Nonequilibrium work methods for determining potentials of mean force (PMF) w(z) have recently gained popularity as an alternative to standard equilibrium based methods. Introduced by Kosztin et al., the forward-reverse (FR) method is a bidirectional work method in that it requires the work to be sampled in both forward and reverse directions along the reaction coordinate z. This bidirectional sampling leads to much faster convergence than other nonequilibrium methods such as the Jarzynski equality, and the calculation itself is extremely simple, making the FR method an attractive way of determining the PMF. Presented here is an extension to the FR method that deals with sampling problems along essentially irreversible reaction coordinates. By oscillating a particle as it is steered along a reaction coordinate, both forward and reverse work samples are obtained as the particle progresses. Dubbed the oscillating forward-reverse (OFR) method, this new method overcomes the issue of irreversibility that is present in numerous soft-matter and biological systems, particularly in the stretching or unfolding of proteins. The data analysis of the OFR method is non-trivial however, and to this end a software package named the ‘OFR Analysis Tool’ has been created. This software performs all of the complicated analysis necessary, as well as a complete error analysis that considers correlations in the data, thus streamlining the use of the OFR method for potential end users. Another attractive feature of the FR method is that the dissipative work is collected at the same time as the free energy changes, making it possible to also calculate local diffusion coefficients, D(z), from the same simulation as the PMF through the Stokes-Nernst-Einstein relation Fdrag = −γv, with γ = kB T /D. While working with the OFR method, however, the D(z) results never matched known values or those obtained through other methods, including the mean square displacement (or Einstein) method. After a reformulation of the procedure to obtain D(z), i.e. by including the correct path length and particle speeds, results were obtained that were much closer to the correct values. The results however showed very little variation over the length of the reaction coordinate, even when D(z) was known to vary drastically. It seemed that the highly variable and noncontinuous velocity function of the particle being steered through the “stiff-spring” method was incompatible with the macroscopic definition of the drag coefficient, γ. The drag coefficient requires at most a slowly varying velocity so that the assumption of a linearly related dissipative work remains valid at all times. To address this, a new dynamic constraint steering protocol (DCP) was developed to replace the previously used “stiff-spring” method, now referred to as a dynamic restraint protocol (DRP). We present here the results for diffusion in bulk water, and both the PMF and diffusion results from the permeation of a water molecule through a DPPC membrane. We also consider the issue of ergodicity and sampling, and propose that to obtain an accurate w(z) (and D(z)) from even a moderately complex system, the final result should be a weighted average obtained from numerous pulls. An additional utility of the FR and OFR methods is that the permeability across lipid bilayers can be calculated from w(z) and D(z) using the inhomogeneous solubility-diffusion (ISD) model. As tests, the permeability was first calculated for H2O and O2 through DPPC. From the simulations, the permeability coefficients for H2O were found to be 0.129 ± 0.075 cm/s and 0.141 ± 0.043 cm/s, at 323 K and 350 K respectively, while the permeability coefficients for O2 were 114 ± 40 cm/s and 101 ± 27 cm/s, again at 323 K and 350 K respectively. As a final, more challenging system, the permeability of tyramine – a positively charged trace amine at physiological pH – was calculated. The final value of P = 0.89 ± 0.24 Ang/ns is over two orders of magnitude lower than that obtained from experiment (22 ± 4 Ang/ns), although it is clear that the permeability as calculated through the ISD is extremely sensitive to the PMF, as scaling the PMF by ∼ 20% allowed the simulation and experimental values to agree within uncertainty. With accurate predictions for free energies and permeabilities, the OFR method could potentially be used for many valuable endeavors such as rational drug design.

The goal of the current study was to develop a computational framework for modelling the coupled fluid-structure interaction problem of squeeze films often encountered in MEMS devices. Vibratory MEMS devices such as gyroscopes, RF switches, and 2D resonators often have a thin plate like structure vibrating transversely to a Fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping to the vibrating plate. For accurate modelling of the squeeze film effect, one must account for the coupled fluid-structure interaction. The majority of prior works attempting to address the coupled problem either approximate the mode shape of the vibrating plate or resort to cumbersome iterative solution strategies to address the problem in an indirect way. In the current work, we discuss the development of a fully coupled finite element based numerical scheme to solve the 2D Reynolds equation coupled with the 3D plate elasticity equation in a single step. The squeeze film solver so developed has been implemented into a commercial FEA package NISA as part of its Micro-Systems module. Further, extending on a prior analytical work, the effect of variable ow boundaries for an all sides clamped plate on squeeze film parameters has been thoroughly investigated. The developed FEM based numerical scheme has been used to validate the results of the prior analytical study. The developed numerical scheme models the 2D Reynolds equation thus limiting the model to account for the effects of the fluid volume strictly confined between the structure and the substrate. To study the effect of surrounding fluid volume ANSYS FLOTRAN simulations have been performed by numerically solving the full 3D Navier Stokes equation in the extended fluid domain for the different flow boundary scenarios. Cut-off frequencies are established beyond which one can consider a 2D fluid domain without considerable loss of accuracy. First, a displacement based finite element formulation is presented for the 2D Reynolds equation coupled with the 3D elasticity equation. Both lower order 8 node and higher order 27 node 3D elements are developed. Only a single type of 3D element is used for modelling along with a 2D fluid layer represented by the \wet" face of the 3D structural domain. The results from our numerical model are compared with experimental data from literature for a MEMS cantilever. The results from the 27 node displacement based elements show good agreement with published experimental data. The results from the lower order 8 node displacement based elements however show huge errors even for relatively fine meshes due to locking issues in modelling high aspect ratio structures. This limits the implementation of the displacement based solver in commercial FE packages where the available mesh generators are generally restricted to lower order 3D elements. In order to overcome the limitations faced by lower order elements (primarily locking issues) in modelling high aspect ratio MEMS geometries, a coupled hybrid formulation is developed next. A thorough performance study is presented considering both the hybrid and displacement based elements for lower order 8 node and higher order 27 node ele- ments. The optimal element choice for modelling squeeze film geometries is determined based on the comparative studies. The effect of element aspect ratio for hybrid and displacement based elements are studied and the superiority of hybrid formulation over displacement based formulations is established for lower order 8 node elements. The coupled hybrid nite element formulation developed for lower order elements is implemented in the commercial FEA package NISA. The implementation scheme to integrate the developed coupled hybrid 8 node squeeze film solver into the commercial FEA package is discussed. The pre-integration analysis and subsequent requirement gaps are first investigated. Based on the gap analysis, certain GUI modifications are undertaken and parser programs are developed to re-format data according to NISA input requirements. Certain special features are included in the package to aid in post processing data analysis by MEMS designers such as \frequency sweep" and \node of interest" selection. As a case study for validation, we also present the modelling of a MEMS cantilever and show that the simulation results from our software are in good agreement with experimental data reported in the literature. Finally as a case study, an extension of a prior analytical work, which studies the effect of varying flow boundaries on squeeze film parameters, is discussed. Explanations are provided for the findings reported in the prior analytical work. The concept of using variation in flow boundaries as a frequency tuning tool is introduced. The analytical results are validated with the coupled numerical scheme discussed before, by considering imposed mode shape for an all sides clamped plate as prescribed displacement to the fluid domain. The simulated results are used to study the intricacies in squeeze film damping and stiffness variations with respect to spatial changes in the fluid flow boundary conditions. In particular, it has been shown that the boundary venting conditions can be used effectively to tune the dynamic response of a micromechanical structure over a fairly large range of frequencies and somewhat smaller range of squeeze film damping. Next, the effect of the surrounding fluid volume for various venting conditions is studied. ANSYS FLOTRAN is used to solve for the full 3D Navier Stokes equation over the extended fluid domain. Results from the extended domain study are used to determine cut-off frequencies beyond which one need not resort to an extended mesh study, and yet be within 5% accuracy of the full extended mesh model.

O presente trabalho apresenta um estudo numérico bidimensional sobre a otimização da geometria de um dispositivo conversor de energia das ondas do mar em energia elétrica. O objetivo principal é, através da modelagem computacional de um dispositivo cujo principio de funcionamento é o de Coluna de Água Oscilante (CAO) e do emprego de Constructal Design, maximizar a conversão da energia das ondas do mar em energia elétrica. Essa técnica é baseada na Teoria Constructal. O aspecto inédito deste trabalho, em relação aos estudos disponíveis na literatura, é o fato de levar em conta o clima de ondas de uma dada região e, a partir disso, dimensionar o dispositivo de modo que ele tenha um desempenho otimizado. Para tanto, foi empregado o método Constructal Design, os graus de liberdade empregados são: H1/L (razão entre a altura e o comprimento da câmara CAO) e H3 (profundidade de submersão do dispositivo CAO). A relação H2/l (razão entre altura e comprimento da chaminé de saída da câmara CAO) é considerada um parâmetro fixo. Foram realizados estudos levando em conta uma onda em escala de laboratório e um espectro de ondas real. Foi também realizado um estudo sobre a influência da perda de carga da turbina através de uma restrição física. Para a solução numérica foi empregado um código comercial de dinâmica dos fluidos computacional, FLUENT®, baseado no Método de Volumes Finitos (MVF). A geometria e a geração a malha foi realizada no software GAMBIT®. O modelo multifásico Volume of Fluid (VOF) é aplicado no tratamento da interação água-ar. O domínio computacional é representado por um tanque de ondas com o dispositivo CAO acoplado. Os resultados obtidos mostram que é possível estabelecer uma razão de H1/L ótimo, conhecendo-se o clima de ondas, ou seja, o recomendável é que esta razão seja igual a quatro vezes a altura da onda dividido pelo comprimento da onda incidente. / The present work presents a two-dimensional numerical study about the geometric optimization of an ocean Wave Energy Converter (WEC) into electrical energy. The main goal is, through computational modeling of a device whose operating principle is the Oscillating Water Column (OWC) and from employment Constructal Design, to maximize the conversion of energy of ocean waves into electricity. This technique is based on Constructal Theory. The inedited aspect of this work comparing to the available studies is that it takes into account the wave climate of a given region to design the device so that it achieves optimum performance. Constructal Design is employed varying the degrees of freedom H1/L (ratio between the height and length of OWC chamber) and H3 (lip submergence). While the relation H2/l (ratio between height and length of chimney) is kept fixed. Studies were performed considering a wave on a laboratory scale and a spectrum of real waves. Yet a study of the influence of the turbine pressure losses was performed using a physical constraint. For the numerical solution it is used the Computational Fluid Dynamic (CFD) commercial code FLUENT®, based on the Finite Volume Method (FVM). The geometry and mesh generation was performed in GAMBIT ® software. The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The computational domain is represented by an OWC device coupled with the wave tank. The results show that it is possible to establish a relationship of H1 / L optimum, if the wave climate is know. It is recommended that this ratio be equal to four times the height of the wave divided by the length of the incident wave.

O presente trabalho tem como objetivo maximizar a potência hidropneumática convertida num dispositivo do tipo Coluna d'Água Oscilante (CAO). Para fazê-lo, o método Constructal Design é aplicado para aprimorar a geometria e a profundidade de submersão do dispositivo. No desenvolvimento do método Constructal são propostos e analisados três graus de liberdade: H1/L (razão entre a altura e comprimento da câmara do dispositivo CAO), H2/l (razão entre a altura da câmara e o comprimento da chaminé) e H3 (profundidade de submersão do dispositivo CAO). As restrições do problema (parâmetros constantes) são a área da câmara A1 e a área total do dispositivo CAO A2. O domínio computacional consiste de um dispositivo CAO inserido num tanque que é submetido a ondas na escala real. A malha é desenvolvida no software Ansys Icem®. O código de Dinâmica dos Fluidos Computacional Ansys Fluent® é empregado para encontrar a solução numérica a qual é baseada no método dos Volumes Finitos. O modelo multifásico Volume of Fluid (VOF) é usado na interação das fases água-ar. Os resultados indicam que a potência hidropneumática máxima obtida é de 190 W para razões de H1/L, H2/l e H3 iguais a 0,135, 6,0 e 9,5 m respectivamente. Por outro lado, o menor valor obtido da potência hidropneumática é de quase 11 W, o que mostra a utilidade do método Constructal, para fornecer uma relação entre o clima de ondas de um lugar determinado e as dimensões ótimas do dispositivo CAO. / The present work aims to maximize the hydropneumatic power converted in an Oscillating Water Column (OWC) device. To do this, Constructal Design is applied to optimize its geometry and submergence. For the development of Constructal method, it has been proposed and analyzed three degrees of freedom: H1/ L (ratio between the height and length of OWC chamber), H2/l (ratio between height and length of chimney), and H3 (submergence). The problem constraints (fixed parameters) are total area of the OWC chamber A1 and total area of OWC device A2. The computational domain consists of an OWC inserted in a tank where waves in a real scale are generated. The mesh is developed in ANSYS ICEM®. The Computational Fluid Dynamics code FLUENT® is used to find the numerical solution which is based on Finite Volume Method (FVM). The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The results show that the maximum hydropneumatic power obtained was 190 W for H1/L, H2/l e H3 ratios equal to 0.135, 6.0 and 9.5 m respectively. In contrast, the smaller value obtained for the hydropneumatic power is almost 11 W. So, it shows the utility of Constructal Method which provides a relationship between the wave climate of a particular place and the optimal dimensions for the OWC device.

A conversão da energia das ondas dos oceanos em energia elétrica é uma alternativa para o problema da falta de combustíveis fósseis. Uma das possibilidades de aproveitamento é através de dispositivos cujo princípio de funcionamento é o de Coluna de Água Oscilante (CAO). No presente trabalho o objetivo é, através da modelagem computacional e do emprego do Design Construtal, maximizar a potência hidropneumática de um dispositivo conversor de energia das ondas do mar do tipo CAO. São analisados diferentes eixos da restrição física, no formato elíptico, que representa a turbina, e duas formas geométricas na região de transição entre a câmara hidropneumática e a chaminé do dispositivo CAO: trapezoidal e semicircular. Considerando um domínio bidimensional, as restrições para estes problemas são: Área da restrição elíptica (AR), Área total do dispositivo (AT) e razão entre a área da restrição elíptica e a área total (ϕn). Os graus de liberdade analisados são: a razão entre os comprimentos dos eixos da restrição elíptica (d1/d2) para o caso da restrição física da turbina, o ângulo de inclinação da parede (α) para o caso com região de transição trapezoidal, o raio (r) e H2/l (razão entre altura e comprimento da chaminé de saída da câmara CAO) para o caso com região de transição semicircular. Para a solução numérica é empregado um código de dinâmica dos fluidos computacional, FLUENT®, baseado no Método de Volumes Finitos (MVF). O modelo multifásico Volume of Fluid (VOF) é aplicado no tratamento da interação água-ar. O domínio computacional é representado por um tanque de ondas com um dispositivo CAO acoplado. Os resultados obtidos indicam que, para o estudo da região de transição trapezoidal o desempenho do conversor tem aproximadamente o mesmo desempenho para todas as geometrias estudadas. A região de transição semicircular, apresenta resultados para os quais foi possível otimizar a potência hidropneumática. O estudo da turbina indica que foi possível determinar uma geometria capaz de converter a energia da onda incidente ao dispositivo, sem que ocorresse a obstrução do escoamento de ar na chaminé do dispositivo CAO. Assim, mostra-se a relação entre o método Design Construtal e o clima de ondas na definição das dimensões que maximizam a potência hidropneumática. / The conversion of ocean’s wave energy into electrical energy is an alternative for the scarcity of fossil fuels. One of the possibilities of energy use is through devices, whose operating principle is the Oscillating Water Column (OWC). In this work the aim is, through computer modeling and the Constructal Design, to maximize hydropneumatic power of a power converter device type OWC. Different axes of physical constraint with elliptical shape, representing the effect of the turbine , are analyzed. Two geometric shapes in the transition region between the hydropneumatic chamber and the chimney OWC device, trapezoidal and semicircular, are also analyzed. Considering a two-dimensional domain the restrictions for this problem are: Elliptical restriction area (AR), Total area device (AT) and the ratio between the area of the elliptical restraint and the total area (ϕn). The considered degrees of freedom are: the ratio between the lengths of the axes (d1/d2) of the elliptical restraint, for the turbine’s physical constraint case, the inclination angle (α) of the wall for the trapezoidal transition case, and the radius (r) and H2/l (ratio between height and length of output chimney CAO) for the semicircular transition region case. For the numerical solution, a commercial code of computational fluid dynamics, FLUENT®, which is based on the Finite Volume Method (FVM), is employed. The multiphase model Volume of Fluid (VOF) is applied in the treatment of water-air interaction. The computational domain is represented by a wave tank with a fixed OWC device. The obtained results indicate that, for the study of the trapezoidal transition region, the performance of converter don’t seems to be compensatory only by changing the geometry of the trapezoidal area. However, for the semicircular transition region, it was possible to optimize a hydropneumatic power. The study of turbine effect indicates a geometry capable of converting the energy of the incident wave to the device, without obstructing the air flow in the chimney of de OWC, showing the relationship between the Constructal Design method and the wave climate in the definition of the dimensions that maximize the hydropneumatic power.

O presente trabalho apresenta um estudo numérico bidimensional sobre a otimização da geometria de um dispositivo conversor de energia das ondas do mar em energia elétrica. O objetivo principal é, através da modelagem computacional de um dispositivo cujo principio de funcionamento é o de Coluna de Água Oscilante (CAO) e do emprego de Constructal Design, maximizar a conversão da energia das ondas do mar em energia elétrica. Essa técnica é baseada na Teoria Constructal. O aspecto inédito deste trabalho, em relação aos estudos disponíveis na literatura, é o fato de levar em conta o clima de ondas de uma dada região e, a partir disso, dimensionar o dispositivo de modo que ele tenha um desempenho otimizado. Para tanto, foi empregado o método Constructal Design, os graus de liberdade empregados são: H1/L (razão entre a altura e o comprimento da câmara CAO) e H3 (profundidade de submersão do dispositivo CAO). A relação H2/l (razão entre altura e comprimento da chaminé de saída da câmara CAO) é considerada um parâmetro fixo. Foram realizados estudos levando em conta uma onda em escala de laboratório e um espectro de ondas real. Foi também realizado um estudo sobre a influência da perda de carga da turbina através de uma restrição física. Para a solução numérica foi empregado um código comercial de dinâmica dos fluidos computacional, FLUENT®, baseado no Método de Volumes Finitos (MVF). A geometria e a geração a malha foi realizada no software GAMBIT®. O modelo multifásico Volume of Fluid (VOF) é aplicado no tratamento da interação água-ar. O domínio computacional é representado por um tanque de ondas com o dispositivo CAO acoplado. Os resultados obtidos mostram que é possível estabelecer uma razão de H1/L ótimo, conhecendo-se o clima de ondas, ou seja, o recomendável é que esta razão seja igual a quatro vezes a altura da onda dividido pelo comprimento da onda incidente. / The present work presents a two-dimensional numerical study about the geometric optimization of an ocean Wave Energy Converter (WEC) into electrical energy. The main goal is, through computational modeling of a device whose operating principle is the Oscillating Water Column (OWC) and from employment Constructal Design, to maximize the conversion of energy of ocean waves into electricity. This technique is based on Constructal Theory. The inedited aspect of this work comparing to the available studies is that it takes into account the wave climate of a given region to design the device so that it achieves optimum performance. Constructal Design is employed varying the degrees of freedom H1/L (ratio between the height and length of OWC chamber) and H3 (lip submergence). While the relation H2/l (ratio between height and length of chimney) is kept fixed. Studies were performed considering a wave on a laboratory scale and a spectrum of real waves. Yet a study of the influence of the turbine pressure losses was performed using a physical constraint. For the numerical solution it is used the Computational Fluid Dynamic (CFD) commercial code FLUENT®, based on the Finite Volume Method (FVM). The geometry and mesh generation was performed in GAMBIT ® software. The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The computational domain is represented by an OWC device coupled with the wave tank. The results show that it is possible to establish a relationship of H1 / L optimum, if the wave climate is know. It is recommended that this ratio be equal to four times the height of the wave divided by the length of the incident wave.

A conversão da energia das ondas dos oceanos em energia elétrica é uma alternativa para o problema da falta de combustíveis fósseis. Uma das possibilidades de aproveitamento é através de dispositivos cujo princípio de funcionamento é o de Coluna de Água Oscilante (CAO). No presente trabalho o objetivo é, através da modelagem computacional e do emprego do Design Construtal, maximizar a potência hidropneumática de um dispositivo conversor de energia das ondas do mar do tipo CAO. São analisados diferentes eixos da restrição física, no formato elíptico, que representa a turbina, e duas formas geométricas na região de transição entre a câmara hidropneumática e a chaminé do dispositivo CAO: trapezoidal e semicircular. Considerando um domínio bidimensional, as restrições para estes problemas são: Área da restrição elíptica (AR), Área total do dispositivo (AT) e razão entre a área da restrição elíptica e a área total (ϕn). Os graus de liberdade analisados são: a razão entre os comprimentos dos eixos da restrição elíptica (d1/d2) para o caso da restrição física da turbina, o ângulo de inclinação da parede (α) para o caso com região de transição trapezoidal, o raio (r) e H2/l (razão entre altura e comprimento da chaminé de saída da câmara CAO) para o caso com região de transição semicircular. Para a solução numérica é empregado um código de dinâmica dos fluidos computacional, FLUENT®, baseado no Método de Volumes Finitos (MVF). O modelo multifásico Volume of Fluid (VOF) é aplicado no tratamento da interação água-ar. O domínio computacional é representado por um tanque de ondas com um dispositivo CAO acoplado. Os resultados obtidos indicam que, para o estudo da região de transição trapezoidal o desempenho do conversor tem aproximadamente o mesmo desempenho para todas as geometrias estudadas. A região de transição semicircular, apresenta resultados para os quais foi possível otimizar a potência hidropneumática. O estudo da turbina indica que foi possível determinar uma geometria capaz de converter a energia da onda incidente ao dispositivo, sem que ocorresse a obstrução do escoamento de ar na chaminé do dispositivo CAO. Assim, mostra-se a relação entre o método Design Construtal e o clima de ondas na definição das dimensões que maximizam a potência hidropneumática. / The conversion of ocean’s wave energy into electrical energy is an alternative for the scarcity of fossil fuels. One of the possibilities of energy use is through devices, whose operating principle is the Oscillating Water Column (OWC). In this work the aim is, through computer modeling and the Constructal Design, to maximize hydropneumatic power of a power converter device type OWC. Different axes of physical constraint with elliptical shape, representing the effect of the turbine , are analyzed. Two geometric shapes in the transition region between the hydropneumatic chamber and the chimney OWC device, trapezoidal and semicircular, are also analyzed. Considering a two-dimensional domain the restrictions for this problem are: Elliptical restriction area (AR), Total area device (AT) and the ratio between the area of the elliptical restraint and the total area (ϕn). The considered degrees of freedom are: the ratio between the lengths of the axes (d1/d2) of the elliptical restraint, for the turbine’s physical constraint case, the inclination angle (α) of the wall for the trapezoidal transition case, and the radius (r) and H2/l (ratio between height and length of output chimney CAO) for the semicircular transition region case. For the numerical solution, a commercial code of computational fluid dynamics, FLUENT®, which is based on the Finite Volume Method (FVM), is employed. The multiphase model Volume of Fluid (VOF) is applied in the treatment of water-air interaction. The computational domain is represented by a wave tank with a fixed OWC device. The obtained results indicate that, for the study of the trapezoidal transition region, the performance of converter don’t seems to be compensatory only by changing the geometry of the trapezoidal area. However, for the semicircular transition region, it was possible to optimize a hydropneumatic power. The study of turbine effect indicates a geometry capable of converting the energy of the incident wave to the device, without obstructing the air flow in the chimney of de OWC, showing the relationship between the Constructal Design method and the wave climate in the definition of the dimensions that maximize the hydropneumatic power.

O presente trabalho tem como objetivo maximizar a potência hidropneumática convertida num dispositivo do tipo Coluna d'Água Oscilante (CAO). Para fazê-lo, o método Constructal Design é aplicado para aprimorar a geometria e a profundidade de submersão do dispositivo. No desenvolvimento do método Constructal são propostos e analisados três graus de liberdade: H1/L (razão entre a altura e comprimento da câmara do dispositivo CAO), H2/l (razão entre a altura da câmara e o comprimento da chaminé) e H3 (profundidade de submersão do dispositivo CAO). As restrições do problema (parâmetros constantes) são a área da câmara A1 e a área total do dispositivo CAO A2. O domínio computacional consiste de um dispositivo CAO inserido num tanque que é submetido a ondas na escala real. A malha é desenvolvida no software Ansys Icem®. O código de Dinâmica dos Fluidos Computacional Ansys Fluent® é empregado para encontrar a solução numérica a qual é baseada no método dos Volumes Finitos. O modelo multifásico Volume of Fluid (VOF) é usado na interação das fases água-ar. Os resultados indicam que a potência hidropneumática máxima obtida é de 190 W para razões de H1/L, H2/l e H3 iguais a 0,135, 6,0 e 9,5 m respectivamente. Por outro lado, o menor valor obtido da potência hidropneumática é de quase 11 W, o que mostra a utilidade do método Constructal, para fornecer uma relação entre o clima de ondas de um lugar determinado e as dimensões ótimas do dispositivo CAO. / The present work aims to maximize the hydropneumatic power converted in an Oscillating Water Column (OWC) device. To do this, Constructal Design is applied to optimize its geometry and submergence. For the development of Constructal method, it has been proposed and analyzed three degrees of freedom: H1/ L (ratio between the height and length of OWC chamber), H2/l (ratio between height and length of chimney), and H3 (submergence). The problem constraints (fixed parameters) are total area of the OWC chamber A1 and total area of OWC device A2. The computational domain consists of an OWC inserted in a tank where waves in a real scale are generated. The mesh is developed in ANSYS ICEM®. The Computational Fluid Dynamics code FLUENT® is used to find the numerical solution which is based on Finite Volume Method (FVM). The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The results show that the maximum hydropneumatic power obtained was 190 W for H1/L, H2/l e H3 ratios equal to 0.135, 6.0 and 9.5 m respectively. In contrast, the smaller value obtained for the hydropneumatic power is almost 11 W. So, it shows the utility of Constructal Method which provides a relationship between the wave climate of a particular place and the optimal dimensions for the OWC device.

O presente trabalho tem como objetivo maximizar a potência hidropneumática convertida num dispositivo do tipo Coluna d'Água Oscilante (CAO). Para fazê-lo, o método Constructal Design é aplicado para aprimorar a geometria e a profundidade de submersão do dispositivo. No desenvolvimento do método Constructal são propostos e analisados três graus de liberdade: H1/L (razão entre a altura e comprimento da câmara do dispositivo CAO), H2/l (razão entre a altura da câmara e o comprimento da chaminé) e H3 (profundidade de submersão do dispositivo CAO). As restrições do problema (parâmetros constantes) são a área da câmara A1 e a área total do dispositivo CAO A2. O domínio computacional consiste de um dispositivo CAO inserido num tanque que é submetido a ondas na escala real. A malha é desenvolvida no software Ansys Icem®. O código de Dinâmica dos Fluidos Computacional Ansys Fluent® é empregado para encontrar a solução numérica a qual é baseada no método dos Volumes Finitos. O modelo multifásico Volume of Fluid (VOF) é usado na interação das fases água-ar. Os resultados indicam que a potência hidropneumática máxima obtida é de 190 W para razões de H1/L, H2/l e H3 iguais a 0,135, 6,0 e 9,5 m respectivamente. Por outro lado, o menor valor obtido da potência hidropneumática é de quase 11 W, o que mostra a utilidade do método Constructal, para fornecer uma relação entre o clima de ondas de um lugar determinado e as dimensões ótimas do dispositivo CAO. / The present work aims to maximize the hydropneumatic power converted in an Oscillating Water Column (OWC) device. To do this, Constructal Design is applied to optimize its geometry and submergence. For the development of Constructal method, it has been proposed and analyzed three degrees of freedom: H1/ L (ratio between the height and length of OWC chamber), H2/l (ratio between height and length of chimney), and H3 (submergence). The problem constraints (fixed parameters) are total area of the OWC chamber A1 and total area of OWC device A2. The computational domain consists of an OWC inserted in a tank where waves in a real scale are generated. The mesh is developed in ANSYS ICEM®. The Computational Fluid Dynamics code FLUENT® is used to find the numerical solution which is based on Finite Volume Method (FVM). The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The results show that the maximum hydropneumatic power obtained was 190 W for H1/L, H2/l e H3 ratios equal to 0.135, 6.0 and 9.5 m respectively. In contrast, the smaller value obtained for the hydropneumatic power is almost 11 W. So, it shows the utility of Constructal Method which provides a relationship between the wave climate of a particular place and the optimal dimensions for the OWC device.

O presente trabalho apresenta um estudo numérico bidimensional sobre a otimização da geometria de um dispositivo conversor de energia das ondas do mar em energia elétrica. O objetivo principal é, através da modelagem computacional de um dispositivo cujo principio de funcionamento é o de Coluna de Água Oscilante (CAO) e do emprego de Constructal Design, maximizar a conversão da energia das ondas do mar em energia elétrica. Essa técnica é baseada na Teoria Constructal. O aspecto inédito deste trabalho, em relação aos estudos disponíveis na literatura, é o fato de levar em conta o clima de ondas de uma dada região e, a partir disso, dimensionar o dispositivo de modo que ele tenha um desempenho otimizado. Para tanto, foi empregado o método Constructal Design, os graus de liberdade empregados são: H1/L (razão entre a altura e o comprimento da câmara CAO) e H3 (profundidade de submersão do dispositivo CAO). A relação H2/l (razão entre altura e comprimento da chaminé de saída da câmara CAO) é considerada um parâmetro fixo. Foram realizados estudos levando em conta uma onda em escala de laboratório e um espectro de ondas real. Foi também realizado um estudo sobre a influência da perda de carga da turbina através de uma restrição física. Para a solução numérica foi empregado um código comercial de dinâmica dos fluidos computacional, FLUENT®, baseado no Método de Volumes Finitos (MVF). A geometria e a geração a malha foi realizada no software GAMBIT®. O modelo multifásico Volume of Fluid (VOF) é aplicado no tratamento da interação água-ar. O domínio computacional é representado por um tanque de ondas com o dispositivo CAO acoplado. Os resultados obtidos mostram que é possível estabelecer uma razão de H1/L ótimo, conhecendo-se o clima de ondas, ou seja, o recomendável é que esta razão seja igual a quatro vezes a altura da onda dividido pelo comprimento da onda incidente. / The present work presents a two-dimensional numerical study about the geometric optimization of an ocean Wave Energy Converter (WEC) into electrical energy. The main goal is, through computational modeling of a device whose operating principle is the Oscillating Water Column (OWC) and from employment Constructal Design, to maximize the conversion of energy of ocean waves into electricity. This technique is based on Constructal Theory. The inedited aspect of this work comparing to the available studies is that it takes into account the wave climate of a given region to design the device so that it achieves optimum performance. Constructal Design is employed varying the degrees of freedom H1/L (ratio between the height and length of OWC chamber) and H3 (lip submergence). While the relation H2/l (ratio between height and length of chimney) is kept fixed. Studies were performed considering a wave on a laboratory scale and a spectrum of real waves. Yet a study of the influence of the turbine pressure losses was performed using a physical constraint. For the numerical solution it is used the Computational Fluid Dynamic (CFD) commercial code FLUENT®, based on the Finite Volume Method (FVM). The geometry and mesh generation was performed in GAMBIT ® software. The multiphasic Volume of Fluid (VOF) model is applied to tackle with the water-air interaction. The computational domain is represented by an OWC device coupled with the wave tank. The results show that it is possible to establish a relationship of H1 / L optimum, if the wave climate is know. It is recommended that this ratio be equal to four times the height of the wave divided by the length of the incident wave.