Liquid-metal-cooled fast reactors are under development worldwide, with the aim to contribute to an increased sustainable nuclear future. These reactors often employ wire-wrapped fuel assemblies in the core. For the safety assessment of such reactors, a reasonable prediction of the flow and temperature field in the fuel assemblies is required, both for operational as well as for accidental conditions. This is usually achieved using a combination of experimental work and various types of numerical simulations. This paper describes the collaborative work performed by European partners with respect to the effect of blockages in wire-wrapped fuel assemblies.To begin with, results for an unblocked situation are presented for experiments and simulations, showing satisfactory comparisons. After that, initial work performed on solid blockages is described. It is shown that the first simulations of such blockages showed large discrepancies with the experimental results. As a result, a number of sensitivity analyses revealed the major contributors to these discrepancies, which led to the design of a porous blockage experiment and simulation campaign, which at the same time was more representative of the postulated reactor conditions. Finally, the results of the porous blockage campaign are shown.

Direct Numerical Simulation (DNS) is performed for a pressurized thermal shock scenario in a reactor downcomer geometry. In the present work, a simplified representative geometry is adopted where cold fluid injected from a square duct is injected in a planar downcomer. A secondary hot inlet at the top of the downcomer is employed to enforce a downward flow of the injected emergency core cooling water, to mimic the effect of density driven flow. The Reynolds number of the impinging flow, based on bulk velocity and duct height, equals 12,500, while a unity Prandtl number fluid is used. The simulation is performed for two thermal boundary conditions, namely an isotemperature condition and an adiabatic condition, representing the two extreme scenarios of a conjugate heat transfer problem. The instantaneous and mean fields are first analysed in order to study the flow pattern and formation of vortical structures within the downcomer. The impinging flow is deflected radially outwards in the vicinity of the barrel wall, which then interacts with the surrounding hot fluid forming large vortical structures and bringing the cold fluid back to the vessel wall. The mixing of flow and penetration of colder temperatures in the downcomer is observed to be greatly influenced by interaction of these vortical structures. The descending cold plume in the downcomer is observed to form three branches separated by low-speed regions. The maximum values of turbulent kinetic energy are observed only in the vicinity of flow impingement, while high values of its production and dissipation are also observed within the shear layers of the descending plume. The maximum values of temperature fluctuations are found at the interface of the descending cold plume and surrounding hot fluid, while relatively high values are also seen at the locations of large vortical strucutres. Anisotropy in turbulence is also analysed using the componentality contour approach and a modified barycentric colour mapping scheme. Also reported herein is a comparison of mean and statistical profiles with those at lower Reynolds number reported in the literature. At higher Reynolds number, the cold impinging jet is deflected farther outwards in the downcomer. The locations of peak fluctuations in velocity and temperature are also farther away from the impingement. The magnitudes of fluctuating temperature and turbulent kinetic energy are observed to be higher for the present higher Reynolds number case. The peak Nusselt number at the barrel wall is observed to scale with a factor of Re1/2 in the present configuration.

Liquid metal-cooled reactors are expected to play an important role in the future nuclear energy landscape, thanks in part to their higher fuel utilization rates compared to conventional water-cooled reactors. These reactors are typically cooled using sodium or lead (alloys), which have low Prandtl numbers, making the modeling of heat transfer in these reactors challenging. The use of the Simple Gradient Diffusion Hypothesis (SGDH) for the calculation of the turbulent heat flux has become a standard computational fluid dynamics practice because of the reasonable results obtained with this approach for many fluids. However, the SGDH is known to give inaccurate results for low-Prandtl-number fluids. In order to overcome this limitation of the SGDH, an Algebraic Heat Flux Model (AHFM) was developed in recent years that can improve the accuracy of heat flux modeling in low-Prandtl-number fluids. In previous works, this model's coefficients were computed from global flow parameters such as the Reynolds number, which may not necessarily be known in advance and may even be impossible to define in transient analyses or complex flow configurations. In this work, we propose an alternative formulation of the AHFM coefficients, in which they are calculated automatically from local turbulence parameters. We validate this new formulation with direct numerical simulation results in several different forced convection flow configurations and demonstrate that it provides an improvement in the prediction of the mean temperature field compared to the SGDH. Additionally, we show that the new formulation, despite the automatization of the coefficients, performs at least as well as the original AHFM formulation for the selected cases at low Prandtl numbers.

Turbulent heat transfer is a complex phenomenon, which has become the focus of turbulence modelling research in recent years. The closure of turbulent heat flux has conventionally been approached by the so-called eddy diffusivity approach in its most trivial version, the Reynolds analogy. While this approach provides a simple and efficient closure, it lacks accuracy when the similarity hypothesis between thermal and momentum fields is less justified, i.e. in presence of low Prandtl number fluids, such as liquid metals, for which the high molecular diffusivity compared to the kinematic viscosity leads to larger thermal turbulent structures compared to the momentum ones. The thermal turbulence modelling of this kind of fluids is further challenged by the scarcity of reference data. The present paper discusses the recent advancements in the heat flux modelling approaches, including closures for local turbulent Prandtl number, algebraic models and other higher-order models with special attention to low-Prandtl cases. Although these recently developed models provide a better alternative to the conventional approach, they also suffer from limitations of their own, and their validation is still ongoing. The present paper provides a thorough review of these shortcomings, including the need for calibration, the need for a priori knowledge of flow and heat transfer regimes, isotropic nature, lack of wall-modelling, together with their applicability to industrial cases. Another major criteria to rank such models is their applicability to complex flow configurations where multiple flow regimes exist in a single flow domain. Global efforts are under way order to develop and validate a universal turbulent heat flux modelling approach. A brief account of such efforts in the international community is also presented herein. Rigorous testing and validation of such modelling approaches is required, preferably in an integral flow case over complex reactor-scale geometries, before they can be widely used by the nuclear design and development community.

The multi-year research program carried out by NRG and funded by the Dutch ministry of economic affairs and climate is called ‘Program for Innovation and cOmpetence development for NuclEar infrastructurE and Research’ (PIONEER). The program comprises seven themes, i.e. long term operation, nuclear modelling and simulation, nuclear safety and compliance, fuels & materials, radioactive waste management, radiation protection, and innovative nuclear systems. One of the pillars in the theme of innovative nuclear systems is fast reactor research, particularly in the field of thermal hydraulics. This paper provides an overview of all fast reactor thermal hydraulics activities in the program, covering development and validation of System Thermal Hydraulics (STH) and 3D (engineering as well as high-fidelity) Computational Fluid Dynamics (CFD) codes and simulation approaches. Applications range from fundamental turbulent heat transport to core, pool and system thermal hydraulics. With the recent improvements in computational infrastructure and power, also further developments of multi-scale and multi-physics computational approaches are being integrated in the PIONEER program. A generic coupling tool ‘myMuscle’ is under development which is introduced in this paper. Recent results and current developments are presented together with an outlook for the results to be expected at the end of the current multi-year program and beyond.

Direct Numerical Simulation (DNS) of fully-developed flow and heat transfer is performed for a bare rod bundle with a low pitch-to-diameter ratio using the highly-scalabale spectral element code Nek50 0 0. The simulation is performed at a Reynolds number, Reh, based on the bulk velocity and hydraulic diameter, of 9800, with iso-temperature and iso-flux thermal boundary conditions and Prandtl numbers 0.025, 1.0 and 2.0. The mean velocity and temperature statistics are first validated against the experimental mea-surements of Hooper et al. (1983) and complementary DNS results of Lai et al. (2019) which are reported in the literature at a higher Reh of 22,600. The mean flow and temperature are demonstrated a similar behaviour at the present low Renolds number and the higher Reynolds number of Lai et al. (2019), in-dicating the Reynolds number scaling of the mean flow. The anisotropy of the flow is illustrated using distribution of normal and Reynolds stresses, and the Lumley invariant map. It is shown that the turbu-lence in the subchannel region is characteristic of wall-bounded turbulent flows such as channel flows. In the narrow gap, however, turbulence is suppressed, only enhanced in the streamwise direction due to flow pulsations. Further, temperature statistics with both thermal boundary conditions are presented, demonstrating the effect of the Prandtl number on the mean and fluctuating quantities. The temperature statistics with iso-temperature wall boundary conditions, not reported in literature before, are shown to behave differently in the interstitial subchannel region and the narrow gap between two rods. The distri-bution of turbulent heat flux is also presented. The streamwise component of turbulent heat flux is again shown to be enhanced, in comparison to the same in the subchannel. The pulsating motion of flow across the narrow gap is discussed further. A frequency analysis of the velocity in the narrow gap elucidates the frequency of flow pulsations. Unlike mean flow statistics, the flow pulsations are shown to exhibit a low Reynolds number effect. The reference DNS data presented in the present work, complementary to that of Lai et al. (2019), serves as a benchmark against which lower order turbulence models may be further developed or improved. In particular, the newly presented anisotropy data and the turbulence heat flux data are essential for further development, improvement and validation of turbulent heat transfer models at different Prandtl numbers.(c) 2023 Elsevier Ltd. All rights reserved.

With the increase in computational power, High Fidelity (HiFi) simulations become increasingly important to nuclear thermal hydraulics for fundamental understanding of turbulent flow and heat transfer phenomena and for further development and validation of engineering CFD models. We consider Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES) as HiFi analyses. In this paper, we present an overview of single-phase and two-phase flow DNS simulations relevant for nuclear reactor safety and design purposes. In order to limit the scope, this overview has a focus on DNS simulations of fully turbulent non-reacting incompressible flows. LES approaches are briefly mentioned in certain areas, where LES-to-DNS upgrade is expected to happen in the near future. We first explain the concept of DNS and related concepts like Under-resolved DNS (UDNS) and quasi-DNS (q-DNS). Subsequently, we present the numerical methods which are generally used for HiFi simulations. A wider span of numerical methods can be observed in single-phase flow simulations than in two-phase flow simulations, where the later require additional algorithms for tracking of the interfaces between the two phases. Consequently, two-phase DNS simulations are not immune to modelling errors, and are much more complex than their single-phase counterparts. Next, an overview is given of single-phase flow DNS simulations. We start with basic cases like turbulent channel and pipe flows, which are mainly useful for development and validation of less detailed engineering CFD models. We continue with more recent and more complex cases like, e.g., flows in a rod bundle and a pebble bed, which are directly applicable in nuclear engineering. Next, an overview of two-phase flow HiFi simulations is presented in a similar fashion. The importance of the availability of the presented HiFi simulations is explained by addressing their role for further development and validation of engineering CFD models which are used for the eventual industrial applications. The importance of HiFi simulation data, complementary to experimental data, for uncertainty quantification and machine learning is explained. Finally, future challenges for HiFi simulations, especially for two-phase flow, are elucidated.

Several investigations have been undertaken to study the velocity and temperature fields associated with the thermal mixing between fluids, and resulting thermal striping in a T-junction. However, the available experimental databases are not sufficient to describe the involved physics in adequate detail, and, due to experimental limitations, accurate data on velocity and temperature fluctuations in regions close to the wall are not available. Computational Fluid Dynamics (CFD) can play an important role in predicting such complex flow features. However, predicting complex thermal fatigue phenomena is a challenge for the available momentum and heat flux turbulence models. Furthermore, such models need to be extensively validated. The aim of the present work is to design a reference numerical experiment for Direct Numerical Simulation (DNS) of a thermal fatigue scenario using Reynolds-Averaged Navier-Stokes (RANS) simulations. First, the feasibility of scaling down the Reynolds number from experimental cases to a computationally-feasible range is investigated. The junction corner shape is also modified to a slightly rounded corner, ensuring that the underlying fundamental physical phenomena of turbulence and thermal mixing flow features are preserved. Finally, the pipe lengths of the model were calibrated to ensure there would be no interference of the upstream developing region and the outlet boundary conditions on the thermal mixing at the junction. A sample under-resolved DNS case, with unity and low-Prandtl number passive temperature scalars, with iso-temperature, iso-flux and mixed (Robin) wall boundary conditions, are presented. This proof-of-concept simulation contributes to the finalization of the set-up for fully-resolved DNS with respect to the computational grid size selection and transient characteristics.

Two-phase flows may occur in many regimes, ranging from dispersed flow, slug or plug flow to stratified flow. To capture all those regimes with a monolithic approach, a so-called all-regime two-phase model should be developed. This paper presents such an all-regime two-phase modeling approach called Four-Field Large Interface Simulation (FF-LIS), in which we consistently consider two phases (gas and liquid) which can both be either resolved or sub-grid, resulting in four fields. The efficacy of this approach hinges on the accuracy with which the inter-scale mass, momentum and energy transfer terms between dispersed and resolved regimes are captured. In this paper, we introduce three phenomenological mechanisms to control the inter-scale transfer: absorption, break-up and coalescence. The separation of multiphase scales allows for the explicit modeling of transfer between them, whereas other methods often rely on an algebraic regime map in which transfer between scales is accounted for implicitly. We apply FF-LIS to the simulation of both bubbly and fully resolved single bubble flow, as a way of validating FF-LIS in those two two-phase limits. Next, the transfer terms are illustrated by simulation of bubbles rising in a column. As the bubble concentration increases, it is shown that a transfer from sub-grid to resolved occurs. Finally, we apply FF-LIS to the simulation of two-phase horizontal pipe flow in which the several flow regimes, depending on the superficial velocities, are recovered, and to the simulation of a plunging jet in which FF-LIS is shown to produce an entrained bubble plume. FF-LIS presents a computational platform for faithful two-phase resolved and sub-grid simulation of relevant real-world two-phase problems, and allows two-phase modelers for the explicit control on what can be resolved, and what should be sub-grid.

Hybrid multiphase flows are flows with both dispersed phase and large scale structures, and generally have a wide range of interfacial length scales. Such flows are common in industrial flow problems and nuclear engineering applications. Appropriate modelling of these scales, ranging from the dispersed to the segregated flow regime, becomes important as they all contribute to the overall behaviour of the flow physics. Conventional two-fluid, two-field Eulerian-Eulerian solvers have been known to neglect important aspects of flow physics and are unable to reproduce such hybrid flows. A systematic benchmark of a hybrid solver named Hybrid Dispresed-Large Interface Solver (HD-LIS) is presented here. A flow regime map based on the gas volume fraction is utilised in the present solver in order to distinguish between dispersed and segregated flow regimes and for application of the appropriate physical models and numerical schemes in each regime. The modelling of segregated regime includes an appropriate drag force, interface compression scheme, and turbulence damping, while modelling of the dispersed regime considers both drag and non-drag momentum exchange forces. In addition, the use of total variation diminishing (TVD) numerical schemes and semi-implicit temporal discretization approach ensures boundedness and robustness of the solver. The present benchmark includes a wide spectrum of test cases, selected to test the ability of the solver in fundamental modelling of dispersed phase or large scale interfaces These validation cases include single bubble and droplet dynamics, flow regimes transition (between dispersed and plug flows), free-surface impact jet, and two phase shear flows. It is shown that the present solver is able to qualitatively reproduce both dispersed and segregated flow physics well. As will be demonstrated, HD-LIS differs from other existing Eulerian-Eulerian two-fluid solvers which are reported in literature in respect to the applied numerical schemes and physical models. This selection of schemes and models is shown to make the solver suitable for modelling of underlying flow physics exhibited by dispersed flows and large-scale interfaces. Although the validation cases presented herein offer limited flow complexity, the present solver is considered a step towards a more comprehensive hybrid solver.

One of the main issues in the context of the safety assessment of liquid metal-cooled reactors is flow blockages in fuel sub-assemblies. CFD modelling may be used to predict the temperature and velocity fields inside a fuel assembly under blocked and unblocked conditions. However, the computational cost requirements make it infeasible to model the complete assembly using the resolved RANS, LES or DNS approaches. To this end, a reduced-resolution RANS approach of an assembly is presented and validated in this paper. In order to reproduce and compare with experimental data, the 19-pin hexagonal fuel assembly of the NACIE-UP facility at ENEA in Italy has been selected for the present simulation study. For the flow blockage, a 6-pin edge-type blockage is selected similar to that used in the experimental facility. During the pre-test simulation study, wall-resolved RANS simulations are performed for the unblocked flow conditions. Using the wall-resolved RANS simulations as reference, a mesh sensitivity is performed by subsequently reducing the wall and bulk resolutions. As the blocked flow condition requires transient simulations, the resolution study is only performed for the unblocked flow condition to reduce the computational effort. It is shown that the approach may be used to reproduce the temperature and velocity fields similar to that in wall-resolved simulations within tolerance limits, but at a fraction of the computational cost. Experimental data for unblocked and blocked flow conditions has been made available for the Blocked Fuel Pin Simulator (BFPS) section at the NACIE-UP facility. These experimental data are used to validate the reduced-resolution approach in the post-test analysis. The difference between the present results and the experimental data is attributed for and quantified. Consistent with the literature, two main effects of flow blockages are identified. A local temperature hotspot is observed in the wake of the blockage caused by the coolant recirculation zone. The global effect of temperature peak is observed at the end of the active length downstream of the blockage, caused by the lower mass flow rates in the blocked sub-channels. For the unblocked flow condition, the maximum difference compared to the experimental data is estimated to be 11%. While the error in prediction of the local temperature hotspot and peak temperature at the end of active length is estimated to be 25% and 12%, respectively, for the partially-blocked flow condition. Finally, based on the 19-pin model, the feasibility of the reduced-resolution approach for the complete 127-pin assembly of ALFRED demo reactor is demonstrated. In addition to the unblocked flow condition, the approach is also used for blocked grid spacer conditions. Consistent with the results of NACIE bundle, the two main effects - local and global - of the flow blockage are also observed here. The local effect of temperature hotspot behind the blockage is observed to be dominant for the larger blockage, while the global effect of peak temperature downstream of the blockage is observed to be proportional to the size of the flow blockage.

Most fuel assemblies in a liquid metal fast reactors (LMFRs) are surrounded by wrapper tubes, usually arranged in a hexagonal arrangement. The heat transfer across these wrapper walls between sub-assemblies, due to the inter-wrapper flow (IWF), can play a vital role in reducing peak cladding temperatures during flow blockage or flow reduction scenarios, particularly during the passive heat decay removal. This is specific to each LMFR design. CFD analyses of different flow and power conditions may provide essential understanding of the physics and efficacy of heat removal due to IWF. However, the partially-or fully-blocked fuel assemblies lead to highly transient nature of the flow, which can dramatically increase the computational requirements of the simulations making it infeasible to compute using well resolved CFD approaches. In this context, a reduced-resolution RANS model of the influence of IWF is validated in this paper. The three 7-pin hexagonal bundles of the KALLA facility at KIT in Germany are used to model the IWF experimentally. In the computational model, three adjacent bundles along with the inter-wrapper region between them are modelled, where the pins in each bundle are spaced using wire wraps. Wall-resolved RANS simulations are first performed as reference simulations. As the modelling of natural convection is more sensitive to mesh resolution, only this case is used for the resolution sensitivity study. In order to further reduce the computational effort of the sensitivity study, only one wire-pitch length of the inter-wrapper region with two adjacent bundles is used. The resolution is reduced separately in the bundle, the inter-wrapper region and the solid structures, to better understand the effect of mesh resolution. It is demonstrated that the reduced-resolution approach may be used to predict the temperatures in the inter-wrapper region fairly well. After the reduced-resolution approach is optimised for the natural convection case, the approach is validated against experimental data of the KALLA facility. Experimental cases representing different flow blockages have been reproduced using reduced resolution RANS for the purpose of validation. Both qualitative and quantitative comparison and analyses are presented in terms of temperature field. The difference between the model and the experimental data is attributed for and quantified. It is noted that the temperature fields in the bundle and inter-wrapper region are predicted fairly well by the present computational model. However, the local heat flux to the inter-wrapper region is under-predicted by roughly 15-18%, while the total power transported by the IWF is under-predicted by about 6-11% for the present cases. The present model is observed to over-predict the maximum temperature hot-spot in the bundle by roughly 18-33%. It is demonstrated that this gross over-prediction is due to the absence of modelling of conjugate heat transfer in the rods and wires. If the solid wires and pin claddings are modelled, this over-prediction is reduced to roughly 12%. It is shown that a reduced-resolution scheme substantially reduces the computational costs, with a minor difference in prediction of heat transfer in comparison to a wall-resolved mesh.

Knowledge of the heat transport in the core is important for design and safety assessment of all nuclear reactors including liquid metal cooled reactors. In the past, design and safety calculations with respect heat transport in the core for such liquid metal cooled reactors were largely one-dimensional and based on experimental data. Nowadays, with modern state-of-the-art computer power and tools, three-dimensional Computational Fluid Dynamics (CFD) simulations allow designers and safety specialists to obtain much more detailed information on the heat transport in liquid metal cooled fuel assemblies, obviously supported by necessary experimental campaigns. This may lead to new insights possibly decreasing the safety margins. To this respect, an overview will be provided on the necessary activities in the frame of design and safety support using CFD for liquid metal reactors accompanied and illustrated by examples from NRG in the Netherlands. These examples include validation efforts for fuel assemblies as they are designed on the drawing board for 'cold' conditions. However, in reality, even under normal operational condition, a fuel assembly may deform. Therefore, an assessment of the effect of deformations resulting from operational conditions is necessary and will be shown. Another aspect possibly occurring during operational conditions is vibration. State-of-the-art coupled CFD and finite element method fluid structure interaction techniques have been developed and applied to a wire wrapped fuel assembly, providing insights in the vibration behavior of such assemblies. However, design and safety analysts will not only have to cope with operational conditions, but also have to show the heat transport behavior under accident conditions. For this, an assessment of the effect of internal and inlet blockages will be presented.

The two-fluid Euler-Euler model can be used for the description of co-existing stratified and dispersed multiphase flow within one flow domain. For realistic engineering applications, turbulence is often modeled in the Reynolds-averaged Navier-Stokes (RANS) framework where closure of the Reynolds stresses is mostly achieved using the turbulent viscosity formulation. It is a well-known problem that at large-scale interfaces between two phases such turbulence modeling breaks down as turbulent viscosity in the vicinity of an interface is over-predicted. To address this issue, we adopt the Egorov approach (Egorov et al., 2014) which locally damps turbulence near the interface. This model is based upon the idea that at a large-scale interface the lighter phase may see the heavier phase much like a solid wall, suggesting a wall-like treatment of turbulent dissipation at the interface. The implementation of the model inside a two-phase formulation of the k-epsilon model is discussed, and shown to give good predictions of interfacial turbulence in co-current stratified two-phase flow. The Egorov approach is extended to the k-epsilon model, which may be relevant for a large array of engineering applications in which the k-epsilon model is more effective than the k-epsilon model. It is shown that the non-dimensional Egorov approach coefficient is grid dependent. We introduce a new formulation of the interfacial damping term in the two-fluid Euler-Euler model which gives more consistent results for different computational grids in comparison to the original formulation of the Egorov approach. This feature, as well as its straightforward implementation in both the k-epsilon and k-epsilon models, make the new model useful to a large array of multiphase engineering problems in which interfacial turbulence damping is relevant.

Large-eddy simulations of turbulent channel flow subjected to a step-like acceleration have been performed to investigate the effect of high Reynolds number ratios on the transient behaviour of turbulence. It is shown that the response of the flow exhibits the same fundamental characteristics described in He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102 and vol. 764, 2015, pp. 395–427)—a three-stage response resembling that of the bypass transition of boundary layer flows. The features of transition are seen to become more striking as the Re-ratio increases—the elongated streaks become stronger and longer, and the initial turbulent spot sites at the onset of transition become increasingly sparse. The critical Reynolds number of transition and the transition period Reynolds number for those cases are shown to deviate from the trends of He & Seddighi (2015). The high Re-ratio cases show double peaks in the transient response of streamwise fluctuation profiles shortly after the onset of transition. Conditionally-averaged turbulent statistics based on a λ_2-criterion are used to show that the two peaks in the fluctuation profiles are due to separate contributions of the active and inactive regions of turbulence generation. The peak closer to the wall is attributed to the generation of “new” turbulence in the active region, whereas the peak farther away from the wall is attributed to the elongated streaks in the inactive region. In the low Re-ratio cases, the peaks of these two regions are close to each other during the entire transient, resulting in a single peak in the domain-averaged profile.

In this paper, we report a combined experimental and LES study of transient flow in a rectangular channel accelerating from an initial turbulent flow following the opening of the control valve. We show that this transient flow undergoes a process of laminar-turbulent transition even though the initial flow is turbulent. This is consistent with the findings from the numerical studies of idealised flow transients (He & Seddighi 2013, 2015 and Seddighi et al 2014). The transient flow is characterised by a time developing laminar-like boundary layer, which later becomes unstable and breaks up into turbulence. This process is similar to the bypass transition of spatially developing boundary layer.