Particle Image Velocimetry measurements of the liquid velocity fields in the flow over the backward-facing step were performed in the same flow configuration as in the existing Direct Numerical Simulation (DNS). The experiment and the simulation were performed in an identical cross-section geometry with step expansion rate 2.25 and the square shape of the outlet duct at the Reynolds number in an inlet part of the section 7100. The experiment was performed in transparent test section, 1.2 m long, with 20 × 45 mm2 cross-section upstream and 45 × 45 mm2 downstream, while a domain that was three times shorter was used in the DNS. A 2D-2C PIV system with a single high-speed camera and a pulse laser was used for a series of two-dimensional measurements of the velocity field at several cross-sections from two different perspectives. Variables analyzed in the experiment are time-averaged fluid velocities, velocity RMS fluctuations and two components of the Reynolds stress tensor. The key novelty is the comparison of two very accurate approaches, PIV and DNS, in the same cross-section geometry. Comparison of the similarities, and especially the differences between the two approaches, elucidates uncertainties of both studies and answers the question on what kind of agreement is expected when two very accurate approaches are compared.

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

The backward facing step geometry (BFS) is a representative geometry for sudden expansions in pipe, duct and channel flows. While this type of geometry by itself is not a part of engineering components, the flow separation and the accompanying flow features present in a BFS are of great importance when designing manifolds, heat exchangers or fuel bundles. In the frame of EU Horizon 2020 project SESAME, an extensive effort has been put forward to gain more insights into the flow and thermal features in a BFS geometry for low-Prandtl number fluids. The main motivation behind this effort is two-fold: to generate a reference database by means of experiments and high fidelity simulations, and accordingly utilize the reference database to validate and/or improve the turbulence models in engineering applications. In this paper, we present a broad description of the experimental facility and its expected capabilities, as well as the results of numerical efforts. The experimental results will be obtained in the DITEFA 2 facility of KIT with a GaInSn eutectic alloy. The expansion ratio of the BFS in the experiment is set to 2 and the geometry has one heated wall. Unlike the vast majority of the BFS experiments found in the literature, the present BFS experiment has an outflow in a shape of a square, that is, the width and height of the outflow are approximately the same. Second, a direct numerical simulation (DNS) is performed with a passive scalar and for an expansion ratio of 2.25. Similar to the experiment, the shape of the outflow is a square and the average flow is three-dimensional. Conjugate heat transfer DNS is performed for the heated solid walls, while the unheated walls were neglected. Finally, this reference DNS data is used to validate a LES and an advanced RANS modelling approach.

Turbulent heat transfer is an extremely complex phe nomenon that has challenged turbulence modellers over various decades. In the recent past, several attempts have been made for the assessment and further development/calibration of t he available turbulent heat flux modelling approaches. One of the main hampering factors with respect to the further assessment of these modelling approaches is the lack of reference data, i.e. experimental or numerical via the use of Direct Numerical Simulations (DNS). Within the fram ework of the EU SESAME and MYRTE projects, an extensive and collaborative effort has been put forward to generate a wide range of reference data, both experimental and numerical, to fill this gap. In parallel, this data has been used to validate and/or improve the classical and s ophi ticated turbulent heat flux modelling approaches. This article reports the experimental and DNS datab ase that has been generated within these projects for various low-Prandtl flow configuration s in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with low-Prandtl fluids, and a forced convection planar jet case with two differen t Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wall-bounded mixed convection flow at low-Prandtl number with varying Richardson number ( Ri) values; a wall-bounded mixed convection flow in a bare rod bundle configuration f r two different Reynolds numbers; a forced convection in a confined backward facing step (BFS) for two different Prandtl fluids; a forced convection impinging jet for three different Prandt l fluids corresponding to two different Reynolds numbers of the fully developed planar turb ulent jet; a mixed-convection cold-hot-cold The 18 International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-18) Log Number: 000 Portland, Oregon, USA, August 18 22, 2019 triple jet configuration corresponding to Ri=0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection i nfinite wire-wrapped fuel assembly. This wide range of reference data is used to evalua te, v lidate and/or further develop different turbulent heat flux modelling approaches, namely si mple gradient diffusion hypothesis based on constant and variable turbulent Prandtl number; exp licit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastl y, this article will highlight the current challenges and perspectives of the available turbul ence models, in different codes, for the accurate prediction of flow and heat transfer in lo w-Prandtl fluids.

In this paper, we present the profiles, together with statistical uncertainties of turbulent heat flux, obtained in the recently performed Direct Numerical Simulation (DNS) of flow of two liquid metals over a confined backward facing step. This work is a continuation of work that was performed within the European project SESAME. The presented profiles are obtained in the whole domain, while the uncertainty is analysed in 49 pre chosen points throughout the domain. The analysis is performed over at most 10 million time step or equivalently of around 5000 dimensionless time units. The turbulent heat flux is important for development of new turbulence models with less accurate methods for simulating flow properties, such as RANS methods, based on averaged Navier-Stokes equations. The DNS was performed with the Nek5000 code. The most notable feature of this code is the use of spectral elements to solve for velocity, temperature and any other passive scalar. It is an open source code developed by the Argonne National Laboratory. Two Prandtl fluids were simulated (Pr = 0.005 and Pr = 0.1), although due to brevity, we only show uncertainty results for the lower Prandtl number. We found significant differences in results for turbulent heat flux between the two fluids. The positions of minimal and maximal values differ significantly. The estimated relative uncertainty remains high even after 10 million time steps. Nevertheless, within the uncertainty bounds, we can observe symmetries and anti-symmetries, which are appropriate for the nature of the flow in a confined backward facing step.

The critical review discusses the most accurate methods for description of turbulent flows: the computationally very expensive direct numerical simulation (DNS) and slightly less accurate and slightly less expensive large eddy simulation (LES) methods. Both methods have found their way into nuclear thermal hydraulics as tools for studies of the fundamental mechanisms of turbulence and turbulent heat transfer. In the first section of this critical review, both methods are briefly introduced in parallel with the basic properties of the turbulent flows. The focus is on the DNS method, the so-called quasi-DNS approach, and the coarsest turbulence modeling approach discussed in this work, which is still on the very small-scale, wall-resolved LES. Other, coarser turbulence modeling approaches (such as wall-modeled LES, Reynolds Averaged Navier-Stokes (RANS)/LES hybrids, or RANS) are beyond the scope of the present work. Section II answers the question: "How do the DNS and LES methods work?" A short discussion of the computational requirements, numerical approaches, and computational tools is included. Section III is about the interpretation of the DNS and LES results and statistical uncertainties. Sections IV and V give some examples of the DNS and wall-resolved LES results relevant for nuclear thermal hydraulics. The last section lists the conclusions and some of the challenges that might be tackled with the most accurate techniques like DNS and LES.

The paper presents the direct numerical simulation (DNS) of a confined backward facing (BFS) step geometry with a flow of two fluids with Prandtl numbers 0.005 and 0.1. The expansion ratio of the BFS geometry is equal to 2.25 and the outflow of the geometry has a shape of a rectangle. The geometry is surrounded by no-slip walls and has no periodic boundaries. Additionally, a step wall and a heater are simulated, which are thermally coupled with each other and to the fluid domain. A recycling boundary condition is used to achieve a fully turbulent inflow boundary condition with a constant mass flow rate. The friction Reynolds number of the flow in the channel before the step is around 207 and the Reynolds number based on the bulk velocity at the inflow and the hydraulic diameter of the inflow is approximately 7100. The reattachment zone was found at about 7.9 step heights downstream of the step. Because the step is confined in the span-wise direction, the average flow exhibits strong 3D features. These features significantly increase the averaging times to achieve sufficiently low statistical uncertainties of flow properties. The DNS is performed with moderate spatial resolution on 30 million grid points, however, it took very long averaging time and 8 million time steps to obtain acceptable statistical uncertainties. In the paper we explore the 3D features and give first and second order statistics for flow and thermal fields, which are relevant for the validation of RANS modelling approach. To this regard, an advanced and well calibrated turbulent heat flux model, called AHFM-NRG+, is selected for validation in this paper. (C) 2019 Elsevier Ltd. All rights reserved.

Turbulent heat transfer is a complex phenomenon that has challenged turbulence modellers over various decades. In this regard, in the recent past, several attempts have been made for the assessment and further development/calibration of the available turbulent heat flux modelling approaches. One of the main hampering factors with respect to the further assessment of these modelling approaches is the lack of reference data. In the framework of the EU SESAME and MYRTE projects, an extensive effort has been put forward to generate a wide range of reference data, both experimental and numerical, to fill this gap. In that context, this article reports the numerical database that has been generated within these projects for various liquid metal flow configurations in different flow regimes. These high fidelity numerical data include seven different flow configurations: a wall-bounded mixed convection flow at low Prandtl number with varying Richardson number (R-i) values; a wall-bounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jets; a mixed-convection cold-hot-cold triple jet configuration corresponding to R-i = 0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. These high-fidelity numerical databases will serve the further development of turbulent heat transfer models by providing unique, new and detailed data for the thermal-hydraulic behaviour of liquid metals in various flow configurations.

Liquid velocity fields in the flow over the backward facing step were measured with the Particle Image Velocimetry (PIV) technique. A transparent experiment test section with the geometry of backward facing step flow and the length of 1.2 meter was designed. The experimental campaign described in the present work was performed in turbulent flow with Reynolds numbers around 7100. Commercial system from LaVision with a single high speed camera and a pulse laser was used for a series of two-dimensional measurements of the velocity field at several cross-sections from two different perspectives. The experimental setup and the results presented in this work are expected to be useful for comparison with accurate numerical simulations.

In this paper, we present the statistical uncertainties in the results of direct numerical simulation of thermal and fluid fluctuations in a flow of liquid metal past a backward-facing step (BFS) with finite dimensions and solid walls. Since the turbulent flow has chaotic temporal oscillations, the flow is compared to experiments and other tools by using statistical quantities. However, such reductions introduce uncertainties that are reduced with the number of steps and length of simulation. We analysed the statistical convergence of our simulation in 49 chosen points through approximately 10 million time steps or around 5000 dimensionless time units. Simulations are performed with the Nek5000 code. The most notable feature of this code is the use of spectral elements to solve for velocity, temperature and any other passive scalar. It is an open source code developed by the Argonne National Laboratory. Spectral element method is a hybrid method between a finite element method and a collocation spectral method. The method divides the computational domain into finite elements, within which a spectral method is used to solve for variables. This method allows for the use of spectral method in irregularly shaped geometries and to perform direct numerical simulations in such geometries. The key finding of our analysis are significant statistical uncertainties, which would only diminish with extremely long integration times. The integration time in the simulation is already very long and corresponds to roughly 40 min measurement in a corresponding experiment.

Particle Image Velocimetry (PIV) is an increasingly popular technique for measuring liquid velocity fields, based on cross-correlation of subsequent images of microscopic particles moving along with the liquid. As such, we intend to use it for measurements of boiling phenomena. A simple flow experiment with the geometry of backward facing step flow was proposed herein. Transparent test section with the length of one meter was built and turbulent flows with low Reynolds numbers were observed. Commercial system from LaVision with a single high speed camera and a pulse laser was used for two-dimensional measurements of the velocity field. Experiments in the test section with aspect ratio of 2.25 were performed at Reynolds number of 5700. The experimental setup and the results are presented.

In this paper, we present the direct numerical simulations of thermal fluctuations in walls and in turbulent flow of liquid metal flowing past a backward-facing step (BFS) with finite dimensions and solid walls. The simulations are performed in three dimensions at Reynolds number based on hydraulic radius of 7089 and Prandtl number equal to 0.005. The temperature field is a passive scalar in our simulations. Simulations were performed with the spectral element code Nek5000. The reattachment zone was found to be approximately 7.9 step heights after the step. This work is part of work that is performed within the SESAME project of Horizon2020 research programme and is a continuation of research at our department.

In this paper we present the preliminary results of direct numerical simulations of a turbulent flow of a liquid metal past the backward-facing step (BFS) with finite dimensions. The BFS geometry can be visualised as a channel where one of the walls has a shape of a step. The flow is flowing from the narrower part to the wider part. The simulations are performed in three dimensions.For the inflow boundary condition over the BFS, a fully developed turbulent velocity field is used. To obtain this fully developed turbulent inflow, a recycling boundary condition is used with which a plane of velocity values from the middle of domain is copied and used to set the inflow boundary condition.Simulations are performed with the NEK5000 code. The most notable feature of this code is the use of spectral elements to solve for velocity, temperature and any other passive scalar. It is an open source code developed by the Argonne National Laboratory.Spectral element method is a hybrid method between finite element method and a collocation spectral method. The method divides the computational domain into finite elements, within which a spectral method is used to solve for variables. This method allows for the use of spectral method in irregularly shaped geometries and to perform direct numerical simulations in such geometries.We performed some preliminary analysis of the calculated friction Reynolds number and the velocity profile before the step. Some analysis of the reattachment of flow was also performed.The main purpose of this work is to test the numerical set-up to later perform calculations with temperature field as a passive scalar. Dimensional walls with internal heating will be added to simulate the heat production in the walls.This work is part of our contribution to the SESAME project of Horizon2020 research programme.

Phenix was a prototype fast breeder reactor that was in operation between the year 1973 and 2009. It was a pool-type reactor cooled with liquid sodium. The net power generating capacity was around 230 MW and the breeding ratio of about 1.12. Because of high thermal conductivity of sodium and liquid metals in general, thermal fluctuations in the liquid can penetrate into adjacent structures with low attenuation. Due to the turbulent nature of the flow, the thermal fluctuations at some point have a typical frequency of 1 Hz. Together with high thermal conductivity these thermal loads cause quick ageing of materials. In this paper we present the direct numerical simulations of fully developed turbulent flow in a channel between two plates with finite dimensions. The outer walls of solid plates are heated with constant flux. In the two other directions, periodic boundary conditions are used. To thermally couple the walls with the fluid, conjugate heat transfer model is used. To compare the results to the past results, gravity is neglected and the temperature is a passive scalar. Simulations are performed with the Nek5000 code. The most notable feature of this code is the use of spectral elements to solve for velocity, temperature and any other passive scalar. Results are compared with simulations based on spectral schemes performed within the THINS EU project between 2010 and 2014. This work is part of work that is performed within the SESAME project of Horizon2020 research programme and is a continuation of research at our department.

In this paper we present preliminary results of condensation induced slug formation and propagation in a horizontal pipe. The pipe is partially filled with cold liquid ammonia at the begining and hot gaseous ammonia is inlet. 3D simulations of two-phase flows with the Hughes-Duffey correlation for predicting condensation were performed for three test cases.

In this paper we simulate the flow in the differentially heated cavity with ratio of height to width equal to 8. The method used is spectral and is similar to one used by Xin and Le Quere in 2002. Instead of using Chebyshev polynomials, we used trigonometric functions to describe spatial distribution of the folw. At Rayleigh number 3.4 x 10(5) only one periodic solution was found. Our results differ from the Chebyshev method by a few percent.

It is well known that turbulent temperature fluctuations penetrate into the heated wall that is being cooled with a turbulent flow. The present work represents a theoretical analysis of the heated slab that is being cooled with turbulent flow from both sides. Results of the direct numerical simulations predict penetration of the turbulent temperature fluctuations into the solid wall. For a sufficiently thick slab, temperature fluctuations from both sides of the slab do not interfere. As the slab gets thinner, fluctuations from both sides interfere and tend to a finite value as the slab thickness limits toward zero. Due to the non-coherent turbulent flows on each side of the slab, thermal fluctuations in the zero-thickness slab are actually lower than in the case of the zero-thickness wall, which is heated by the same turbulent flow from a single side and is isolated on the other side. Spectral numerical scheme was used for Direct Numerical Simulation of fully developed channel flow that is cooling the idealized slab heated with constant volumetric heat source. Implemented boundary conditions for liquid and solid energy equations correspond to the geometry that can be found in some experimental nuclear reactors with fuel in the form of parallel slabs. Periodicity of streamwise and spanwise directions was assumed for velocity and passive scalar temperature field. For temperature, periodicity of the computational domain was assumed also in the wall-normal direction. Most of the simulations were performed at constant friction Reynolds number 180 and Prandtl number 1 with various geometrical and material properties of the heated slab. Some additional analyses were performed also at friction Reynolds number 395 and Prandtl numbers 0.1 and 10.

In this paper we in part recreate simulations in the 8:1 differentially heated cavity that were carried out by Xin and Le Quere [1]. Their method uses second order time stepping scheme and Chebyshev collocation method for spatial dimensions. Our results with the same method differ for about 10(-4) from theirs. We further performed simulations using a method based on trigonometric functions for spatial dimensions. Results using the latter method differ for about few percent compared to results in [1].