Applied Mathematics Commons^™

Accuracy Analysis For Kolmogorov Entropy Used In Studying The Chaotic Dynamics Of Cfb Reactors Based On Solids Concentration Fluctuations, Samwel V. Manyele

Tanzania Journal of Engineering and Technology (TJET)

A study on the chaotic dynamics of a high flux circulating fluidized bed (CFB) riser (10-m high and 76-mm i.d.) using the maximum likelihood estimate of the Kolmogorov entropy (KML) is reported. The signals used were measured by using a solids concentration fiber optic probe, accuracy of which is reported based on statistical analysis. The sensitivity analysis of the parameters used for computing KML was conducted to identify optimum settings, based on the standard error, s(KML) and the nature of PDF of the b-values from the reconstructed phase space trajectories. The length of time series, N, sampling frequency, fs, and …

Study Of Multibody Dynamics Using Matlab, Kalyani Soman

Mechanical & Aerospace Engineering Theses & Dissertations

Research in computational dynamics has gained importance in the past few years because of the demand for analysis and simulation of various multi-body systems in the growing mechanical and aerospace industry. These multi-body systems are made of individual bodies that are interconnected via mechanical joints. Mathematically, these joints that connect the bodies can be described as constraint equations imposed upon the motions of the involved free bodies. This process will result in an equation of motion expressed in the form of a differential-algebraic equation. It is the main objective of this thesis to develop a solution algorithm that can take …

Predictive Control Of A Munition Using Low-Speed Linear Theory, Nathan Slegers

Faculty Publications - Biomedical, Mechanical, and Civil Engineering

"Modified linear theory provides reasonable impact predictions at high speeds. However, for typical small UAS mission speeds, less than 20-m/s impact errors were substantial due to large angles of attack and pitch rates. Low-speed linear theory was developed by including higher-order terms involving w and q that modified linear theory neglects. As a result, the angle of attack, pitch, and yaw predictions are significantly improved, leading to accurate impact predictions even at very low speeds. A predictive control scheme was developed to reduce dispersion using control surfaces near the tail. The predictive controller uses low-speed linear theory to rapidly predict …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Mikhail Khenner

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …

Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian

Mechanical Engineering Faculty Research

RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …

Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor

Tanzania Journal of Engineering and Technology (TJET)

This paper reports on a research project conducted with an objective of identifying and assessing various approaches used by different computer users (Management, System Administrators and end users) in Tanzania to combat computer viruses (CVs), and to assess users' awareness level on CVs. Specifically, the study aimed at assessing the awareness level on CVs to the Tanzanian business community; analyze the socio -economic impact caused by CVs in Tanzania and; assess existing methods, capacity and limitations on controlling CVs in Tanzania. Data was collected using both questionnaires and interview from financial institutions such as NBC and BOT, and telecommunications sector …

Validation Of Finite Element Beam Models, Pavan R. Madhineni

Mechanical & Aerospace Engineering Theses & Dissertations

Finite Element (FE) methods these days are becoming very popular to predict the responses of structures in industries, such as the aerospace and automobile industries. When there is a new design or modification of an existing design, the product must be tested to fulfill the criterion projected by the industry or external agencies before it can be launched. The product must be checked for each and every aspect, and every minute detail of each of the external forces. Hence, it becomes very important to carry out the model validation on the product.

This thesis describes validation of finite element (FE) …

Investigation And Applications Of Latin Hypercube Sampling Methods, Prashant K. Patel

Mechanical & Aerospace Engineering Theses & Dissertations

The Latin hypercube sampling method, sometimes called the stratified sampling method, is a commonly used variance reduction method. Recently, the optimal Latin hypercube sampling method (OLH) and the modified optimal Latin hypercube sampling method (MOLH) are introduced in the literature, which use the genetic algorithm to adjust the distance between sampled points.

This paper will compare the basic Latin hypercube, the optimal Latin hypercube and the modified optimal Latin hypercube methods for generating the sample points for statistical application and curve fitting, in te1ms of accuracy and efficiency. Analytical and structural examples are used in this thesis to facilitate the …

Application Of Meshless Methods For Thermal Analysis, Darrell Pepper, Bozidar Sarler

Mechanical Engineering Faculty Research

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) — which are simple to implement — for thermal problems. Radial basis functions are the natural generalization of univariate polynomial splines to a multivariate setting that work for arbitrary geometry with high dimensions. RBF functions depend only on the distance from some center point. …

Transient Non-Linear Heat Conduction Solution By A Dual Reciprocity Boundary Element Method With An Effective Posteriori Error Estimator, Eduardo Divo, Alain J. Kassab

Publications

A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach.

Review Of The Product Development Process And Information Flow In The Manufacturing Industry: Problems And A Possible Wav Forward, E Opiyo

Tanzania Journal of Engineering and Technology (TJET)

No abstract provided.

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Simulation Of Engineering Systems Described By High-Index Dae And Discontinuous Ode Using Single Step Methods, Marc Compere

Publications

This dissertation presents numerical methods for solving two classes of or-dinary diferential equations (ODE) based on single-step integration meth-ods. The first class of equations addressed describes the mechanical dynamics of constrained multibody systems. These equations are ordinary differential equations (ODE) subject to algebraic constraints. Accordinly they are called differential-algebraic equations (DAE).

Specific contributions made in this area include an explicit transforma-tion between the Hessenberg index-3 form for constrained mechanical systems to a canonical state-space form used in the nonlinear control communities. A hybrid solution method was developed that incorporates both sliding-mode control (SMC) from the controls literature and post-stabilization from …

Overview Of Fuzzy Logic, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The presentation includes a brief introduction to fuzzy logic and fuzzy logic controllers. These concepts are illustrated by an example of an autonomous vehicle controller.

Comparison Of Two Distributed Fuzzy Logic Controllers For Flexible-Link Manipulators, Linda Z. Shi, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The paper suggests that fuzzy logic controllers present a computationally efficient and robust alternative to conventional controllers. The paper presents two possible structures for the distributed fuzzy logic controller of a single-link flexible manipulator. A linear quadratic regulator method is used to prove the effectiveness of fuzzy logic controllers.

Design Of Fuzzy Logic Controllers For Optimal Performance, Mohamed Trabia

Mechanical Engineering Faculty Presentations

While fuzzy logic controllers are generally robust, the performance of a system whose behavior is not well understood, or that has a large number of coupled inputs and outputs, may be less than optimal. In this paper, nonlinear programming techniques are used to improve the performance of a fuzzy logic controller for navigating an autonomous vehicle.

Eddy Structures Induced Within A Wedge By A Honing Circular Arc, C. P. Hills

Articles

In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as …

Eddies Induced In Cylindrical Containers By A Rotating End Wall, Christopher Hills

Articles

The flow generated in a viscous liquid contained in a cylindrical geometry by a rotating end wall is considered. Recent numerical and experimental work has established several distinct phases of the motion when fluid inertia plays a significant role. The current paper, however, establishes the nature of the flow in the thus far neglected low Reynolds number regime. Explicitly, by employing biorthogonality relations appropriate to the current geometry, it is shown that a sequence of exponentially decaying eddies extends outward from the rotating end wall. The cellular structure is a manifestation of the dominance of complex eigensolutions to the homogeneous …

Rotary Honing: A Variant Of The Taylor Paint-Scraper Problem, Christopher Hills, H. Moffatt

Articles

The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' …

Application Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Arton Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Art, Silas Kajuna

Tanzania Journal of Engineering and Technology (TJET)

Vibration is one of the techniques employed in the determination of dynamic properties of fruits and vegetables. It entails generation of a mechanical or acoustic vibrational signal which is propagated through the flesh of the agricultural material. A transducer is either attached or held close to the specimen to monitor the propagation of the signal through the specimen. The manner in which the signal is transmitted through the material is analyzed, and the dynamic properties of the specimen which relate to its firmness or its internal being are derived. The technique has been around for the past 30 years or …

Correlation Of Finite Element Prediction And Experimental Measurements Of Aircraft Panel Structural Vibration, Olaf L. Storaasli

Mechanical & Aerospace Engineering Theses & Dissertations

With the rapid development of computational capabilities and the implementation of complex tools for commercial finite element programs, predicting structural dynamics and related acoustics of complex structures is presently achievable. Structural finite element modeling is a design tool widely utilized for analysis of problems of all kinds. However, high frequency vibration of complex structures, such as the reinforced aircraft panel used for this study, currently does not correlate well with experimental measurements using conventional modeling methods. An investigation into the commonly used modeling techniques as well as the new tools of commercial finite element analysis packages for the prediction of …

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter

All HMC Faculty Publications and Research

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex c_v is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (c_v→∞) and numerically …

Msda A Machinery Selection Decision Aid For Stubble Management Practices, Linda Leonard, Andrew Green

Grain and other field crops published reports

MSDA is a user friendly program developed to help farmers predict stubble outcomes before acting on their management practice. This manual is an accompaniment to a computer program designed on Micorsoft Excel-macros. Its aim is to help farmers assess their current machinery and stubble handling ability and view options that may be adopted as best practice for their properties.

The program is designed with the complete season in mind. Information is gathered on the full complement of machinery used from harvest through to seeding, to allow farmers to see all choices available and enable them to choose the best system …

Implementation Of A Multiblock Sensitivity Analysis Method In Numerical Aerodynamic Shape Optimization, James Matthew Lacasse

Mechanical & Aerospace Engineering Theses & Dissertations

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations, Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies.

The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from …