Flávio C . Bannwart | Universidade Estadual de Campinas (original) (raw)

Papers by Flávio C . Bannwart

International Journal of Thermal Sciences, Oct 1, 2017

This paper aims to study the effects of air variable properties in the transient case of the clas... more This paper aims to study the effects of air variable properties in the transient case of the classical differentially heated square cavity problem. A SIMPLE algorithm using a low Mach number approximation is applied for coupling the heat and momentum transport equations, which are discretized by the finite volume method. A fully implicit scheme is used for time discretization. The numerical code is validated with benchmark results obtaining a maximum deviation of 0.13% in the average Nusselt number for the non-Boussinesq approach. The temperature and velocity fields as well as the local Nusselt number are numerically studied for Rayleigh numbers ranging between 10 4-10 7. A temperature difference of 720 K is considered. We have found that the effects of variable properties are especially relevant along the flow development period, amongst which the average Nusselt number, for instance, differs up to roughly 10% with respect to the constant properties case; in contrast, once in steady state regime, such a difference remains less important and is no longer oscillating, resulting around 2%. An investigation is therefore put forward covering additional effects under regard of the principle of energy conservation, such as the time evolution of the total energy and its components for both transient regime and steady state cases. Excepting for the kinetic energy, the internal, potential and total energies are consistently and significantly higher for the case of variable properties; a suitable discussion is provided.

Dedico esta tese à minha filha que logo vai nascer. Je dédie cette thèse à ma fille qui naîtra bi... more Dedico esta tese à minha filha que logo vai nascer. Je dédie cette thèse à ma fille qui naîtra bientôt. I dedicate this thesis to my daughter who will be born soon.

Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. These acou... more Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. These acoustic waves can be used to induce cooling (thermo-acoustic refrigeration) or generate electricity (thermo-acoustic generator). This conversion is due to the thermo-viscous interaction between the acoustically oscillating gas medium within a porous material, referred to as a regenerator, and the pore internal walls. Although there has been significant progress in the development of efficient thermo-acoustic systems, their relatively low efficiency and the nonlinearity associated with more severe working conditions remain their major issues. Therefore, it is a major potential area of research. In this study, a one-stage travelling-wave thermo-acoustic engine has been modelled using DeltaEC. The simulation was performed by considering various input heat to the hot heat exchanger within the range of 8.2 to 227.91W, and sixty (60) datasets were generated. These data were used to build an Artificial Neural Network (ANN) model. The comparison between the output data extracted from the DeltaEC simulation and the results predicted from the ANN model was done. Both of the results obtained are in good agreement and prove that the ANN can be suitable for predicting configurations that were not previously simulated.

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Dec 20, 2021

General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equati... more General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equations are deduced for the case of a simply supported beam submitted to uniformly distributed static load. Both solutions are confronted against Ansys software results, taken as reference, leading to the corresponding particular fractional solutions. As expected, both particular solutions converge to the Ansys results for small deflections and beam with high-aspect ratio, while, for opposite geometrical features, the fractional Timoshenko-Ehrenfest solution performs slightly better, kept the linear elasticity. The shear effects are realized in the fractional order transformation of the Euler-Bernoulli model; besides, from comparative analysis, other physical effects in the structure may be present in the fractional order. Resumo. Soluções fracionárias gerais para as equações diferenciais de Euler-Bernoulli e Timoshenko-Ehrenfest são deduzidas para o caso de uma viga biapoiada submetida a uma carga estática uniformemente distribuída. Ambas as soluções são confrontadas com os resultados do software Ansys, tomado como referência, levandoàs soluções fracionárias particulares correspondentes. Como esperado, ambas as soluções específicas convergem para os resultados do Ansys para pequenas deflexões e vigas de alta razão de aspecto, enquanto que, na geometria oposta, a solução fracionária de Timoshenko-Ehrenfest tem um desempenho ligeiramente melhor, mantida a elasticidade linear. Os efeitos de cisalhamento são constatados na transformação de ordem fracionária do modelo de Euler-Bernoulli; além disso, a partir da análise comparativa, outros efeitos físicos na estrutura podem estar presentes na ordem fracionária.

Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.

Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.

17th Brazilian Congress of Thermal Sciences and Engineering, 2018

MATEC Web of Conferences

Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. This conve... more Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. This conversion is due to the thermo-viscous interaction between the acoustically oscillating gas fluid within a porous medium, referred to as a regenerator, and the pore internal walls. The thermo-acoustic approach is proposed in this study as an alternative sustainable solution for addressing the issue of electricity in remote areas of developing countries. This approach is environmentally friendly as it utilises air as the working medium and therefore does not generate harmful emissions. In this study, a two-stage travelling-wave thermo-acoustic engine has been modelled using DeltaEC. The simulation was performed by considering various input heat for both of the engine stages. The heat input for the first stage was set within the range of 359.48 to 455.75W, while in the second stage was within the range of 1307.99 to 1656.35W. Hundred (100) data were generated. This dataset was used to build an...

Trends in Computational and Applied Mathematics

Euler-Bernoulli (EB) and Timoshenko-Ehrenfest (TE) theories model simple beams under linear const... more Euler-Bernoulli (EB) and Timoshenko-Ehrenfest (TE) theories model simple beams under linear constraints. But even keeping these constraints, specific structural effects in real applications compromise the accuracy of the models, such as stress concentration due to force reactions on the support contacts or bucking, for example. Both EB and TE solutions assume planar cross sections and structural stability, and therefore do not address those particular effects; the interest in using them is to explore the conditions under which shear effects are significant or not. Numerical solutions such as the ones obtained from the Finite Element Method (FEM) reach structural effects quite well, depending on the complexity of the problem and degree of refinement. However, although accurate, the numerical solutions do not distinguish whethera particular effect is on charge or not; they implicitly encompass all of them as a whole. To diagnose them for simple beams, analytical solutions such as EB o...

C.Q.D. - Revista Eletrônica Paulista de Matemática

Simply supported prismatic beams submitted to uniformly distributed static load are modeled in th... more Simply supported prismatic beams submitted to uniformly distributed static load are modeled in the ANSYS environment under linear elasticity limits. However, the beam deflection profile may behave in disagreement with the predictions from either Euler-Bernoulli (EB) or even Timoshenko-Ehrenfest (TE) linear theories, depending on the load magnitude and geometrical properties of the cross section. Careful examination on the ANSYS stress output data reveals, for those cases, local stress concentrations on the support contacts areas due to the intensive force reactions, which end up affecting the resulting transversal deflection along the entire beam, although the linear regime is ensured for all finite elements. Another way to verify these effects is to employ fractional calculus modeling on the EB or TE equations so that to confront the general fractional solutions with the ANSYS deflection outputs, which leads to a fractional order model whenever the stress concentration is present. The deviation of the fractional order with respect to the integer order of reference allows to measure the degree of relevance of the supporting reactions on the structure behavior. Both EB and TE theories lead to similar results, whose only difference relies on the shear effects already predicted analytically in the TE modeling, which may also be estimated on its magnitude by comparison using fractional calculus. Several case studies have been conducted and led to the development of a new estimate for structural analysis.

Simply supported prismatic beams submitted to uniformly distributed static load are modeled in th... more Simply supported prismatic beams submitted to uniformly distributed static load are modeled in the ANSYS environment under linear elasticity limits. However, the beam deflection profile may behave in disagreement with the predictions from either Euler-Bernoulli (EB) or even Timoshenko-Ehrenfest (TE) linear theories, depending on the load magnitude and geometrical properties of the cross section. Careful examination on the ANSYS stress output data reveals, for those cases, local stress concentrations on the support contacts areas due to the intensive force reactions, which end up affecting the resulting transversal deflection along the entire beam, although the linear regime is ensured for all finite elements. Another way to verify these effects is to employ fractional calculus modeling on the EB or TE equations so that to confront the general fractional solutions with the ANSYS deflection outputs, which leads to a fractional order model whenever the stress concentration is present. The deviation of the fractional order with respect to the integer order of reference allows to measure the degree of relevance of the supporting reactions on the structure behavior. Both EB and TE theories lead to similar results, whose only difference relies on the shear effects already predicted analytically in the TE modeling, which may also be estimated on its magnitude by comparison using fractional calculus. Several case studies have been conducted and led to the development of a new estimate for structural analysis.

o comportamento dinâmico da fundacao de turbogrupos pode afetar significativamente a resposta em ... more o comportamento dinâmico da fundacao de turbogrupos pode afetar significativamente a resposta em frequencia de algumas maquinas rotativas. Assim, no intuito de se avaliar corretamente o comportamento vibratorio do sistema dinâmico como um todo, e importante considerar as forcas atuantes entre o rotor e a fundacao. Nesse sentido, ha muitas tecnicas matematicas baseadas na estimativa da matriz de impedância mecânica da fundacao. Cada termo dessa matriz pode ser escrito como uma funcao dos seus parâmetros modais e da velocidade de rotacao do rotor. No entanto, a medicao da resposta em frequencia de uma fundacao isolada, excitada por uma forca conhecida, frequentemente nao e disponivel. Entretanto, ha algumas tecnicas de modelagem que independem dessa disponibilidade, e permitem a identificacao dos parâmetros modais da fundacao: frequencias naturais, fatores de amortecimento e massas modais. Dois metodos de identificacao sao descritos, baseados em funcoes de minimizacao, sendo que um deles e mais aprofundadamente aplicado. Tais funcoes lidam com comparacoes entre as respostas em frequencia nos pontos de conexao (mancais hidrodinâmicos) entre rotor e fundacao, obtidas pelos deslocamentos absolutos e relativos medidos, e pelos seus respectivos valores analiticos, calculados atraves de modelagem matematica. Minimizando-se as funcoes objetivo que relacionam os dados, sao determinados os parâmetros modais em questao. Para se efetuar a funcao de minimizacao citada, sao tomados dois metodos numericos de procura sistematica de parâmetros modais. Ambos sao apresentados e aplicados Abstract

Procceedings of the 18th Brazilian Congress of Thermal Sciences and Engineering, 2020

The thermoacoustic engine onsets due to the spontaneous thermoviscous interaction between an acou... more The thermoacoustic engine onsets due to the spontaneous thermoviscous interaction between an acoustic particle and the surface of a solid substrate, ignited when the latter is submitted to a sufficiently high temperature gradient along the direction of acoustic propagation within a waveguide. This effect, namely thermoacoustic, consists in a conversion of thermal into acoustic energy, whose magnitude is proportional to the area of exposition for the interaction, besides other factors. In this way, the porous material in the thermoacoustic core (TAC) is a key point within the engine as it increases the total available area, provided by the pore internal walls. This study consists in a simulation and analysis of a previously conceived and experimentally characterized thermoacoustic engine in the transfer matrix context, from another work, in the free software DeltaEC environment -under Rott’s approach context. Once the simulated model matches the real engine, we expect to disclosure variables that until then were hidden in the original data within the measured transfer matrices of the thermoacoustic core (TTAC), such as the temperature profile along the device, heat and acoustic power, among others. So far, we have reached some degree of approximation. In the sequence, the goal of this investigation is to enable the editing of variables in the simulation and even in the transfer matrix itself, deliberately changing its coefficients. Based on the arbitrary performance of the engine, this altered TTAC may indicate corresponding changes, via inverse problem, in the porous material such as geometric parameters or thermophysical properties. Therefore, the resulting model may be a tool to potentially improve the performance of real systems in the stage of design.

25th International Congress of Mechanical Engineering, 2019

The performance of thermoacoustic devices, either engines or refrigerators, depends essentially o... more The performance of thermoacoustic devices, either engines or refrigerators, depends essentially on the design of its main component: the thermoacoustic core (TAC), which comprises a porous material, heat exchangers and a thermal buffer tube. Usual porous materials of the most efficient devices are complex in its internal geometry, which makes convenient its experimental characterization as an implicit component of the entire TAC, to be treated as a black box in the form of a transfer matrix. From this measured data, a particular TAC can then be inserted into a simulated waveguide network so that to constitute a thermoacoustic engine (TAE), whose performance can be analytically predicted from usual transfer matrix relations. Nonetheless, selecting the best porous material for a certain TAE configuration by experimental means is highly time demanding due to the laborious iterative process involved. On the other hand, for complex porous materials, analytical or numerical approaches are so far impractical. The purpose of this work is to explore experimental data from previous works, where TAC acoustic transfer matrices had been measured, aiming to circumvent the need of such iterative experimental process in the quest for a better porous material. Those matrices are adequate and directly edited with close observation of the resulting new simulated - and artificial - performance. They are evaluated with respect to the actual physical system and corresponding boundary conditions by contrasting their values to the real transfer matrix data. The corresponding determinant, which measures the degree of nonreciprocity, is proposed as reference for selecting the synthesized transfer matrices as a preceding step toward the optimal design of porous materials from an inverse problem approach.

17th Brazilian Congress of Thermal Sciences and Engineering, 2018

Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic os... more Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic oscillations in a working gas confined within a tubular network, whose configuration may lead to either standing or traveling waves. Its main segment is the thermoacoustic core (TAC), defined as the waveguide interval where the temperature gradient is inhomogeneous and, if sufficiently high, generates the acoustic field. The thermoacoustic phenomenon occurs within the open pores of its main component: stack or regenerator. From the transfer matrix of the TAC filled with a specific porous material, different engines can be designed by varying the lengths of the other waveguide segments, and their energetic performances estimated. Therefore, an optimization can be carried out by pursuing the best waveguide configuration for each TAC. However, such procedures may be time-demanding as they follow a forward problem for each sample of porous material under investigation, and the chances of achieving a good TAC design may not be favored in this trial and error process. As an attempt to improve the criteria for porous material selection, we explore in this work an inverse problem: the synthesis of the TAC transfer matrix from an arbitrary engine performance. Previous experimental data from TACs of two different porous materials are analyzed for a standing wave engine configuration. Each transfer coefficient is disturbed in both amplitude and phase in simulations so that to evaluate the effects on the thermoacoustic gain. The resulting artificial matrices lead to better energetic performances and rise discussions toward the feasibility of the corresponding porous materials.

ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the freque... more ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the frequency response of some rotating machines. So, in order to evaluate correctly the vibrational behaviour of the whole system, it is important to consider the forces acting between the machine supports and foundation. On this way, there are many mathematical techniques based on the evaluation of the foundation mechanical impedance matrix. Each term of this matrix can be described as a function of the foundation modal parameters and the machine rotational speed. Nevertheless, the measurement of the only foundation frequency response due to a known exciting force is often not available. Fortunately, there are some modelling technics that supply such needs, allowing the foundation modal parameters identification, also in particular conditions: natural frequencies, vibrational modes and their respective generalized masses, stiffnesses and dampings. Two methods for these case-studies identification are applied here, and both deal with minimization functions, which will be briefly presented. These functions are based on the comparison between the frequency response at the connecting points between rotor and foundation (journal bearings), obtained by measuring absolute and relative displacements, and the respective analitical ones, obtained by a mathematical model. Minimizing objective functions that relate these data, the foundation modal parameters are determined. These procedures allow to get information enough about the foundation. For complex structures, the methods can be particularly advantageous over the analytical methods (the FEM, in this case, can take too much computational costs). As a final result, the total system (rotor, bearings and foundation) frequency response can be calculated for the system externally excited by unbalancing forces of the rotor. The first method deals with comparisons between the forces acting on the foundation and the forces due to the foundation vibrations. After some iterations, the forces tend to equalize themselves for the correct foundation modal parameters identified. The measurements required are the absolute connecting points displacements measured at the bearings housing. It is also required that the number of normal modes of the supporting structure (foundation) must be equal to the number of degrees of freedom associated to the connecting points. The second method involves iterations and comparisons between displacements. The measurements required here are the relative displacements at the bearings, obtained through the absolute displacements of the rotor and the bearings at the connecting points. It is not necessary to know the exciting forces, and the number of normal modes does not need to be equal to the degrees of freedom, since the foundation modal matrix is not inverted here. Besides, it is proposed an optimization of the modal parameters systematical searching numerical method.

ABSTRACT This paper deals with two numerical methods applied to a method for modal parameters ide... more ABSTRACT This paper deals with two numerical methods applied to a method for modal parameters identification of turbomachinery foundation. The identification method evaluates the modal parameters of the foundation structures using rotor and supports vibration data, dealing with comparisons between analytical and experimental frequency responses. The numerical methods were designed to process a required minimization function, by the identification method, trying to be as fast and as accurate as possible. One of these two methods is new and proceeds in a good agreement with the expected results.

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2021

General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equati... more General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equations are deduced for the case of a simply supported beam submitted to uniformly distributed static load. Both solutions are confronted against Ansys software results, taken as reference, leading to the corresponding particular fractional solutions. As expected, both particular solutions converge to the Ansys results for small deflections and beam with high-aspect ratio, while, for opposite geometrical features, the fractional Timoshenko-Ehrenfest solution performs slightly better, kept the linear elasticity. The shear effects are realized in the fractional order transformation of the Euler-Bernoulli model; besides, from comparative analysis, other physical effects in the structure may be present in the fractional order.

International Journal of Thermal Sciences, Oct 1, 2017

This paper aims to study the effects of air variable properties in the transient case of the clas... more This paper aims to study the effects of air variable properties in the transient case of the classical differentially heated square cavity problem. A SIMPLE algorithm using a low Mach number approximation is applied for coupling the heat and momentum transport equations, which are discretized by the finite volume method. A fully implicit scheme is used for time discretization. The numerical code is validated with benchmark results obtaining a maximum deviation of 0.13% in the average Nusselt number for the non-Boussinesq approach. The temperature and velocity fields as well as the local Nusselt number are numerically studied for Rayleigh numbers ranging between 10 4-10 7. A temperature difference of 720 K is considered. We have found that the effects of variable properties are especially relevant along the flow development period, amongst which the average Nusselt number, for instance, differs up to roughly 10% with respect to the constant properties case; in contrast, once in steady state regime, such a difference remains less important and is no longer oscillating, resulting around 2%. An investigation is therefore put forward covering additional effects under regard of the principle of energy conservation, such as the time evolution of the total energy and its components for both transient regime and steady state cases. Excepting for the kinetic energy, the internal, potential and total energies are consistently and significantly higher for the case of variable properties; a suitable discussion is provided.

Dedico esta tese à minha filha que logo vai nascer. Je dédie cette thèse à ma fille qui naîtra bi... more Dedico esta tese à minha filha que logo vai nascer. Je dédie cette thèse à ma fille qui naîtra bientôt. I dedicate this thesis to my daughter who will be born soon.

Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. These acou... more Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. These acoustic waves can be used to induce cooling (thermo-acoustic refrigeration) or generate electricity (thermo-acoustic generator). This conversion is due to the thermo-viscous interaction between the acoustically oscillating gas medium within a porous material, referred to as a regenerator, and the pore internal walls. Although there has been significant progress in the development of efficient thermo-acoustic systems, their relatively low efficiency and the nonlinearity associated with more severe working conditions remain their major issues. Therefore, it is a major potential area of research. In this study, a one-stage travelling-wave thermo-acoustic engine has been modelled using DeltaEC. The simulation was performed by considering various input heat to the hot heat exchanger within the range of 8.2 to 227.91W, and sixty (60) datasets were generated. These data were used to build an Artificial Neural Network (ANN) model. The comparison between the output data extracted from the DeltaEC simulation and the results predicted from the ANN model was done. Both of the results obtained are in good agreement and prove that the ANN can be suitable for predicting configurations that were not previously simulated.

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Dec 20, 2021

General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equati... more General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equations are deduced for the case of a simply supported beam submitted to uniformly distributed static load. Both solutions are confronted against Ansys software results, taken as reference, leading to the corresponding particular fractional solutions. As expected, both particular solutions converge to the Ansys results for small deflections and beam with high-aspect ratio, while, for opposite geometrical features, the fractional Timoshenko-Ehrenfest solution performs slightly better, kept the linear elasticity. The shear effects are realized in the fractional order transformation of the Euler-Bernoulli model; besides, from comparative analysis, other physical effects in the structure may be present in the fractional order. Resumo. Soluções fracionárias gerais para as equações diferenciais de Euler-Bernoulli e Timoshenko-Ehrenfest são deduzidas para o caso de uma viga biapoiada submetida a uma carga estática uniformemente distribuída. Ambas as soluções são confrontadas com os resultados do software Ansys, tomado como referência, levandoàs soluções fracionárias particulares correspondentes. Como esperado, ambas as soluções específicas convergem para os resultados do Ansys para pequenas deflexões e vigas de alta razão de aspecto, enquanto que, na geometria oposta, a solução fracionária de Timoshenko-Ehrenfest tem um desempenho ligeiramente melhor, mantida a elasticidade linear. Os efeitos de cisalhamento são constatados na transformação de ordem fracionária do modelo de Euler-Bernoulli; além disso, a partir da análise comparativa, outros efeitos físicos na estrutura podem estar presentes na ordem fracionária.

Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.

Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and w... more Maine (LAUM),France, under the frame of a co-tutelage agreement between these universities, and with the financial and infrastructural support from the Brazilian funding agency CAPES, from LAUM, and from UNICAMP, to which I am deeply grateful. I would like to thank M. Yves Aurégan, Research Director CNRS, and M. Joël Gilbert, Director of LAUM, for being welcome during the two years period that I lived in Le Mans as a Ph.D. Student. Writing this "Acknowledgments"essay is not a simple task. To accomplish this doctorate I depended on so many people, in so particularly different ways, that I can be sure that I will be unfair in my following words. But what I am indeed sure of is that I will do my best. What those forgotten or insufficiently acknowledged people can be sure of is that, even though not fairly mentioned here, they are imprinted in my heart.

17th Brazilian Congress of Thermal Sciences and Engineering, 2018

MATEC Web of Conferences

Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. This conve... more Thermo-acoustic systems can convert thermal energy into acoustic waves and vice-versa. This conversion is due to the thermo-viscous interaction between the acoustically oscillating gas fluid within a porous medium, referred to as a regenerator, and the pore internal walls. The thermo-acoustic approach is proposed in this study as an alternative sustainable solution for addressing the issue of electricity in remote areas of developing countries. This approach is environmentally friendly as it utilises air as the working medium and therefore does not generate harmful emissions. In this study, a two-stage travelling-wave thermo-acoustic engine has been modelled using DeltaEC. The simulation was performed by considering various input heat for both of the engine stages. The heat input for the first stage was set within the range of 359.48 to 455.75W, while in the second stage was within the range of 1307.99 to 1656.35W. Hundred (100) data were generated. This dataset was used to build an...

Trends in Computational and Applied Mathematics

Euler-Bernoulli (EB) and Timoshenko-Ehrenfest (TE) theories model simple beams under linear const... more Euler-Bernoulli (EB) and Timoshenko-Ehrenfest (TE) theories model simple beams under linear constraints. But even keeping these constraints, specific structural effects in real applications compromise the accuracy of the models, such as stress concentration due to force reactions on the support contacts or bucking, for example. Both EB and TE solutions assume planar cross sections and structural stability, and therefore do not address those particular effects; the interest in using them is to explore the conditions under which shear effects are significant or not. Numerical solutions such as the ones obtained from the Finite Element Method (FEM) reach structural effects quite well, depending on the complexity of the problem and degree of refinement. However, although accurate, the numerical solutions do not distinguish whethera particular effect is on charge or not; they implicitly encompass all of them as a whole. To diagnose them for simple beams, analytical solutions such as EB o...

C.Q.D. - Revista Eletrônica Paulista de Matemática

Simply supported prismatic beams submitted to uniformly distributed static load are modeled in th... more Simply supported prismatic beams submitted to uniformly distributed static load are modeled in the ANSYS environment under linear elasticity limits. However, the beam deflection profile may behave in disagreement with the predictions from either Euler-Bernoulli (EB) or even Timoshenko-Ehrenfest (TE) linear theories, depending on the load magnitude and geometrical properties of the cross section. Careful examination on the ANSYS stress output data reveals, for those cases, local stress concentrations on the support contacts areas due to the intensive force reactions, which end up affecting the resulting transversal deflection along the entire beam, although the linear regime is ensured for all finite elements. Another way to verify these effects is to employ fractional calculus modeling on the EB or TE equations so that to confront the general fractional solutions with the ANSYS deflection outputs, which leads to a fractional order model whenever the stress concentration is present. The deviation of the fractional order with respect to the integer order of reference allows to measure the degree of relevance of the supporting reactions on the structure behavior. Both EB and TE theories lead to similar results, whose only difference relies on the shear effects already predicted analytically in the TE modeling, which may also be estimated on its magnitude by comparison using fractional calculus. Several case studies have been conducted and led to the development of a new estimate for structural analysis.

Simply supported prismatic beams submitted to uniformly distributed static load are modeled in th... more Simply supported prismatic beams submitted to uniformly distributed static load are modeled in the ANSYS environment under linear elasticity limits. However, the beam deflection profile may behave in disagreement with the predictions from either Euler-Bernoulli (EB) or even Timoshenko-Ehrenfest (TE) linear theories, depending on the load magnitude and geometrical properties of the cross section. Careful examination on the ANSYS stress output data reveals, for those cases, local stress concentrations on the support contacts areas due to the intensive force reactions, which end up affecting the resulting transversal deflection along the entire beam, although the linear regime is ensured for all finite elements. Another way to verify these effects is to employ fractional calculus modeling on the EB or TE equations so that to confront the general fractional solutions with the ANSYS deflection outputs, which leads to a fractional order model whenever the stress concentration is present. The deviation of the fractional order with respect to the integer order of reference allows to measure the degree of relevance of the supporting reactions on the structure behavior. Both EB and TE theories lead to similar results, whose only difference relies on the shear effects already predicted analytically in the TE modeling, which may also be estimated on its magnitude by comparison using fractional calculus. Several case studies have been conducted and led to the development of a new estimate for structural analysis.

o comportamento dinâmico da fundacao de turbogrupos pode afetar significativamente a resposta em ... more o comportamento dinâmico da fundacao de turbogrupos pode afetar significativamente a resposta em frequencia de algumas maquinas rotativas. Assim, no intuito de se avaliar corretamente o comportamento vibratorio do sistema dinâmico como um todo, e importante considerar as forcas atuantes entre o rotor e a fundacao. Nesse sentido, ha muitas tecnicas matematicas baseadas na estimativa da matriz de impedância mecânica da fundacao. Cada termo dessa matriz pode ser escrito como uma funcao dos seus parâmetros modais e da velocidade de rotacao do rotor. No entanto, a medicao da resposta em frequencia de uma fundacao isolada, excitada por uma forca conhecida, frequentemente nao e disponivel. Entretanto, ha algumas tecnicas de modelagem que independem dessa disponibilidade, e permitem a identificacao dos parâmetros modais da fundacao: frequencias naturais, fatores de amortecimento e massas modais. Dois metodos de identificacao sao descritos, baseados em funcoes de minimizacao, sendo que um deles e mais aprofundadamente aplicado. Tais funcoes lidam com comparacoes entre as respostas em frequencia nos pontos de conexao (mancais hidrodinâmicos) entre rotor e fundacao, obtidas pelos deslocamentos absolutos e relativos medidos, e pelos seus respectivos valores analiticos, calculados atraves de modelagem matematica. Minimizando-se as funcoes objetivo que relacionam os dados, sao determinados os parâmetros modais em questao. Para se efetuar a funcao de minimizacao citada, sao tomados dois metodos numericos de procura sistematica de parâmetros modais. Ambos sao apresentados e aplicados Abstract

Procceedings of the 18th Brazilian Congress of Thermal Sciences and Engineering, 2020

The thermoacoustic engine onsets due to the spontaneous thermoviscous interaction between an acou... more The thermoacoustic engine onsets due to the spontaneous thermoviscous interaction between an acoustic particle and the surface of a solid substrate, ignited when the latter is submitted to a sufficiently high temperature gradient along the direction of acoustic propagation within a waveguide. This effect, namely thermoacoustic, consists in a conversion of thermal into acoustic energy, whose magnitude is proportional to the area of exposition for the interaction, besides other factors. In this way, the porous material in the thermoacoustic core (TAC) is a key point within the engine as it increases the total available area, provided by the pore internal walls. This study consists in a simulation and analysis of a previously conceived and experimentally characterized thermoacoustic engine in the transfer matrix context, from another work, in the free software DeltaEC environment -under Rott’s approach context. Once the simulated model matches the real engine, we expect to disclosure variables that until then were hidden in the original data within the measured transfer matrices of the thermoacoustic core (TTAC), such as the temperature profile along the device, heat and acoustic power, among others. So far, we have reached some degree of approximation. In the sequence, the goal of this investigation is to enable the editing of variables in the simulation and even in the transfer matrix itself, deliberately changing its coefficients. Based on the arbitrary performance of the engine, this altered TTAC may indicate corresponding changes, via inverse problem, in the porous material such as geometric parameters or thermophysical properties. Therefore, the resulting model may be a tool to potentially improve the performance of real systems in the stage of design.

25th International Congress of Mechanical Engineering, 2019

The performance of thermoacoustic devices, either engines or refrigerators, depends essentially o... more The performance of thermoacoustic devices, either engines or refrigerators, depends essentially on the design of its main component: the thermoacoustic core (TAC), which comprises a porous material, heat exchangers and a thermal buffer tube. Usual porous materials of the most efficient devices are complex in its internal geometry, which makes convenient its experimental characterization as an implicit component of the entire TAC, to be treated as a black box in the form of a transfer matrix. From this measured data, a particular TAC can then be inserted into a simulated waveguide network so that to constitute a thermoacoustic engine (TAE), whose performance can be analytically predicted from usual transfer matrix relations. Nonetheless, selecting the best porous material for a certain TAE configuration by experimental means is highly time demanding due to the laborious iterative process involved. On the other hand, for complex porous materials, analytical or numerical approaches are so far impractical. The purpose of this work is to explore experimental data from previous works, where TAC acoustic transfer matrices had been measured, aiming to circumvent the need of such iterative experimental process in the quest for a better porous material. Those matrices are adequate and directly edited with close observation of the resulting new simulated - and artificial - performance. They are evaluated with respect to the actual physical system and corresponding boundary conditions by contrasting their values to the real transfer matrix data. The corresponding determinant, which measures the degree of nonreciprocity, is proposed as reference for selecting the synthesized transfer matrices as a preceding step toward the optimal design of porous materials from an inverse problem approach.

17th Brazilian Congress of Thermal Sciences and Engineering, 2018

Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic os... more Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic oscillations in a working gas confined within a tubular network, whose configuration may lead to either standing or traveling waves. Its main segment is the thermoacoustic core (TAC), defined as the waveguide interval where the temperature gradient is inhomogeneous and, if sufficiently high, generates the acoustic field. The thermoacoustic phenomenon occurs within the open pores of its main component: stack or regenerator. From the transfer matrix of the TAC filled with a specific porous material, different engines can be designed by varying the lengths of the other waveguide segments, and their energetic performances estimated. Therefore, an optimization can be carried out by pursuing the best waveguide configuration for each TAC. However, such procedures may be time-demanding as they follow a forward problem for each sample of porous material under investigation, and the chances of achieving a good TAC design may not be favored in this trial and error process. As an attempt to improve the criteria for porous material selection, we explore in this work an inverse problem: the synthesis of the TAC transfer matrix from an arbitrary engine performance. Previous experimental data from TACs of two different porous materials are analyzed for a standing wave engine configuration. Each transfer coefficient is disturbed in both amplitude and phase in simulations so that to evaluate the effects on the thermoacoustic gain. The resulting artificial matrices lead to better energetic performances and rise discussions toward the feasibility of the corresponding porous materials.

ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the freque... more ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the frequency response of some rotating machines. So, in order to evaluate correctly the vibrational behaviour of the whole system, it is important to consider the forces acting between the machine supports and foundation. On this way, there are many mathematical techniques based on the evaluation of the foundation mechanical impedance matrix. Each term of this matrix can be described as a function of the foundation modal parameters and the machine rotational speed. Nevertheless, the measurement of the only foundation frequency response due to a known exciting force is often not available. Fortunately, there are some modelling technics that supply such needs, allowing the foundation modal parameters identification, also in particular conditions: natural frequencies, vibrational modes and their respective generalized masses, stiffnesses and dampings. Two methods for these case-studies identification are applied here, and both deal with minimization functions, which will be briefly presented. These functions are based on the comparison between the frequency response at the connecting points between rotor and foundation (journal bearings), obtained by measuring absolute and relative displacements, and the respective analitical ones, obtained by a mathematical model. Minimizing objective functions that relate these data, the foundation modal parameters are determined. These procedures allow to get information enough about the foundation. For complex structures, the methods can be particularly advantageous over the analytical methods (the FEM, in this case, can take too much computational costs). As a final result, the total system (rotor, bearings and foundation) frequency response can be calculated for the system externally excited by unbalancing forces of the rotor. The first method deals with comparisons between the forces acting on the foundation and the forces due to the foundation vibrations. After some iterations, the forces tend to equalize themselves for the correct foundation modal parameters identified. The measurements required are the absolute connecting points displacements measured at the bearings housing. It is also required that the number of normal modes of the supporting structure (foundation) must be equal to the number of degrees of freedom associated to the connecting points. The second method involves iterations and comparisons between displacements. The measurements required here are the relative displacements at the bearings, obtained through the absolute displacements of the rotor and the bearings at the connecting points. It is not necessary to know the exciting forces, and the number of normal modes does not need to be equal to the degrees of freedom, since the foundation modal matrix is not inverted here. Besides, it is proposed an optimization of the modal parameters systematical searching numerical method.

ABSTRACT This paper deals with two numerical methods applied to a method for modal parameters ide... more ABSTRACT This paper deals with two numerical methods applied to a method for modal parameters identification of turbomachinery foundation. The identification method evaluates the modal parameters of the foundation structures using rotor and supports vibration data, dealing with comparisons between analytical and experimental frequency responses. The numerical methods were designed to process a required minimization function, by the identification method, trying to be as fast and as accurate as possible. One of these two methods is new and proceeds in a good agreement with the expected results.

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2021

General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equati... more General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equations are deduced for the case of a simply supported beam submitted to uniformly distributed static load. Both solutions are confronted against Ansys software results, taken as reference, leading to the corresponding particular fractional solutions. As expected, both particular solutions converge to the Ansys results for small deflections and beam with high-aspect ratio, while, for opposite geometrical features, the fractional Timoshenko-Ehrenfest solution performs slightly better, kept the linear elasticity. The shear effects are realized in the fractional order transformation of the Euler-Bernoulli model; besides, from comparative analysis, other physical effects in the structure may be present in the fractional order.

18th Brazilian Congress of Thermal Sciences and Engineering, 2020

The performance of thermoacoustic devices, either engines or refrigerators, depends essentially o... more The performance of thermoacoustic devices, either engines or refrigerators, depends essentially on the design of its main component: the thermoacoustic core (TAC), which comprises a porous material, heat exchangers and a thermal buffer tube. Usual porous materials of the most efficient devices are complex in its internal geometry, which makes convenient its experimental characterization as an implicit component of the entire TAC, to be treated as a black box in the form of a transfer matrix. From this measured data, a particular TAC can then be inserted into a simulated waveguide network so that to constitute a thermoacoustic engine (TAE), whose performance can be analytically predicted from usual transfer matrix relations. Nonetheless, selecting the best porous material for a certain TAE configuration by experimental means is highly time demanding due to the laborious iterative process involved. On the other hand, for complex porous materials, analytical or numerical approaches are so far impractical. The purpose of this work is to explore experimental data from previous works, where TAC acoustic transfer matrices had been measured, aiming to circumvent the need of such iterative experimental process in the quest for a better porous material. Those matrices are adequate and directly edited with close observation of the resulting new simulated - and artificial - performance. They are evaluated with respect to the actual physical system and corresponding boundary conditions by contrasting their values to the real transfer matrix data. The corresponding determinant, which measures the degree of nonreciprocity, is proposed as reference for selecting the synthesized transfer matrices as a preceding step toward the optimal design of porous materials from an inverse problem approach.

ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the freque... more ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the frequency response of some rotating machines. So, in order to evaluate correctly the vibrational behaviour of the whole system, it is important to consider the forces acting between the machine supports and foundation. On this way, there are many mathematical techniques based on the evaluation of the foundation mechanical impedance matrix. Each term of this matrix can be described as a function of the foundation modal parameters and the machine rotational speed. Nevertheless, the measurement of the only foundation frequency response due to a known exciting force is often not available. Fortunately, there are some modelling technics that supply such needs, allowing the foundation modal parameters identification, also in particular conditions: natural frequencies, vibrational modes and their respective generalized masses, stiffnesses and dampings. Two methods for these case-studies identification are applied here, and both deal with minimization functions, which will be briefly presented. These functions are based on the comparison between the frequency response at the connecting points between rotor and foundation (journal bearings), obtained by measuring absolute and relative displacements, and the respective analitical ones, obtained by a mathematical model. Minimizing objective functions that relate these data, the foundation modal parameters are determined. These procedures allow to get information enough about the foundation. For complex structures, the methods can be particularly advantageous over the analytical methods (the FEM, in this case, can take too much computational costs). As a final result, the total system (rotor, bearings and foundation) frequency response can be calculated for the system externally excited by unbalancing forces of the rotor. The first method deals with comparisons between the forces acting on the foundation and the forces due to the foundation vibrations. After some iterations, the forces tend to equalize themselves for the correct foundation modal parameters identified. The measurements required are the absolute connecting points displacements measured at the bearings housing. It is also required that the number of normal modes of the supporting structure (foundation) must be equal to the number of degrees of freedom associated to the connecting points. The second method involves iterations and comparisons between displacements. The measurements required here are the relative displacements at the bearings, obtained through the absolute displacements of the rotor and the bearings at the connecting points. It is not necessary to know the exciting forces, and the number of normal modes does not need to be equal to the degrees of freedom, since the foundation modal matrix is not inverted here. Besides, it is proposed an optimization of the modal parameters systematical searching numerical method.

ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the freque... more ABSTRACT The dynamic behaviour of a turbomachinery foundation can significantly affect the frequency response of some rotating machines. So, in order to evaluate correctly the vibrational behaviour of the whole system, it is important to consider the forces acting between the machine supports and foundation. On this way, there are many mathematical techniques based on the evaluation of the foundation mechanical impedance matrix. Each term of this matrix can be described as a function of the foundation modal parameters and the machine rotational speed. Nevertheless, the measurement of the only foundation frequency response due to a known exciting force is often not available. Fortunately, there are some modelling technics that supply such needs, allowing the foundation modal parameters identification, also in particular conditions: natural frequencies, vibrational modes and their respective generalized masses, stiffnesses and dampings. Two methods for these case-studies identification are applied here, and both deal with minimization functions, which will be briefly presented. These functions are based on the comparison between the frequency response at the connecting points between rotor and foundation (journal bearings), obtained by measuring absolute and relative displacements, and the respective analitical ones, obtained by a mathematical model. Minimizing objective functions that relate these data, the foundation modal parameters are determined. These procedures allow to get information enough about the foundation. For complex structures, the methods can be particularly advantageous over the analytical methods (the FEM, in this case, can take too much computational costs). As a final result, the total system (rotor, bearings and foundation) frequency response can be calculated for the system externally excited by unbalancing forces of the rotor. The first method deals with comparisons between the forces acting on the foundation and the forces due to the foundation vibrations. After some iterations, the forces tend to equalize themselves for the correct foundation modal parameters identified. The measurements required are the absolute connecting points displacements measured at the bearings housing. It is also required that the number of normal modes of the supporting structure (foundation) must be equal to the number of degrees of freedom associated to the connecting points. The second method involves iterations and comparisons between displacements. The measurements required here are the relative displacements at the bearings, obtained through the absolute displacements of the rotor and the bearings at the connecting points. It is not necessary to know the exciting forces, and the number of normal modes does not need to be equal to the degrees of freedom, since the foundation modal matrix is not inverted here. Besides, it is proposed an optimization of the modal parameters systematical searching numerical method.

Thermoacoustic engines are often investigated as viable alternatives for energy regeneration. The... more Thermoacoustic engines are often investigated as viable alternatives for energy regeneration. The most widely used analytical model for pressure wave propagation in thermoacoustic devices is the second order linear model developed by Nikolaus Rott. In this work, we propose a generalization of Rott's equation under the regard of fractional order calculus; we also propose a solution for this generalized equation for a specific domain. Simulations of thermoacoustic engines verify this solution and indicate potential advantages of a continuously variable order, adjustable with experimental data, as it may cover nonlinearities and effects of geometrical complexities present in test rigs. Therefore, the resulting model may better fit real systems, which leads to more accurate designing.

Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic os... more Thermoacoustic engines convert thermal into mechanical energy by means of spontaneous acoustic oscillations in a working gas confined within a tubular network, whose configuration may lead to either standing or traveling waves. Its main segment is the thermoacoustic core (TAC), defined as the waveguide interval where the temperature gradient is inhomogeneous and, if sufficiently high, generates the acoustic field. The thermoacoustic phenomenon occurs within the open pores of its main component: stack or regenerator. From the transfer matrix of the TAC filled with a specific porous material, different engines can be designed by varying the lengths of the other waveguide segments, and their energetic performances estimated. Therefore, an optimization can be carried out by pursuing the best waveguide configuration for each TAC. However, such procedures may be time-demanding as they follow a forward problem for each sample of porous material under investigation, and the chances of achieving a good TAC design may not be favored in this trial and error process. As an attempt to improve the criteria for porous material selection, we explore in this work an inverse problem: the synthesis of the TAC transfer matrix from an arbitrary engine performance. Previous experimental data from TACs of two different porous materials are analyzed for a standing wave engine configuration. Each transfer coefficient is disturbed in both amplitude and phase in simulations so that to evaluate the effects on the thermoacoustic gain. The resulting artificial matrices lead to better energetic performances and rise discussions toward the feasibility of the corresponding porous materials.