Numerical simulation and flow analysis of an elbow diffuser

Numerical simulation of the unsteady turbulent flow in a three-dimensional elbow diffuser is performed. The investigation is carried out with a commercial finite volume solver implementing the Reynolds averaged Navier-Stokes equations. Against the background of current research in DNS and LES, the modeling of most practically relevant turbulent flows continues to be based on this system of equations. For this reason it is important to evaluate the limitations of the Reynolds averaging approach with the associated turbulence modeling, in particular for the prediction of time-dependent flows. Verification and validation are presented; detailed measurements are compared with computations. While a great deal of research has focused on draft tube design, relatively little is known about the complex flow features present. The flow is analyzed over a wide range of operating conditions including part load. Topological changes in the flow patterns with the global characteristics of the diffuser are presented. Visualization provides extra insight into the complex flow. Forced and self-sustained time-dependent flow phenomena are captured. Falling into these categories are flow field fluctuations introduced by the runner, self-sustained vortex shedding phenomena, and the typical rotating helical vortex observed at part load. Additionally, the linear stability of measured inlet profiles is investigated, providing a fuller understanding of the basic instability mechanism.

Simulation of shear-driven flows

Roland Bouffanais

The research work reported in the present dissertation is aimed at the analysis of complex physical phenomena involving instabilities and nonlinearities occurring in fluids through state-of-the-art numerical modeling. Solutions of intricate fluid physics problems are devised in two particularly arduous situations: fluid domains with moving boundaries and the high-Reynolds-number regime dominated by nonlinear convective effects. Shear-driven flows of incompressible Newtonian fluids enclosed in cavities of varying geometries are thoroughly investigated in the two following frameworks: transition with a free surface and confined turbulence. The physical system we consider is made of an incompressible Newtonian fluid filling a bounded, or partially bounded cavity. A series of shear-driven flows are easily generated by setting in motion some part of the container boundary. These driven-cavity flows are not only technologically important, they are of great scientific interest because they display almost all physical fluid phenomena that can possibly occur in incompressible flows, and this in the simplest geometrical settings. Thus corner eddies, secondary flows, longitudinal vortices, complex three-dimensional patterns, chaotic particle motions, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same geometry. This facilitates the comparison of results from experiments, analysis, and computation over the whole range of Reynolds numbers. The flows under consideration are part of a larger class of confined flows driven by linear or angular momentum gradients. This dissertation reports a detailed study of a novel numerical method developed for the simulation of an unsteady free-surface flow in three-space-dimensions. This method relies on a moving-grid technique to solve the Navier-Stokes equations expressed in the arbitrary Lagrangian-Eulerian (ALE) kinematics and discretized by the spectral element method. A comprehensive analysis of the continuous and discretized formulations of the general problem in the ALE frame, with nonlinear, non-homogeneous and unsteady boundary conditions is presented. In this dissertation, we first consider in the internal turbulent flow of a fluid enclosed in a bounded cubical cavity driven by the constant translation of its lid. The solution of this flow relied on large-eddy simulations, which served to improve our physical understanding of this complex flow dynamics. Subsequently, a novel subgrid model based on approximate deconvolution methods coupled with a dynamic mixed scale model was devised. The large-eddy simulation of the lid-driven cubical cavity flow based on this novel subgrid model has shown improvements over traditional subgrid-viscosity type of models. Finally a new interpretation of approximate deconvolution models when used with implicit filtering as a way to approximate the projective grid filter was given. This led to the introduction of the grid filter models. Through the use of a newly-developed method of numerical simulation, in this dissertation we solve unsteady flows with a flat and moving free-surface in the transitional regime. These flows are the incompressible flow of a viscous fluid enclosed in a cylindrical container with an open top surface and driven by the steady rotation of the bottom wall. New flow states are investigated based on the fully three-dimensional solution of the Navier-Stokes equations for these free-surface cylindrical swirling flows, without resorting to any symmetry properties unlike all other results available in the literature. To our knowledge, this study delivers the most general available results for this free-surface problem due to its original mathematical treatment. This second part of the dissertation is a basic research task directed at increasing our understanding of the influence of the presence of a free surface on the intricate transitional flow dynamics of shear-driven flows.

EPFL2007

Grid Filter Models for the Large Eddy Simulation of Fluid Flows

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.

EPFL2010

Approximation numérique des écoulements turbulents dans des cuves d'électrolyse de l'aluminium

Jonathan Rochat

Aluminium is a metal extracted from bauxite ore using electrolysis process in cells of big size. A huge electric current goes in the cell through an electrolytic bath and aluminium liquid. These currents generate strong magnetic forces that allow the bath and the aluminium to move. A good knowledge of these turbulent flows is very important to optimize the process. The purpose of this thesis is to study and simulate turbulent flows in the aluminium smelting process. These flows are solved numerically with a finite element method. In particular, the Navier-Stokes equations for bifluid flows with free moving interface are solved numerically. In the first part of this work, we develop some mixing-length models that take into account the effects of the wall. A theoretical mathematical study shows the validity of these models and we give some recommendation on the choice of the parameters of the computation. In the second part we study the resolution of the Navier-Stokes equations. The study focuses on algorithms that decouple the computation of the speed and pressure, commonly called projection method or Chorin-Temam algorithm. The final section provides answers on the relevance of wall modelling and projection methods in numerical simulation of turbulent flows in the aluminium smelting process. In particular, we obtain a numerical model that produces a realistic flow with a reasonable CPU time and we discuss the choice of certain parameters involved in the different models.