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Publication# Large eddy simulation of particulate flow inside a differentially heated cavity

Christoph Bosshard, Abdelouahab Dehbi, Michel Deville, Emmanuel Leriche, Alfredo Soldati

*Elsevier, *2014

Article

Article

Résumé

In nuclear safety, some severe accident scenarios lead to the presence of fission products in aerosol form in the closed containment atmosphere. It is important to understand the particle depletion process to estimate the risk of a release of radioactivity to the environment should a containment break occur. As a model for the containment, we use the three-dimensional differentially heated cavity problem. The differentially heated cavity is a cubical box with a hot wall and a cold wall on vertical opposite sides. On the other walls of the cube we have adiabatic boundary conditions. For the velocity field the no-slip boundary condition is applied. The flow of the air in the cavity is described by the Boussinesq equations. The method used to simulate the turbulent flow is the large eddy simulation (LES) where the dynamics of the large eddies is resolved by the computational grid and the small eddies are modelled by the introduction of subgrid scale quantities using a filter function. Particle trajectories are computed using the Lagrangian particle tracking method, including the relevant forces (drag, gravity, thermophoresis). Four different sets with each set containing one million particles and diameters of 10 mu m, 15 mu m, 25 mu m and 35 mu m are simulated. Simulation results for the flow field and particle sizes from 15 mu m to 35 mu m are compared to previous results from direct numerical simulation (DNS). The integration time of the LES is three times longer and the smallest particles have been simulated only in the LES. Particle statistics in the LES and the DNS were similar and the settling rates were practically identical. It was found that for this type of flow no model was necessary for the influence of the unresolved flow scales on the particle motions. This can be explained by the dominant nature of gravity settling compared to turbophoresis which is negligible for the particle sizes of the present study. (C) 2013 Elsevier B.V. All rights reserved.

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Concepts associés (25)

Direct numerical simulation

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the

Turbulence

vignette|Léonard de Vinci s'est notamment passionné pour l'étude de la turbulence.
La turbulence désigne l'état de l'écoulement d'un fluide, liquide ou gaz, dans lequel la vitesse présente en tout poi

Simulation des grandes structures de la turbulence

La simulation des grandes structures de la turbulence (SGS ou en anglais LES pour Large Eddy Simulation) est une méthode utilisée en modélisation de la turbulence. Elle consiste à filtrer les petite

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In nuclear safety, most severe accident scenarios lead to the presence of fission products in aerosol form in the closed containment atmosphere. It is important to understand the particle depletion process to estimate the risk of a release of radioactivity to the environment should a containment break occur. As a model for the containment, we use the three-dimensional differentially heated cavity (DHC) problem. DHC is a cubical box with a hot wall and a cold wall on vertical opposite sides. On the other walls of the cube we have adiabatic boundary conditions. For the velocity field the no-slip boundary condition is valid. The flow of the air in the cavity is described by the Boussinesq equations. Complex flow patterns develop and the flow characteristics depend on the non-dimensional Rayleigh and Prandtl numbers. The predominant flow type in the DHC is a turbulent natural convection flow. This work aims at reaching Rayleigh numbers and turbulent levels as high as possible given the available computational resources. The method used to simulate the turbulent flow is the large eddy simulation (LES) where the dynamics of the large eddies is resolved by the computational grid and the small eddies are modelled by the introduction of subgrid scale quantities using a filter function. Numerically, the LES equations are discretized by the spectral element method. Particle trajectories are computed using the Lagrangian particle tracking method, including the relevant forces (drag, gravity, thermophoresis). Four different particle sets with each set containing one million particles and diameters of 10 μm, 15 μm, 25 μm and 35 μm are simulated. The complexity and the size of the large three-dimensional problem requires the use of massively parallel supercomputers. Spectral element methods are naturally suitable for parallelisation by distributing the elements among the processors. For the Lagrangian particle tracking we use a method where equal numbers of particles are assigned to every processor. The flow field is broadcast and every particle processor tracks the assigned particles, a procedure which leads to a perfect load balancing. Simulation results for the flow field and particle sizes from 15 μm to 35 μm at a Rayleigh number of 109 are compared to previous results from a direct numerical simulation. First order statistics of the LES flow fields are in very good agreement with the direct numerical simulation while the agreement of second order moments is fair. Also the turbulent structures associated to the maximum of turbulent kinetic energy production are correctly reproduced. Particle statistics in the LES and the direct numerical simulation were similar and the settling rates practically identical. Contrary to previous particle simulations in LES, it was found that no model was necessary for the influence of the unresolved flow scales on the particle motions. This can be explained, because the important settling mechanism is through gravity and particle deposition at the walls by turbophoresis is negligible.

Marc Anthony David Habisreutinger

In fluid mechanics, turbulence can occur in very simple flow geometries, for Newtonian fluids and without the need for additional flow conditions such as temperature gradients or chemical reactions. In standard cases, intuitive assumptions on the physics of the subgrid scales coupled with the classical theories of turbulence can be well suited for subgrid modelling in large eddy simulation. However, considering more complex situations such as elastic or plasmas turbulence, the behaviour of the subgrid scales is not clearly identified, certainly not as intuitive and the corresponding theories are not available yet. The question is how to proceed when the functional modelling, which imposes a known behaviour to the subgrid scales of the flow, is not possible. For instance, this issue could be overcome using deconvolution-based subgrid models which aim at a partial recovery of the original quantities from their filtered counterpart. In principle, functional modelling is avoided by attempting to invert the filtering operator applied to the governing equations. However, this apparent advantage is completely lost since these models are usually coupled with auxiliary approaches, directly based on functional modelling, in order to account for the interactions with the scales which are not representable on the coarse spatial discretization used for large eddy simulation. The driving motivation of this work is to suppress the need for this secondary modelling which would allow to extend the use of deconvolution-based models to the large eddy simulation of flows whose behaviour of subgrid scales is not identified. Considering the effects of the coarse numerical discretization as the only effective filter applied to the macroscopic equations, an interpretation of the deconvolution models as a way to approximate the effect of the scales lost by numerical discretization on the resolved scales of the flow is demonstrated. Consequently, a new category of subgrid models, the grid filter models, is defined and gives a theoretical justification to the use of deconvolution models for the entire subgrid modelling process. In this perspective, a general method for the computation of the convolution filter which models the effect of the grid filter on the computable scales of the solution is proposed, thereby addressing the key issue of the numerical discretization in large eddy simulation. This modelling approach is validated performing the large eddy simulation of the incompressible flow of a Newtonian fluid in a lid-driven cubical cavity. Comparisons with classical subgrid models allow to assess the validity of this modelling approach and the suppression of the need for functional modelling. In order to extend the validity domain of the grid filter models, the large eddy simulation of an elastic turbulence problem is envisaged. Numerical simulations of elastic turbulence are limited by numerical instabilities which are particularly stringent at high elasticity. Moreover, the computational burden resulting from the required space-time resolutions is significantly increased as compared to the Newtonian case. Consequently, available direct numerical simulations are restricted to periodic and two-dimensional cases. Among these studies, the large eddy simulation of the viscoelastic Kolmogorov flow is chosen as benchmark problem.

In the last years, the correlation between air pollution and health issues related to respiratory, cardiovascular and digestive systems has become evident. Today, urban aerosols raise the interest of both scientific community and public opinion. METAS, the Swiss Federal Institute of Metrology, takes part in AeroTox, a European Union’s research project involving the development of a reference aerosol calibration infrastructure - a so-called mixing chamber. In this chamber, pure air and particles are injected on top and the resulting aerosol is sampled at the bottom. The quality of this aerosol is assessed according to its concentration homogeneity: the purpose of this master’s project is to improve it. In addition, two research questions were addressed. How much can the mixing chamber dimensions be reduced without affecting the concentration homogeneity? Dimensions are crucial because the mixing chamber must be transportable. Also, how much can the flow rates be reduced without affecting the concentration homogeneity? Computational Fluid Dynamics (CFD) simulations and experiments were employed. Numerical simulations were performed in COMSOL Multiphysics, implementing a particle tracing and a diluted species model. This allowed to investigate the structure of the flow and the involved mixing mechanisms: diffusion, convection and turbulent dispersion. However, only the diluted species model was successful. The simulated concentration at the outlet is perfectly homogeneous. Experiments were carried out using two particle size distributions: NaCl (size peak at 80 nm) and Polystyrene Latex (PSL, size peak at 900 nm). Empirical data validate simulations and show a concentration homogeneity within 5%. Furthermore, uncertainty on the measurements is of 4.24%: the simulated concentration homogeneity thus lies within the uncertainty of the experimental findings. Moreover, experiments show that salt particles reach a higher concentration homogeneity than PSL particles. Finally, in case of salt particles, experiments prove that the flow rates can be halved and even equalized and the length of the mixing chamber can be reduced to 50% without drastically affecting the concentration homogeneity.

2020