In engineering systems operating under high Schmidt (Sc) or Prandtl (Pr) number flow conditions, the demand for near-wall mesh refinement increases significantly, underscoring the need for cost-effective modeling approaches that avoid additional computational overhead. Existing models, which are predominantly designed for low-Sc flows, overlook temporal filtering effects, resulting in inaccuracies in theoretical description and mass transfer predictions. This paper addresses the impact of high Sc or Pr by refining the single-layer scalar diffusivity model. It introduces a switch between scalar filtering and eddy viscosity-dominated regions, leveraging two parameters: κ Sc, accounting for temporal filtering effects, and κ Re, addressing variations in Reynolds number. In addition, we adopted a complementary outer layer term to model the upwarding trend in low frictional Reynolds number condition. Using the two-layer model with unity Sc and/or Pr, a close agreement with the von-Kármán constant in the velocity boundary layer was observed. The modified model demonstrated strong agreement with scalar profiles across a broad range of Sc and friction Reynolds numbers (Reτ) in direct numerical simulation and large eddy simulation data, demonstrating its accuracy at low Reτ and predictive performance at high Reτ. The two-layer model improves the prediction of turbulent mass transfer, providing better alignment with high Sc engineering correlations than existing wall model approach. This study provides valuable insight for modeling the mass and heat transfer processes under high Sc or Pr conditions.

This study investigates near-wall diffusive flux modeling for passive scalar transport in turbulent flows with high Schmidt (Sc) or Prandtl (Pr) numbers. Under these conditions, the diffusion boundary layer becomes significantly thinner than the velocity boundary layer. Capturing the concentration boundary layer presents challenges due to additional scaling in the viscous-diffusive regime. For DNS, mesh resolution requirements to capture passive scalar behavior near the wall are more stringent than those for Kolmogorov scales in pure hydrodynamics investigations. Consequently, wall-resolved approaches in both RANS and WMLES demand excessive wall refinement, limiting their practicality for high Reynolds numbers and industrial applications. In this work, we focus on turbulent flow without an adverse pressure gradient. Existing wall models fail to provide accurate estimates of wall diffusive flux for passive scalar transport at high Sc. This failure arises from the breakdown of the assumption of eddy diffusivity asymptotic behavior. Using such models for simulating surface processes (e.g., flow-accelerated corrosion) in RANS and WMLES can lead to non-negligible errors. Our study introduces a two-layer scalar diffusivity model to enhance wall modeling capabilities in passive scalar transport at high Sc or Pr numbers.

Flow-accelerated corrosion and erosion (FACE) phenomena can be crucial for performance of structural elements in heavy liquid metal (HLM) cooled reactor systems. Existing experimental observations indicate that turbulent flow characteristic can affect FACE, but there is no quantitative data that can be used for model development and validation. Main recirculation pump impellers, which operate at high relative velocities and rotational flow conditions can be especially vulnerable to FACE. For comparison, the core internals operate at lower velocities and in axial flow conditions, but at higher temperatures and neutron fluence. Hence, systematic experimental data is needed to improve our knowledge on FACE phenomena. The Separate Effect Test Facility for Flow-Accelerated Corrosion and Erosion (SEFACE) is designed to obtain such experimental data including high relative velocities (up 20 ms−1) and high temperatures (400 to 550 °C) of liquid lead. This article focuses on the hydrodynamic design of SEFACE. The aim of the design is to achieve well defined flow conditions for experiments and ensure safe operation of the facility. First, we examine three design concepts (i.e., forced convection loop, rotating cylinder, and rotating disk) and motivate the choice of the rotating disk approach for SEFACE. Second, we discuss different design options, i.e., a confined rotor–stator test chamber and the unconfined rotating disk configuration. We used Reynolds-Averaged Navier Stokes (RANS) calculations to identify and solve the issues stemming from the high rotational speed. These include, for instance, lead free surface deformation, radial pressure buildup, and axial bending forces due to asymmetric test chamber. The CFD-derived torque and power predictions in rotor–stator and rotating disk systems are verified with selected empirical turbulent friction factor correlations or/and DNS calculations. We demonstrate that the developed hydrodynamic design of SEFACE solves identified issues and enables obtaining experimental data under well-defined flow conditions. The findings are deemed to also be applicable to the design of rotating disk-type FACE installations for other liquid mediums.

Long-term material compatibility in heavy liquid metal (HLM) remains a challenge for the successful deployment of HLM-based technologies. Flow-accelerated corrosion and erosion (FACE) phenomena can lead to continual material deterioration, which needs to be considered throughout the reactor design stage. Nonetheless, known experimental data are inadequate to cover all the prototypical flow regimes during LFR's operation. Modelling of the FAC/FACE phenomena remains mostly in lumped parameter/subchannel scales, where the FAC model is coupled to the bulk flow of the pipe or subchannel. These methodologies might produce a sufficient prediction for the core internals; however, this might not be suitable for the pump impeller due to comparatively greater relative velocity and the occurrence of transient flow patterns near the rotating impeller. To establish an understanding of the connection between turbulence and FACE, the liquid lead-based Separate Effect Flow Accelerated Corrosion and Erosion (SEFACE) facility is currently under design at KTH in the framework of the Sustainable Nuclear Energy Research In Sweden (SUNRISE) project. SEFACE attempts to investigate FACE phenomena in the liquid lead and produce quantifiable validation data for model development. The paper divides itself into two parts. Part I refers to the study of operational conditions in SEFACE via Reynolds Averaged Navier Stokes (RANS) simulation, while Part II deals with the recent attempt on modelling time-dependent flow shear on rotating disks based on large eddy simulation (LES). The paper begins with a brief review of prior studies on flow-accelerated corrosion. Following that, the SEFACE facility's design concept is laid out considering several physical and operational constraints. A periodic wedge of the SEFACE test chamber is chosen to examine the facility's time-averaged behaviour. The k-ω shear stress transport (SST) model was employed for the simulations. The torque prediction on the rotating disk system is verified with the empirical frictional factor prediction. The latest hydrodynamic design enables SEFACE to be spun at 1200 revolutions per minute (corresponding to a maximum velocity of 21 m/s) without causing free surface deformation or excessive pressure. SEFACE permits the collecting of experimental data under the effect of various relative velocities in a single experiment round. The second part of the paper focuses on a recent attempt to determine the wall shear stress distribution on a rotating disk using wall-modelled large eddy simulation (WMLES S-Omega). The obtained amplitude and frequency of wall shear stress fluctuations will aid model development in future.

Monte Carlo criticality calculations of large, loosely-coupled problems are long known to suffer from slow convergence of the tally errors due to cycle-to-cycle fission source correlations. In several recent studies, it was suggested that these correlations could be possibly attributed to the neutron clustering phenomenon that is visible in calculations with a small number of neutrons per iteration cycle (batch size). Nevertheless, other studies have also shown the error convergence rate in such loosely-coupled problems to be batch size-independent during active criticality cycles. Here, we aim to address this inconsistency by studying the error convergence in a large number of test calculations, varying the neutron batch size from small to large. In our tests, we have observed that the presence of visible neutron clusters does not increase the cycle-to-cycle fission source correlations and does not worsen the convergence rate of the tally errors.

This paper describes the design, implementation and characterisation of an Autonomous Reactivity Control (ARC) system in a small modular lead-cooled fast reactor. The aim of this work was to demonstrate the applicability of the ARC system and to study its dynamic behaviour during an anticipated transient without scram. A simplified one-dimensional model was developed to calculate the heat transfer within the ARC system, and the reactivity worth as a function of the neutron poison’s insertion into the active core was obtained via static neutronic calculations. By coupling the aforementioned models, the ARC’s time-dependent reactivity was derived as a function of the coolant outlet temperature variation. This model was implemented into the BELLA multi-point dynamics code and transient simulations were run. A control rod ejection accident was studied leading to an unprotected transient overpower scenario, in which 350 pcm reactivity was inserted during one second. It was shown that the ARC system provides a forceful negative reactivity feedback and that steady-state temperatures after the transient were reduced by almost 300 K compared to an identical transient without its action. In this scenario, the ARC system managed to stabilise the coolant outlet temperature at a value 100 K above nominal conditions. The implementation of an ARC system provided the reactor with a passively actuated self-regulating reactivity control system able to insert large amounts of negative reactivity in a short amount of time.

This thesis presents a compilation of work focused on Monte Carlo crit-icality, kinetics and burnup calculations in reactor physics. Performing suchcalculations usually comes at a high computing cost. Therefore, the main mo-tivation behind the presented work is lowering the computing cost of MonteCarlo calculations. To this end, three new methods for improving the comput-ing efficiency are proposed: a method for neutron population control in MonteCarlo criticality calculations; a hybrid stochastic-deterministic response ma-trix method for reactor kinetics calculations; and an optimisation method forMonte Carlo burnup calculations.

The first method gradually increases the neutron population size over thesuccessive cycles in Monte Carlo criticality calculations. This enables fasterfission source iterations at the beginning of a calculation where the sourcemay contain errors from the initial cycle while at the same time preventingthe source bias from dominating the error later in the calculation. The methodis tested on a set of full-core PWR criticality calculations.

The second method is based on the response matrix formalism which de-scribes a system by a set of response functions. The response functions arecomputed during Monte Carlo criticality calculations. These functions arethen used in a deterministic set of equations for solving a space-time depen-dent problem. The method is demonstrated on a set of absorber movementtransients in a PWR-type mini-core.

The third method sets the time step length and the number of neutronhistories simulated during each time step of Monte Carlo burnup calculationsaccording to the fraction of the computing cost assigned to the depletion solu-tions (and other procedures that are repeatedly executed before starting theactive cycles) and the overall computing cost of a Monte Carlo burnup calcu-lation. Optimal values of this fraction are studied in a set of test calculations.

Additionally, numerical tests on tally error convergence in Monte Carlocriticality calculations and stability of Monte Carlo burnup calculations arepresented. The context and the outcomes of the work are summarized inthe main body of the thesis while the details are presented in the appendedpublications.

Denna avhandling presenterar en sammanställning av arbete fokuseratpå Monte Carlo-kriticitets, kinetik och utbränningsberäkningar inom reak-torfysik. Att utföra sådana beräkningar innebär vanligtvis en hög datorkost-nad. Därför är den främsta motivationen bakom det presenterade arbetet attsänka beräkningskostnaden för Monte Carlo-beräkningar. För detta ändamålföreslås tre nya metoder för att förbättra beräkningseffektiviteten: en me-tod för neutronpopulationskontroll i Monte Carlo-kriticitetsberäkningar; enstokastisk-deterministisk responsmatrismetod för reaktorkinetikberäkningar;och en optimeringsmetod för Monte Carlo-utbränningsberäkningar.

Den första metoden ökar gradvis neutronpopulationens storlek över de påvarandra följande cyklerna i Monte Carlo-kriticitetsberäkningar. Detta möj-liggör en snabbare iteration av klyvningskällan i början av en beräkning därkällan kan innehålla fel från den inledande cykeln samtidigt som källförskjut-ningen förhindras från att dominera felet senare i beräkningen. Metoden testaspå en uppsättning helhärdskriticitesberäkningar i en PWR.

Den andra metoden är baserad på responsmatrisformalismen som beskri-ver ett system med en uppsättning responsfunktioner. Responsfunktionernaberäknas vid Monte Carlo-kriticitetsberäkningar. Dessa funktioner användssedan i en deterministisk uppsättning ekvationer för att lösa ett rum- ochtidsberoende problem. Metoden demonstreras på en uppsättning styrstavs-transienter i en minihärd av PWR-typ.

Den tredje metoden anger tidsstegslängden och antalet neutronhistori-er som simuleras under varje tidssteg i Monte Carlo-utbränningsberäkningarenligt andelen av beräkningskostnaden som tilldelas utbränningslösningarna(och andra procedurer som utförs upprepade gånger innan de aktiva cyklernastartas) och den totala beräkningskostnaden för en Monte Carlo-utbrännings-beräkning. Optimala värden för denna andel studeras i en uppsättning test-beräkningar.

Dessutom presenteras numeriska tester för felkonvergens i Monte Carlo-kriticitetsberäkningar och stabiliteten för Monte Carlo-utbränningsberäkningar.Kontexten och resultaten av arbetet sammanfattas i avhandlingens huvuddelmedan detaljerna presenteras i de bifogade publikationerna.

Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.

Passive safety systems in a nuclear reactor allow to simplify the overall plant design, beside improving economics and reliability, which are considered to be among the salient goals of advanced Generation IV reactors. This work focuses on investigating the application of a self-actuated, gravity-driven shutdown system in a small lead-cooled fast reactor and its dynamic response to an initiating event. The reactor thermal-hydraulics and neutronics assessment were performed in advance. According to a first-order approximation approach, the passive insertion of shutdown assembly was assumed to be influenced primarily by three forces: gravitational, buoyancy and fluid drag. A system of kinematic equations were formulated a priori and a MATLAB program was developed to determine the dynamics of the assembly. Identifying the delicate nature of the balance of forces, sensitivity analysis for coolant channel velocities and assembly foot densities yielded an optimal system model that resulted in successful passive shutdown. Transient safety studies, using the multi-point dynamics code BELLA, showed that the gravity-driven system acts remarkably well, even when accounting for a brief delay in self-actuation. Ultimately the reactor is brought to a sub-critical state while respecting technological constraints.

Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.