Orientador: Carlos Alberto Gasparetto / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-08T22:28:21Z (GMT). No. of bitstreams: 1 Ohata_SueliMarie_D.pdf: 1133009 bytes, checksum: d9e555381242748bb00e413dc46b8c7d (MD5) Previous issue date: 2007 / Resumo: Os reatores de recirculação representam uma tecnologia alternativa muito atraente para o processo de hidrogenação, tecnologia esta ainda não totalmente desenvolvida para a hidrogenação de óleos vegetais. Os reatores convencionais utilizados no processo de hidrogenação possuem agitação mecânica, sistema de injeção de hidrogênio na base, e necessitam de condições mais severas de operação, como a temperatura e a pressão. Em um reator que opera num sistema de recirculação, um ejetor tipo Venturi e utilizado, o qual proporciona uma grande transferência de massa entre as fases presentes, dispensando a agitação mecânica, alem de requerer quantidades menores de catalisador, demandar menos hidrogênio e trabalhar com pressão, temperatura e tempo de reação menor. Foram encontradas poucas informações na literatura a respeito do processo de hidrogenação de óleos vegetais através do reator de recirculação, desta forma, o objetivo deste trabalho foi analisar o processo de hidrogenação de óleo de soja em um reator de recirculação através da modelagem e simulação. Para a formulação do modelo que descreve este sistema, foram considerados os fenômenos de transferência de massa, alem da cinética da reação. A partir das equações obtidas, propos-se uma metodologia para solucionar o sistema de equações diferenciais que descrevem o sistema. Foram propostos dois modelos para o estudo: reator em batelada, resolvido analiticamente e uma associação de um reator CSTR em serie com um PFR com dispersão axial, resolvido pelo método da colocação ortogonal. Ambos os modelos descreveram adequadamente o processo de hidrogenação nas condições estudadas / Abstract: Loop reactors represent a very attractive alternative technology to the hydrogenation process, but this technology was not totally developed for the hydrogenation of vegetable oils. The conventional reactors used for the hydrogenation process have mechanical agitation, system of injection of hydrogen in the basis and they need more severe conditions of operation, as the temperature and the pressure. In a reactor that operates in a system loop, an ejector type Venturi is used, which provides an high mass transfer rate between the present phases, without mechanical agitation, needs less catalyst, demands less hydrogen and works with lower values of pressure, temperature and time of reaction. There is very little information in the literature about the hydrogenation process of vegetable oils in a loop reactor, thus, the purpose of this study was to analyse of the process of hydrogenation of soybean oil in a loop reactor by modelling and simulation. For the formulation of the model that describes this system, the phenomena of mass transfer and kinetics of the reaction were considered. From the balance equations, a method was considered to solve the system of differential equations that describe the system. Two models of reactors were proposed for the study: batch reactor, solved analytically and an association of a reactor CSTR in series with a PFR with axial dispersion, solved by orthogonal collocation method. Both models described the process of hydrogenation appropriately in the studied conditions / Doutorado / Doutor em Engenharia de Alimentos

This paper presents conora, a robust trajectory optimization software utilizing orthogonal collocation methods for ascending rocket stages, targeting applications in early phases of mission design. The proposed methodology leverages orthogonal collocation techniques, preferred over the multitude of available options for their robustness to inaccuracies in the initial guess. This, together with low amount of available data about the ascent profile, often makes preliminary optimization considerably complex, extremely case-specific and, consequently, very time consuming. The software here implemented addresses the problem of maximizing the payload mass of a rocket by providing the required flexibility to adapt to any mission scenario disregarding of the celestial body, launch site, vehicle design and target orbit. Proper functionality is demonstrated by replicating existing missions, simplifying and reducing to the bare minimum the number of inputs. Ariane V ascending to GTO, Electron launch to SSO, ALTO mission to LEO, Apollo XI Lunar Module ascent and Starship take-off to LMO are the multifaceted mission scenarios selected to demonstrate the capabilities of conora, resulting in accurate injection into orbit and relatively close estimation of optimized payload masses. The obtained outcomes grow more valuable when considering the small amount of inputs provided, the simplicity of the utilized physical model and the strong assumptions considered. The whole software development process followed a V-model, from requirement definition, passing by the actual implementation, to thorough code testing of each conora’s module. 64 are the number of identified top level requirements, for a verification process elaborated via more than 270 tests, from unit to system level. The entire work was performed in the context of an internship at DLR, at the Institute of Space Systems in Bremen, Germany. / Denna uppsats presenterar conora, en robust mjukvara för optimeringen av flygbanor, via användningen av ortogonala kollokationsmetoder för stigande raketsteg, med fokus på applikationer inom de tidiga faserna av uppdragets utformning. Den förslagna metodiken använder ortogonala kollokationsmetoder, som föredras över konkurrerande metoder för dess robusthet mot fel och osäkerheter i initial gissningen. Detta, tillsammans med lite tillgängliga data kring stigningsprofilen gör att preliminära optimeringar blir komplexa, extremt fallspecifika och därmed också väldigt tidskrävande. Mjukvaran har implementerats för att hantera maximering av nyttolastsmassan på en raket genom att bidra med den krävda flexibiliteten att anpassas till olika uppdragsscenarier, oavsett himlakropp, uppskjutningsplats, farkostsdesign eller given omloppsbana. Korrekt funktionalitet demonstreras genom att replikera nutida uppdrag, genom att förenkla och reducera till den lägsta mängd inmatningsvariabler. Ariane Vs uppstigning till GTO, Elektrons uppskjutning till SSO, ALTO uppdrag till LEO, Apollo XI Lunar Modules uppskjutning och Starships uppskjutning till LMO är de mångfasetterade uppdragsscenarion valda för att demonstrera conoras kapacitet. Resultatet visar på träffsäkra injektioner till omloppsbana och relativt bra uppskattning av optimerad nyttolastsmassa. Resultatet blir mer värdefullt när man tar hänsyn den lilla mängden inmatningsvariabler, enkelheten av de använda fysiska modellerna och de starka antaganden som gjorts. Hela mjukvarans utvecklingsprocess följde en V-modell, från kravskrivning, genom implementationen, till genomgående kodtestning av varje modul i conora. 64 krav på högsta nivå identifierades, för en verifikationsprocess utvecklad via mer än 270 tester, från enhets- till systemnivå. Hela arbetet utfördes inom ett praktikantarbete vid DLR, vid avdelningen för rymdsystem i Bremen, Tyskland.

Bound state systems consisting of three nonrelativistic particles are numerically studied. Calculations are performed employing two-body and three-body forces as input in the Hamiltonian in order to study the role or contribution of three-body forces to the binding in these systems. The resulting differential Faddeev equations are solved as three-dimensional equations in the two Jacobi coordinates and the angle between them, as opposed to the usual partial wave expansion approach. By expanding the wave function as a sum of the products of spline functions in each of the three coordinates, and using the orthogonal collocation procedure, the equations are transformed into an eigenvalue problem. The matrices in the aforementioned eigenvalue equations are generally of large order. In order to solve these matrix equations with modest and optimal computer memory and storage, we employ the iterative Restarted Arnoldi Algorithm in conjunction with the so-called tensor trick method. Furthermore, we incorporate a polynomial accelerator in the algorithm to obtain rapid convergence. We applied the method to obtain the binding energies of Triton, Carbon-12, and Ozone molecule. / Physics / M.Sc (Physics)

This thesis investigates novel algorithms for enabling the use of first-principle electrochemical models for battery monitoring and control in advanced battery management systems (BMSs). Specifically, the fast solution and state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional (P2D) model are investigated. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the P2D model is then used in combination with an extended Kalman filter (EKF) algorithm modified for differential-algebraic equations (DAEs) to estimate the states of the model, e.g. lithium concentrations, overpotential. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200s despite a 30% error on battery initial state-of-charge (SoC) and additive measurement noise with 10mV and 0.5°C standard deviations. The parameter accuracy of such first-principle models is of utmost importance for the trustworthy estimation of internal battery electrochemical states. Therefore, the identifiability of the simpler single particle (SP) electrochemical model is investigated both in principle and in practice. Grouping parameters and partially non-dimensionalising the SP model equations in order to understand the maximum expected degrees of freedom in the problem reveals that there are only six unique parameters in the SP model. The structural identifiability is then examined by asking whether the transfer function of the linearised SP model is unique. It is found that the model is unique provided that the electrode open circuit voltage curves have a non-zero gradient, the parameters are ordered, and that the behaviour of the kinetics of each electrode is lumped together into a single parameter which is the charge transfer resistance. The practical estimation of the SP model parameters from frequency-domain experimental data obtained by electrochemical impedance spectroscopy (EIS) is then investigated and shows that estimation at a single SoC is insufficient to obtain satisfactory results and EIS data at multiple SoCs must be combined.

Bound state systems consisting of three nonrelativistic particles are numerically studied. Calculations are performed employing two-body and three-body forces as input in the Hamiltonian in order to study the role or contribution of three-body forces to the binding in these systems. The resulting differential Faddeev equations are solved as three-dimensional equations in the two Jacobi coordinates and the angle between them, as opposed to the usual partial wave expansion approach. By expanding the wave function as a sum of the products of spline functions in each of the three coordinates, and using the orthogonal collocation procedure, the equations are transformed into an eigenvalue problem. The matrices in the aforementioned eigenvalue equations are generally of large order. In order to solve these matrix equations with modest and optimal computer memory and storage, we employ the iterative Restarted Arnoldi Algorithm in conjunction with the so-called tensor trick method. Furthermore, we incorporate a polynomial accelerator in the algorithm to obtain rapid convergence. We applied the method to obtain the binding energies of Triton, Carbon-12, and Ozone molecule. / Physics / M.Sc (Physics)

Made available in DSpace on 2016-06-02T19:56:56Z (GMT). No. of bitstreams: 1 6271.pdf: 1816121 bytes, checksum: 358e1c3f7d194a552db21ddb44f4761c (MD5) Previous issue date: 2014-08-28 / Financiadora de Estudos e Projetos / In general, the chemical processes can be represented using mathematical models, in the case of lumped systems include ordinary differential equations, or, partial differential equations, when distributed parameter systems using methods is necessary in both cases numerical resolution in these models, with the purpose to simulate, analyze and control the process. The implementation of control systems in chemical processes, brings with it many advantages, among these, the improvement and stability in production rates, ensuring product quality and the possibility of a safe operation of the process. Thus, in the last 30 years, different control methodologies were developed, one of the most used techniques, the Model Predictive Control Based on. Its success is due to the fact that this type of control accepts constraints on input variables and process output, determining the future of this movement, while optimizing an objective function can lead to the output of the process until the desired set point. The objective of this project is to implement the Model Predictive Controller with Nonlinear (CPNL ) for a reactor pulp bleaching by the use of chlorine dioxide, whose mathematical model is comprised of partial differential equations, thus being a model parameter distributed. Implementation of the controller, the plant is discretized by the Finite Difference Method and the process model is solved with the technique of Orthogonal Collocation. The integration of the resulting ordinary differential equations systems is performed by the method of Runge-Kutta. The Predictive Controller was compared with a Controller Proportional-Integral (PI). Studies have shown that CPNL has better performance, with faster response and values of the Integral Absolute Error (IAE) and Integral Square Error (ISE) smaller than those calculated for the PI controller. / Em geral, os processos químicos podem ser representados mediante modelos matemáticos que, no caso dos sistemas de parâmetros concentrados, incluem equações diferenciais ordinárias, ou então, equações diferenciais parciais, quando são sistemas de parâmetros distribuídos, sendo necessário nos dois casos o uso de métodos numéricos na resolução destes modelos, com a finalidade de simular, analisar e controlar o processo. A implementação de sistemas de controle em processos químicos, traz consigo múltiplas vantagens, entre essas, a melhora e a estabilidade nas taxas de produção, a garantia da qualidade do produto e a possibilidade de uma operação segura do processo. Desta forma, nos últimos 30 anos, foram desenvolvidas diferentes metodologias de controle, sendo uma das técnicas mais empregadas, o Controle Preditivo Baseado no Modelo. Seu sucesso se deve ao fato de que este tipo de controle aceita restrições nas variáveis de entrada e saída do processo, determinando os movimentos futuros deste, além de otimizar uma função objetivo para conseguir levar a saída do processo até o Set-Point desejado. Assim, o objetivo deste projeto é implementar o Controlador Preditivo com Modelo Não Linear (CPNL ) para um reator de branqueamento de celulose, mediante o uso de dióxido cloro, cujo modelo matemático está constituído por equações diferenciais parciais, sendo assim, um modelo de parâmetros distribuídos. Na implementação do controlador, a planta é discretizada, mediante o Método das Diferenças Finitas e o modelo do processo é resolvido com a técnica de Colocação Ortogonal. A integração dos sistemas de equações diferenciais ordinárias resultantes é realizada mediante o método de Runge- Kutta. O Controlador Preditivo foi comparado com um Controlador Proporcional-Integral (PI). Os estudos mostraram que o CPNL possui melhor desempenho, apresentando uma resposta mais rápida e valores da Integral do Erro Absoluto (IAE) e a Integral do Erro Quadrático (ISE) menores que os calculados para o controlador PI.

No

In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca. / Physics / M. Sc. (Physics)

<p>This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction.</p><p>The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user.</p><p>In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process.</p>

This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction. The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user. In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process. / QC 20101020