Fluid flows through rod bundles are observed in many nuclear applications, such as in the core of Gen IV liquid metal fast breeder nuclear reactors (LMFBR). One of the main features of this configuration is the appearance of flow fluctuations in the rod gaps due to the velocity difference in the sub-channels between the rods. On one side, these pulsations are beneficial as they enhance the heat exchange between the rods and the fluid. On the other side, the fluid pulsations might induce vibrations of the flexible fuel rods, a mechanism generally referred to as Flow Induced Vibrations (FIV). Over time, this might result in mechanical fatigue of the rods and rod fretting, which eventually can compromise their structural integrity. Within the SESAME framework, a joint work between Delft University of Technology (TU Delft), Ghent University (UGent), and NRG has been carried out with the aim of performing experimental measurements of FIV in a 7-rods bundle and validate numerical simulations against the obtained experimental data. The experiments performed by TU Delft consisted of a gravity-driven flow through a 7-rods, hexagonal bundle with a pitch-to-diameter ratio P/D=1.11. A section of 200 mm of the central rod was made out of silicone, of which 100 mm were flexible. Flow measurements have been carried out with Laser Doppler Anemometry (LDA) whereas a high-speed camera has measured the vibrations induced on the silicone rod. The numerical simulations made use of the Unsteady Reynolds-averaged Navier-Stokes equations (URANS) approach for the turbulence modelling, and of strongly coupled algorithms for the solution of the fluid-structure interaction (FSI) problems. The measured frequency of the flow pulsations, as well as the mean rod displacement and vibration frequency, have been used to carry out the benchmark.

In this work, Fluid-Structure Interaction (FSI) simulations are performed to study Flow Induced Vibrations (FIV) of nuclear fuel rods using the commercial code STAR-CCM+. The Navier-Stokes equations are solved on deforming grids with the Arbitrary Eulerian-Lagrangian (ALE) formulation. The finite element method is used to solve the linear elastic problem for the structure. The two solvers are tightly coupled together with the Gauss-Seidel method to solve the FSI problem. The first part of the work focuses on the FIV of a single rod. Two types of rods are considered: 1) a bare rod and 2) a rod with a wire spacer helically wrapped around its external surface. For the case of the bare rod configuration, the effects of the working fluid on the dynamics is investigated and a correlation for the frequencies as function of density is proposed. The second part of the work focuses on the analysis of FIV for two different configurations of bare seven-rod bundle. One of the main features of the considered configurations is the appearance of axial flow fluctuations in the rod gaps due to the velocity difference in the sub-channels between the rods. Therefore, this part of the work focuses on the study of the effect of the velocity pulsations on the vibrations of the rods.

In this work, the effects of different working fluids on the dynamics of vibrating rods in fluid flows is investigated by means of Fluid–Structure Interaction (FSI) simulations. Different fluids with a wide range of density and viscosity are considered. For each of these fluids, FSI simulations are performed to extract the modal parameters of the system. The turbulent fluid flow is modeled by means of the URANS (Unsteady Reynolds-averaged Navier–Stokes) approach, whereas the rod is modeled as an elastic solid. The two-way coupling FSI solver implemented in the commercial code STAR-CCM+ is used to perform the numerical simulations. The computed modal parameters are first used to evaluate the added mass and the added damping of the rod for the different fluid flows. Subsequently, a correlation that predicts the variation of the added mass and added damping with the fluid density and fluid viscosity is proposed. It is found that the added mass varies linearly with the fluid density and is independent of the fluid viscosity. The added mass coefficient for the system considered in this work is close to the unitary value. The added damping is a non-linear function of both fluid density and viscosity. Finally, a Rayleigh damping model to include added damping effects in a structural solver is proposed. The proposed correlation predicts very well the added mass effects. The added damping effects are also predicted reasonably well, especially for lower values of fluid density and viscosity.

In this work, an advanced solver for the simulation of Fluid-Structure Interaction (FSI) problems for nuclear applications is presented. The numerical framework, called as NRG-FSIFOAM, uses a Finite Volume (FV) fluid solver and a Finite Element (FE) structural solver coupled together with a partitioned approach. State-of-the-art implicit coupling algorithms are used in order to increase the accuracy and the stability of the solver for low solid-to-fluid density ratio, i.e. strongly coupled, FSI problems. Furthermore, the solver offers significant advantages with respect to traditional approaches for the solution of turbulent flows because it is equipped with an advanced algorithm to predict pressure fluctuations without the necessity to perform high fidelity simulations. This approach, called as Pressure Fluctuation Model (PFM), uses a stochastic model to generate velocity fluctuations that satisfy the mean turbulent quantities: the corresponding fluctuating pressure field is computed from the Poisson's equation. The pressure fluctuation field complements the mean pressure field computed with URANS models and it is then used as a part of the external forcing for the structural problem. This solver is first tested against benchmark FSI problems with laminar flows. Subsequently, it is used to simulate flow induced vibrations of cylindrical fuel rods in turbulent water and liquid metal flows and to simulate the vibrations of a cantilever beam in turbulent water flow. (C) 2019 Elsevier Ltd. All rights reserved.

In this study, fluid–structure interaction (FSI) simulations of a single cylindrical rod in axial turbulent flows of water and liquid metal are performed. Two types of rods are considered: (1) a bare rod and (2) a rod with a wire spacer helically wrapped around its external surface. The effects of the working fluid and of the rod type are analyzed for the configuration selected in this work. Considering the effect of the wire spacer, it is found that the dynamics of the displacement of the wire-wrapped rod is very different from that of the bare rod due to the asymmetry in the flow field introduced by the wire spacer. Moreover, the wire spacer has a small effect on the value of the natural frequencies, while larger effects are observed on the value of the damping ratio with the liquid metal fluid. The effect of the wire spacer is then investigated in more detail. To this purpose, dynamic simulations of rod configurations with different values of pitch length are performed. It is found that for an integer rod-to-wire-pitch-length-ratio higher damping ratios are observed, whereas the frequencies are less sensitive to the pitch length. As next step, static FSI analyses are performed to study the effect of different wire spacer configurations on the static deformation of the rods. It is found that the distribution of the forces on the rod follows closely the geometry of the wire spacer wrapped around the rod due to the modification of the flow field produced by the presence of the wire. By means of static simulations, the effect of the rod constraints, working fluids and mesh resolutions are also investigated. Finally, the effect of using different numbers of wire pitches with the same pitch length is investigated.

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.

Large-scale computations play an important role in many engineering and scientific applications. In the nuclear field, in particular, the crucial need for accurate simulations and reliable reference data for validation purposes makes high-fidelity simulations an extremely important tool. Due to the too-large computational resources required, these simulations must be performed on dedicated computational facilities. This paper focuses on the description of the high-performance computing facility at the wierk Computing Centre (CI) in Poland. More specifically, the hardware configuration, software used for on-demand deployment of dedicated subclusters, and queuing systems are described. The computational capabilities at the CI are assessed by performing scalability tests with the massive parallel code NEK5000. The tests assess the influence of the CPU architecture, cooling infrastructure, and interconnection performance on the solver running times. Subsequently, selected applications are presented. These applications concern the direct numerical simulations of mixed convection and fluid flow in a rod bundle. The mean velocity and temperature, the root mean square of the velocity components, and the novel results related to the budgets of turbulent kinetic energy as well the budgets of the wall-normal and streamwise turbulent heat flux are reported for different Prandtl numbers for the mixed convection case. For the rod bundle case an instantaneous temperature for the isothermal and isoflux boundary conditions is reported. Moreover, the frequency of the velocity pulsation has been computed.

In this article, the calibration of a sharp corner T-junction configuration is performed in order to design a direct numerical simulation (DNS) which will provide detailed information about the entire flow and the thermal field. This DNS will represent a valuable resource for the validation and the improvement of different turbulence modelling approaches. The T-junction configuration from the MOTHER project is selected as a starting point. The calibration study is performed by means of several RANS computations to achieve an optimized T-junction which is feasible for a DNS. For the DNS problem, different thermal boundary conditions are tested. In particular, the use of Robin boundary is investigated as alternative to the solution of the expensive conjugate heat transfer problem. These thermal boundary conditions are implemented in the spectral element code NEK5000, and then tested for the DNS of a turbulent channel flow.

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid–Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs – also known as immersed boundary methods – the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid–structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid–structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available.

In this paper, various aspects relevant for nuclear applications of bare rod bundles in axial turbulent flows are studied by means of numerical simulations. The work first investigates the fluid dynamics properties of the flow field in the narrow gaps between the rigid rods and then it focuses on the study of the dynamics of the vibrations of the flexible rods. A two-rod assembly is examined first; the system consists of two identical rods in turbulent axial water flows with a small pith-to-diameter ratio and a large wall-to-diameter ratio. In the case of rigid rods, it is found that the flow field is characterized by the presence of strong axial flow pulsations in the gap between the rods with a characteristic frequency close to that observed in previous experimental works at a similar Reynolds number. Subsequently, strongly coupled numerical fluid-structure interaction (FSI) simulations are performed in order to study the flow induced vibration (FIV) of the rods. It is found that a buckling of the rods occurs because the fluid in the gaps pushes the rods apart which then undergo sustained vibrations because of the velocity fluctuations. Furthermore, due to the hydrodynamic coupling, the vibrations of the rods are not independent from each other but the system vibrates as a whole, as confirmed by the spectral analysis which shows the existence of a pair of frequencies around each of the natural frequencies of the structure in vacuo. A seven-rod assembly with the same pitch-to-diameter ratio of the two-rod case is then studied. Numerical simulations reveal the presence of strong flow pulsations in the gaps, although the frequency of the pulsations is slightly lower that than observed in the two-rod case. In the numerical FSI simulations, a very complicated rod-to-rod interaction is observed with the appearance of large vibrations and buckling deformation.

In this paper, the turbulent mixed convection in a channel flow with differentially heated walls is considered for a fixed Richardson number (Ri(b) = 0.5) and three different Prandtl numbers (Pr = 1, 0.1 and 0.01). Numerical simulations are conducted assuming constant fluid properties and the effect of the buoyancy is taken into account by means of the Boussinesq approximation. Direct Numerical Simulations (DNS) are performed first and the effect of the buoyancy on the first and second order statistics of the fluid and thermal fields is highlighted. Furthermore, it is found that in mixed convection the Prandtl number has a much larger effect on the results than in the case of forced convection. The obtained DNS results are then used as a validation database for two different RANS turbulent heat flux models, i.e. the classical Reynolds analogy and a recently proposed three-equation algebraic heat flux models called AHFM-NRG+. It is observed that, as expected, the Reynolds analogy fails to predict the thermal field even for unitary Prandtl numbers fluids. On the other hand, it is shown that the AHFM-NRG+ is in a reasonable agreement with the reference DNS over the entire range of Prandtl numbers considered in the study. (C) 2018 Elsevier Ltd. All rights reserved.

(Flow induced vibration (FIV) plays an important role in many industrial applications, including nuclear energy. In a nuclear power plant, several components could experience FIV. However, among them, fuel rods are critical because of the combined effects of very slender shapes of the rods and hydrodynamic loads induced by the turbulent flow of the surrounding coolant fluid. In this article, a numerical study of a nuclear fuel rod system is performed using a combined computational fluid dynamics (CFD) and computational structural mechanic (CSM) approach. The selected rod system is representative of an experimental set-up consisting of a single and multiple fuel rods exhibiting strongly coupled non-linear behaviors. As a first step, an operational procedure is proposed to construct a numerical model of the rod to be used in the Fluid-structure interaction (FSI) simulations. The material properties of the model are tuned to match the experimental natural frequencies measured in free air. Despite the structural complexities present in the experiments, the natural frequencies of the rod are correctly reproduced, which is an essential step for the subsequent FIV analysis. Subsequently, the FSI computations are performed and the numerical results are processed to extract the modal parameters of the system in axial turbulent flow regime. Both, one and two rod systems are extensively studied for different flow velocities. The obtained results agree with the measurements and the theory. (C) 2017 Elsevier B.V. All rights reserved.

A computational approach is presented for evaluating shape sensitivities using an innovative embedded boundary method for computational fluid dynamics that mitigates the well-known difficulties associated with meshing, mesh updating and/or re-meshing. It is based on the analytical derivation of relevant semi-discrete gradients of the underlying comprehensive flow solver and associated computational geometry support. The proposed approach is integrated in a gradient-based optimization procedure and exploited to perform aerodynamic shape optimization of complex rigid and aeroelastic configurations. It demonstrates the potential of embedded boundary methods for the multi-disciplinary shape optimization of complex aerodynamic systems, and highlights their practical advantages in terms of flexibility, robustness, and performance.

Recently, there has been a renewed interest in non-boundary-conforming methods for Computational Fluid Dynamics (CFD), also known as Embedded Boundary Methods (EBMs) (for example, see [1, 2, 3]), particularly for flow problems involving complex geometries and FluidStructure Interaction (FSI). Indeed, EBMs are attractive because for CFD applications, they operate on fixed grids that do not have to align with the body surfaces and therefore are simpler to generate, in principle [4]. For FSI problems, EBMs offer an alternative to Arbitrary Lagrangian Eulerian methods that is far more robust with respect to large displacements and rotations, large deformations, and topological changes induced by cracks and other structural changes [5, 6]. However, operating on non body-fitted grids has its own difficulties. Chief among them is the accurate treatment of wall boundary and fluid-structure transmission conditions, which is typically performed on surrogates of the embedded discrete fluid-structure interfaces or some reshaped counterparts of these interfaces. Consequently, many EBMs tend to be at best first-order space-accurate at embedded discrete fluid-structure interfaces, and some are even inconsistent there [7]. For viscous flows, EBMs also tend to suffer from sensitivities with respect to the position and orientation of the embedded discrete interfaces relative to the embedding CFD mesh [8]. Originally developed for the solution of multiphase flow problems [9], the Finite Volume method with Exact two-phase Riemann solvers (FIVER) was transformed in [10, 11] into a genuine EBM for CFD and FSI problems. Its underlying approach constitutes a departure from the traditional EBMs in that it treats the velocity and pressure boundary conditions on the embedded discrete interfaces simultaneously rather than disjointly, enforces the appropriate value of the fluid velocity at a wall and recovers the corresponding value of the pressure at this wall via the exact solution of local, 1D, fluid-structure Riemann problems instead of relying for this purpose exclusively on interpolation or extrapolation, and in that it is applicable not only to Cartesian or structured grids, but also to unstructured meshes. However, the original FIVER method shares the same issues faced by traditional EBMs when it comes to the smoothness of some components of the solution near the embedded discrete interfaces, and to sensitivities with respect to the position and orientation of the embedded discrete interfaces relative to the embedding mesh. In particular, both the first[10] and second-order accurate [12] implementations of the original FIVER method are not able to compute smooth values of the skin friction coefficient on embedded discrete surfaces, when the embedding mesh is not aligned with the outlines of these surfaces, although they are capable of predicting integral quantities such as lift and drag coefficients with a high level of accuracy [13, 14]. Hence, the main objectives of this talk are two-fold. First, to present a novel formulation of FIVER that enhances the accuracy of its original version near embedded discrete surfaces for high Reynolds number turbulent flows, enables its coupling with a wall function model to reduce the grid discretization requirements for such applications, removes its sensitivities to the position and orientation of the embedded discrete surfaces relative to the embedding CFD mesh,

Linear and non-linear Residual Distribution schemes for the discretization of the RANS equations are presented. Non-linear schemes are particularly suited for the discretization of transonic flows due to their capacity to give a monotone approximation of discontinuous solutions without the necessity to add artificial viscosity. A non-linear LU-SGS solver is considered to construct a robust implicit solver for the discretization of two and three-dimensional problems.

This paper deals with the construction of a class of high-order accurateresidual distribution schemes for advection-diffusion problems using conformal meshes.The problems considered range from pure diffusion to pure advection. The approximationof the solution is obtained using standard Lagrangian finite elements andthe total residual of the problem is constructed taking into account both theadvective and the diffusive terms in order to discretize with the same schemeboth parts of the governing equation. To cope with the fact that the normalcomponent of the gradient of the numerical solution is discontinuous acrossthe faces of the elements, the gradient of the numerical solution is reconstructedat each degree of freedom of the grid and then interpolated with the same shapefunctions used for the solution. Linear and nonlinear schemes are constructedand their accuracy is tested with the discretization of advection-diffusionand anisotropic diffusion problems.

A robust and high order accurate Residual Distribution (RD) scheme for the discretization of the steady Navier–Stokes equations is presented. The proposed method is very flexible: it is formulated for unstructured grids, regardless the shape of the elements and the number of spatial dimensions. A continuous approximation of the solution is adopted and standard Lagrangian shape functions are used to construct the discrete space, as in Finite Element methods. The traditional technique for designing RD schemes is adopted: evaluate, for any element, a total residual, split it into nodal residuals sent to the degrees of freedom of the element, solve the non-linear system that has been assembled and then iterate up to convergence. The main issue addressed by the paper is that the technique relies in depth on the continuity of the normal flux across the element boundaries: this is no longer true since the gradient of the state solution appears in the flux, hence continuity is lost when using standard finite element approximations. Naive solution methods lead to very poor accuracy. To cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements, a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution, preserving the optimal accuracy of the method. Linear and non-linear schemes are constructed, and their accuracy is tested with the method of the manufactured solutions. The numerical method is also used for the discretization of smooth and shocked laminar flows in two and three spatial dimensions.

This paper deals with a high-order accurate Residual Distribution scheme for the numerical solution of dense gas flows on unstructured grids. Dense gas-dynamics studies the flow of gases in the thermodynamic region above the upper saturation curve, close to the liquid–vapor critical point. In such conditions, some fluids may exhibit negative values of the fundamental derivative of gas-dynamics, leading to non-classical gas-dynamic behaviors, such as rarefaction shock waves, mixed shock/fan waves, and shock splitting. Due to the complexity in performing reliable experimental studies for non-classical gas-dynamics, accurate numerical simulations of dense gas flows are of paramount importance. In this work, advantages in using high-order methods are highlighted, in terms of number of degrees of freedom and computational time used, for computing the numerical solution with a greater accuracy compared to lower-order methods, even for shocked flows. Several numerical experiments are also performed to assess the influence of the thermodynamic models on the problem solution.