Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Melting heat transfer analysis on magnetohydrodynamics buoyancy convection in an enclosure : a numerical study

Therollof melting heat transfer on magnetohydrodynamic natural convection in a square enclosurewithheatingof the bottom wall is examinednumericallyin this article.The dimensionlessgoverning partial differential equations are transformed into vorticity and stream functionformulationand then solved using the finite difference method(FDM). The effects of thermal Rayleigh number(Ra), melting parameter(M) and Hartmann number(Ha) are illustrated graphically.With an increasing melting parameter and Rayleigh number, the rate of fluid flow and temperature gradients are seen to increase. And in the presence of magnetic field, the temperature gradient reduces and hence the conductionmechanism dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameterin the both cases of heating of bottom wall

Numerical Simulations of Thermal Systems-Applications To Fuel Chemistry, Nanofluid Heat Transfer And Aerosol Particle Transport.

In this dissertation, three topics in thermal systems are investigated: 1) the effect of methyl-ester content on combustion chemistry of a biodiesel surrogate; 2) the effects of non-uniform particle sizes and fluid temperature on heat transfer characteristics of liquid water containing alumina nano-particles; 3) the effects of obstacle arrangements on transport of aerosol particles in channel flows. The investigation focuses on computational modeling and analysis in the above problems. In the first study, a kinetic modeling comparison of methyl butanoate and n-butane, its corresponding alkane, contrasts the combustion of methyl esters and normal alkanes, with the aim of understanding the effect of the methyl ester moiety. A fuel-breakdown model [J. Org. Chem. 2008, 73, 94; J. Phys. Chem. A 2008, 112, 51] is added to existing chemical kinetic mechanisms to improve the prediction of CO2 formation from MB decomposition. Sensitivity and reaction pathway analysis show that the absence of negative temperature coefficient behaviors and reduction of soot precursors can be ascribed to the effect of the methyl ester. The second study analyzes the heat transfer and fluid flow of natural convection in a cavity filled with Al2O3/water nanofluid that operates within differentially heated walls. The Navier-Stokes and energy equations are solved numerically, coupling the model of effective thermal conductivity [J. Phys. D 2006, 39, 4486] and model of effective dynamic viscosity [Appl. Phys. Lett. 2007, 91, 243112]. The numerical simulations explore the range where the heat transfer uncertainties can be affected by the operating conditions of the nanoparticles. Furthermore, the suppressed heat transfer phenomena are in good agreement with the latest experimental data of Ho et al. [Int. J. Therm. Sci. 2010, 49, 1345]. Finally, by using a simple lattice Boltzmann model coupled with a Lagrangian formalism, this study investigates the dispersion and deposition of aerosol particles over staggered obstacles in a two-dimensional channel flow. Particle motion mechanisms considered in the particle phase equation include drag, gravity, lift and Brownian forces. In this study, the results highlight the range of particle dimensions where the particle deposition can be affected by the arrangement of blocks placed in the channel flow.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86287/1/kclin_1.pd

Numerical investigation of particle-fluid interaction system based on discrete element method

This thesis focuses on the numerical investigation of the particle-fluid systems based on the Discrete Element Method (DEM). The whole thesis consists of three parts, in each part we have coupled the DEM with different schemes/solvers on the fluid phase. In the first part, we have coupled DEM with Direct Numerical Simulation (DNS) to study the particle-laden turbulent flow. The effect of collisions on the particle behavior in fully developed turbulent flow in a straight square duct was numerically investigated. Three sizes of particles were considered with diameters equal to 50 µm, 100 µm and 500 µm. Firstly, the particle transportation by turbulent flow was studied in the absence of the gravitational effect. Then, the particle deposition was studied under the effect of the wall-normal gravity force in which the influence of collisions on the particle resuspension rate and the final stage of particle distribution on the duct floor were discussed, respectively. In the second part, we have coupled DEM with Lattice Boltzmann Method (LBM) to study the particle sedimentation in Newtonian laminar flow. A novel combined LBM-IBM-DEM scheme was presented with its application to model the sedimentation of two dimensional circular particles in incompressible Newtonian flows. Case studies of single sphere settling in a cavity, and two particles settling in a channel were carried out, the velocity characteristics of the particle during settling and near the bottom were examined. At last, a numerical example of sedimentation involving 504 particles was finally presented to demonstrate the capability of the combined scheme. Furthermore, a Particulate Immersed Boundary Method (PIBM) for simulating the fluid-particle multiphase flow was presented and assessed in both two and three-dimensional applications. Compared with the conventional IBM, dozens of times speedup in two-dimensional simulation and hundreds of times in three-dimensional simulation can be expected under the same particle and mesh number. Numerical simulations of particle sedimentation in the Newtonian flows were conducted based on a combined LBM - PIBM - DEM showing that the PIBM could capture the feature of the particulate flows in fluid and was indeed a promising scheme for the solution of the fluid-particle interaction problems. In the last part, we have coupled DEM with averaged Navier-Stokes equations (NS) to study the particle transportation and wear process on the pipe wall. A case of pneumatic conveying was utilized to demonstrate the capability of the coupling model. The concrete pumping process was then simulated, where the hydraulic pressure and velocity distribution of the fluid phase were obtained. The frequency of the particles impacting on the bended pipe was monitored, a new time average collision intensity model based on impact force was proposed to investigate the wear process of the elbow. The location of maximum erosive wear damage in elbow was predicted. Furthermore, the influences of slurry velocity, bend orientation and angle of elbow on the puncture point location were discussed.Esta tesis se centra en la investigación numérica de sistemas partícula-líquido basado en la técnica Discrete Element Method (DEM). La tesis consta de tres partes, en cada una de las cuales se ha acoplado el método DEM con diferentes esquemas/solucionadores en la fase fluida. En la primera parte, hemos acoplado los métodos DEM con Direct Numerical Simulation (DNS) para estudiar casos de "particle-laden turbulent flow". Se investigó numéricamente el efecto de las colisiones en el comportamiento de las partículas en el flujo turbulento completamente desarrollado en un conducto cuadrado recto. Tres tamaños de partículas se consideraron con diámetros de 50, 100 y 500 micrometros. En primer lugar, el transporte de partículas por el flujo turbulento se estudió en la ausencia del efecto gravitacional. Entonces, la deposición de partículas se estudió bajo el efecto de la fuerza de gravedad normal a la pared, en el que se discutieron la influencia de la tasa de colisiones en re-suspensión de las partículas y la fase final de la distribución de partículas en el suelo del conducto, respectivamente. En la segunda parte, se ha acoplado los métodos DEM con Lattice Boltzmann Method (LBM) para estudiar la sedimentación de partículas en flujo laminar newtoniano. Un nuevo metodo combinado LBM-IBM-DEM se presentó y ha sido aplicado para modelar la sedimentación de dos partículas circulares bi-dimensionales en flujos Newtonianos incompresibles. Se estudiaron casos de sedimentación en una cavidad de una sola esfera, y sedimentación de dos partículas en un canal, las características de la velocidad de la partícula durante la sedimentación y cerca de la base fueron también examinados. En el último caso, un ejemplo numérico de sedimentación de 504 partículas fue finalmente presentado para demostrar la capacidad del método combinado. Además, se ha presentado un método "Particulate Immersed Boundary Method" (PIBM) para la simulación de flujos multifásicos partícula-fluido y ha sido evaluado en dos y tres dimensiones. En comparación con el método IBM convencional, se puede esperar con el mismo número de partículas y de malla un SpeedUp docenas de veces superior en la simulación bidimensional y cientos de veces en la simulación en tres dimensiones. Se llevaron a cabo simulaciones numéricas de la sedimentación de partículas en los flujos newtonianos basados en una combinación LBM - PIBM - DEM, mostrando que el PIBM podría capturar las características de los flujos de partículas en el líquido y fue en efecto un esquema prometedor para la solución de problemas de interacción fluido-partícula. En la última parte, se ha acoplado el método DEM con las ecuaciones promediadas de Navier-Stokes (NS) para estudiar el transporte de partículas y el proceso de desgaste en la pared de una tubería. Se utilizó un caso de transporte neumático para demostrar la capacidad del modelo acoplado. Entonces se simuló el proceso de bombeo de hormigón, de donde se obtuvo la presión hidráulica y la distribución de la velocidad de la fase fluida. Se monitoreó la frecuencia de impacto de las partículas en la tubería doblada, se propuso un nuevo modelo de intensidad de colisión promediado en tiempo para investigar el proceso de desgaste del codo basado en la fuerza de impacto. Se predijo la ubicación del daño máximo desgaste por erosión en el codo. Además, se examinaron las influencias de la velocidad de pulpa, la orientación y el ángulo de curvatura del codo en la ubicación del punto de punción.Postprint (published version

Transient removal of contaminant from a channel with differentially heated wall of cavity

Cleaning accumulated deposits inside pipe cavity are by disassembling and cleaning it part by part. Hydrodynamic cleaning of the cavity is an alternative method to clean accumulated deposits or contaminants inside the pipe cavity instead of dissembling them part by part is a tedious process or using a solvent which is not suitable in the food processing industry. This study aims to investigate the contaminants removal process from a cavity by resorting to natural flow to clean the deposits in different cavity sizes and includes different heating locations with different flow configurations. An experimental method is used to visualize the flow behaviour inside the cavity of a channel at a large aspect ratio in isothermal conditions. These results are used to validate numerical results obtained in isothermal flow conditions. For numerical study, Constrained Interpolated Profile (CIP) method is used for the advection phase of momentum and energy equation, and central difference is used to solve the non-advection phase of momentum and energy equations. The numerical studies include different aspect ratios (AR), 1 to 4, various Reynolds numbers (Re), 50 to 1000, and different locations of the heated wall inside the cavity (left wall, bottom wall, & right wall) for three different Grashof numbers (Gr), 1000, 10 000, and 100 000. The particles removal percentage at the transient and steady states are then compared and discussed. A larger aspect ratio and a more significant Reynolds number for isothermal conditions will give a higher percentage of contaminants removal except for AR = 4 and Re = 50. This particular flow shows a higher percentage of contaminant removal than AR = 4; Re = 100, 200, and 400. For mixed convection flow, one typical result can be concluded: at small Gr, the contaminant removal percentage is not changing significantly for all different heated wall positions. It is also shown that a more significant aspect ratio will produce a better contaminant removal process, and a higher Grashof number will improve the contaminant removal process. It is also found that when Gr equals 1000 and 10000, there is no significant change in the contaminant removal process and constant heat flux from the bottom wall for Gr = 100,000 gives the highest contaminant removal percentage for every aspect ratio. The highest percentage removal of contaminant is 98.94% for Gr =100 000, AR=4

Lattice Boltzmann Numerical Investigation of Inner Cylindrical Pin-fins Configuration on Nanofluid Natural Convective Heat Transfer in Porous Enclosure

Concerning the geometrical effect of inner cylindrical hot pins, the natural convective heat transfer of nanofluid in a homogenous porous medium in a squared enclosure is numerically studied, using lattice Boltzmann method (LBM). In order to investigate the arrangement of inner cylinders for better heat transfer performance, five different configurations (including one, three, and four pins) were compared, while the total heat transfer area of inner pins were held fixed. Squared cavity walls and inner cylinder’s surfaces were constantly held at cold and warm temperatures, respectively. In our simulation, Brinkman and Forchheimer-extended Darcy models were utilized for isothermal incompressible flow in porous media. The flow and temperature fields were simulated using coupled flow and temperature distribution functions. The effect of porous media was added as a source term in flow distribution functions. The results were validated using previous creditable data, showing relatively good agreements. After brief study of copper nano-particles volume fraction effects, five cases of interest were compared for different values of porosity and Rayleigh number by means of averaged Nusselt number of hot and cold walls; and also local Nusselt number of enclosure walls. Comparison of different cases shows the geometrical dependence of overall heat transfer performance via the average Nusselt number of hot pins strongly depending on their position. The four pin case with diamond arrangement shows the best performance in the light of enclosure walls’ average Nusselt number (heat transfer to cold walls). However, the case with three pins and downward triangular arrangement surprisingly gives promising heat transfer performance. In addition, the results show that natural convective heat transfer and flow field is intensified with increasing Rayleigh number, Darcy number, and porosity

Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity

The transient conjugate natural convection heat transfer in a differentially-heated cavity with a partition of finite thickness and thermal conductivity are investigated numerically over the range of the Rayleigh number from 103 to 108, the thermal conductivity ratio of partition to that of fluid from 0.1 to 1000, and the dimensionless partition thickness from 0.05 to 0.2. An analysis of the obtained temperature contours and profiles, the time for the onset of stratification and the Nusselt number shows that the thermal conductivity ratio effect is significant only over the range of 0.1–10, when the role played by the partition changes, whereas the effect becomes negligible as the thermal conductivity ratio is very large (100 or beyond). It is also found that the scaling relations developed for the non-partitioned cavity are found to be applicable for the partitioned cavity. The results further show that the effect of the partition thickness on heat transfer is significant mainly when the thermal conductivity ratio is small

A Review on Contact and Collision Methods for Multi-body Hydrodynamic problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.Comment: 37 pages, 12 Figure

Numerical predictions of laminar and turbulent forced convection: Lattice Boltzmann simulations using parallel libraries

This paper presents the performance comparison of various parallel lattice Boltzmann codes for simulation of incompressible laminar convection in 2D and 3D channels. Five different parallel libraries namely; matlabpool, pMatlab, GPU-Matlab, OpenMP and OpenMP+OpenMPI were used to parallelize the serial lattice Boltzmann method code. Domain decomposition method was adopted for parallelism for 2D and 3D uniform lattice grids. Bhatnagar-Gross-Krook approximation with lattice types D2Q9, D2Q19 and D2Q5, D2Q6 were considered to solve 2D and 3D fluid flow and heat transfer respectively. Parallel computations were conducted on a workstation and an IBM HPC cluster with 32 nodes. Laminar forced convection in a 2D and turbulent forced convection in a 3D channels was considered as a test case. The performance of parallel LBM codes was compared with serial LBM code. Results show that for a given problem, parallel simulations using matlabpool and pMatlab library perform almost equal. Parallel simulations using C language with OpenMP libraries were 10 times faster than simulations involving Matlab parallel libraries. Parallel simulations with OpenMP+OpenMPI were 0.35 times faster than the reported parallel lattice Boltzmann method code in the literature

Development of a flexible forcing immersed boundary-lattice Boltzmann method and its applications in thermal and particulate flows

Ph.DDOCTOR OF PHILOSOPH