The appearance of macro-segregations in the ingot casting process has led to the development of a solidification model in the Computational Fluid Dynamics software code_saturne. It relies on a mixture model encompassing mass, momentum, energy and solute transport equations. After having implemented this model for the Finite Volume (FV) scheme of code_saturne, it is here implemented for the Compatible Discrete Operator (CDO) framework. The resulting solidification and segregation predictions are validated against an academic test case. Integral and local comparisons are performed and exhibit a good agreement of the CDO approach with results obtained with the FV scheme and with the commercial software SOLID®. Moreover, the CDO approach relying on a strong velocity-pressure coupling brings a significant improvement in terms of robustness with respect to the time step, allowing for faster computations.

Dealing with complex geometries for industrial applications is challenging in computational fluid dynamic workflows. Current developments in scan devices offer the possibility to represent very complex solid geometries in fluid dynamic solvers. This paper proposes a novel approach for reconstructing solid geometry from 3-D scans and flow simulation. Based on a 3-D point cloud, the approach automatically reconstructs the solid surface by including local solid planes in any convex computational cell. An immersed boundary method is then used to impose appropriate boundary conditions on the solid surfaces in the co-located finite volume context. The present approach avoids the complex and time-consuming manual/assisted meshing typical of body-fitted mesh workflows while showing satisfactory robustness and accuracy.

Spillways are hydraulic structures that regulate flow control in dams in order to prevent their failure during floods. Weirs efficiency depends mainly on their crest shape. Currently, their geometry has only been studied empirically due to the complex flow nature. Hence, the aim of this study is to carry out a numerical optimization procedure of the spillway design. Advances in computational fluid dynamics (CFD) allow a better understanding of free surface flows. Code_Saturne, which is a CFD model developed within EDF R&D incorporating a Volume Of Fluid (VOF) method, computes the weir upstream water level for a given flow discharge. Then, a shape optimization methodology was developed to maximize the flow discharge coefficient while at the same time taking into account the damage risk by cavitation of the weir. With the help of a 2D model, the head discharge was minimized while limiting negative pressure appearance along weir crest. The optimization study was based on a gradient descent algorithm and a Bézier curve parametrization of the weir shape. A comparison between the optimal shape hydraulic performances and the standard weir shape highlights a significant gain in the flow discharge of the structure.

Spillways are hydraulic structures that ensure safety and prevent failure of dams. They are designed to regulate flow and evacuate water during floods. Spillways are qualified by their capacity to evacuate water, which is quantified by flow discharge coefficient measurements. Crest weir shape is one of the main parameters that influence spillway efficiency. Currently, their geometry has only been studied empirically due to the complexity of flow. Despite being well studied experimentally, they have not yet undergone a thorough optimization study to enhance their efficiency. The present study aims to increase weir hydraulic performances. To carry out this purpose, a shape optimization methodology based on the Volume Of Fluid (VOF) model of Code_Saturne was developed to maximize flow discharge coefficients while at the same time taking into account damage risk by cavitation of the weir concrete. Conducted first on a 2D model, for a given flow rate, head discharge was minimized while limiting negative pressure appearance along weir crest. The multi-objective shape optimization study was based on a surrogate model by Kriging. In order to alleviate the computational cost, an efficient approach deploying different grid resolutions is proposed. A comparison between the optimal shape hydraulic performances and the standard weir shape highlights a significant improvement in weir efficiency.

The present work uses the Smoothed Particle Hydrodynamics (SPH) meshless numerical method in order to investigate the behaviour of a water sheet falling under gravity by comparing the simulation to the results of an experimental chute of 10m height. The present model is capable of predicting the falling velocity and the trajectory of the water sheet, as observed on the experiment.

Air entrainment within water is a common feature of flows over hydraulic works – spill over a dam, wave breaking on a dike, etc. – and its accurate modeling is a key to better design such structures. The Smoothed Particle Hydrodynamics (SPH) method appears as a natural way to model such highly distorted flows. To avoid computationally prohibitive costs related to the full discretization of bubbles or drops, a mixture model for high density ratio flows relying on a volume-based formulation with relative velocity between phases has first been developed and validated in Fonty et al. (Proceedings of 13th international SPHERIC workshop. Galway, Ireland, 2018; Int J Multiph Flow 111:158–174, 2019. https://doi.org/10.1016/j.ijmultiphaseflow.2018.11.007 ). Instead of having a once and for all assigned phase as in multifluid SPH, each particle now carries both phases through their respective volume fractions. In the present work, in order to handle practical air entrainment application cases, the open boundary formulation described in Ferrand et al. (Comput Phys Commun 210:29–44, 2017. https://doi.org/10.1016/j.cpc.2016.09.009 ) is adapted to this mixture model. Then, after introducing turbulence through a $$k{-}\epsilon$$ model, a specific closure on the air bubbles relative velocity is proposed including a Stokesian drag term and turbulent diffusion. This model is then applied to two cases of air entrainment: a stepped spillway for interfacial aeration and a plunging jet for local aeration. Finally a 3D industrial test case of discharge-control structure at the La Coche power plant (France) is considered. While valuable insights are obtained for the volume fraction field, further investigations are required to improve the modeling of the flow dynamics.

The smoothed particle hydrodynamics (SPH) numerical method is based on two approximations: a smoothing interpolation and a discrete (particle-based) approximation. The smoothing error has been identified in the early years of SPH as being proportional to the square of the smoothing length in the absence of boundaries and using a radial normalised kernel. Here we calculate the exact smoothing error as a function of the kernel standard deviation as a differential operator applied to the interpolated field. The key feature is that this error depends on the kernel Laplace transform. This technique is applied to the main SPH smoothed differential operators (gradient, divergence, pressure Laplacian and viscous forces). The present theory is tested against numerical data for harmonic and Gaussian functions with an excellent agreement. (C) 2019 Elsevier Ltd. All rights reserved.

The numerical modelling of two-phase mixture flows with high density ratios (e.g. water/air) is challenging. Multiphase averaged models with volume fraction representation encompass a simple way of simulating such flows: mixture models with relative velocity between phases. Such approaches were implemented in SPH (Smoothed Particle Hydrodynamics) using a mass-weighted definition of the mixture velocity, but with limited validation. Instead, to handle high density ratios, a mixture model with a volumetric mixture velocity is developed in this work. To avoid conservation issues raised by the discretization of the relative material displacement contribution in the volume fraction equation, a formulation on phase volumes is derived following a finite volume reasoning. Conservativity, realizability, limit behaviour for single-phase flow are the leading principles of this derivation. Volume diffusion is added to prevent development of instabilities due to the colocated nature of SPH. This model is adapted to the semi-analytical SPH wall boundary conditions. Running on GPU, this approach is successfully applied to the separation of phases in a settling tank with low to high density ratios. An analytical solution on a two-phase mixture Poiseuille flow is also used to check the accuracy of the numerical implementation. Then, a Rayleigh-Taylor instability test case is performed to compare with multi-fluid SPH. Finally, a comparison with experimental and numerical data is made on a sand dumping case; this highlights some limits of this mixture model. (C) 2018 Elsevier Ltd. All rights reserved.