion in a typical symmetric damª²break experiment over time. During experiments,a central water column with different heights (h=5 cm,10 cm and 20 cm) was released from the small cylindrical Plexiglas container,which was pulled upward at a velocity of 3 m/s sufficient to obtain a freestanding water column. Then,the liquid sloshed outward to the container walls (
Figure 3ª²3(b)~(e)) and sloshed inward again to pile up at the center of the large container after draining down the walls (
Figure 3ª²3(f)~(h)). The liquid motion was taken by a highª²speed camera that could provide the heights and velocities of sloshing as typical experimental results. Here,it should be noted




Figure 3ª²3Sloshing motion in a typical symmetric damª²break experiment over time (Dc=11 cm,h=20 cm)£Û11£Ý





Figure 3ª²3(Continued)


that in the damª²break experiments,the initial outward slosh and the subsequent inward slosh were both driven by gravity,while in a postulated CDA of SFR,the outward sloshing motion of the liquid pool is generally triggered by a pressure buildup in the pool center,which is different from the inward slosh£Û3£Ý. Nevertheless,some important characteristics of the sloshing motion could still be captured in these experiments.




In the experiments,the outward sloshing motion including the wave pattern at the outer cylinder wall was rather stable£Û11£Ý. However,the structure of the wave was rather complicated due to the interaction between several liquid layers. Then,the converging waves in Figure 3ª²3(f) were highly unstable and were easily disturbed. As shown in Figures 3ª²3 (g) and (h),lots of ¡°liquid fingers¡± piled up from the converging wave and a rather chaotic motion finally resulted in a water peak at the center. After collapsing of the peak,the water sloshed outward again in another cycle with smaller amplitudes. Finally,the sloshing motion was damped.


Table 3ª²1 shows the experimental results for symmetric damª²break experiments. It was found that although the velocity of the waves increased with increasing initial water height h as expected (Cases No.1~3 in Table 3ª²1),the effect was not so pronounced in the comparison to the theoretical calculation  results using the 1D shallow water approximation which obeys the assumption that the water depth of the problem should be much smaller than its length scale£Û11,29£Ý. Furthermore,with the increase of both initial water height and Dc (iª±e. the increase of water mass),the liquid level at the outer wall resulting from the outª²slosh increased and after flow reversal,the height of the central slosh also increased.


Table 3ª²1Experimental results for symmetric damª²break experiments£Û3,11£Ý



Case
No.Dc
/cmh
/cm

Sloshing at outer container wallSloshing at pool center

Arrival
time
at wall/sTime of
maximum
height/sMaximum
height/cmArrival

time at
center/s
Time of
first peak
height/sFirst peak
height/cm

11150ª±24¡À0ª±020ª±34¡À0ª±023ª±0¡À1ª±0¡ª1ª±22¡À0ª±043ª±0¡À1
211100ª±21¡À0ª±020ª±36¡À0ª±029ª±0¡À1ª±0¡ª0ª±84¡À0ª±0425ª±0¡À5
311200ª±20¡À0ª±020ª±42¡À0ª±0216ª±0¡À1ª±0~0ª±740ª±88¡À0ª±0440ª±0¡À5
419100ª±16¡À0ª±020ª±34¡À0ª±0214ª±0¡À1ª±0¡ª0ª±80¡À0ª±0440ª±0¡À6
519200ª±15¡À0ª±020ª±40¡À0ª±0222ª±0¡À1ª±0¡ª0ª±82¡À0ª±0460ª±0¡À10



2. Simulations under symmetric damª²break condition


To simulate symmetric damª²break experiments,SIMMERª²¢ò,AFDM and IVA3,three fluidª²dynamics codes,were firstly tested by Munz and Maschek et al. (1992)£Û3,12£Ý. Recently,SIMMERª²¢ô,FVP method as well as SPH were employed for the simulation of damª²break experiments by Yamano et al. (2012),Guo et al. (2010,2012),Vorobyev et al. (2012) and Jo et al. (2019) respectively£Û13ª²17£Ý. To evaluate the simulation results,the time when the liquid reached the outer container wall,the height of the maximum sloshing at the outer cylinder wall,the time of arrival of the backª²liquid wave at the center,and the maximum sloshing height at the center have been determined in experiments (Table 3ª²1)£Û3£Ý. The simulation results of all these methods are introduced below.

1)  SIMMERª²¢ò and AFDM codes


In the simulation using SIMMERª²¢ò and AFDM codes with Rª²¦Èª²Z cylindrical coordinate,Case 3 in Table 3ª²1 was chosen as a typical example and a grid with step sizes of ¦¤r=¦¤z=1 cm was used except at the location of the surface of the initial water column where ¦¤r=¦¤z=0ª±5 cm£Û3£Ý. For the AFDM code,the secondª²order option (AFD2),the firstª²order donor cell option (AFD1),and the secondª²order option on a fine mesh with ¦¤r/2 and ¦¤z/2 (AFD2F) were applied. The simulation results are shown in Table 3ª²2,while Figures 3ª²4 and 3ª²5 display the volume fraction plots of sloshing process using the SIMMERª²¢ò and AFD2. Here,it should be noted that the free surface of water was not tracked for the reason that both codes simulated sloshing as a twoª²phase flow and the frictions at the pool bottom and walls have not been taken into account£Û3£Ý. For better quantification,reassembly rates were analyzed by comparing the SIMMERª²¢ò as well as AFD2 results and Figure 3ª²6 shows the liquid mass distribution within the radius (volume) of the original water column.


Table 3ª²2Simulation results of SIMMERª²¢ò and AFDM for the typical symmetric damª²break

experiment£Û3£Ý



Code

Sloshing at outer container wallSloshing at pool center

Arrival time
at wall/sMaximum
height/cmArrival time
at center/sMaximal
height/cm

SIMMERª²¢ò0ª±189ª±00ª±6216ª±0
AFD10ª±189ª±00ª±6216ª±0
AFD20ª±1813ª±00ª±6150ª±0
AFD2F0ª±1916ª±00ª±6660ª±0


According to the comparison between the experimental and the simulation results,it could be found that the sloshing heights were underestimated while the sloshing velocities of the leading liquid fronts were overestimated if the firstª²order methods (iª±e. SIMMERª²¢ò and AFD1) were used (Tables 3ª²1 and