LABORATORY SIMULATION OF TURBULENT-LIKE FLOWS

Most turbulence studies up to the present are based on statistical modeling, however, the spatio-temporal flow structure of the turbulence is still largely unexplored. Tur- bulence has been established to have a multi-scale instantaneous streamline structure which influences the energy spectrum and other properties such as dissipation and mixing. In an attempt to further understand the fundamental nature of turbulence and its consequences for efficient mixing, a new class of flows, so called “turbulent-like”, is in- troduced and its spatio-temporal structure of the flows characterised. These flows are generated in the laboratory using a shallow layer of brine and controlled by multi-scale electromagnetic forces resulting from a combination of electric current and a magnetic field created by a fractal permanent magnet distribution. These flows are laminar, yet turbulent-like, in that they have multi-scale streamline topology in the shape of “cat’s eyes” within “cat’s eyes” (or 8’s within 8’s) similar to the known schematic streamline structure of two-dimensional turbulence. Unsteadiness is introduced to the flows by means of time-dependent electrical current. Particle Tracking Velocimetry (PTV) measurements are performed. The technique developed provides highly resolved Eulerian velocity fields in space and time. The analysis focuses on the impact of the forcing frequency, mean intensity and amplitude on various Eulerian and Lagrangian properties of the flows e.g. energy spectrum and fluid element dispersion statistics. Other statistics such as the integral length and time scales are also extracted to characterise the unsteady multi-scale flows. The research outcome provides the analysis of laboratory generated unsteady multi- scale flows which are a tool for the controlled study of complex flow properties related to turbulence and mixing with potential applications as efficient mixers as well as in geophysical, environmental and industrial fields

An instrumented tracer for Lagrangian measurements in Rayleigh-B\'enard convection

We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, and analyse its statistics. Additional use of cameras allow us to track the particle position and to report here the first direct measurement of Lagrangian heat flux transfer in Rayleigh-B{\'e}nard convection. The device shows promise for opening new research in a broad variety of fluid systems.Comment: 14 page

Particle tracking velocimetry and accelerometry (PTVA) measurements applied to quasi-two-dimensional multi-scale flows

Accepted versio

Lagrangian modeling of reactive transport in heterogeneous porous media

Tesi per compendi de publicacions, amb diferents seccions retallades per drets de l'editorFluid flow, solute transport, and chemical reactions in porous media are highly relevant for multiple applications and in several fields of knowledge. Aquifers are a typical example of porous media, but many others exist, like for instance biological tissues or wastewater treatment filters. Modeling and simulation of transport processes in porous media can be done through Lagrangian methods, which have certain advantages with respect to classical Eulerian methods. Among these advantages, a key one is that the solution of the advective transport term does not generate any numerical dispersion or instabilities, not even in those cases that are strongly dominated by advection, as opposed to what happens with classical Eulerian methods. However, the incorporation of chemical reaccions in the Lagrangian modeling context involves additional challenges and considerations with respect to conservative transport modeling. In this thesis, which is presented as a compendium of publications, new techniques are developed for modeling reactive transport of solutes in porous media from a Lagrangian perspective. Throghout the thesis, two different types of numerical particles are studied: mass-particles and fluid-particles. In both cases, continuum-scale dispersion (or at least part of it) is represented by random walks of numerical particles. Also in both cases, reactive transport simulations require interaction between nearby particles, either for directly computing reactions (when mass-particles are used) or for exchanging solutes (in the fluid-particle case). For this reason, a large part of this thesis revolves around the study of kernel functions, whose purpose is to mathematically represent the support volume of (and interaction between) particles. In this thesis it is shown that these functions, optimized using statistical theories of Kernel Density Estimation (KDE), may be used to simulate all kinds of nonlinear reactions with the mass-particle method known as Random Walk Particle Tracking (RWPT). Then, a new approach is developed for locally optimizing the particles' support volume (represented by the kernel bandwidth), such that it adapts its size and shape in time and space to minimize error. Thereafter, this technique is implemented in a hybrid manner in combination with a spatial discretization (binning) to improve its computational efficiency and to allow the incorporation of boundary conditions. Regarding fluid-particles, in this thesis it is shown that two methods that exist in Lagrangian modeling literature (Smoothed Particle Hydrodynamics or SPH, and Mass Transfer Particle Tracking) are mathematically equivalent, and they only differ in the choice of kernel used for the solute exchange between particles, which simulates dispersive transport. Finally, a novel Lagrangian fluid-particle method is developed, with an algorithm based on Multi-Rate Interaction by Exchange with the Mean (MRIEM), which enables to account for local-scale concentration fluctuation effects, as well as their generation, transport and decay. The method is shown capable of reproducing experimental results of reactive transport in a porous medium with locally mixing-limited conditions.El flux de fluids, el transport de soluts, i les reaccions químiques en medis porosos són processos amb una gran rellevància en multitud d'aplicacions i àmbits. Els aqüífers són un típic exemple de medi porós, però n'existeixen molts d'altres, com per exemple els teixits biològics, o els filtres per tractament d'aigües residuals. La modelació i simulació de processos de transport de soluts en medis porosos pot ser duta a terme mitjançant mètodes Lagrangians, que presenten certs avantatges respecte als clàssics mètodes Eulerians. Entre aquests avantatges, un dels principals és que la solució del terme advectiu del transport no genera problemes de dispersió numèrica o inestabilitats, ni tan sols en aquells casos fortament dominats per l'advecció, a diferència del que passa amb els mètodes clàssics Eulerians. No obstant això, la incorporació de reaccions químiques en el context Lagrangià comporta reptes i consideracions addicionals respecte de les del transport conservatiu. En aquesta tesi, presentada en format de compendi de publicacions, es desenvolupen noves tècniques per a modelar el transport reactiu de soluts en medis porosos des d'una perspectiva Lagrangiana. Al llarg de la tesi, s'estudien dos tipus diferents de partícules numèriques: partícules de massa i partícules de fluid. En ambdós casos, la dispersió a l'escala de continuu (o almenys una part de la mateixa) és representada mitjançant desplaçaments aleatoris de les partícules numèriques. També en ambdós casos, les simulacions de transport reactiu requereixen la interacció entre partícules properes, ja sigui per a computar directament les reaccions (quan s'usen partícules de massa) o per a intercanviar soluts (en el cas de partícules de fluid). Per això, gran part de la tesi gira al voltant de l'estudi de les funcions Kernel, les quals tenen la finalitat de representar matemàticament el volum de suport de (i interacció entre) les partícules. En aquesta tesi es demostra que aquestes funcions, optimitzades fent servir teories estadístiques d'estimació de densitat per kernels, poden ser utilitzades per a reproduir tot tipus de reaccions no lineals amb el mètode basat en partícules de massa conegut com a "Random Walk Particle Tracking". Seguidament, es desenvolupa una nova manera d'optimitzar localment el volum de suport de les partícules (representat per l'ample de banda del Kernel), de manera que s'adapti en el temps i l'espai per reduir l'error. Posteriorment, aquesta tècnica és implementada de forma híbrida en combinació amb una discretització espaial per a millorar-ne l'eficiència computacional i possibilitar la incorporació de condicions de contorn. Pel que fa al cas de partícules de fluid, en aquesta tesi es demostra que dos mètodes existents a la literatura ("Smoothed Particle Hydrodynamics" o SPH, i "Mass Transfer Particle Tracking") són matemàticament equivalents, i que es diferencien únicament pel Kernel que es fa servir en l'intercanvi de soluts entre partícules, que simula el transport dispersiu. Finalment, es desenvolupa un nou mètode Lagrangià de partícules de fluid, amb un algoritme basat en Interacció per Intercanvi amb la Mitja a Múltiples Velocitats (MRIEM, per les seves sigles en anglès), que permet reproduir l'efecte de les fluctuacions de concentració a l'escala local, així com la seva generació, transport i destrucció. Es demostra que el mètode és capaç de reproduir resultats experimentals de transport reactiu en un medi porós en condicions limitades per la mescla local.Postprint (published version

Finite Time Lyapunov Exponent Analysis of Model Predictive Control and Reinforcement Learning

Finite-time Lyapunov exponents (FTLEs) provide a powerful approach to compute time-varying analogs of invariant manifolds in unsteady fluid flow fields. These manifolds are useful to visualize the transport mechanisms of passive tracers advecting with the flow. However, many vehicles and mobile sensors are not passive, but are instead actuated according to some intelligent trajectory planning or control law; for example, model predictive control and reinforcement learning are often used to design energy-efficient trajectories in a dynamically changing background flow. In this work, we investigate the use of FTLE on such controlled agents to gain insight into optimal transport routes for navigation in known unsteady flows. We find that these controlled FTLE (cFTLE) coherent structures separate the flow field into different regions with similar costs of transport to the goal location. These separatrices are functions of the planning algorithm's hyper-parameters, such as the optimization time horizon and the cost of actuation. Computing the invariant sets and manifolds of active agent dynamics in dynamic flow fields is useful in the context of robust motion control, hyperparameter tuning, and determining safe and collision-free trajectories for autonomous systems. Moreover, these cFTLE structures provide insight into effective deployment locations for mobile agents with actuation and energy constraints to traverse the ocean or atmosphere.Comment: 22 pages, 12 figure

Study of Motion Control of A Flexible Link

20th century has witnessed massive upsurge in the use of manipulators in several industries especially in space, defense, and medical industries. Among the types of manipulators used, single link manipulators are the most widely used. A single link robotic manipulator is nothing but a link controlled by an actuator to carry out a particular function such as placing a payload from point A to point B. For low power requirements single link manipulators are made up of light weight materials which require flexibility considerations.Flexibility makes the dynamics of the link heavily non-linear which induces vibrations and overshoot. In this project initially the dynamic model of rigid flexible manipulator is explained, then the state space model of the manipulator system is incorporated into MATLAB. The link flexibility is studied by a single beam FEmodel, where expressions for kinetic and potential energyare employed to derive the torqueequation.The 3 flexible link equations are coupled in terms of 3 variables, θ, Ø and v. The tip angle is finally given aslvfor flexible case whereas for the rigid manipulator the tip angle is same as the hub angle θ. Thereforeaccurate computation of v is very important. The joint flexibility is excluded from analysis.Several comparisons were made between the rigid and flexible link for torque requirement. The relation between the trajectory and hub angle is also plotted in a graph.Finally a PD controller taking the errors and its derivative is designed based on the rigid link dynamics

Gaussian Process Model Predictive Control of An Unmanned Quadrotor

The Model Predictive Control (MPC) trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic Gaussian Process (GP) models. This is different from conventional models obtained through Newtonian analysis. A hierarchical control scheme is used to handle the trajectory tracking problem with the translational subsystem in the outer loop and the rotational subsystem in the inner loop. Constrained GP based MPC are formulated separately for both subsystems. The resulting MPC problems are typically nonlinear and non-convex. We derived 15 a GP based local dynamical model that allows these optimization problems to be relaxed to convex ones which can be efficiently solved with a simple active-set algorithm. The performance of the proposed approach is compared with an existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation results show that the two approaches exhibit similar trajectory tracking performance. However, our approach has the advantage of incorporating constraints on the control inputs. In addition, our approach only requires 20% of the computational time for NMPC.Comment: arXiv admin note: text overlap with arXiv:1612.0121

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

Investigation of mixed element hybrid grid-based CFD methods for rotorcraft flow analysis

Accurate first-principles flow prediction is essential to the design and development of rotorcraft, and while current numerical analysis tools can, in theory, model the complete flow field, in practice the accuracy of these tools is limited by various inherent numerical deficiencies. An approach that combines the first-principles physical modeling capability of CFD schemes with the vortex preservation capabilities of Lagrangian vortex methods has been developed recently that controls the numerical diffusion of the rotor wake in a grid-based solver by employing a vorticity-velocity, rather than primitive variable, formulation. Coupling strategies, including variable exchange protocols are evaluated using several unstructured, structured, and Cartesian-grid Reynolds Averaged Navier-Stokes (RANS)/Euler CFD solvers. Results obtained with the hybrid grid-based solvers illustrate the capability of this hybrid method to resolve vortex-dominated flow fields with lower cell counts than pure RANS/Euler methods

Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications

Multi-material physics arise in an innumerable amount of engineering problems. A broadly scoped numerical model is developed and described in this thesis to simulate the dynamic interaction of multi-fluid and solid systems. It is particularly aimed at modelling the interaction of two immiscible fluids with solid structures in a coastal engineering context; however it can be extended to other similar areas of research. The Navier Stokes equations governing the fluids are solved using a combination of finite element (FEM) and control volume finite element (CVFE) discretisations. The sharp interface between the fluids is obtained through the compressive transport of material properties (e.g. material concentration). This behaviour is achieved through the CVFE method and a conveniently limited flux calculation scheme based on the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided, consisting of steady and unsteady flows. To further enhance the method, improve accuracy, and exploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It is essentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined by semi-explicitly solving an iterative functional minimisation problem. A multi-phase approach is used to introduce solid structure modelling. In this approach, solution of the velocity field for the fluid phase is obtained using Model B as explained by Gidaspow (1994, page 151). Interaction between the fluid phase and the solids is achieved through the means of a source term included in the fluid momentum equations. The interacting force is calculated through integration of this source term and adding a buoyancy contribution. The resulting force is passed to an external solid-dynamics model such as the Discrete Element Method (DEM), or the combined Finite Discrete Element Method (FEMDEM). The versatility and novelty of this combined modelling approach stems from its ability to capture the fluid interaction with particles of random size and shape. Each of the three main components of this thesis: the advection scheme, the moving mesh method, and the solid interaction are individually validated, and examples of randomly shaped and sized particles are shown. To conclude the work, the methods are combined together in the context of coastal engineering applications, where the complex coupled problem of waves impacting on breakwater amour units is chosen to demonstrate the simulation possibilities. The three components developed in this thesis significantly extend the application range of already powerful tools, such as Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringing them together for the first time