In a severe accident of light water reactors (LWRs), the molten core materials (corium) may relocate to the lower plenum of the reactor pressure vessel (RPV) and consequently impose significant thermal and mechanical loadings on the lower head of RPV. To mitigate the risk of RPV failure due to the corium attack, the external surface of the RPV lower head can be cooled by water through an in-vessel melt retention (IVMR) strategy. In the conventional IVMR design of pressurized water reactors (PWRs), the external cooling of RPV is realized by flooding the reactor cavity and forming natural circulation boiling across the lower head.  The cooling capacity is bounded by the critical heat flux (CHF) of natural circulation boiling. To overcome limitation of the conventional IVMR measure, an alternative IVMR measure was proposed in this work, which implements an efficient water spray system to cool the external surface of the lower head. 

The study of this doctoral thesis is oriented to examine the feasibility of spray cooling in the alternative IVMR strategy. For this purpose, an extensive investigation on spray cooling of a downward-facing heater surface was accomplished in this thesis, including both experimental and numerical studies on the cooling performance and influential factors that affect performance of multiple spray nozzles. The numerical models with high-fidelity predictive capabilities for multi-nozzle spray cooling of the downward-facing heater surface were validated against the experimental data. The key points of the research and the results are as follows. 

·       In experimental studies, heat transfer characteristics of water spray of an array of 2×2 spray nozzles over a relatively large heater surface were investigated. The effects of surface inclination, nozzle-to-surface distance and flowrate on spray heat transfer were investigated for the first time on the downward-facing heater surface. The heater was made of a 150 μm thick SA302B steel foil with a surface of 120 mm ´ 80 mm. Joule heating was applied by connecting the specimen to the electrodes of a DC power supply of low voltage and high current. Four full-cone pressure-swirl spray nozzles were used in the experiment. The test matrix includes the following variations of parameters: six surface inclinations (between 15 deg and 90 deg), four coolant flowrates, and three nozzle-to-surface distances. The experimental results indicated an efficient cooling potential of the multi-nozzle water spray over the downward-facing heater surface, with a maximum heat removal up to 2.50 MW/m2. The cooling performance was enhanced by increasing flowrate, but the enhancement by flowrate was diminishing after an intermediate flowrate. The surface inclination had a negligible impact on the cooling performance.

·       In numerical studies, simulation models to predict the spray cooling process were developed by adopting a coupled Eulerian-Lagrangian methodology implemented in the open-source CFD code package OpenFOAM. Prior to simulation of experiments, a validation of the models was conducted against analytical solutions of relevant hydrodynamic problems, and the results confirmed the predictive accuracy in liquid film dynamics and spray impingement on inclined surfaces. The predicted liquid film morphology had a good agreement with the experimental observation under adiabatic conditions. 

·       The numerical models were further extended to the modeling of heat transfer, thin film boiling and conjugate heat transfer in the spray cooling problem. The simulation results of full- and partial-coverage of the heater surface by respective 6- and 4-nozzle array showed reasonable agreements with experimental data across various surface inclinations. The validation exercises demonstrated the capability of the numerical approach to model complex multiphase heat transfer phenomena encountered in the spray cooling.

This work did not only improve our understanding of multi-nozzle spray cooling mechanisms over a downward-facing heater surface, but also provided basic experimental data and numerical approach for further assessment of spray cooling application to the IVMR strategy in nuclear reactor safety.

Under svåra haverier av lättvattenreaktorer (LWR) leder till omlokaliseringen av smält kärnbränsle (corium) till reaktortankens nedre plenum till betydande termisk och mekanisk belastning på tanken. För att minska risken för reaktortankhaveri på grund av termisk degradering i konventionella konstruktioner av avancerade tryckvattenreaktorer (PWR) för kvarhållning i reaktortryckkärlet (IVMR) genom översvämning av utrymmet under reaktortanken. Kylkapaciteten begränsas av det kritiska värmeflödet (CHF) av den naturliga cirkulationskokningen. För att öka säkerhetsmarginalerna utöver konventionella metoder föreslår denna doktorsavhandling införandet av ett effektivt sprutkylningssystem som en alternativ metod för kylning av reaktortankens nedre plenum. Genomförandet av sprutbaserad IVMR konceptualiseras genom en undersökning av sprutkylningsmekanismer med varierande lutningar.

Det primära syftet med denna doktorsavhandling är att genomföra experimentella undersökningar av prestandan hos ett sprutkylningssystem och dess  faktorer som påverkar IVMR-strategier. Numeriska modeller med hög precision har utvecklats för att modellera sprutkylning med flera munstycken på en nedåtvänd yta har utvecklats. Studien fokuserar på följande huvudpunkter:

I den experimentella delen undersöktes värmetransportförmpågan hos en 2×2-munstyckegitter (fyra fullkoniska tryckvirvelsprutmunstycken) som påverkade en stor värmeyta riktat nedåt. Effekterna av sex lutningarna (mellan 15 deg–90 deg), avstånd mellan munstycke och yta samt flödeshastighet analyserades för första gången inom IVR-ERVC-applikationer. Testerna utfördes på SA302B med en tjocklek på 150 μm och en yta på 120 mm ´ 80 mm, uppvärmd med Joule-effekten med högström och lågspännings likström. Resultaten visade en maximal kylkapacitet på cirka 2,50 MW/m², med tydlig påverkan av flödeshastighet med optimal prestanda vid medelflöden, medan lutningen hade försumbar effekt.·        En kopplad Euler-Lagrange-metodik implementerades i OpenFOAM för att simulera sprutkylningsprocessen. Modellerna validerades mot teoretiska fall med analytiska lösningar, vilket bekräftade noggrannheten i att uppskatta vätskefilmdynamik vid både sprutpåverkan och lutande ytor innan experimenten simulerades. Den simulerade filmmorfologin hade god överensstämmelse med  experimentella observationer under adiabatiska förhållanden.

·        Modellerna utökades med värmetransport, filmskokning och konjugerad värmetransport i fasta material. Simuleringar av fullständig (6-munstycken) och partiell (4-munstycken) täckning av ytan visade stark korrelation med datan från experimenten över olika lutningar, vilket validerade förmågan att hantera komplexflerfasvärmetransport av sprutkylning.

Denna studie främjar förståelsen av sprutkylningsmekanismer för IVMR-applikationer genom att tillhandahålla empiriska och beräkningsmässiga bevis på flersprutssystemens lämplighet för att hantera extrema termiska belastningar. De validerade modellerna erbjuder ett robust verktyg för framtida säkerhetsanalyser av kärnreaktorer.

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.

The melt infiltration in porous debris is of importance to severe accident prediction and mitigation in nuclear power plants (NPPs), but its mechanism remains elusive. In this study, a computational fluid dynamics (CFD) model is proposed to simulate the evolution of melt infiltration within porous media, incorporating both solidification and melting processes. The CFD model is validated against the experiment (REMCOD facility) and Moving Particle Semi-implicit (MPS) simulation results. Building upon this validated model, the influence of the melt superheat, the initial particle temperature, and its surface wettability on melt infiltration dynamics are mainly analyzed. It is found that increased initial melt superheat enhances melt infiltration length and rate; higher initial particle temperatures promote deeper and faster infiltration, while lower temperatures may result in solidification that blocks further infiltration. Additionally, the wettable particulate bed can enhance melt relocation and heat transfer, but it also accelerates the solidification of the melt, which complicates the infiltration process. Furthermore, phase changes could intensify melt flow instability. This work may expand our understanding of melt infiltration dynamics and pave the way to severe accident modeling in NPPs. 

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.

Motivated by the interest in steam explosion in chemical solutions and seawater, a series of tests were carried out in the MISTEE facility at KTH to investigate steam explosion characteristics as multiple molten droplets of tin were falling through a coolant pool containing deionized water, boric acid solution, neutral solution of boric acid and sodium phosphate, and seawater, separately. The experimental results revealed distinct and complex characteristics of steam explosion of multiple droplets, which were not observed in previous single-droplet steam explosion experiments. The tin melt samples of 5 g and 20 g were employed to formulate different numbers of multiple droplets. In the test with 5 g melt, steam explosion was more energetic at a deeper explosion location − a similar trend found in the single-droplet steam explosion test with 1 g melt. However, the test of 20 g melt did not show a clear trend in a wide range of explosion depth. The peak pressure and impulse increased with increasing mass of melt sample. The steam explosion occurred more closely to the coolant pool surfaces in the seawater and chemical solutions than in deionized water. Steam explosion intensity was significantly reduced in a neutral solution containing 1.2 wt.% boric acid and sodium phosphate. The influence of the chemical solutions on steam explosion was diminishing in the tests with multiple droplets.

The steam explosion plays an essential role in the safety analysis of light water reactors (LWRs). Some studies have demonstrated that the occurrence of steam explosions is dependent on many factors such as melt and coolant temperatures, melt and coolant properties, non -condensable gases, etc. After the Fukushima accident, seawater as an emergency coolant and its impact on fuel coolant interactions are receiving attention. However, there is still little knowledge on the impact of seawater on steam explosion. The present study is intended to examine the effect of coolant salinity on steam explosion through a series of tests with single molten droplet falling in different coolant pools (DI water, and seawater at different salinities from 7.7 g/kg to 35 g/kg). The experimental results reveal that the salinity of coolant significantly influences the probability of spontaneous steam explosion of molten tin droplets. The probability of steam explosion generally increases with increasing salinity from 0 to 17.5 g/kg. The molten droplet in seawater experiences more pronounced deformation at same depth before the vapor film of the droplet collapses. What's more, the peak pressure generated by steam explosion in seawater is notably higher than that in DI water. The fragmentation of molten tin droplet after the explosion is enhanced accordingly.

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.