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Nowadays, as industrial designs are close to their optimal configurations, the challenge lies in the extraction of the last percentages of improvement. This necessitates accurate evaluations of the performance and represents a significant higher computational cost. The present work aims at integrating Large Eddy Simulations in the optimization framework for an accurate evaluation of the flow field. The number of expensive evaluations is kept to a minimum by using the adjoint method for the evaluation of the gradient of the objective function. Divergence of the gradients due to the chaotic flow motion is avoided by an additional step which decouples the Large Eddy Simulations from the gradient calculations. An adaptation process based on a Reynolds Averaged Navier-Stokes simulation is therefore sought to mimic the more accurate Large Eddy Simulation results. The obtained field is then used in combination with an adjoint shape optimization routine. The method is tested on the design of a U-bend for internal cooling channels by minimizing its pressure loss. Starting from an optimized geometry obtained through a classical approach based on RANS evaluations, further improvements of the design are achieved with the application of the proposed strategy when performances are evaluated by means of LES.

The numerical simulation of turbulent heat transfer in complex industrial flows represents a major challenge for RANS models. The impinging jet configuration is a popular test case for turbulence models, due to both the challenging nature of the flow field for the RANS approach and its widespread use in industrial applications. As a consequence, a large number of studies in the literature is dedicated to the assessment of a broad variety of turbulence models in this configuration. In particular, a significant effort has been put into the assessment of different closures for the turbulent momentum flux. In contrast, relatively little attention has been paid to the modelling of the turbulent heat flux term, and the classical Reynolds analogy is almost universally employed for this purpose despite its well-known limitations. Nevertheless, recently there has been a growing interest towards the development and assessment of more advanced closures for the turbulent heat flux. In this context, in the present work six turbulence models relying on different closures for both the turbulent momentum and heat fluxes have been used to simulate a planar impinging jet at unity, moderate and low Prandtl number and thoroughly assessed against a recently published reference DNS database. It is shown that the use of an advanced differential closure for the Reynolds stresses can result in an improvement in the prediction of the flow field. This, in turn, directly results in a more accurate prediction of the mean temperature at unity Prandtl number when the Reynolds analogy is employed for the closure of the turbulent heat flux. On the other hand, the inadequacy of the latter approach appears evident at low Prandtl values, and the necessity to account at least for the variability of the turbulent Prandtl number is demonstrated. It is then inferred that the most promising approach for such complex cases is represented by the combined use of anisotropic models for both the turbulent flow and the thermal fields.

The correct prediction of the flow field is of crucial importance to drive numerical optimization to a real improvement of a design. For this purpose, different numerical approaches can be used to study the fluid dynamics characteristics and the performance of the design. In particular, in the present work the Reynolds-averaged Navier–Stokes and large eddy simulation approach are compared for an internal aerodynamic application. The obtained solutions are validated against experiments through a quantitative and qualitative comparison, i.e. pressure measurements and particle image velocimetry flow visualizations, respectively.

The E-SCAPE (European SCAled Pool Experiment) facility at the Belgian nuclear research center SCK•CEN is a thermal hydraulic 1/6th-scale model of the MYRRHA reactor with an electrical core simulator and cooled by LBE. The E-SCAPE facility provides experimental feedback to the designers on the forced and natural flow patterns, flow mixing and stratification during operational and accidental conditions. In addition, it provides valuable data for validation of the computational techniques for their use with LBE and in the design of MYRRHA. In terms of momentum field, one of the most important integral quantity to reproduce is the pressure drop in the system which has a direct consequence on the evolution of the mass flows and determines the free-surface levels in transient scenarios. In this paper, a detailed CFD study is performed on the flow in the E-SCAPE core region with the aim on predicting the correct pressure drop. Different numerical representation of the core geometry have been modeled and subjected to validation against experimental results from E-SCAPE. Special attention has been addressed to the choice of geometric simplifications and numerical models for accurate representation of the core of the E-SCAPE pool facility.

Numerical analysis of the thermohydraulic behavior of the innovative flexible fast spectrum research reactor, MYRRHA, under design by the Belgian Nuclear Research Center (SCK•CEN) is a very challenging task. The primary coolant of the reactor is Lead Bismuth Eutectic, LBE, which is an opaque heavy liquid metal with low Prandtl number. The simulation tool needs to involve many complex physical phenomena to be able to predict accurately the flow and thermal field in the pool type reactor. In the past few years, within the frame of a collaboration between SCK•CEN and the von Karman Institute, a new platform, MyrrhaFoam, was developed based on the open source simulation environment, OpenFOAM. The current tool can deal with incompressible buoyancy corrected steady/unsteady single phase flows. It takes into account conjugate heat transfer in the solid parts which is mandatory due to the expected high temperature gradients between the different parts of the reactor. The temperature dependent properties of LBE are also considered. MyrrhaFoam is supplemented with the most relevant thermal turbulence models for low Prandtl number liquids up to date.

Performing good-quality computational fluid dynamics (CFD) simulations is not an easy task as the CFD engineer has to judge whether the results of the simulation can be trusted. While reality is continuous in space and time, computers work in the discrete domain. This chapter refers in the basis to generic existing CFD best practice guidelines but elaborates on the specific guidelines that arise from the simulation of liquid metals. The guidelines are provided following the structure of simulation, that is, preprocessing, simulation (or processing), and postprocessing. Finally, the most relevant guidelines specific for nuclear liquid-metal CFD simulations are summarized.

The European Scaled Pool Experiment (E-SCAPE) is a 1/6th-scale thermal hydraulic model of the MYRRHA reactor and has been developed within the European framework programs THINS and MYRTE. MYRRHA is a multi-purpose hybrid pool-type research reactor cooled with lead-bismuth eutectic (LBE) that is under design at the Belgian nuclear research center SCK•CEN. The experiments from the E-SCAPE facility are essential for the design and licensing of MYRRHA. On the one hand, the experimental data from E-SCAPE directly provide information to the designers on the flow patterns and heat transport in the LBE in the upper and lower plena of the reactor. On the other hand, the experimental data from E-SCAPE enable qualification of thermal hydraulic computer codes used for analyzing the flow and heat transport in the MYRRHA reactor. The accuracy of codes rely on the underlying modelling approaches, whose validity can only be assessed by comparing them with relevant experimental data. Given the rare conditions present in heavy liquid cooled nuclear reactors, the possibility to compare complete pool simulations with experimental data is a unique opportunity. This paper presents the modelling approaches and first results of the pre-test analyses performed for E-SCAPE by NRG, SCK•CEN and VKI using Computational Fluid Dynamics (CFD). The CFD analyses of NRG are performed with the STAR-CCM + code, at SCK•CEN with the ANSYS CFX code and at VKI OpenFOAM is used. A first comparison of the results obtained with three different CFD codes for flow and heat transport in the E-SCAPE pool is presented and, where possible, validated against experimental results.

The present paper describes the application of local perturbations in Large Eddy Simulation to enhance transition to turbulence applied on the heated wall of a natural convection boundary layer. Simulations are carried out with a Prandtl number P r = 0.71 and a maximum Grashof number of G r = 4.1 × 10 11 . The purpose of this work is to accelerate the transition process in the numerical domain, reducing the needed simulation effort to reach the turbulent regime in a natural convection boundary layer flow. A parametric study has been performed to identify the fastest transition to turbulence in the proposed technique. The obtained results are compared with experimental, empirical and other numerical reference data to assess the method’s performance. The analysis of the transition method contemplates its effect in the mean flow field, as well as in the resolved Reynolds stresses and turbulent heat fluxes.

The pressure loss reduction inside the U-bends of internal cooling channels is of crucial importance to increase the performance of cooling systems of gas turbines. The optimization technique proposed in the present work is based on the continuous adjoint shape method and is implemented in the OpenFOAM open-source framework. The calculated gradients of the objective function are linked to a node-based constrained morphing routine, allowing the modification of the shape towards an optimum design with minimal pressure loss. The integration with a robust mesh morpher solver leads to successive automatic steps towards the design improvement. Design modifications take into account constraints and limitations related to the chosen design. The feasibility of the design is guaranteed by the application of a smoothing function with the aim to avoid rough external surfaces.

Following the Fukushima-Daiichi accident, many countries decided to strengthen the safety systems of their nuclear power plants in order to increase the capabilities of managing severe nuclear accidents. To achieve this goal detailed analysis of postulated design and beyond-design-basis accidents is essential. The main tools available for the analysis of these complex scenarios are Advanced Lumped Parameters (LP) and Computational Fluid Dynamics (CFD) codes. Currently, the most limiting factor in the application of these tools is their validation. This activity is performed in support of the development and validation of a CFD model, built in the numerical environment of OpenFOAM, for hydrogen behavior in the containment of Light Water Reactors. For validation purpose, numerical simulations of the erosion of a light gas stratification by means of a hot air jet have been performed, and results of the simulations were analysed and compared against experimental results obtained by Ritterath (2012) in the MiniPanda facility. Two different scenarios have been considered, each characterized by a different value of the mass flow rate of the jet used to erode the stratification.

The development of Gen IV nuclear reactors entails research oh heavy liquid metals, which are considered as appropriate coolant agents due to their high thermal conductivity and favorable nuclear safety characteristics. These fluids are characterized by a very low Prandtl number (between 0.006 and 0.025). During the design of such reactors, the scenarios of maintenance or loss-of-flow accidents consider a pure natural convection loop inside the reactor. The CFD modeling of the momentum and heat transfer must contemplate natural convection in low Prandtl number fluids, however in literature these flow configurations are not usual. This is why in the present article, Large Eddy Simulations over a natural convection boundary layer at Pr = 0.025 are presented and described. Turbulence is triggered by adding a perturbation in the boundary layer. The adopted numerical approach is validated through a Large Eddy Simulation at Pr = 0.71 , where heat transfer, friction coefficient and mean and turbulent flow fields are compared with measurements in literature. Once turbulence is reached in the Pr = 0.025 boundary layer, flow characteristics as Nusselt number, skin friction coefficient and turbulent profiles are calculated and compared with the Pr = 0.71 simulation to assess the effect of Prandtl number on heat and momentum transfer.

Thermal-hydraulics is recognized as a key safety challenge in the development of liquid metal cooled reactors. At nominal operating conditions, the Prandtl number of liquid metals which are used as primary coolants, such as lead and sodium, is very low: typically of the order of 0.025–0.001. Obtaining an accurate prediction of the turbulent heat transfer at such a low Prandtl number is not an easy task for the standard turbulence models and has challenged the modellers over several decades. In the framework of the EU SESAME project, an effort has been put forward to assess and/or further develop/calibrate different turbulent heat flux closures. In this regard, the present article reports an assessment of four different turbulent heat flux closures for applications involving low-Prandtl fluids. These closures include: (i) the Reynolds analogy based on a constant turbulent Prandtl number (ii) a four-equation explicit algebraic heat flux model (AHFM) (ii) a three-equation implicit AHFM called AHFM-NRG and (iv) a non-linear second-order heat flux model called Turbulence Model for Buoyant Flows (TMBF). The performance of these turbulence models has been assessed in three different test cases against high-fidelity numerical reference data been generated within the SESAME project. The three test cases are: a natural Rayleigh-Benard convection flow, a mixed convection planar channel flow and a forced convection impinging jet flow. The shortcomings of the classical Reynolds analogy approach for low-Prandtl fluids in all flow regimes are highlighted; hence, more advanced and well-calibrated closures are recommended.

The temperature perturbation method (TPM) is used as an alternative technique to the classical velocity perturbations to generate inflow turbulence for LES or DNS simulations. The TPM consists in seeding the flow with random temperature perturbations which, through a buoyancy triggered mechanism, will induce the creation of turbulent structures. Naturally, this implies that the physical buoyancy effects need to be sufficiently strong, which has limited up to now its application to atmospheric flows. The proposed modification makes it applicable to a wider variety of wall-bounded flows, that would involve much smaller length scales than in the atmosphere. In this novel approach, a perturbation zone is defined at the entrance of the domain, along which an artificial local Richardson number is applied so that buoyancy effects are sufficiently strong to create turbulence. The TPM is implemented in the incompressible solver of OpenFOAM v2.3 with buoyancy effects and tested on a plane channel flow at R e τ = 395 . Prior to testing, periodic channel flow results are obtained to represent the reference fully developed turbulent state. The perturbation zone is divided into a fully active zone, where buoyancy is maximum, and a transition zone, needed to insure a smooth progression back to zero buoyancy. Several perturbation functions are applied to modulate these artificial effects, in order to identify the function that most efficiently pre-mixes the flow, thus preventing stratification effects from slowing down the flow recovery. Thereafter, the transition length and the artificial local Richardson number are optimized, based on wall shear stress recovery. Moreover, the effect of the perturbation frequency on not only the flow solution but also the energy spectra is examined in order to prevent the technique from contaminating the energy content. The flow development is compared to the synthetic turbulence generator method of Xie and Castro [1] in terms of the recovery distances of both the wall shear stress and the Reynolds stresses. The optimized method appears to be efficient with a flow that reaches equilibrium and a good quality energy spectra after about 15 δ . Although this final length remains similar to that obtained by competing methods, the optimized TPM benefits from a greater flexibility since only first-order statistics are required as input. Therefore, it can be applied without prior knowledge of second order moments or integral length scales, making it directly applicable to a wide variety of flows.

This article deals with the discretization of linearized Euler equations by multidimensional upwind residual distribution methods. Linearized Euler equations are applied to model the propagation of sound in the domain where no source of sound is present and where the analogy methods such as Ffowcs―Williams can not be used because of gradients in the mean flow. The residual distribution method leads to a class of schemes that shares properties of both finite element method and finite volume method. In particular, the schemes used here are multidimensional upwind, which make them very attractive because of their low cross-dissipation. First, the discretization method is introduced as an alternative method for computational aeroacoustic applications on unstructured grids. The residual distribution method is then analyzed analytically for wave propagation. Next it is applied to linearized Euler equations with proper acoustic boundary conditions, and finally verifiedon test cases having exact solution.

In this article, the results of aeroacoustic cases obtained by high-order methods are presented. One internal and one external case are considered. The internal case is a transonic cavity. It has been computed by three parters, namely FOI-LiU (Linkoping University), University of Stuttgart (USTUTT) and Dassault Aviation (DASSAV). FOI-LiU has computed with their higher order accurate finite difference solver using a block structured grid. Comparisons are made to reference calculations using an unstructured grid with Edge. USTUTT uses a high order discontinuous Galerkin spectral element code for the final high-order computations and a mixed modal/nodal DG code for the baseline computations. Dassault Aviation uses their in-house stabilized finite element code Aether, both for the reference and the higher-order computations. In both instances unstructured tetrehedral grids are used. The external case is a quasi-two dimensional generic wing and flap configuration defined in the VALIANT FP7 project. Two institutions were involved in the high-order simulation of this low-Mach number test case, M = 0.15, Central Institute of Aero- and Hydrodynamics, TsAGI, and the von Karman Institute, VKI. In the following, the acoustic predictions corresponding to the two test cases will be described.

Imposing subsonic outlet boundary conditions for compressible ow simulations is still a challenging problem, since spurious re ections are occurring if unsteady disturbances leaving the domain. Most of the non-re ecting boundary conditions can be found in the literature performing very well if only acoustic perturbations are considered, but they are less e ective if there are vortical structures passing through the boundaries. This issue is true for both inlets and outlets, but in the current paper just outlets are considered in 2D and 3D. In the literature these spurious waves due to unsteady perturbation passing though the boundaries are called re ections. However, if a vortical structure is leaving the domain, the acoustic waves propagating back to the solution domain are rather created. In this sense, the original characteristic equations are modi ed such that the source terms responsible for these spurious waves could be identi ed and deactivated. In such a way, the vortical disturbances can pass the boundaries and therefore no more bu er zone is needed. In this paper, we used this approach to design non-re ecting outlet using residual distribution schemes to solve the bulk ow. We have developed the new boundary condition for both Linearized Euler Equations and Navier-Stokes Equations.

This article is dedicated to the design of high order residual distributive schemes for unsteady problems. We use a space-time strategy, which means that the time is considered as a third dimension. To achieve high order both in space and in time, we use prismatic elements having (k+1) levels, each level being a P k element. The first section is dedicated to the deign of space-time schemes on such elements. The second section presents the performances on different type of problems. In particular, we look at a discontinuous problem on Euler equations and two problems of propagation of sound using Linearised Euler equations.

This article deals with the discretization of Linearized Euler Equations (LEEs) by multidimensional upwind Residual Distribution methods. Linearized Euler equations are applied in the domain where there is no source of sound and the analogy methods such as Ffowcs-Williams can not be used because of gradients in the mean flow. Residual distribution method is a class of schemes that is in between finite-element and finite-volume. In particular, the schemes that we use are multidimensional upwind which make them very attractive because of their very low cross-dissipation. First, we define the formulation of the LEEs that we choose to use. Then, we focus on the residual schemes and we describe two ways of discretizing unsteady problems. The third part presents a wave number of those schemes. Finally, we show the advantage of these schemes on several acoustic problems.

The project aimed to clarify the hydrogeological circumstances of a urineral water well. Nowadays the well produces water from 12m depth, but previously it was known as natural spring. Before the project the origin of the water was unknown, so the planning of the mise of the production rate and the delineation of the protection area could not based on actual data. To provide the needed data, detailed geological mapping, processing archive and new geophysical data, water table determination and chemical analysis were performed. This paper deals mainly with the geophysical aspects of this integrated geologicalgeophysical work.

Various geoelectrical measurements have been widely used for bauxite and coal prospecting in the Hungarian Transdanubian Central Range for decades. These mountain form a syncline structure, bauxite deposits can be found in their central part in tectonically preformed karstic depressions of resistive Mesozoic -mainly Upper Triassic- carbonates. Conductive Cenozoic formations including coal beds cover the bauxite lenses and the basement. This resistivity contrast and the approximately 1-D model allow to determine the depth to the basement and to distinguish the main structural units in the study area using geoelectrical methods.

The current paper describes the loss of flow (LOF) transient investigated in the MYRRHA reactor by the means of Computational Fluid Dynamics. This scenario is starting from the nominal operation case then the two pumps stop simultaneously. An unsteady solution with resolved interface was considered with calculating conjugate heat transfer through the relevant structures. Due to a postulated event (e.g. loss of the electric grid) the pumps are not powered anymore stops. After the detection of the problem (temperature difference above the core rises with 20 degree) the reactor power is stopped by the safety rods (delay of 1 s). The fuel elements, however, continue to generate residual heat according to the decay heat curve. Due to the loss of the pumps, the pressure difference between the cold and the hot plenum is decreasing, which result in a gravitational flow equilibrating the two free surfaces to the same level. The objective of the work was to determine the flow through the core during the coast down of the pumps and eventual flow reversal into the pump/heat-exchanger box due to the gravitational flow. The simulation revealed that after losing power, the LBE flow reverses into the pumps in less than 0.1 s according to the simulations. In the core there is a brief moment of reverse flow, too, but only after the core is scrammed, therefore, the loss of cold LBE flow is not causing overheat. Once the core is scrammed, the position of the maximum temperature in the system shifts to the Above Core Structure, where the residual hot plume rising from the core impinges to the Above Core Upper Closure. The levels of the lower and upper plenum equilibrate roughly 20 s after the pump failure event.

This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various low-Prandtl flow configurations 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 different 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 and forced convection flow in a bare rod bundle configuration for two different Reynolds numbers; 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 jet; a mixed-convection cold-hot-cold triple jet configuration corresponding to Ri=0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in low-Prandtl fluids. © 2019 American Nuclear Society. All rights reserved.