Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems

Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction–diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models

A hybrid lagrangian-eulerian approach for simulation of bubble dynamics

A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolution: (i) fully resolved simulations (FRS) wherein the bubble dynamics and deformation are completely resolved, and (ii) subgrid, discrete bubble model where the bubbles are not resolved by the computational grid. For fully resolved simulations, a novel approach combining a particle-based, mesh-free technique with a finite-volume flow solver, is developed. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. Interpolation kernel based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Unlike front-tracking methods, connectivity between the marker points is not necessary. For underresolved bubbles, a mixture-theory based Eulerian-Lagrangian approach accounting for volumetric displacements due to bubble motion and size variations is developed. The bubble dynamics is modeled by Rayleigh-Plesset equations using an adaptive timestepping scheme. A detailed verification and validation study of both approaches is performed to test the accuracy of the method on a variety of single and multiple bubble problems to show good predictive capability. Interaction of bubbles with a traveling vortex tube is simulated and compared with experimental data of Sridhar and Katz [1] to show good agreement.http://deepblue.lib.umich.edu/bitstream/2027.42/84270/1/CAV2009-final74.pd

Verification and Validation of Numerical Modelling Approaches Pertinent to Stomach Modelling

The digestive system is vital to the human body. Over many decades, scientists have been investigating the food breakdown mechanisms inside the stomach through in vivo human and animal studies and in vitro experiments. Due to recent improvements in computing speed and algorithm development, computational modelling has become a viable option to investigate in-body processes. Such in silico models are more easily controlled to investigate individual variables, do not require invasive physical experiments, and can provide valuable insights into the local physics of gastric flow. There is a huge potential for numerical approaches in stomach modelling as they can provide a comprehensive understanding of the complex flow and chemistry in the stomach. However, to make sure the numerical methods are accurate and reliable, rigorous verification and validation are essential as part of model development. A significant focus of this thesis was on verifying and validating the numerical modelling approaches pertinent to stomach modellin

Analysis of the suction chamber of external gear pumps and their influence on cavitation and volumetric efficiency

Hydraulic machines are faced with increasingly severe performance requirements. The need to design smaller and more powerful machines rotating at higher speeds in order to provide increasing efficiencies, has to face a major limitation: cavitation. A two-dimensional numerical approach, by means of Computational Fluid Dynamics (CFD), has been developed for studying the effect of cavitation in the volumetric efficiency of external gear pumps. Several cavitation models and grid deformation algorithms have been studied, and a method for simulating the contact between solid boundaries has been developed. The velocity field in the inlet chamber has also been experimentally measured by means of Time-Resolved Particle Image Velocimetry (TRPIV) and results have been compared to the numerical ones in order to validate the accuracy of the model. Our two-dimensional model is not able to predict the real volumetric efficiency of the pump, since several simplifications are involved in it. Nevertheless, this model shows to be valid to understand the complex flow patterns that take place inside the pump and to study the influence of cavitation on volumetric efficiency. The influence of the rotational speed of the pump has been analyzed, as well as the effect of the geometry of the inlet chamber, the working pressure, the inlet pressure loss factor, and the flow leakage through the radial clearances of the pump between gears and casing

An embedded boundary approach for simulation of reacting flow problems in complex geometries with moving and stationary boundaries

Many useful engineering devices involve moving boundaries interacting with a reacting compressible flow. Examples of such applications include propulsion systems with moving components such as Internal Combustion (IC) engines, hypersonic propulsive devices such as Oblique Detonation Wave (ODW) engines and solid rocket motors involving regressing propellant surfaces. Computational Fluid Dynamics (CFD) can be effectively employed to study these systems. However, conventional numerical methods face several difficulties related to grid generation, treatment of moving boundaries, lack of adequate grid resolution at an affordable computational cost, and shortcomings in closure models required for Large Eddy Simulation (LES). This thesis demonstrates new accurate numerical models and subgrid closures for LES of problems in non-trivial geometries with moving boundaries. A new high-order adaptive cut-cell based embedded boundary method is developed for viscous flows, which can provide a smooth and accurate reconstruction to predict the near-wall shear stress and pressure distribution. The method can achieve a high order of accuracy even under adverse geometrical constraints such as narrow gaps and sharp corners due to a novel and robust cell clustering algorithm. This algorithm also enforces the stability of the numerical scheme in the presence of arbitrary low volume cells formed in the cell cutting process. Additionally, an extended cell clustering approach, which can achieve exact conservation of mass, momentum, and energy is proposed for moving boundaries. The embedded boundary method is built on a massively parallel framework that performs block structured Adaptive Mesh Refinement (AMR) by interfacing with the BoxLib open source library. This modeling framework is then applied to study fundamental physics in high-speed propulsion systems, for example, shock-turbulence interactions, flame-turbulence interaction, and flame/detonation stabilization in a reacting system. LES using the multilevel subgrid closure for flow and chemistry is used to study flame anchoring in a transverse reacting jet in cross flow. Important mechanisms that stabilize the flame are identified and shown to be consistent with past observations from experiments and using direct numerical simulations (DNS) but obtained here using much coarser grid LES. Finally, to demonstrate the ability of the methodology to simulate moving bodies in a reactive system, DNS of a hypersonic projectile fired into a reacting flow is performed to reveal key effects of pressure on the stabilization of detonation ahead of the projectile.Ph.D

Concept innovant d'échangeur/réacteur multifonctionnel par contrôle dynamique passif par générateurs de vorticité flexibles

The aim of this study is to investigate the use of fluid-structure interaction (FSI) to improve heat transfer and mixing performances in multi-functional heat exchangers/reactors, and to evaluate configuration designs where the main target is to produce and maintain self-sustained oscillations of flexible vortex generators. At first, two dimensional laminar flow studies are numerically investigated. The results show that a minimum of three alternating flaps is needed to produce an instability that leads to large displacement oscillations. However, the introduction of two co-planar flaps upstream destabilizes the flow by creating periodic forces that act on the alternating downstream flaps. Hence, this results in artificially increasing the reduced velocity that will induce the alternating flaps to be in a lock-in state. Thus in this case, large displacement amplitudes are created with two alternating flaps only. The free flaps oscillations produce vortices of higher strength which have a positive impact on heat transfer and mixing. Secondly, a three dimensional HEV configuration with flexible trapezoidal vortex generators inclined with an angle of 45◦ with respect to the wall and reversed opposite to the flow direction is numerically investigated. Fast Fourier Transformation is applied on the temporal variation of the Proper Orthogonal Decomposition (POD) coefficientswhich displays a dominant peak in the flow and corresponds to the vortices periodic formation and detachment. This dominant frequency synchronizes well with the structural oscillation frequency and the fundamental frequency of the tabs reaching a lock-in state and leading to large oscillation amplitudes.Le but de cette étude est d’étudier l’utilisation d’interactions fluide-structure (FSI) pour améliorer le transfert de chaleur et les performances de mélange dans des échangeurs-réacteurs multifonctionnels, et d’évaluer des configurations pour lesquelles l’objectif est de produire et de maintenir un régime dynamique auto-entretenu d’oscillations des générateurs de tourbillons flexibles. Dans un premier temps, deux études numériques ont été réalisées pour des écoulements laminaires bidimensionnels. Les résultats montrent qu’un minimum de trois générateurs de tourbillons alternés est nécessaire pour produire une instabilité qui engendre les oscillations de larges amplitudes. L’ajout de deux promoteurs coplanaires en amont déstabilise l’écoulement en créant des forces périodiques agissant sur les générateurs de tourbillons en aval. Il en résulte une augmentation de la vitesse réduite qui impose un blocage en fréquence des oscillations des générateurs de tourbillons en aval. Dans cette configuration, des oscillations de larges amplitudes sont obtenues pour uniquement deux générateurs de tourbillons en aval. Les oscillations des générateurs de tourbillons produisent une vorticité intense qui a une incidence positive que le transfert de chaleur et sur le mélange. Dans un second temps, une configuration tridimensionnelle HEV incluant des générateurs de tourbillons trapézoïdaux flexibles orientés a 45◦ vers l’amont est étudiée par simulations numériques. Une analyse FFT réalisée sur les coefficients issus d’une analyse POD montre un pic fréquentiel correspondant aux formations et lâchers tourbillonnaires périodiques. Cette fréquence dominante correspond bien au mode propre d’oscillation des générateurs de tourbillons et engendre ainsi de larges amplitudes d’oscillations