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Rod bundle flows are commonplace in nuclear engineering, and are present in light water reactors (LWRs) as well as other more advanced concepts. Inhomogeneities in the bundle cross section can lead to complex flow phenomena, including varying local conditions of turbulence. Despite the decades of numerical and experimental investigations regarding this topic, and the importance of elucidating the physics of the flow field, to date there are few publicly available direct numerical simulations (DNS) of the flow in multiple-pin rod bundles. Thus a multiple-pin DNS study can provide significant value toward reaching a deeper understanding of the flow physics, as well as a reference simulation for development of various reduced-resolution analysis techniques. To this end, DNS of the flow in a square 5 × 5 rod bundle at Reynolds number of 19,000 has been performed using the highly-parallel spectral element code Nek5000. The geometrical dimensions were representative of typical LWR fuel designs. The DNS was designed using microscales estimated from an advanced Reynolds-Averaged Navier-Stokes (RANS) model. Characteristics of the velocity field, Reynolds stresses, and anisotropy are presented in detail for various regions of the bundle. The turbulent kinetic energy budget is also presented and discussed.

PetscSF, the communication component of the Portable, Extensible Toolkit for Scientific Computation (PETSc), is designed to provide PETSc's communication infrastructure suitable for exascale computers that utilize GPUs and other accelerators. PetscSF provides a simple application programming interface (API) for managing common communication patterns in scientific computations by using a star-forest graph representation. PetscSF supports several implementations based on MPI and NVSHMEM, whose selection is based on the characteristics of the application or the target architecture. An efficient and portable model for network and intra-node communication is essential for implementing large-scale applications. The Message Passing Interface, which has been the de facto standard for distributed memory systems, has developed into a large complex API that does not yet provide high performance on the emerging heterogeneous CPU-GPU-based exascale systems. In this paper, we discuss the design of PetscSF, how it can overcome some difficulties of working directly with MPI on GPUs, and we demonstrate its performance, scalability, and novel features., Comment: 12 pages, 12 figures

Postprocessing and storage of large data sets represent one of the main computational bottlenecks in computational fluid dynamics. We assume that the accuracy necessary for computation is higher than needed for postprocessing. Therefore, in the current work we assess thresholds for data reduction as required by the most common data analysis tools used in the study of fluid flow phenomena, specifically wall-bounded turbulence. These thresholds are imposed a priori by the user in L2-norm, and we assess a set of parameters to identify the minimum accuracy requirements. The method considered in the present work is the discrete Legendre transform (DLT), which we evaluate in the computation of turbulence statistics, spectral analysis and resilience for cases highly-sensitive to the initial conditions. Maximum acceptable compression ratios of the original data have been found to be around 97%, depending on the application purpose. The new method outperforms downsampling, as well as the previously explored data truncation method based on discrete Chebyshev transform (DCT).

Rod bundle flows are prevalent in nuclear engineering for both light water reactors (LWR) and advanced reactor concepts. Unlike canonical channel flow, the flow in rod bundles presents some unique characteristics, notably due to the inhomogeneous cross section which can present different local conditions of turbulence as well as localized effects characteristic of external flows. Despite the ubiquity of rod-bundle flows and the decades of experimental and numerical knowledge acquired in this field, high-fidelity datasets of multiple-pin configurations are still relatively sparse due to the computational cost involved in generating them at relevant Reynolds numbers. These datasets are of great value as they allow for assessment of the reliability of various turbulence models, as well as allow for a deeper understanding of the flow physics. We present Large Eddy Simulations (LES) of the flow at Reynolds number 19,000 in a square 5 × 5 rod bundle representative of LWR fuel generated by the flow solver Nek5000. We consider standard configurations as well as configurations where the central pin is replaced with a control rod guide thimble, and analyze the flow fields in detail. The accuracy of the LES of the base 5 × 5 configuration is established by comparing against Direct Numerical Simulation (DNS) results. We compare the LES results from Nek5000 with an advanced Reynolds Stress model from STAR-CCM+, which shows good agreement in the wide gaps with larger discrepancies in the narrow gaps. In particular, evidence of gap vortex streets and changes in the turbulence structure are seen in the edge subchannels and in the narrow thimble gaps in LES, but are not predicted by STAR-CCM+.

Swirl-switching is a low-frequency oscillatory phenomenon which affects the Dean vortices in bent pipes and may cause fatigue in piping systems. Despite thirty years worth of research, the mechanism that causes these oscillations and the frequencies that characterise them remain unclear. Here we show that a three-dimensional wave-like structure is responsible for the low-frequency switching of the dominant Dean vortex. The present study, performed via direct numerical simulation, focuses on the turbulent flow through a $90^{\circ }$ pipe bend preceded and followed by straight pipe segments. A pipe with curvature 0.3 (defined as ratio between pipe radius and bend radius) is studied for a bulk Reynolds number $Re=11\,700$, corresponding to a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\approx 360$. Synthetic turbulence is generated at the inflow section and used instead of the classical recycling method in order to avoid the interference between recycling and swirl-switching frequencies. The flow field is analysed by three-dimensional proper orthogonal decomposition (POD) which for the first time allows the identification of the source of swirl-switching: a wave-like structure that originates in the pipe bend. Contrary to some previous studies, the flow in the upstream pipe does not show any direct influence on the swirl-switching modes. Our analysis further shows that a three-dimensional characterisation of the modes is crucial to understand the mechanism, and that reconstructions based on two-dimensional POD modes are incomplete.

BoomerAMG, the algebraic multigrid solver from the hypre library, is used to solve a coarse grid problem which is part of the preconditioning strategy for the pressure equation arising from the numerical resolution of the Navier–Stokes equations. A set of optimal parameters for the setup phase is determined and used for selected strong scaling tests on two different supercomputers, namely Mira and Hazel Hen, on up to 131, 072 compute cores. The results are compared to an existing algebraic multigrid solver, designed specifically for the coarse grid problem at hand. It is shown that the BoomerAMG solver is fast and scalable, and that performance depends on the computer architecture. The test cases considered are the turbulent flow past a NACA4412 airfoil and the turbulent flow inside wire-tapped pin bundles.

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use., Comment: 22 pages, 10 figures Added figures to explain the initialization strategy, fixed typos, updated abstract and modified title to make it more self explanatory

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.

When performing computational fluid dynamics (CFD) simulations of complex flows, the a priori knowledge of the flow physics and the location of the dominant flow features are usually unknown. For this reason, the development of adaptive remeshing techniques is crucial for large-scale computational problems. Some work has been made recently to provide Nek5000 with adaptive mesh refinement (AMR) capabilities in order to facilitate the generation of the grid and push forward the limit in terms of problem size and complexity [10].

The field of computational fluid dynamics (CFD) is data intensive, particularly for high-fidelity simulations. Direct and large-eddy simulations (DNS and LES), which are framed in this high-fidelity regime, require to capture a wide range of flow scales, a fact that leads to a high number of degrees of freedom. Besides the computational bottleneck, brought by the size of the problem, a slightly overlooked issue is the manipulation of the data. High amounts of disk space and also the slow speed of I/O (input/output) impose limitations on large-scale simulations. Typically the computational requirements for proper resolution of the flow structures are far higher than those of post-processing. To mitigate such shortcomings we employ a lossy data compression procedure, and track the reduction that occurs for various levels of truncation of the data set.

Large eddy simulation (LES) of an experimental benchmark investigating buoyant mixing among two fluids is developed for verification and validation. Flow physics involve a completely closed system where after a valve is opened, two initially stationary fluids with different densities are allowed to mix. The Boussinesq approximation and low-Mach equations are coded into spectral element code Nek5000 to predict the buoyancy forces, and miscibility is accounted for using the advection-diffusion equation for concentration. Due to computational costs of higher order solutions, current analysis consists of initial flow development after the valve is opened. Minor differences between the models and Schmidt number are found within the turbulent spectrum and time integrated quantities. Moreover, solutions for higher polynomial orders are compared to quantify error due to spatial discretization. Error estimates using a posteriori spectral derivation of truncation and quadrature error are also calculated. Validation with particle image velocimetry (PIV) reveals good prediction of both average and fluctuating components of the primary flow within the cold leg but less accurate results in the downcomer. It is concluded that instabilities due to resolving more of the interface using the high molecular Schmidt number is essential for accurately predicting this type of flow.

Thermal striping is of particular significance in nuclear reactor applications, primarily in sodium cooled fast reactors. The mixing chamber of the upper plenum of a nuclear reactor can be subjected to thermal striping unless designed such that the coolant is sufficiently mixed prior to reaching the top wall of the upper plenum. In order to conduct a systematic analysis of this phenomenon a simplified experimental set-up was designed and built at Argonne National Laboratory. In a parallel effort a similar simulation was conducted using the spectral-element code Nek5000. The set-up consists of two turbulent jets entering a rectangular tank via two hexagonal inlets, the interesting phenomena being the mixing within the tank. Two different inlet geometries were studied previously, both experimentally and via high-fidelity large-eddy simulations reporting various turbulent statistical quantities. To further assess the flow behavior we hereby perform a Proper Orthogonal Decomposition (POD) to identify the most dominant energetic modes and quantify their impact on the top wall of the upper plenum. The POD analysis of the experimental data in both inlet geometrical configurations is compared with LES and presented to highlight the impact of geometry on the velocity and thermal fields. We find a qualitative coherence between both simulation and experiment, characterized by a strong backflow in the weakly stable geometry, as indicated by the first mode, and the presence of three stagnation points in the strongly stable geometry setup. Also we identify a pairing of modes 1 and 3 with higher frequency than the second mode. This pairing is opposite in the two flow configurations leading to a faster decay of one of the jets in one case and a stable flow in the other.

The study of flows over spherical bluff bodies is relevant in engineering systems such as nuclear power reactors. These flows exhibit complex spatial and temporal behavior due to the presence of significant streamwise curvature that leads to boundary layer separation and reattachment, and the turbulence phenomena associated with these effects. In this study, we present results for flow over one and two spheres in free-stream conditions at Reynolds number 1,000, which corresponds to a turbulent-flow regime. The goal of the study was to verify our simulation methodology and develop an initial understanding regarding the spatial and temporal effects of additional spheres in close proximity to the canonical single-sphere case. Based on our results, we find that additional spheres significantly alter the behavior of the flow. The addition of a second sphere suppresses vortex formation, while the temporal correlation between points in the wake is also reduced.

Adaptive mesh refinement is performed in the framework of the spectral element method augmented by approaches to error estimation and control. The h-refinement technique is used for adapting the me ...

A set of accurate quadrature rules applicable to a class of integrable functions with isolated singularities is designed and analysed theoretically in one and two dimensions. These quadrature rules ...

We review a number of aspects of the transitional and turbulent flow in bent pipes, obtained at KTH using the spectral-element code Nek5000. This flow, sometimes also called Dean flow, is characterised by the appearance of Dean vortices, which arise due to the action of the centrifugal force in the bend. We start with reviewing recent stability analysis in the toroidal flow, and conclude that for all curvatures \(\delta >0\) an exponential instability is present at a bulk Reynolds number of about 4000. Further increasing the Reynolds number lets the flow go through a region with potential sub straight and sublaminar drag. An analysis using proper orthogonal decomposition (POD) reveals that wave-like motions are still present in the otherwise turbulent flow. Upon further increasing Re, the in-plane Dean vortices lead to a modulation of turbulence depending on the azimuthal position. The flow is then dominated by low-frequency so-called swirl-switching motion. This motion is studied in both a periodic and spatially developing framework. Finally, the effect of Dean vortices on Lagrangian inertial particles is studied.

Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom’s method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls.

The aim of this paper is to present a mathematical model for vertical extrapolation of the wind speed gathered from a perspective site under study. The least squares methodology is used for wind speed profile calculation. The proposed model will be applied on the sets of measured data taken at three representative heights. Because the measurements heights are significantly lower than turbine hub height the method is needed in order to obtain a synthetic set of data at a desired height. The validation of the model show that pre-processing the measurement data using this tool ensure a better estimate of the vertical wind profile compared to existing analytical models for extrapolating wind speeds to higher heights at a site.

In this work we report the results of DNSs and LESs of the turbulent flow through hexagonal ducts at friction Reynolds numbers based on centerplane wall shear and duct half-height Reτ,c ≃ 180, 360, and 550. The evolution of the Fanning friction factor f with Re is in very good agreement with experimental measurements. A significant disagreement between the DNS and previous RANS simulations was found in the prediction of the in-plane velocity, and is explained through the inability of the RANS model to properly reproduce the secondary flow present in the hexagon. The kinetic energy of the secondary flow integrated over the cross-sectional area 〈K〉yz decreases with Re in the hexagon, whereas it remains constant with Re in square ducts at comparable Reynolds numbers. Close connection between the values of Reynolds stress uw¯ on the horizontal wall close to the corner and the interaction of bursting events between the horizontal and inclined walls is found. This interaction leads to the formation of the secon...

The model parameters of photovoltaic (PV) cell depend on the environmental conditions, especially are function of the temperature and the irradiance values of the site where the panel is placed. In this paper the performances of PV cells/panels are analysed related to the different temperature and irradiance levels by using the circuit sensitivity. Therefore the model parameters of the equivalent circuits for PV cells and their typical connections are modelled by first order sensitivity relations. LabViEW and MatLab software procedures are implemented in order to prove the theoretical models, and to provide numerical examples taken from real case on PV cells.

This paper presents an original method for topological determination of network functions for linear and reciprocal multi-ports networks with a great number of nodes and edges. The algorithm has five steps in order to simplify the description of each multi-port and the multi-ports interconnection, and to reduce the network by successive procedures based on linear circuit equivalence properties. An efficient algorithm for topological determination of network functions for different input-output ports of the interconnected multi-ports networks is used.