A generalized 1D particle transport method for convection diffusion reaction model

This work is devoted to the development of numerical method to deal with convection diffusion dominated problem with reaction term, non - stiff chemical reaction and stiff chemical reaction. The technique is based on the unifying Eulerian - Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves created by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that, each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients (steep fronts) and discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that, the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consumer when compared with other classical technique e.g., method of lines. Apart from this advantage, the particle transport method can be used to simulate problems that involve movingsteep/smooth fronts such as separation of two or more elements in the system.

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Effective diffusivity and convective mass transfer coefficient during the drying of bananas

In this article, a methodology is used for the simultaneous determination of the effective diffusivity and the convective mass transfer coefficient in porous solids, which can be considered as an infinite cylinder during drying. Two models are used for optimization and drying simulation: model 1 (constant volume and diffusivity, with equilibrium boundary condition), and model 2 (constant volume and diffusivity with convective boundary condition). Optimization algorithms based on the inverse method were coupled to the analytical solutions, and these solutions can be adjusted to experimental data of the drying kinetics. An application of optimization methodology was made to describe the drying kinetics of whole bananas, using experimental data available in the literature. The statistical indicators enable to affirm that the solution of diffusion equation with convective boundary condition generates results superior than those with the equilibrium boundary condition.

Estimation of transpiration of the 'Valencia' orange young plant using thermal dissipation probe method

Most studies on measures of transpiration of plants, especially woody fruit, relies on methods of heat supply in the trunk. This study aimed to calibrate the Thermal Dissipation Probe Method (TDP) to estimate the transpiration, study the effects of natural thermal gradients and determine the relation between outside diameter and area of xylem in 'Valencia' orange young plants. TDP were installed in 40 orange plants of 15 months old, planted in boxes of 500 L, in a greenhouse. It was tested the correction of the natural thermal differences (DTN) for the estimation based on two unheated probes. The area of the conductive section was related to the outside diameter of the stem by means of polynomial regression. The equation for estimation of sap flow was calibrated having as standard lysimeter measures of a representative plant. The angular coefficient of the equation for estimating sap flow was adjusted by minimizing the absolute deviation between the sap flow and daily transpiration measured by lysimeter. Based on these results, it was concluded that the method of TDP, adjusting the original calibration and correction of the DTN, was effective in transpiration assessment.

Estimation of evaporation in the Banabuiú dam, in the state of Ceará, Brazil, by different combined methods, derived from the Penman equation

The state of Ceará, Brazil, has 75% of its area covered by Brazilian semiarid, with its peculiar features. In this state, the dams are constituted in water structure of strategic importance, ensuring, both in time and space, the development and supply of water to population. However, construction of reservoirs results in various impacts that should be carefully observed when deciding on their implementation. One of the impacts identified as negative is the increased evaporation, which constitutes a major component of water balance in reservoirs, especially in arid regions. Several methods for estimating evaporation have been proposed over time, many of them deriving from the Penman equation. This study evaluated six different methods for estimating evaporation in order to determine the most suitable for use in hydrological models for water balance in reservoirs in the state of Ceará. The tested methods were proposed by Penman, Kohler-Nordenson-Fox, Priestley-Taylor, deBruim-Keijman, Brutsaert-Stricker and deBruim. The methods presented good performance when tested for water balance during the dry season, and the Priestley-Taylor was the most appropriate, since the data from de simulated water balance with evaporation estimated by this method were the closest of the water balance data observed from measures of reservoir level and the elevation-volume curve provided by the Company of Management of Water Resources of the state of Ceará - COGERH.

Comparison of diffusion models for description of osmotic dehydration of radish slices dipped in brine

ABSTRACT This paper aims at describing the osmotic dehydration of radish cut into cylindrical pieces, using one- and two-dimensional analytical solutions of diffusion equation with boundary conditions of the first and third kind. These solutions were coupled with an optimizer to determine the process parameters, using experimental data. Three models were proposed to describe the osmotic dehydration of radish slices in brine at low temperature. The two-dimensional model with boundary condition of the third kind well described the kinetics of mass transfers, and it enabled prediction of moisture and solid distributions at any given time.

A Soft Contact Collision Method For Real-Time Simulation of Triangularized Geometries in Multibody Dynamics

When modeling machines in their natural working environment collisions become a very important feature in terms of simulation accuracy. By expanding the simulation to include the operation environment, the need for a general collision model that is able to handle a wide variety of cases has become central in the development of simulation environments. With the addition of the operating environment the challenges for the collision modeling method also change. More simultaneous contacts with more objects occur in more complicated situations. This means that the real-time requirement becomes more difficult to meet. Common problems in current collision modeling methods include for example dependency on the geometry shape or mesh density, calculation need increasing exponentially in respect to the number of contacts, the lack of a proper friction model and failures due to certain configurations like closed kinematic loops. All these problems mean that the current modeling methods will fail in certain situations. A method that would not fail in any situation is not very realistic but improvements can be made over the current methods.

The bifurcational behaviour of the spatially distributed Rayleigh equation

At the present work the bifurcational behaviour of the solutions of Rayleigh equation and corresponding spatially distributed system is being analysed. The conditions of oscillatory and monotonic loss of stability are obtained. In the case of oscillatory loss of stability, the analysis of linear spectral problem is being performed. For nonlinear problem, recurrent formulas for the general term of the asymptotic approximation of the self-oscillations are found, the stability of the periodic mode is analysed. Lyapunov-Schmidt method is being used for asymptotic approximation. The correlation between periodic solutions of ODE and PDE is being investigated. The influence of the diffusion on the frequency of self-oscillations is being analysed. Several numerical experiments are being performed in order to support theoretical findings.

QT interval in healthy dogs: which method of correcting the QT interval in dogs is appropriate for use in small animal clinics?

The electrocardiography (ECG) QT interval is influenced by fluctuations in heart rate (HR) what may lead to misinterpretation of its length. Considering that alterations in QT interval length reflect abnormalities of the ventricular repolarisation which predispose to occurrence of arrhythmias, this variable must be properly evaluated. The aim of this work is to determine which method of correcting the QT interval is the most appropriate for dogs regarding different ranges of normal HR (different breeds). Healthy adult dogs (n=130; German Shepherd, Boxer, Pit Bull Terrier, and Poodle) were submitted to ECG examination and QT intervals were determined in triplicates from the bipolar limb II lead and corrected for the effects of HR through the application of three published formulae involving quadratic, cubic or linear regression. The mean corrected QT values (QTc) obtained using the diverse formulae were significantly different (ρ<0.05), while those derived according to the equation QTcV = QT + 0.087(1- RR) were the most consistent (linear regression). QTcV values were strongly correlated (r=0.83) with the QT interval and showed a coefficient of variation of 8.37% and a 95% confidence interval of 0.22-0.23 s. Owing to its simplicity and reliability, the QTcV was considered the most appropriate to be used for the correction of QT interval in dogs.

A temperature predicting model for manufacturing processes requiring coiling

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Lagrangian multipliers for coast-arcs of optimum space trajectories

Some properties of generalized canonical systems - special dynamical systems described by a Hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. A complete closed-form solution for Lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. Classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. For circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Panel Method Formulation for Oscillating Airfoils in Sonic Flow

The mathematical model for two-dimensional unsteady sonic flow, based on the classical diffusion equation with imaginary coefficient, is presented and discussed. The main purpose is to develop a rigorous formulation in order to bring into light the correspondence between the sonic, supersonic and subsonic panel method theory. Source and doublet integrals are obtained and Laplace transformation demonstrates that, in fact, the source integral is the solution of the doublet integral equation. It is shown that the doublet-only formulation reduces to a Volterra integral equation of the first kind and a numerical method is proposed in order to solve it. To the authors' knowledge this is the first reported solution to the unsteady sonic thin airfoil problem through the use of doublet singularities. Comparisons with the source-only formulation are shown for the problem of a flat plate in combined harmonic heaving and pitching motion.

Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.