CURRENT THEMES IN ENGINEERING SCIENCE 2009: Selected Presentations at the World Congress on Engineering‐2009

Oscillations of a Spacecraft with a Vertical Elastic Tether
View Description Hide DescriptionThe motion about a center of mass of a spacecraft with a vertical elastic tethered system under the action of the gravitational moment and small periodic tethered force at a circular orbit is studied. The mathematical model is derived using Lagrange’s equations including tether vibrations and oscillations of the spacecraft relatively to the proper mass center. The paper contains bifurcation analysis, phase space study, and analytic solutions for separatrixes. The considered mechanical system performs chaotic motion near separatrixes under the influence of small disturbances. The Melnikov method gives a criterion for homo/heteroclinic chaos in terms of system parameters. Results of the study can be useful for the analysis of gravitational stabilization systems with space tethers and for studying the behavior of a spacecraft with a deployed tether.

Application of Control Volume Method Using the Voronoi Tessellation in Numerical Modelling of Solidification Process
View Description Hide DescriptionThe paper presents the method to analyse the thermal processes occurring in the cast composite solidification. The cast is formed by a bundle of parallel fibres randomly immersed in a host metal matrix. The heat is transferred from the metal matrix and absorbed by the fibres. The objective of this paper is to evaluate the volumetric fraction of the fibres for which the solidification of the metal matrix occurs only due to the presence of fibres playing a role of internal chills. Our method is to compute Voronoi diagrams with Voronoi regions representing the geometric location of the fibres in the metal matrix and to use these regions as control volumes within a variant of the Control Volume Method.

Hamiltonian Dynamics of Spider‐Type Multirotor Rigid Bodies Systems
View Description Hide DescriptionThis paper sets out to develop a spider‐type multiple‐rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor‐equipped rays, so it was called a “Spider‐type System,” also it can be called “Rotary Hedgehog.” These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer‐Deprit canonical variables. These variables allow obtaining exact solution for hetero‐ and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.

Method of Multiple Orthogonalities for Vibration Problems
View Description Hide DescriptionThe modeling of vibration problems is of great importance in engineering and mathematical physics. A widely spread method of analyzing such problems is the variational method. The simplest and advanced vibration models are represented using the examples of a long and thick rod. Two kinds of eigenfunction orthogonality are proved and the corresponding norms are used to derive Green’s function that gives rise to the analytical solution of these problems. The method can be easily generalized to a broad class of hyperbolic problems.

Cournot competition between a non‐profit firm and a for‐profit firm with uncertainty
View Description Hide DescriptionIn this paper, we consider a Cournot competition between a nonprofit firm and a for‐profit firm in a homogeneous goods market, with uncertain demand. Given an asymmetric tax schedule, we compute explicitly the Bayesian‐Nash equilibrium. Furthermore, we analyze the effects of the tax rate and the degree of altruistic preference on market equilibrium outcomes.

Manufacturing and Examination of Metallic Femoral Heads
View Description Hide DescriptionIn the last years new methods have been investigated for the manufacturing of artificial implants for hip joints. For some parts of these implants, like femoral heads, the method of high speed machining is used for manufacture. In this paper was investigated the connection between cutting parameters and forces, in high speed turning of metallic femoral heads. This method is widely used in the industry combined with hard part machining, and leads to better surface roughness and to decreasing of cutting time. Also investigate as the connection of the surface roughness in this manufacturing method with the measuring of the spheres using Atomic Force Microscopy according to the Standard ISO 7206.

Simulation of Erosive Effects of Sand Particle Impacts in Axial Turbomachinery
View Description Hide DescriptionThe erosion resulting from sand ingestion into an axial turbomachinery is predicted using a Lagrangian particle tracking model. This simulation takes into account the effects of turbulence and endwalls vorticities on particles, random size distribution and rebound of particles. The governing equations of particle motion through stationary and rotating parts are solved in a stepwise manner separately from the flow field. Particles tracking and impacts are predicted in different cells of the computational domain based on the finite element method. A semi‐empirical erosion correlation is used to predict erosion areas based on impacts condition. The simulations results obtained for different positions of the rotor blade revealed that the main impacted areas are found over the blade leading edge corner and an area of the pressure side extending towards and over the tip, in addition to a strip along the leading edge of the suction side.

Optimal Stopping Rules For Some Blackjack Type Problems
View Description Hide DescriptionThe paper deals with a class of optimal stopping problems having some features of blackjack type games. A decision maker observes sequentially the values of a finite sequence of non‐negative random variables. After each observation he decides whether to stop or to continue. If he decides to stop, he obtains a payoff dependent on the sum of already observed values. The greater the sum, the more the decision maker gains, unless the sum exceeds a positive number limit given in the problem. If so, the decision maker loses all or part of his payoff. A sufficient condition for existence of a simple optimal stopping rule for such problems is formulated. Then some special cases are considered in detail. Some numerical examples and practical questions are discussed as well.

Tensile and Creep Behavior of Extruded Al MMCs
View Description Hide DescriptionComposites of AA6063 Al alloy reinforced with SiC particles were prepared by the vortex method. Hot extrusion was carried out for the as cast composites with a reduction in area of 25%. Tensile and creep behavior of as‐cast and extruded composites were studied at elevated temperatures. Tensile tests carried out at room temperature showed that for the as‐cast composites, the addition of up to 10% by weight improves the strength but reduces ductility. Further addition of reduces the strength and ductility of the composites. At 150 and 300° C the matrix alloy exhibits higher strength than the composites. Extrusion generally raised the strength of the composites at both room and elevated temperatures. Time rupture creep tests carried out at 300° C showed that the composites exhibit higher creep resistance as compared to the matrix alloy except at relatively low stresses where the matrix has a better creep resistance. Extrusion improved the resistance of composites to creep rupture.

Non‐Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics
View Description Hide DescriptionOne of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two‐dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two‐dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non‐singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Intracavity Dynamics in Mode‐Locked Lasers
View Description Hide DescriptionWe present a theoretical description of the generation of ultra‐short, high‐energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra‐cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra‐cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self‐similar behavior to be governed by the porous media equation with a rapidly‐varying, mean‐zero diffusion coefficient whose solution is the well‐known Barenblatt similarity solution with parabolic profile.

A Multigrid Block Krylov Subspace Spectral Method for Variable‐Coefficient Elliptic PDE
View Description Hide DescriptionKrylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time‐dependent variable‐coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this same approach to time‐independent PDE of the form where L is an elliptic differential operator. Numerical results demonstrate the effectiveness of this approach, in conjunction with residual correction applied on progressively finer grids, for Poisson’s equation and the Helmholtz equation.

Fundamental Flaws In The Derivation Of Stevens’ Law For Taste Within Norwich’s Entropy Theory of Perception
View Description Hide DescriptionNorwich’s Entropy Theory of Perception (1975‐present) is a general theory of perception, based on Shannon’s Information Theory. Among many bold claims, the Entropy Theory presents a truly astounding result: that Stevens’ Law with an Index of 1, an empirical power relation of direct proportionality between perceived taste intensity and stimulus concentration, arises from theory alone. Norwich’s theorizing starts with several extraordinary hypotheses. First, “multiple, parallel receptor‐neuron units” without collaterals “carry essentially the same message to the brain,” i.e. the rate‐level curves are identical. Second, sensation is proportional to firing rate. Third, firing rate is proportional to the taste receptor’s “resolvable uncertainty.” Fourth, the “resolvable uncertainty” is obtained from Shannon’s Information Theory. Finally, “resolvable uncertainty” also depends upon the microscopic thermodynamic density fluctuation of the tasted solute. Norwich proves that density fluctuation is density variance, which is proportional to solute concentration, all based on the theory of fluctuations in fluid composition from Tolman’s classic physics text, “The Principles of Statistical Mechanics.” Altogether, according to Norwich, perceived taste intensity is theoretically proportional to solute concentration. Such a universal rule for taste, one that is independent of solute identity, personal physiological differences, and psychophysical task, is truly remarkable and is well‐deserving of scrutiny. Norwich’s crucial step was the derivation of density variance. That step was meticulously reconstructed here. It transpires that the appropriate fluctuation is Tolman’s mean‐square fractional density fluctuation, not density variance as used by Norwich. Tolman’s algebra yields a “Stevens Index” of rather than 1. As “Stevens Index” empirically always exceeds zero, the Index of suggests that it is risky to infer psychophysical laws of sensory response from information theory and stimulus physics while ignoring empirical biological transformations, such as sensory transduction. Indeed, it raises doubts as to whether the Entropy Theory actually describes psychophysical laws at all.

Numerical and Experimental Design Study of a Regenerative Pump
View Description Hide DescriptionThis paper presents the use of a commercial CFD code to simulate the flow‐field within the regenerative pump and compare the CFD results with new experimental data. Regenerative pumps are the subject of increased interest in industry as these pumps are low cost, low specific speed, compact and able to deliver high heads with stable performance characteristics. The complex flow‐field within the regenerative pump represents a considerable challenge to detailed mathematical modelling. This paper also presents a novel rapid manufacturing process used to consider the effect of impeller geometry changes on the pump efficiency. Ten modified impeller blade profiles, relative to a standard radial configuration, were evaluated. The CFD performance results demonstrate reasonable agreement with the experimental tests. The CFD results also demonstrate that it is possible to represent the helical flow field for the pump which has only been witnessed in experimental flow visualisation until now. The ability to use CFD modelling in conjunction with rapid manufacturing techniques has meant that more complex impeller geometry configurations can now be assessed with better understanding of the flow‐field and resulting efficiency.

Upper Limits for Power Yield in Thermal, Chemical, and Electrochemical Systems
View Description Hide DescriptionWe consider modeling and power optimization of energy converters, such as thermal, solar and chemical engines and fuel cells. Thermodynamic principles lead to expressions for converter’s efficiency and generated power. Efficiency equations serve to solve the problems of upgrading or downgrading a resource. Power yield is a cumulative effect in a system consisting of a resource, engines, and an infinite bath. While optimization of steady state systems requires using the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. The primary result of static optimization is the upper limit of power, whereas that of dynamic optimization is a finite‐rate counterpart of classical reversible work (exergy). The latter quantity depends on the end state coordinates and a dissipation index, h, which is the Hamiltonian of the problem of minimum entropy production. In reacting systems, an active part of chemical affinity constitutes a major component of the overall efficiency. The theory is also applied to fuel cells regarded as electrochemical flow engines. Enhanced bounds on power yield follow, which are stronger than those predicted by the reversible work potential.

Monte Carlo Method for Predicting a Physically Based Drop Size Distribution Evolution of a Spray
View Description Hide DescriptionWe report in this paper a method for predicting the evolution of a physically based drop size distribution of a spray, by coupling the Maximum Entropy Formalism and the Monte Carlo scheme. Using the discrete or continuous population balance equation, a Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After deriving a kernel for coalescence, we solve the time dependent drop size distribution equation using a Monte Carlo method. We apply the method to the spray of a new print‐head known as a Spray On Demand (SOD) device; the process exploits ultrasonic spray generation via a Faraday instability where the fluid/structure interaction causing the instability is described by a modified Hamilton’s principle. This has led to a physically‐based approach for predicting the initial drop size distribution within the framework of the Maximum Entropy Formalism (MEF): a three‐parameter generalized Gamma distribution is chosen by using conservation of mass and energy. The calculation of the drop size distribution evolution by Monte Carlo method shows the effect of spray droplets coalescence both on the number‐based or volume‐based drop size distributions.

Back Matter for Volume 1220
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