Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Modelling of Pseudo Hydrostatic Force in Two – Phase Flow with Different Layers

In the study of solid-in-liquid flow, shear stress is important in determining the force that is acting on the pipe wall. In case of homogenous suspension solid-in-liquid flow, the properties can be considered as mixture properties with constant concentration profile across the flow area. In the moving bed of particles with variable concentration, the shear estimation is not directly predictable and there is no existing clear mathematical formula to achieve this objective. In the present work, the method of finding the force acted on the pipe wall by the particles in the layer, which is termed the dry force will be presented using a method called the “pseudo hydrostatic pressure” method. To attain the equation for the dry force, a mathematical approach is taken with the assumptions that the flow is a horizontal, two-phase pipe flow (solid-liquid), incompressible and it is at steady-state. For initial study, only Newtonian fluid is to be considered in the case. The two-layer approach is taken whereby the flow will consist of one upper suspended layer of particles in the fluid, and the bottom layer which is the moving bed of particles. Thus, the developed mathematical model can be applicable in solving for the shear force in horizontal two-phase flows

Computational Eulerian Hydrodynamics and Galilean Invariance

Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We demonstrate that Eulerian hydrodynamics methods do converge to a Galilean-invariant solution, provided a well-defined convergent solution exists. Specifically, we show that numerical diffusion, resulting from diffusion-like terms in the discretized hydrodynamical equations solved by Eulerian methods, accounts for the effects previously identified as evidence for the Galilean non-invariance of these methods. These velocity-dependent diffusive terms lead to different results for different bulk velocities when the spatial resolution of the simulation is kept fixed, but their effect becomes negligible as the resolution of the simulation is increased to obtain a converged solution. In particular, we find that Kelvin-Helmholtz instabilities develop properly in realistic Eulerian calculations regardless of the bulk velocity provided the problem is simulated with sufficient resolution (a factor of 2-4 increase compared to the case without bulk flows for realistic velocities). Our results reiterate that high-resolution Eulerian methods can perform well and obtain a convergent solution, even in the presence of highly supersonic bulk flows.Comment: Version accepted by MNRAS Oct 2, 2009. Figures degraded. For high-resolution color figures and movies of the numerical simulations, please visit http://www.astro.caltech.edu/~brant/Site/Computational_Eulerian_Hydrodynamics_and_Galilean_Invariance.htm

Flow Assessment Using Optical Coherence Microscopy Based Particle Image Velocimetry

Congenital heart diseases (CHDs) are the most common forms of congenital malformation in newborns. Among all types of CHDs, a large portion is contributed by malformation of endocardial cushion malformation during early heart development. Although the etiology of endocardial cushion malformation is unclear, it is a result of interactions between genetic and environmental factors has been confirmed. There is hypothesis indicating that malformation of endocardial cushion is caused by altered shear stress conditions where in cushion forming area the shear stress is supposed to be high compare with other area in congenital heart. However it is difficult to justify due to lack of in vivo imaging modality that is able to monitor structure and hemodynamic conditions simultaneously and over long time period. To address this problem, we present an optical coherence microscopy based particle image velocimetry system. This system is capable of invasively imaging biological sample structures at micrometer resolution and providing velocity information at the same time. With this imaging set up we successfully assessed velocity profile in a microfluidic system with simultaneous structure details demonstration of the microfluidic channel. Both flow measurement and structural information were verified using conventional microscopy. As a result, OCM-based PIV imaging modality not only makes it feasible to study in detail the process of congenital heart remodeling in response to environmental alterations, but also provides new options for measuring fluid flow in live tissue

Development of Numerical Methods for Accurate and Efficient Scale-Resolving Simulations

Hybrid RANS (Reynolds-Averaged Navier-Stokes)-LES (Large-Eddy Simulation) techniques are considered to be sufficiently accurate and computationally affordable for the aeronautical industry. Scale-resolving simulations is a powerful tool that can accurately predict complex unsteady compressible high-Reynolds-number turbulent flows, as often encountered aeronautical applications. However, since the turbulent scales are resolved instead of modeled, higher demand is placed on the underlying numerical methods used in the simulations.This thesis explores and develops numerical methods suitable for hybrid RANS-LES. The methods are implemented in the Computational Fluid Dynamics (CFD) solver M-Edge, a compressible unstructured node-centered edge-based solver. A low-dissipative, low-dispersive numerical scheme was calibrated and verified in LES of turbulent channel flow and Decaying Homogeneous Isotropic Turbulent (DHIT). It was shown that numerical dissipation and dispersion needs to be carefully tuned, in order to accurately predict resolved turbulent stresses and the correct decay of turbulent kinetic energy. The reported results are in good agreement with reference DNS and experimental data.The optimized numerical scheme was then applied to simulate developing hybrid RANS-LES turbulent channel flow. In order to mitigate the grey area region in the LES zone, a Synthetic Turbulence Generator (STG) was applied at the RANS-LES interface. It was shown that using upstream turbulent statistics from a precursor LES or RANS, the recovery length of the skin friction coefficient could be reduced to just a few boundary layer thicknesses.A new implicit gradient reconstruction scheme suitable for node-centered solvers was proposed. It was shown that the reconstruction scheme achieves fourth-order scaling on regular grids and third-order scaling on irregular grid for an analytical academic case. The Navier-Stokes Characteristic Boundary Condition (NSCBC) was implemented and verified for transport of an analytical vortex. It was shown that special boundary treatment is needed for transporting turbulent structures through the boundary with minimal reflections

Beyond Shallow Water: appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer Theory

International audienceWe study the flow of a thin layer of fluid over a flat surface. Commonly, the 1-D Shallow-water or Saint-Venant set of equations are used to compute the solution of such flows. These simplified equations may be obtained through the integration of the Navier-Stokes equations over the depth of the fluid, but their solution requires the introduction of constitutive relations based on strict hypothesis on the flow régime. Here, we present an approach based on a kind of boundary layer system with hydrostatic pressure. This relaxes the need for closure relations which are instead obtained as solutions of the computation. It is then demonstrated that the corresponding closures are very dependent on the type of flow considered, for example laminar viscous slumps or hydraulic jumps. This has important practical consequences as far as the applicability of standard closures is concerned

Study on the Homogenization Speed in a Tank Equipped with Maxblend Impeller

Le but de ce travail est de caractériser expérimentalement la performance du mélangeur Maxblend dans le cas de suspensions solides. De par le très grand nombre d’applications industrielles qui utilisent le mélange solide-liquide, d'importants efforts ont été mis en œuvre pour améliorer la compréhension de cette opération. Le principal objectif du mélange solide-liquide est de créer et de maintenir l'homogénéisation de la suspension. De telles opérations étant généralement réalisées dans des cuves agitées mécaniquement, le choix d'un agitateur à haute performance est primordial pour assurer à la fois la dispersion des particules et leur suspension. L'agitateur Maxblend est un des plus efficaces parmi la nouvelle génération de mélangeur. Il est composé d’une large pale, située au bas de la cuve, et d'une grille sur la partie supérieure. La pale joue le rôle d'une pompe et la grille permet de créer la dispersion. Le mélangeur Maxblend est une alternative intéressante aux agitateurs raclant et est utilisé dans différents procédés, allant de la dispersion de gaz à la polymérisation. Dans ce travail, une étude expérimentale a été réalisée pour caractériser la performance d’un système de mélange équipé d’un agitateur Maxblend et d’une cuve cylindrique, dans le cas des fluides newtoniens. La vitesse d'homogénéisation (NH), correspondant à la vitesse critique pour obtenir une suspension uniforme, est mesurée par tomographie à résistance électrique. Le travail expérimental a permis d’obtenir, pour diverses viscosités de fluides, la puissance consommée et le temps de mélange. De plus, l’impact de la géométrie de la cuve, de l'espace entre le fond de la cuve et l'agitateur, ainsi que la quantité de solide sur l’efficacité de l’agitateur à générer la suspension ont été étudiés. En se basant sur ces résultats, il est possible de confirmer que le Maxblend est un mélangeur performant, puisqu’il permet d’obtenir une suspension uniforme, un temps de mélange court avec une faible consommation d'énergie. Mots clé: Mélange, Suspension, Solide-Liquide, Maxblend, Newtonien, fluide visqueux, Suspension homogène. ---------- The goal of this work is to characterize experimentally the performance of a Maxblend impeller for solid suspensions. Significant efforts have been devoted to better understand the solid liquid mixing phenomena, because of the large number of industrial applications of this operation. The major objective of solid-liquid mixing is to first create and then maintain homogenous slurry conditions. Such operations are commonly carried out in tanks stirred by suitable mechanical agitators. The important point in designing a solid-liquid suspension is choosing a high performance impeller for achieving both the dispersion of the particles and their suspension, at the same time. The Maxblend impeller is one of the most efficient kinds of the new generation impellers. It is composed of a large bottom paddle and an upper grid. The paddle acts as a pump and the grid provides dispersion capabilities. The Maxblend impeller represents an interesting alternative to close clearance impellers and it has been used in many different processes ranging from gas dispersion to polymerizations. In this study, an experimental investigation is carried out to characterize the mixing performance, for Newtonian fluids in a cylindrical tank equipped with a Maxblend impeller. The homogenization speed (NH) is introduced as the critical speed for the uniform suspension and it is measured by Electrical Resistance Tomography. The experimental work consisted in obtaining the power consumption and the mixing time for various liquid viscosities in Maxblend. Also the effects of vessel geometry, off-bottom clearance and solid loading on solid suspension efficiency are investigated. According to the results, it can be confirmed that Maxblend is an interesting technology to obtain a uniform suspension in light of short mixing time and low power consumption. Key Words: Mixing, Suspension, Solid-Liquid, Maxblend, Newtonian, Viscous fluid, Homogeneous suspensio