In this thesis, the Smoothed Particle Hydrodynamics (SPH) method is applied to elastic dynamics and fracture. More specifically, two coupling methods are presented which make use of both the Eulerian and Total Lagrangian formulations. These coupling methods are intended for problems whereby SPH particles, which constitute the domain, are required to convert from a Total Lagrangian kernel to an Eulerian kernel once a damage criterion is activated. The conservation equations are derived for the Eulerian and Total Lagrangian formulations, in a consistent manner which naturally presents the conditions required for the conservation of momentum and energy. These derivations are written such that they make no use of the symmetrical nature of the kernel function or the anti-symmetrical nature of the kernel function gradient. The conservation of momentum and energy is then enforced, along with improving the consistency of the formulations, by implementing the mixed kernel-and-gradient correction. This mixed correction can be applied to both the Eulerian and Total Lagrangian formulations without detracting from the energy and momentum preserving properties provided that the kernel gradient anti-symmetry property is not exploited. The symmetry terms, which are often found in SPH, are included in the derivation of the conservation equations. This is done both to reduce the number of calculations required and to simplify the first coupling procedure. Both coupled formulations are further expanded by highlighting how artificial viscosity can be introduced. A disadvantage of the first coupling method, this being the incompatibility with artificial stress, is also detailed. The equations of state and the plasticity and damage models used in this work are outlined. Additionally, a number of practical details concerning numerical implementation are given. These include the coupled implementations of ghost particle boundary conditions, memory storage, OpenMP implementation, and the Predict, Evaluate, Correct (PEC) form of leapfrog time integration used. Lastly, the proposed formulations and models are verified and validated. This is done by modelling progressively more complex simulations that verify individual aspects of the formulations. Either analytical or experimental results are used for validation where possible. The final simulations highlight how high velocity impacts can be modelled using the proposed coupled mixed correction Eulerian Total Lagrangian SPH method.

Controlled cooling is an important part of steel production industry that affects the properties of the outcome steel. Many of the researches done in controlled cooling are experimental. Due to progress in the numerical techniques and high cost of experimental works in this field the numerical work seems more feasible. Heat transfer analysis is the necessary element of successful controlled cooling and ultimately achievement of novel properties in steel. Heat transfer on the surface of the plate normally contains different regimes such as film boiling, nucleate boiling, transition boiling and radiation heat transfer. This makes the analysis more complicated. In order to perform the heat transfer analysis often empirical correlations are being used. In these correlations the velocity and pressure within the fluid domain is involved. Therefore in order to obtain a better understanding of heat transfer process, study of hydrodynamics of the fluid becomes necessary. Circular jet due to its high efficiency has been used vastly in the industry. Although some experimental studies of round jet arrays have been done, yet the characteristics of a single jet with industrial geometric and flow parameters on the surface of a flat plate is not fully understood. Study of hydrodynamics of the jet impingement is the first step to achieve better understanding of heat transfer process. Finite element method as a popular numerical method has been used vastly to simulate different domains. Traditional approaches of finite element method, Lagrangian and Eulerian, each has its own benefits and drawbacks. Lagrangian approach has been used widely in solid domains and Eulerian approach has been widely used in fluid fields. Jet impingement problem, due to its unknown free surface and the change in the boundary, falls in the category of special problems and none of the traditional approaches is suitable for this application. The Arbitrary Lagrangian Eulerian (ALE) formulation has emerged as a technique that can alleviate many of the shortcomings of the traditional Lagrangian and Eulerian formulations in handling these types of problems. Using the ALE formulation the computational grid need not adhere to the material (Lagrangian) nor be fixed in space (Eulerian) but can be moved arbitrarily. Two distinct techniques are being used to implement the ALE formulation, namely the operator split approach and the fully coupled approach. This thesis presents a fully coupled ALE formulation for the simulation of flow field. ALE form of Navier-Stokes equations are derived from the basic principles of continuum mechanics and conservation laws in the fluid. These formulations are then converted in to ALE finite element equations for the fluid flow. The axi-symmetric form of these equations are then derived in order to be used for jet impingement application. In the ALE Formulation as the mesh or the computational grid can move independent of the material and space, an additional set of unknowns representing mesh movement appears in the equations. Prescribing a mesh motion scheme in order to define these unknowns is problem-dependent and has not been yet generalized for all applications. After investigating different methods, the Winslow method is chosen for jet impingement application. This method is based on adding a specific set of partial differential Equations(Laplace equations) to the existing equations in order to obtain enough equations for the unknowns. Then these set of PDEs are converted to finite element equations and derived in axi-symmetric form to be used in jet impingement application. These equations together with the field equations are then applied to jet impingement problem. Due to the number of equations and nonlinearity of the field equations the solution of the problem faces some challenges in terms of convergence characteristics and modeling strategies. Some suggestions are made to deal with these challenges and convergence problems. Finally the numerical treatment and results of analyzing hydrodynamics of the Jet Impingement is presented. The work in this thesis is confined to the numerical simulation of the jet impingement and the specifications of an industrial test setup only have been used in order to obtain the parameters of the numerical model. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Fluidized bed reactor technology has been widely adopted within the industry as vital component for numerous manufacturing, power generation and gasification processes due to its enhanced mixing characteristics. Computational modeling of fluidized bed hydrodynamics is a significant challenge that has to be tackled for increasing predictive accuracy. The distributor plate of a fluidized bed is typically modeled using a uniform inlet condition, when in reality the inlet is non-uniform inlet. The regions of bed mass that do not fluidize because of the non-uniform inlet conditions form deadzones and remain static between the jets. A new model based on the mass that contributes to the pressure drop is proposed to model a fluidized bed, and has been investigated for a cylindrical reactor for glass beads, ceramic single solids particles, and glass-ceramic, and ceramic-ceramic binary mixtures. The adjusted mass model was shown to accurately predict fluidization characteristics such as pressure drop and minimum fluidization velocity. The effectiveness of the adjusted mass model was further illustrated by applying it to fluidized beds containing coal, switchgrass, poplar wood, and cornstover biomass particles and coal-biomass binary mixtures. The adjusted mass model was further analyzed for bed expansion heights of different mixtures, and for solids distribution by analyzing the solids volume fraction. The effect of increasing the percent biomass in the mixture was also investigated. To further model the non-uniform inlet condition, two different distributor configurations with 5 and 9 jets was considered for a quasi-2D bed, and simulations were performed in both 2D and 3D. Fluidization characteristics and mixing of the bed were analyzed for the simulation. Furthermore, the deadzones formed due to multiple jet configurations of the distributor are quantified and their distributions over the plate were analyzed. / Ph. D.

An Euler tour of a hypergraph is a closed walk that traverses every edge exactly once; if a hypergraph admits such a walk, then it is called eulerian. Although this notion is one of the progenitors of graph theory --- dating back to the eighteenth century --- treatment of this subject has only begun on hypergraphs in the last decade. Other authors have produced results about rank-2 universal cycles and 1-overlap cycles, which are equivalent to our definition of Euler tours. In contrast, an Euler family is a collection of nontrivial closed walks that jointly traverse every edge of the hypergraph exactly once and cannot be concatenated simply. Since an Euler tour is an Euler family comprising a single walk, having an Euler family is a weaker attribute than being eulerian; we call a hypergraph quasi-eulerian if it admits an Euler family. Due to a result of Lovász, it can be much easier to determine that some classes of hypergraphs are quasi-eulerian, rather than eulerian; in this thesis, we present some techniques that allow us to make the leap from quasi-eulerian to eulerian. A triple system of order n and index λ (denoted TS(n,λ)) is a 3-uniform hypergraph in which every pair of vertices lies together in exactly λ edges. A Steiner triple system of order n is a TS(n,1). We first give a proof that every TS(n,λ) with λ ⩾ 2 is eulerian. Other authors have already shown that every such triple system is quasi-eulerian, so we modify an Euler family in order to show that an Euler tour must exist. We then give a proof that every Steiner triple system (barring the degenerate TS(3,1)) is eulerian. We achieve this by first constructing a near-Hamilton cycle out of some of the edges, then demonstrating that the hypergraph consisting of the remaining edges has a decomposition into closed walks in which each edge is traversed exactly once. In order to extend these results on triple systems, we define a type of hypergraph called an ℓ-covering k-hypergraph, a k-uniform hypergraph in which every ℓ-subset of the vertices lie together in at least one edge. We generalize the techniques used earlier on TS(n,λ) with λ ⩾ 2 and define interchanging cycles. Such cycles allow us to transform an Euler family into another Euler family, preferably of smaller cardinality. We first prove that all 2-covering 3-hypergraphs are eulerian by starting with an Euler family that has the minimum cardinality possible, then demonstrating that if there are two or more walks in the Euler family, then we can rework two or more of them into a single walk. We then use this result to prove by induction that, for k ⩾ 3, all (k-1)-covering k-hypergraphs are eulerian. We attempt to extend these results further to all ℓ-covering k-hypergraphs for ℓ ⩾ 2 and k ⩾ 3. Using the same induction technique as before, we only need to give a result for 2-covering k-hypergraphs. We are able to use Lovász's condition and some counting techniques to show that these are all quasi-eulerian. Finally, we give some constructive results on hypergraphs with small edge cuts. There has been analogous work by other authors on hypergraphs with small vertex cuts. We reduce the problem of finding an Euler tour in a hypergraph to finding an Euler tour in each of the connected components of the edge-deleted subhypergraph, then show how these individual Euler tours can be concatenated.

Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered.

In this thesis we consider two sets of combinatorial structures defined on an Eulerian graph: the Eulerian orientations and Euler tours. We are interested in the computational problems of counting (computing the number of elements in the set) and sampling (generating a random element of the set). Specifically, we are interested in the question of when there exists an efficient algorithm for counting or sampling the elements of either set. The Eulerian orientations of a number of classes of planar lattices are of practical significance as they correspond to configurations of certain models studied in statistical physics. In 1992 Mihail and Winkler showed that counting Eulerian orientations of a general Eulerian graph is #P-complete and demonstrated that the problem of sampling an Eulerian orientation can be reduced to the tractable problem of sampling a perfect matching of a bipartite graph. We present a proof that this problem remains #Pcomplete when the input is restricted to being a planar graph, and analyse a natural algorithm for generating random Eulerian orientations of one of the afore-mentioned planar lattices. Moreover, we make some progress towards classifying the range of planar graphs on which this algorithm is rapidly mixing by exhibiting an infinite class of planar graphs for which the algorithm will always take an exponential amount of time to converge. The problem of counting the Euler tours of undirected graphs has proven to be less amenable to analysis than that of Eulerian orientations. Although it has been known for many years that the number of Euler tours of any directed graph can be computed in polynomial time, until recently very little was known about the complexity of counting Euler tours of an undirected graph. Brightwell and Winkler showed that this problem is #P-complete in 2005 and, apart from a few very simple examples, e.g., series-parellel graphs, there are no known tractable cases, nor are there any good reasons to believe the problem to be intractable. Moreover, despite several unsuccessful attempts, there has been no progress made on the question of approximability. Indeed, this problem was considered to be one of the more difficult open problems in approximate counting since long before the complexity of exact counting was resolved. By considering a randomised input model, we are able to show that a very simple algorithm can sample or approximately count the Euler tours of almost every d-in/d-out directed graph in expected polynomial time. Then, we present some partial results towards showing that this algorithm can be used to sample or approximately count the Euler tours of almost every 2d-regular graph in expected polynomial time. We also provide some empirical evidence to support the unproven conjecture required to obtain this result. As a sideresult of this work, we obtain an asymptotic characterisation of the distribution of the number of Eulerian orientations of a random 2d-regular graph.

No description available.

The safety and security of liquefied natural gas (LNG) facilities has prompted the need for continued study of LNG mitigation systems. Water spray systems are widely recognized as an effective measure for dispersing LNG vapor clouds. Currently, there are no engineering guidelines available for water curtain applications in the LNG industry due to a lack of understanding of the complex interactions between the LNG vapor cloud and water droplets. This research applies computational fluid dynamics (CFD) modeling to investigate the forced dispersion of LNG vapor using upward-oriented full-cone spray nozzles. A Eulerian-Lagrangian approach was applied to simulate the energy and momentum exchange between the continuous (gas flow) and discrete (droplets) phases. Discussed are the physical parameters that are essential inputs to the CFD simulation of the water spray-LNG system. The experimental data collected from the Mary Kay O’Connor Process Safety Center’s outdoor LNG spill work in March 2009 at the Brayton Fire Training Field were used to calibrate the physical parameters. The physical mechanisms of the water spray application were investigated using LNG forced dispersion modeling. The effects of momentum imparting from the droplets to the air- vapor mixture, thermal transfer between the two phases (droplet/vapor) and effects of various levels of air entrainment rates on the behavior of the LNG vapors are evaluated. Lastly, the key parametric dependences of the design elements for an effective water curtain system are investigated. The effects of different droplet sizes, droplet temperatures, nozzle cone angles, and installation configurations of water spray applications on LNG vapor behavior are analyzed. This work aims to investigate the complex interaction of the water droplet-LNG vapor system, which will serve in developing guidelines and establishing engineering criteria for a site-specific LNG mitigation system. Finally, the potentials of applying CFD modeling in providing guidance for setting up the design criteria for an effective forced mitigation system as an integrated safety element for LNG facilities are discussed.

No description available.

Thesis (M. Sc.)--Carleton University, 2005. / Includes bibliographical references (p. 47-48). Also available in electronic format on the Internet.