Simulation of the mixing process in FCIs with hydrodynamic fragmentation model

Available online at www.sciencedirect.comNUCLEARScienceDirectSCIENCEANDTECHNIQUESNuclear Science and Techniques, VoL.18, No.4 (2007) 242 246Simulation of the mixing process in FCIs with hydrodynamicfragmentation modelLIN Qian CAO Xuewu(School of Nuclear Science and Engineering, Shanghai Jiaotong Untversit, Shanghai 200240, China)Abstract Fuel Coolant Interactions (FCIs) are important issues in nuclear reactor severe accident analysis. In FCIs,fragmentation model of molten droplets is a key factor to estimate degree of possiblc damage. In this paper, the mix-ing process in FCIs is studied by the simulation of MEXA experiment with hydrodynamic fragmentation model. Theresult shows that hydrodynamic fragmentacion model underestimales the fragmentation rate of high temperature mol-ten droplets under the condition of low Weber numbers. It is concluded that models bascd on thermal fragmentationmechanism should be adopted to analyze the FCI process and its consequence.Key words Severe accident, FCI, Molten fuel droplel, Fragmentation, MIXACLC number TL364+.41IntroductionIn this study, validity of the hydrodynamic frag-mentation model under the condition of low WeberFuel Coolant Interactions (FCIs), numercallynumbers is tested and evaluated through the simulationstudied in recent years, are important issues in nuclearof the MIXA 06 experiment.lol The mixing process inreactor severe accident analysis. In FCIs, the fragmen-FCIs is investigated.tation of high-temperature molten droplets contactingwith low-temperature coolant in the mixing process isDescription of experimentused to estimate degree of possible damage, and is asey factor to determine the ratio of heat transferred toMIXA are simulated experiments of the mixingpower. The development and venification of modelsstudy of FCIs, which were performed at Winfrithfor fundamental processes in FCIs request aTechnology Centre in conjunction with the CHYMESmulti-phase, multi component, and fluid-dynamicscode development and validation effor./ " The proc-computer code. Currently, bydrodynamic fragmenta-ess involves pouring kilograms of thermitically gener-tion models (such as Taylor type correlation, Pilch andated UO2 melts (81% uranium dioxide and 19% mo-Erdman's correlation, etc.)n.2] are employed for FCIslybdenum metal at 3600 K) into a near-saturated waternumerical studies. They are developed based on rela-pool of square section of 0.37m (side)x0.6 m (depth).tive velocity of droplets to coolant liquid. StudiesS.4A droplet former is employed to produce a stream ofshow that, in high Weber number cases, hydrodynamicdroplets with diameter of 6 mm, and a cylindrical skirtmechanism dominates the fragmentation process. Withis used to control the stream to a diameter of 0.12 m.In the MIXA-06 experiment, 3 kg of molten ura-low Weber numbers, however, thermnal fragmentationmechanism may dominate the fragmentation process,5nia were released. The melt droplets pour lasts for awhich is caused by vapor film collapse or surface so-total time of 1.0 s. The vessel is left open to the at-lidification of the melt droplets.中国煤花Iniadl pessureu is0.1*YHCNMHGSupported by National Natural Scieace Foundaio of China (No.50576050)E-mail: stulqgsju.du.cnReceived date: 2007-01-22No.4LIN Qian et al: Simulation of the mixing process in FCIs with hydrodynamic fragmentation model243MPa in the experiment and the water is itilly heatedmodel becomes the main factor. The surface area is ato around the saturated temperature.function of the radius of droplets and fragments, whichis related to the fragmentation of droplets, so in this3Geometry and initial conditionspaper the ftont advancement of droplet stream is indi-In this simulation, the geometry and initial condi-rectly dominated by the fragmentation mode] em-ployed in the calculation.tions are mostly consistent with the experiment parameters, but a few differences were made to optimize4.1 Base casethe computer calculation.Bascally, Tay!or correlation (hydrodynamicThe experimental vessel with square-section ismodeled as an axis-symmetric cylindrical volume withfragmentation model) is employed to model the frag-the same cross sectional area as the real vessel in amentation of the droplets. In this model, the equilib-radius of 0.21 m. The total height of calculation regionrium radius of droplets is calculated as:is 1.5 m with 0.6 m of water, and rest of the volume isWeqσr=(1)just air, left open to outside, as shown in Fig.1.2ρ.Av2where Ov is the relative velocity difference betweenAir .droplet and coolant, σ is the surface tension, Pc is the↓density of coolant and Wecr is the critical Weber num-Molten fuelUO2 3600 Kber, a dimensionless number to describe when the melt3 kg/sdroplet starts to fragmentize. The default value of crnti-Released time 1scal Weber number are fixed to 12 previously!"In calculating the Base case, the initial radius ofthe melt droplets is set to 0.003 m, radius of the drop-lets during their falling and fragmentation in water iscalculated by Eq.(1), and the minimum radius of the371Kmelt droplets is set to 0.001 m, which is corresponding0.21mto the average value estimated from experiment data.By the calculation, the front advancements of theFig.1 Geometric model.stream of melt droplets in water from the simulationFor all calculations, an initial melt droplet diand experiment are plotted in Fig.2, which shows thatameter of 6 mm is specified. The material of meltthe calculated penetration rate of the droplet stream isdroplets is simulated by 100% UO2. A stream of the●Base casemelt droplets, with a volume fraction of 0.05, flows■Expermentinto the vessel ata rate of 3 kg/s in a time interval of50 t1.0s.■Experiment4 Calculation and discussionThe calculated result mainly contains the fllingof melt droplet stream in water, namely, the front ad-Base casevancement of melt droplets stream, which is a perfect善expression of the mixing region in FCIs. The frontadvancement of the droplet stream is dominated by thedrag ceoffcient between the droplets and liquid cool-中国煤化工.0.3ant, the heat transfer coefficient and the surface area ofMHCNMHGthe droplets. Because the former two cofficients wereFig.2 Simulated front advancements of the stream of meltestimated in previous studies,8.91 the surface areadroplets in water in Base case.244NUCLEAR SCIENCE AND TECHNIQUESVol.18faster than that from the experiment. This means thatments of the stream of melt droplets in Case 2 andthe surface area of the droplets, and fragmentation rateBase case are shown in Fig.4. Although the fragmenta-of the droplets, are underestimated.tion time is very short, the front advancement does notchange t0o much in these two cases, which shows that4.2 Parametric casesthis parameter does not work in the calculation ofSeveral parametric cases were carried out basedthese cases.on the Base case to investigate the influence of the, F Base casefragmentation model on the mixing region related to，F Experiment▲Case 2the fragmentation model.50Case 1: Because size distribution of the dropletcould not be obtained from the calculation and in BaseExperimentcase the radius of the fragments was set to 0.001 m,one did not know that during the penetration whether30 ↓Base caseor not the fragment size reaches the value. Therefore,the minimum radius of the fragments was set to 0.0005m instead of 0.001 m in Case 1, and Taylor correlationwas also employed. The front advancements of theCase 2stream of melt droplets in water in Case 1 and Base10case are plotted in Fig.3, which suggests that the cal-Time1sculated penetration rates of the stream of droplets areFig.4 Simulated front advancements of the stream of meltalmost the same in both cases. The calculated resultsdropiets in water in Case 2 and Base case.suggest that during the penetration, the radius of mostCases 3 and 4: The critical Weber number wasfragments does not reach the average value of 0.001 mset to 0.12. The time constant multiplier for the Weberas estimated from the experiment. This means that thebreakup of the melt droplets was set to 1.0 and 0.001,Taylor correlation fragmentation model underestimatesrespectively, to see which parameter in the Taylor typethe fragmentation rate in the simulated experiment.correlation for the fragmentation of droplets affects the60-Base casefragmentation rate. The front advancement of thedroplets is plotted in Fig.5. It was found that when thecnitical Weber number was 12, with a short fragmenta-tion time, the front advancement of melt droplets didExpenimentnot change; but when the critical Weber number is0.12 and fragmentation time was reduced 1000 times,Base casethe penetration rate reduced greatly. These can be seen30 |in the results of Case 4.The simulated results suggest that the critical”20IWeber number and the fragmentation time may be theCase 1factors affecting the fragmentation rate in the simula-tion of the experiment. The calculation shows that in0.).20.3the experiment, the Weber number of the droplets inFig.3 Simulated front advancements of the stream of meltthe system is around or less than 12. This means thatdroplets in water in Case 1 and Base case.part of the fragmentation process of the droplets dur-Case 2: The difference between Case 2 and Base中国煤化工lence a reduction ofcase is that a time constant multiplier of 0.001 for thethCHCNMHGalts suggest that un-Weber breakup of the melt droplets was added to in-der tir wnuun M iww wwui umbers the hydrody-vestigate influence of the fragmentation time in Taylornamic fragmentation model could not describe thecorrelation on the mixing region. The front advance- fragmentation rate of the melt droplets.No.4LIN Qian et al: Simulation of the mixing process in FCls with hydrodynamic fragmentation model24560 i60,= Base caseH Base case.I F Experiment+ Experiment* Case 3A Case 55(ExperimentCase 4后4(4030e2Base case20 |10Case 5Case 30.1).20.0.4TIme/sTimel sFig.5 Simulated front advancements of the stream of meltFig.6 Simulated front advancements of the stream of meltdroplets in water in Case 3 and Case 4..droplets in water in Case 5.Case 5: This is designed to understand influencer Base caset Experimentof the current fragmentation model on the mixing re-. ACase6gion by obtaining different front advancements of thesodroplet stream induced by the current fragmentationCase 6model. Both the initial and final radii of the melt40 fdroplets were 0.003 m in the mixing region, i.e. with-out fragmentation of the droplets. The front advance-30.ments of the melt droplet stream are plotted in Fig.6. Itshows that the front advancement of the melt droplets20一in Case 5 was faster than that of the experiment and●Base case. The calculated results indicate that theTaylor correlation fragmentation model works in the00.1 .0.20.3simulation of the experiment, but the fragmentationTime/srate is underestimated.Fig.7 Simulated front advancements of the stream of meltCase 6: The fragmentation of the droplets in Casedroplets in water in Case 6.6 was modeled by setting the minimum and maximumradi of the melt droplets to 0.001 m in the mixing re-. Case 6gion. This means that the droplets entering into the, Experiment1e!“. Case7water region would be fragmented immediately into. Case 8small parts of 0.002 m in diameter. The front ad-vancements of the melt droplet stream in water in thesimulation and the experiment are plotted in Fig.7. Itshows that calculated penetration rate of the dropletstream is slower than that of the experiment and BaseCase 7case. The results indicate that the fragmentation rate ofthe droplets is overestimated by the fragmentationmodel. The real fragmentation rate of the droplets in中国煤化工the experiment is between Base case and Case 6.Cases 7 and 8: The fragmentation model of meltHCNMHGdroplets in both cases had the same minimum ancFig.8 Simulated front advancements of the stream of meltmaximum radi of melt droplets in the mixing region.droplets in water in Case 7 & Case 8.246NUCLEAR SCIENCE AND TECHNIQUESVol.18The minimum radius of droplets was set to 0.0015 mdynamic fragmentation model underestimates the sur-and 0.0007m respectively in the two cases to calculateface area of the droplets in the simulation of the ex-size effect of the fragmented droplets on the mixingperiment with low Weber numbers.region. The front advancements of melt droplets areSince the fragmentation model affects the mixingplotted in Fig.8. It shows that the front advancement isregion in FCIs and the estimation of energy conversionsensitive to minimum radius of the melt droplets.as well, a good fragmentation model is needed to theCase 9: This is designed to understand the dif-simulation codes to study the molten material interac-ference between the Pilch and Erdman's correlation 001tion with coolant.for the droplet fragmentation and the Taylor correla-Referencestion in Base case. The front advancements of thedroplet stream are plotted in Fig.9, in which no differ-l Kondo S A, Brear D J, Tobita Y, et al. Status and achieve-ence can be found between the two hydrodynamicment of asessment program for SIMMER-IHI, a multi-fragmentation models.phase, multicomponent code for LMFR safety analysis,60Proceedings of Eighth Intemaional Topical Meeting on一Base case上ExperimentNuclcar Reactor Thermal-Hydraulics, 1997, Japan.Morita K, Kondo S A, Tobita Y, et al. SIMMER-II appli-5cation to fuel-coolant interactions, Proceedings of theExperiment0ECD/CSNI Specialists Meeting on Fuel-Coolant Interac-g 40tions, 1997, Japan.Berthoud G Crecy F, Meignen R. Description of premix-ing with the MC3D Codc including molten jet behaviorCase 9modeling; Comparison with FARO Experiment results,20Proceedings of the OECD/CSNI Spccialsts Meeting onBase caseFuel- Coolant Interactions, 1997, Japan.10Corradini M L, Kim B J, Oh M D. Progress in Nuclear.3Energy, 1988, 22(1): 1-117.Time/sCronenberg A W, Grolmest M A. Nuclear Safety, 1975,Fig.9 Simulated front advancements of the stream of meltdroplets in water in Case 9.16(6): 683-700.By simulating the Base case and parametric cases,6 Denhar M K, Tyler A P. Fletcher D F. Experiments of themixing of molten uranium dioxode with water and initialwe found that the front advancement of the melt drop-comparison with CHYMES code calculations, Procecdingslet stream in experiment was underestimated by Taylortype fragmentation model. Paranetric investigationof Fifth International Topical Meeting on Nuclear ReactorThermnal-Hydraulics, 1992, USA.also shows that hydrodynamic fragmentation modelFletcher D F, Denham M K. Validation of the CHYMESunderestimate the fragmentation rate and the radius ofmixing model, Procedings OECD/CSNI Specialistsfragments. These may be related to the fact that hy-Meeting on Fuel-Coolant Interactions, 1993, USA.drodynamic fragmentation models were developedbased on relative velocity of droplets to coolant liquid.8 Meyer L QUEOS: An experimental investigation of thepremixing phase with hot spheres, Proceedings of EighthUnder low Weber numbers and high temperatures, theIntermational Topical Meeting on Nuclear Reactor Ther-relative velocity will not be the main factor.mal-Hydraulics, 1997, Japan.5 Conclusions9 Cao X W, 'Tobita Y. Jourmal of Nuclear Science and Tech-nology, 2001, 38(9): 721-728.In this paper, the hydrodynamic fragmentation中国煤化工Joumal of Muliphase,model is estimated under condition of low WeberMYHCNMHGnumbers through the simulation of the MIXA-06 ex-periments. The calculated results show that the hydro-