To enhance the thermal safety limits, the present study experimentally investigates the performance of spray cooling on a downward-facing surface. The experiments were conducted on the KTH-SPAYCOR facility. It employs four pressure-swirl full-cone nozzles arranged in a 2 x 2 array to produce a multi-spray pattern on a thin SA302B foil with a relatively large surface area of 120 mm x 80 mm. The tests were carried out under steadystate conditions, achieved through stepwise increments in surface heat flux, until the onset of dry spots or ultimate burnout was detected. Seven tests were performed to examine the effects of nozzle-to-surface distance and the flowrate, while maintaining a fixed surface inclination angle of 30 degrees. The cooling mechanism combines direct droplet impingement and flushing by water film. The experimental results demonstrated the potential applicability of the multi-nozzle array system for cooling large surface areas, such as the reactor pressure vessel lower head. Specifically, the cooling limit was observed to enhance with increasing NTSD and flowrate, reaching a peak value of 2.33 MW/m2 at a flow rate of 13 lpm. However, a slight decline in the cooling limit was noted when the flowrate exceeded this optimal flowrate. Additionally, increasing NTSD and flowrate enhanced the uniformity of the heater temperature distribution. To demonstrate the system's performance under high heat flux conditions, the ultimate critical heat flux was measured at flow rates of 10 lpm and 13 lpm, yielding values at 1.97 MW/m2 and 2.50 MW/m2, respectively.

During severe core meltdown accidents of a light water reactor (LWR), the core melt (molten corium) may fall into a water pool, resulting in molten fuel coolant interactions (FCI). Quantitative understanding of FCI phenomena is paramount to corium risk assessment of LWRs such as Nordic boiling water reactors which employ reactor cavity flooding as severe accident management strategy (SAMS). Melt jet breakup and droplet fragmentation play an important role in FCI, affecting debris coolability and steam explosion energetics which are considered in ex-vessel corium risk assessment. The present study is concerned with numerical simulation of melt jet breakup in a water pool using a multiphase computational fluid dynamics (MCFD) approach where a coupled Level Set and Volume of Fluid (CLSVOF) method is used to capture melt-coolant interfaces. The focus is placed on the prediction of interface instabilities and jet breakup length, and their influential factors (melt materials, jet diameter, fall height, in-pool structures, multiple jets and pitch/diameter ratio). The simulation results are compared with the data of the DEFOR-M tests carried out at KTH. There is a good agreement between simulation and experiment, in terms of jet deformation pattern and jet breakup length. It is also found that the jet breakup length is different from the values predicted by well-known correlations (e.g., Taylor's, Epstein Fauske's and Matsuo's). Based on the experimental and numerical data, a new correlation for the jet breakup length is developed in the similar formula of the Satio's correlation.

An experimental study on multi-nozzle spray cooling of a downward-facing heater surface has been carried out in the SPAYCOR facility at KTH, to provide data assessing the feasibility of spray cooling for in-vessel melt retention (IVR) in light water reactors. To help understand the characteristics and influential factors of the liquid film formed on the heater surface in spray, a numerical study on the dynamics of an isothermal liquid film on the heater surface has also been performed by adopting the OpenFOAM platform, and Eulerian and Lagrangian methods for liquid film and droplets, respectively. The present study is an extension of the previous modeling from hydrodynamics to thermal-hydraulics of the spray cooling problem, via adding heat flux of the heater and two convective heat transfer models between the heater wall and the liquid film. Moreover, droplets-film interaction model is modified. The SPAYCOR experiment is simulated by the numerical models, and the simulation results show a good agreement between the numerical and experimental data, in particular when the modified droplets-film interaction model is applied. After the validation of the numerical models against the SPAYCOR experiment, the numerical models are employed to investigate influential factors on heat transfer, such as mass flux, nozzle-to-surface distance, and nozzle matrix layout. The results indicate that heat transfer is enhanced by increasing mass flux and decreasing nozzle-to-surface distance, and the change of nozzle matrix from inline to staggered layout has little impact on heat removal capacity or temperature distribution of the multi-nozzle spray cooling.

In the context of severe accidents, considerable research efforts throughout the world are currently directed towards ex-vessel corium behavior. The NEA Reduction of Severe Accident Uncertainties (ROSAU) project aims to reduce knowledge gaps and uncertainties associated with two areas: the spreading of core melt in the containment cavity as well as ex-vessel core melt and debris coolability. One pre-test and five large underwater melt spread tests (MST) with molten prototypic material in a newly designed facility are conducted at the Argonne National Laboratory (ANL) in the United States, under the co-ordination with the US Nuclear Regulatory Commission. Part of KTH contributions is to provide numerical results with the developed Moving Particle Semi-implicit (MPS) method code, with specific focus on the temperature distribution and leading-edge progression. The MST-0 and MST-2, conducted in a dry and wet spreading channel, are simulated in the present study. The predicted temperature by MPS code indicates a noticeable decrease at the melt leading edge and a slow decrease in bulk melt in both simulations. Additionally, it is found that the MPS code underestimates the melt average thickness in both simulations due to the absence of a debris porosity model. Overall, the simulation results suggest that the MPS code predicts the melt leading-edge progression and immobilization for all the tests.

A new experimental study (aka SPAYCOR-S2) on multi-nozzle spray cooling of a downward-facing heater surface is conducted on the SPAYCOR facility at KTH, to provide data assessing the feasibility of spray cooling for in- vessel melt retention (IVR) in light water reactors. It is intended to investigate the potential for reducing the number of nozzles for spray cooling of an 80 mm x 120 mm surface, from the 2 x 3 nozzle array in the previous study (Bandaru, 2021) to a 2 x 2 nozzle array in the present study. Given the same heater surface, the pitch-to- diameter ratio is enlarged in a 2 x 2 nozzle array, resulting a partial coverage of the spray cones of four nozzles, in contrast with the 2 x 3 nozzle array where the heater surface was fully covered by six-nozzle spray. The tests focus on the cooling performance of such partial coverage of multi-nozzle spray and the effects of heater surface's inclination angle. The experimental results reveal that the inclination angle of the heat surface has a negligible impact on cooling capacity, although it is slightly higher on the surface inclined at 90 degrees degrees than on the surfaces inclined at 45 degrees degrees or 60 degrees. degrees . The maximum steady heat flux of the 2 x 2 nozzle array at its minimum spray flowrate is determined as 1.96 MW/m2. 2 . A numerical study on the spray cooling of the 2 x 2 nozzle array is also performed with models in OpenFOAM, which are extended from our previous development (Fang, 2023) by adding models for thin-film boiling and conjugate heat transfer in solid. For validation of the numerical study, the spray cooling of the heater surface inclined at various degrees is simulated, and the results are compared with those of experiment. The simulation generally shows good correspondence with experiments.

A numerical model to simulate molten metal relocation with phase change is proposed, coupling the level-set method to track the metal-gas interface and an enthalpy-porosity model to handle phase changes between solid and liquid metal. This coupling simultaneously solves the evolution of the metal-gas interface and liquid-solid metal. The numerical model is validated by a melting experiment involving a Sn–Bi eutectic alloy on a copper substrate, wherein the alloy's transient morphology and spreading diameter are measured. The numerical simulation effectively replicates the observed melting and spreading behaviors of the metal on the solid surface. Further validations, including a melt infiltration simulation and experiment, are consistent with findings from previous research. These simulations affirm the model's capability and efficiency in accurately representing the dynamics of melt relocation across various geometries, even within complex porous structures.

During a severe accident of light water reactors (LWR), melt penetration in a debris bed (also called infiltration) may occur due to the failure of a crust which accommodates a molten pool over the debris bed, or due to earlier re-melting of metallic components (i.e., Zr and Fe) which has lower melting points than oxidic ones (i.e., UO2 and ZrO2) of corium debris. Although understanding and modeling of melt infiltration plays a significant role in the prediction of severe accident progression, little work has been done in this respect due to its complexity. To fill this knowledge gap, the present study develops a Moving Particle Semi-implicit (MPS) code with various models representing key physics in melt infiltration. REMCOD experiment, recently carried out at KTH, has been simulated to validate the updated MPS code. The comparative results show that the melt infiltration in the tests can be reproduced by the MPS code. For a debris bed of cylindrical particles, the melt infiltration process in the experiment can be predicted by using Sauter mean diameter of the particles in the simulation. The code is also applied to investigate the influences of important parameters on the melt infiltration, and it is found that contact angle has little impact on melt penetration process in the case of debris beds with large pore sizes.

During a core meltdown severe accident (SA) of light water reactors (LWRs), melt penetration in porous media (so-called melt infiltration) may occur due to melt relocation on top of a debris bed, or after dryout and re-melting of metallic particles containing steel and Zr, and then remelting of more refractory oxidic particles containing fuel and oxidized Zr in a hot zone of a debris bed. Both in-vessel and ex-vessel phases of SA progression may involve melt infiltration. For instance, if a debris bed in the lower head of reactor pressure vessel (RPV) is uncoolable, melt infiltration occurs due to corium debris remelting and can affect RPV failure mode and place. After the lower head failure, molten corium discharges from the RPV, leading to melt spreading in the reactor cavity if the cavity floor is dry or covered by a shallow water pool. In the case of deep water pool below the RPV, remelting of uncoolable debris bed can also result in melt spreading under the water. Clearly, modeling of melt infiltration and spreading are paramount not only to the prediction of severe accident progression, but also for the analyses of corium coolability and retention. In spite of their importance, insufficient work has been done in mechanistic modeling of the phenomena.

The objective of this doctoral thesis is to provide high-fidelity predictive capabilities for melt infiltration and spreading, which can be employed to substantiate the understanding of melt infiltration in the RPV and melt spreading in the reactor cavity. The focus of the work is to develop a computational code with multi-physics models for modeling specific phenomena important to melt infiltration and melt spreading. The models and code are based on the Moving Particle Semi-implicit (MPS) method, starting from two-dimensional representation and progressing with three-dimensional simulations.

The thesis first describes the MPS method which is a mesh free method suitable for free-surface flow. The governing equations including mass, momentum and energy conservation equations are discretized with particle interaction models, such as gradient model and Laplacian model. Furthermore, models for viscosity and phase change, surface tension and wettability are implemented in the code. Additional models of multi-phase flow, crust formation, and film boiling heat transfer are added for relevant applications.

The developed MPS code is then validated against various experiments for analyses of in-vessel melt infiltration, and ex-vessel melt spreading in dry and underwater conditions. In particular, three numerical studies have been conducted to investigate the capabilities of the MPS code for prediction of melt infiltration, melt spreading under dry condition and melt spreading under water. The key points from the numerical studies are as follows.  

• The MPS code is applied to predict melt infiltration phenomena in various particulate beds employed in the REMCOD experiments carried out at KTH-NPS with corium simulant materials. The wettability model is implemented, which is characterized by the contact angle between the melt and the debris bed. The REMCOD-E09-C4 and E09-C2 tests are calculated in which melt penetrates through hot debris beds with spherical particles and cylindrical particles, respectively.  Then, the MPS code is applied to simulate the REMCOD-E08-C4 test in which the debris bed temperature is below the melting point of melt, thereby the solidification occurs. The results suggest that the melt infiltration process in the experiment with cylindrical particles can be predicted by using Sauter mean diameter. Additionally, the simulation shows a good agreement with the tests.

• The MPS code is further extended and employed for the dry spreading test. A modified crust formation model has been proposed based on rigid body assumption to keep the dynamic shape of crust, which is appropriate for the crust formed at the top surface. Two tests conducted at KTH are simulated as one-dimensional and two-dimensional spreading schemes, respectively. These simulations concentrate on hydrodynamic motion and heat transfer while ignoring the associated phenomena such as MCCI and generation of gaseous concrete decomposition products. The results illustrate the capability of the MPS code predicting melt leading-edge progression and spread thickness in dry cavity.

• The MPS code capabilities are further extended to model the specific phenomena appearing during melt spreading over substrates under a water layer, such as multiphase flow and film boiling heat transfer. A smoothing scheme is proposed to replace the real properties of interfacial particles for multiphase flow. The film boiling heat transfer is calculated along the film boiling regime of the boiling curve. For validation, the updated MPS code is then employed to simulate the S3E-2MWS-Ox-1 and PULiMS-E9 tests, which are conducted at KTH. These simulations focus on investigating the thermal-hydraulic characteristics of 1D and 2D melt underwater spreading, and they predict the leading edge progression and terminal spread thickness well.

In general, the developed MPS code offers a novel approach to predict melt infiltration in the RPV and melt spreading in the reactor cavity with high fidelity. The insight from the simulations helps the understanding of corium coolability and retention.

Vid svåra haverier med härdsmälta i lättvattenreaktorer kan smältan penetrera porösa material (infiltration av smälta) då smältan förflyttas ner ovanpå fragmenterade härdrester eller efter torrkokning och återsmältning av metalliska partiklar med stål och zirkonium eller mer eldfasta oxidpartiklar med bränsle och oxiderad zirkonium i en het region av en bädd av fragmenterade härdrester. Infiltration av smälta kan uppstå både i och utanför reaktortryckkärlet under förloppet av ett svårt haveri. Om en bädd av härdrester i reaktortryckkärlets nedre plenum exempelvis är okylbar, uppstår infiltration av smälta på grund av återsmältning av härdrester som kan inverka på reaktortryckkärlets brottmekanism och brottställe. Efter brott rinner smältan ur reaktortryckkärlet och sprids ut på golvet i utrymmet under reaktortanken om golvet är torrt eller täckt av grunt vatten. Med en djup vattennivå under reaktortanken kan återsmältning av okylbara härdrester också resultera i att smältan sprids ut under vattnet. Det är uppenbart att modellering av smältinfiltration och smältspridning är avgörande inte bara för att förutsäga svåra haveriers utveckling, utan också för analyser av härdresternas kylbarhet och kvarhållning i reaktortryckkärlet. Trots betydelsen av infiltrering och spridning är det arbete som hittills genomförts inom mekanistisk modellering av infiltrationsfenomenen otillräckligt.

Syftet med denna doktorsavhandling är att utveckla verklighetsnära prognosverktyg för smältinfiltration och -spridning, vilka kan användas för att underbygga förståelsen av smältinfiltration i reaktortanken och i utrymmet under den. Fokus för arbetet är att utveckla en beräkningskod med multifysik-modeller för modellering av specifika fenomen som är viktiga för smältinfiltration och smältspridning. Modellerna och koden är baserade på metoden eng. Moving Particle Semi-implicit (MPS), med utgångspunkt från tvådimensionell representation och vidare utveckling till tredimensionella simuleringar.

Avhandlingen beskriver först MPS-metoden som är en nätfri (eng. meshfree) metod lämplig för flöde med fri yta (eng. free-surface flow). De tillämpade ekvationerna, inklusive ekvationer för massans, rörelsemängdens och energins bevarande, diskretiseras med partikelinteraktionsmodeller, såsom gradientmodell och Laplace-operator-modell (eng. Laplacian model). Vidare är modeller för viskositet och fasförändring, ytspänning och vätbarhet implementerade i koden. Ytterligare modeller läggs till för flerfasflöde, formation av skorpa och värmeöverföring genom filmkokning för relevanta tillämpningar.

Den utvecklade MPS-koden valideras sedan mot olika experiment för analyser av smältinfiltration i reaktortanken, och i utrymmet under reaktortanken under torra och våta förhållanden. I synnerhet har tre separata numeriska studier genomförts för att undersöka MPS-kodens möjligheter för prognoser av smältinfiltration, smältspridning under torrt tillstånd och smältspridning under vatten. Huvudpunkterna från de tre numeriska studierna är följande.

• MPS-koden tillämpas för att förutsäga smältinfiltrationsfenomen i olika partikelbäddar som använts i REMCOD-experimenten utförda vid KTH-NPS med simulerade härdmaterial. Vätbarhetsmodellen, som kännetecknas av kontaktvinkeln mellan smältan och bädden av fragmenterade härdrester, är implementerad. REMCOD-E09-C4- och E09-C2-testerna beräknas där smältan tränger igenom heta fragmentbäddar med sfäriska respektive cylindriska partiklar. Sedan tillämpas MPS-koden för att simulera REMCOD-E08-C4-testet där bäddens temperatur understiger smältans smältpunkt, varigenom smältan stelnar. Resultaten tyder på att smältinfiltrationsprocessen i experimentet med cylindriska partiklar kan förutsägas genom att använda Sauterdiametern. Dessutom visar simuleringen en god överensstämmelse med testerna.

• MPS-koden utökas ytterligare och tillämpas för testet med spridning på torr yta. En modifierad modell för bildning av skorpa har föreslagits baserat på ett stelkroppsantagande för att behålla skorpans dynamiska form, vilket är lämpligt för den skorpa som bildas på den övre ytan. Två tester utförda vid KTH simuleras som endimensionella respektive tvådimensionella spridningssystem. Dessa simuleringar koncentrerar sig på hydrodynamisk rörelse och värmeöverföring samtidigt som man bortser från tillhörande fenomen som reaktioner mellan smälta och betong (MCCI) och produktion av gasformiga betongnedbrytningsprodukter. Resultaten påvisar förmågan hos MPS-koden att förutsäga smältfrontens utbredning och spridningstjocklek i ett torrt utrymme.

• MPS-kodfunktionerna utökas ytterligare för att modellera de specifika fenomen som uppstår under smältspridning över substrat under ett vattenskikt, såsom flerfasflöde och värmeöverföring vid filmkokning. En utjämningsmetod (eng. smoothing scheme) föreslås för att ersätta de verkliga egenskaperna hos partiklar i gränsytan för flerfasflöde. Värmeöverföring genom filmkokning beräknas längs kokkurvans filmkokningsregion. För validering används sedan den uppdaterade MPS-koden för att simulera testerna S3E-2MWS-Ox-1 och PULiMS-E9, som genomförts på KTH. Dessa simuleringar fokuserar på att undersöka de termohydrauliska karaktäristika hos smältspridning under vatten i 1D och 2D, och de förutsäger smältfrontens utbredning och den slutliga tjockleken hos smältan väl.

Generellt sett erbjuder den utvecklade MPS-koden ett nytt sätt att förutsäga smältinfiltration och smältspridning i reaktortryckkärlet respektive utrymmet under reaktortanken med hög tillförlitlighet. Insikten från simuleringarna bidrar till förståelsen av härdsmältans kylbarhet och kvarhållning i reaktortryckkärlet.

During postulated severe accidents in a light water reactor (LWR), the core melt (corium) may relocate to the lower head and fail the reactor pressure vessel (RPV). The corium is expected to undergo fuel coolant interactions (FCI) if the reactor cavity is flooded with water. Both FCI energetics and resulting debris bed coolability are of paramount importance to reactor safety, since the ex-vessel corium poses a threat to the containment integrity if steam explosion occurs or the debris bed is uncoolable, leading to release of radioactive fission products to the environment. The present study is intended to quantify the characteristics of a debris bed resulting from FCI, which are crucial to debris bed coolability. Different from the previous studies with only oxidic materials, various materials, including metallic ones of Sn, Sn-Bi and Zn as well as oxidic one of Bi2O3-WO3, were employed as the simulants of corium (mixture of UO2/ZrO2/Zr/Fe) in the present study to investigate the effects of melt materials, melt superheat and coolant subcooling on debris bed formation in a water pool. High-speed photography was applied to visualize melt jet breakup, droplets fragmentation, as well as fragments sedimentation on the pool floor. Other obtained data are debris bed shape (profile) and porosity, as well as morphology and size distri-bution of debris particles. The comparative results of various tests provided insights toward filling the knowledge gap on debris bed characteristics under different melt materials and compositions.

Simulation of melt underwater spreading process is important to the assessment of ex-vessel core melt (corium) risk, since such process may occur and affect corium behavior and coolability during severe accidents of a light water reactor whose cavity is flooded with water prior to the failure of the reactor pressure vessel. This study is concerned with numerical simulation of melt underwater spreading by using the Moving Particle Semi-implicit (MPS) code previously developed at KTH for melt spreading on dry substrates. The code capabilities are further extended to model the specific phenomena appearing in melt spreading over substrates under a water layer, such as multiphase flow and film boiling heat transfer. The S3E-2MWS-Ox-1 and PULiMS-E9 tests conducted at KTH for melt underwater spreading are used to validate the new code capabilities. The leading edge progression and final shape of the melt in both tests are reasonably predicted by the simulation, indicating the further developed MPS code is capable of simulating melt underwater spreading.