Analysis of Geometric Variation of Three Degrees of Freedom through the Constructal Design Method for a Oscillating Water Column Device with Double Hidropneumatic Chamber

2019 ◽  
Vol 396 ◽  
pp. 22-31
Author(s):  
Yuri T.B. Lima ◽  
Mateus das Neves Gomes ◽  
Camila F. Cardozo ◽  
Liércio André Isoldi ◽  
Elizaldo D. Santos ◽  
...  
Keyword(s):  
Water Column ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Design Method ◽  
Geometric Optimization ◽  
Oscillating Water Column ◽  
Constructal Design ◽  
Wave Energy Converters ◽  
Volume Method ◽  
Geometric Variation

This paper presents a biphasic two-dimensional numerical study of sea wave energy converters with operating principle being Oscillating Water Column (CAO) devices with two couples chambers. For the study of the geometric optimization, the Constructal Design method is applied in association with the exhaustive search method to determine the geometric arrangement that leads to the greatest hydropneumatic power available. The objective function is the maximization of hydropneumatic power converted by the device. The constraints of the problem are the inflow volumes of the hydropneumatic chamber (VE1, VE2), the total volumes (VT1, VT2) and the thicknesses of the device columns (e1, e3). The degrees of freedom analyzed were H1/L1(ratio between height and length of the hydropneumatic chamber of the first device), H2/L2 (ratio between height and length of the hydropneumatic chamber of the second device), H2 (height of the column dividing the two devices) and e2 (thickness of the column dividing the devices). In the present work the degree of freedom H6 (depth of immersion of the device) is kept constant and equal to H6 = 9.86 m. The Finite Volume Method (FVM) was used in the numerical solution of the equations employed. For the treatment of the interaction between the air and water phases, the Volume of Fluid (VOF) method was applied. The results show that the maximum hydropneumatic power available was 5715.2 W obtained for degrees of freedom H1/L1 = H2/L2 = 0.2613 and e2 = 2.22 m. The case of lower performance has a power value equal to 4818.5 W with degrees of freedom equal to H1/L1 = H2/L2 = 0.2613 and e2 = 0.1 m.

Numerical Study of the Effect of the Relative Depth on the Overtopping Wave Energy Converters According to Constructal Design

2014 ◽  
Vol 348 ◽  
pp. 232-244 ◽  
Author(s):  
Elizaldo Domingues dos Santos ◽  
Bianca Neves Machado ◽  
Marcos Moisés Zanella ◽  
Mateus das Neves Gomes ◽  
Jeferson Avila Souza ◽  
...  
Keyword(s):  
Wave Energy ◽  
Numerical Study ◽  
Strong Dependence ◽  
Geometric Optimization ◽  
Relative Depth ◽  
Multiphase Model ◽  
Constructal Design ◽  
Wave Energy Converters ◽  
Low Head ◽  
Volume Method

The conversion of wave energy in electrical one has been increasingly studied. One example of wave energy converter (WEC) is the overtopping device. Its main operational principle consists of a ramp which guides the incoming waves into a reservoir raised slightly above the sea level. The accumulated water in the reservoir flows through a low head turbine generating electricity. In this sense, it is performed a numerical study concerned with the geometric optimization of an overtopping WEC for various relative depths:d/λ = 0.3, 0.5 and 0.62, by means of Constructal Design. The main purpose is to evaluate the effect of the relative depth on the design of the ramp geometry (ratio between the ramp height and its length:H1/L1) as well as, investigate the shape which leads to the highest amount of water that insides the reservoir. In the present simulations, the conservation equations of mass, momentum and one equation for the transport of volumetric fraction are solved with the finite volume method (FVM). To tackle with water-air mixture, the multiphase model Volume of Fluid (VOF) is used. Results showed that the optimal shape, (H1/L1)o, has a strong dependence of the relative depth, i.e., there is no universal shape that leads to the best performance of an overtopping device for several wave conditions.

scholarly journals GEOMETRIC EVALUATION OF FOUR STAGGERED CYLINDERS ARRAY SUBJECTED TO FORCED CONVECTIVE FLOWS BY MEANS OF CONSTRUCTAL DESIGN

2019 ◽  
Vol 18 (1) ◽  
pp. 57
Author(s):  
A. P. D. Aghenese ◽  
F. B. Teixeira ◽  
L. A. O. Rocha ◽  
L. A. Isoldi ◽  
J. F. Prolo Filho ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Study ◽  
Design Method ◽  
Fluid Dynamic ◽  
Working Fluid ◽  
Convective Flows ◽  
Constructal Design ◽  
Staggered Arrangement ◽  
Forced Convective Flow ◽  
Volume Method

This work presents a numerical study on the geometric evaluation of forced convective flows over four staggered arrangement of four cylinders. The forced convective flow is considered incompressible, two-dimensional, laminar and unsteady. Geometry varies according to Constructal Design method. The objectives are the maximization of Nusselt number (NuD) and minimization of drag coefficient (CD) between the cylinders and the surrounding flow. Simulations were performed considering Reynolds numbers of ReD = 10, 40 and 150 and air as working fluid, i.e., Prandtl number is assumed Pr = 0.71. The problem presents three degrees of freedom: ST/D (ratio between transversal pitch of the intermediate cylinders and the cylinders diameter), SL1/D (ratio between the frontal and intermediate cylinders longitudinal pitch and the cylinders diameter) and SL2/D (ratio between the intermediate and posterior cylinders longitudinal pitch and the cylinders diameter). However, SL1/D and SL2/D measures were kept fixed at 1.5 and ST/D varies in the range 1.5 ≤ ST/D ≤ 5.0. The conservation equations of mass, momentum and energy conservation are solved with the Finite Volume Method (FVM). Optimal results for fluid-dynamic study in all ReD cases occurred for the lowest values of ST/D, i.e., (ST/D)o,f = 1.5. For thermal analysis, NuD behavior was assessed, where optimal results for ReD = 10 and 40 occurred for the highest values of ST/D, whilst, for ReD = 150, the optimal value was achieved for the intermediate ratio of ST/D = 4.0.

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

2021 ◽  
Vol 407 ◽  
pp. 128-137
Author(s):  
Vinícius Bloss ◽  
Camila Fernandes Cardozo ◽  
Flávia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Ocean Waves ◽  
Response Surfaces ◽  
Oscillating Water Column ◽  
Promising Source ◽  
Three Degrees Of Freedom

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

Numerical and Geometrical Analysis of the Onshore Oscillating Water Column Wave Energy with a Ramp

2021 ◽  
Vol 412 ◽  
pp. 11-26
Author(s):  
Marla Rodrigues Oliveira ◽  
Elizaldo Domingues Santos ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
Mateus das Neves Gomes
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Design Method ◽  
Geometric Analysis ◽  
Relative Difference ◽  
Front Wall ◽  
Multiphase Model ◽  
Oscillating Water Column ◽  
Worst Case

This study is about a two-dimensional numerical analysis of the influence of a ramp in front on an oscillating water column wave energy converter (OWC-WEC). The main purpose was to evaluate, numerically and geometrically, the effect of using a ramp variation in relation to the frontal wall on the hydropneumatic power of the OWC-WEC. The constructal design method was applied for geometric analysis. The problem had a geometric constraint: the area of the ramp (A2) and two degrees of freedom: H2 / L2 (ratio of the height and length of the ramp) and L4 (the distance of the ramp concerning the OWC-WEC front wall). In numerical simulations, the equations of conservation of mass, momentum, and an equation for the transport of volumetric fraction were solved using the finite volume method (FVM). The multiphase model volume of fluid (VOF) was applied for the air-water interaction. Thus, the increase in the H2/L2 ratio resulted in a decrease of the root mean square (RMS) of the available hydropneumatic power (Phyd). By varying the distance L4, the better case was = 6 m and / = 0.025 and the worst case was = 1 m and / = 0.2. The relative difference between the better RMS Phyd = 150.7957 W and the worst Phyd = 73.1164 W reached up to a hundred and six percent.

scholarly journals Numerical Analysis of the Influence of Geometry on a Large Scale Onshore Oscillating Water Column Device with Associated Seabed Ramp

2020 ◽  
Vol 15 (6) ◽  
pp. 873-884
Author(s):  
Max Letzow ◽  
Giulio Lorenzini ◽  
Dante Vinícius Eloy Barbosa ◽  
Ricardo Gabriel Hübner ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Water Column ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Volume Fraction ◽  
Design Method ◽  
Length Ratio ◽  
Oscillating Water Column ◽  
Two Phase ◽  
Worst Case ◽  
Vof Model

The current study aims to perform a geometrical investigation of an onshore Oscillating Water Column (OWC) on a large scale. The Constructal Design method is employed, aiming to maximize its available power. The OWC is subjected to two constraints (areas of the chamber and ramp below the chamber); and three degrees of freedom: height/length ratio of the chamber (H1/L1), height/length ratio of the ramp (H2/L2), and submersion of the frontal wall of the chamber (H3). A laminar, unsteady, incompressible, and two-phase flow was adopted, solving conservation equations of mass, momentum, and transport of water-air volume fraction using Finite Volume Method (FVM) and Volume of Fluid (VOF) model. The global optimal geometry led to a twice maximized available power 37.3% higher than the best case without the seabed ramp below the chamber and seven times better than the worst case. Concerning the sensibility of geometry, results indicated that the chamber geometry, given by ratio H1/L1, over the available power (P) was strongly affected by the ramp ratio H2/L2. Moreover, the behavior of the effect of H2/L2 over the once maximized available power (Pm) and corresponding optimal shape of the chamber, (H1/L1)o, changed dramatically for two different magnitudes of H3 investigated.

scholarly journals CONSTRUCTAL DESIGN OF A VORTEX TUBE FOR SEVERAL INLET STAGNATION PRESSURES

2012 ◽  
Vol 11 (1-2) ◽  
pp. 85 ◽  
Author(s):  
C. H. Marques ◽  
L. A. Isoldi ◽  
E. D. Dos Santos ◽  
L. A. O. Rocha
Keyword(s):  
Turbulent Flows ◽  
Degrees Of Freedom ◽  
Vortex Tube ◽  
Numerical Study ◽  
Cylindrical Tube ◽  
Navier Stokes ◽  
Working Fluid ◽  
Computational Domain ◽  
Constructal Design ◽  
Volume Method

The present paper shows a numerical study concerned with the geometrical optimization of a vortex tube device by means of Constructal Design for several inlet stagnation pressures. In the present study, it is evaluated a vortex tube with two-dimensional axisymmetric computational domain with dry air as the working fluid. The compressible and turbulent flows are numerically solved with the commercial CFD package FLUENT, which is based on the Finite Volume Method. The turbulence is tackled with the k-ε model into the Reynolds Averaged Navier-Stokes (RANS) approach. The geometry has one global restriction, the total volume of the cylindrical tube, and four degrees of freedom: d3/D (the ratio between the diameter of the cold outlet and the diameter of the vortex tube), d1/D (the ratio between the diameter of the inlet nozzle and the diameter of the vortex tube), L2/L (the ratio between the length of the hot exit annulus and the length of the vortextube) and D/L (the ratio between the diameter of the vortex tube and its length). The degree of freedom L2/L will be represented here by the cold mass fraction (yc). In the present work it is optimized the degrees of freedom yc and d3/D while the other degrees of freedom and the global restriction are kept fixed. The purpose here is to maximize the amount of energy extracted from the cold region (cooling effect) for several geometries, as well as, investigate the influence of the inlet stagnation pressure over the optimal geometries. Results showed an increase of the twice maximized cooling heat transfer rate of nearly 330 % from 300 kPa to 700 kPa. Moreover, the optimization showed a higher dependence of (d3/D)o for the lower range of inlet pressures, while the optimization is more dependent of yc,oo for higher inlet stagnation pressures.

Geometric Evaluation of Forced Convective Flows across an Arrangement of Four Circular Cylinders

2017 ◽  
Vol 372 ◽  
pp. 110-121
Author(s):  
Martim dos Santos Pereira ◽  
Bruno Costa Feijó ◽  
Filipe Branco Teixeira ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Degrees Of Freedom ◽  
Design Method ◽  
Great Influence ◽  
Circular Cylinders ◽  
Constructal Design ◽  
Prandtl Numbers ◽  
Forced Convective Flow ◽  
Volume Method ◽  
Four Cylinders

The present study consists in a numerical evaluation of an arrangement formed by four cylinders submitted to an unsteady, two-dimensional, incompressible, laminar and forced convective flow. The geometric evaluation is performed through the Constructal Design method. The problem has two restrictions given by the sum of the area of ​​the cylinders and one occupation area and has three degrees of freedom: ST1/D (the ratio between the transverse pitch of the frontal cylinders and the diameter of the cylinders), ST2/D (the ratio between the transverse pitch of the posterior cylinders and the diameter of the cylinders) and SL/D (ratio between the longitudinal pitch of the frontal and posterior cylinders and the diameter of the cylinders). For all simulations the Reynolds number is kept constant, ReD = 100, and two different Prandtl numbers of Pr = 0.71 and 5.83 are considered, which simulates respectively the use of air and water as a fluid. The conservation equations of mass, momentum and energy are solved with the Finite Volume Method (FVM). The main objective is to evaluate the effect of the degrees of freedom on the drag coefficient (CD) and the Nusselt number (NuD) between the cylinders and the surrounding flow, as well as the optimal ST2/D values ​​for three ratios of ST1/D = 1.5, 3.0 and 4.0, these results being obtained for ratios of SL/D = 1.5 and 4.0. Results showed that the ratio changes of ST1/D and ST2/D have a great influence on the drag coefficients and on the Nusselt number of the arrangement formed by the four cylinders, as well as on the geometries leading to the best fluid dynamics and thermal performance.

Constructal Design Applied to a Channel with Triangular Fins Submitted to Forced Convection

2017 ◽  
Vol 372 ◽  
pp. 152-162 ◽  
Author(s):  
Bruno Costa Feijó ◽  
Martim dos Santos Pereira ◽  
Filipe Branco Teixeira ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Forced Convection ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Design Method ◽  
Convection Heat Transfer ◽  
Lower Surface ◽  
Worst Case ◽  
Constructal Design

The purpose of this work is to present a numerical study of a two-dimensional channel with two triangular fins submitted to a laminar flow with forced convection heat transfer, evaluating the geometry of the first fin through the Constructal Design method. The main objectives are to maximize the heat transfer rate and minimize the pressure difference between the inlet and outlet flow of the channel for different dimensions of the first channel fin, considering the same Reynolds (ReH = 100) and Prandtl numbers (Pr = 0.71). The problem is subjected to three constraints given by the channel area, fin area and maximum occupancy area of ​​each fin. The system has three degrees of freedom. The first is given by the ratio between height and length of the channel, which is kept fixed, H/L = 0.0625. The other two are the ratio between height and width of the upstream fin base (H3/L3) positioned on the lower surface of the channel, and the ratio between height and width of the downstream fin (H4/L4) positioned on the upper surface of the channel, which is also kept fixed, H4/L4 = 1.11. The problem is simulated for three different values ​​of the fraction area of upstream fin (φ1 = 0.1, 0.2 and 0.3). For the numerical approach of the problem, the conservation equations of mass, momentum and energy are solved using the finite volume method (MVF). The results showed that a ratio of φ1 = 0.2 is the one that best meets the proposed multi-objective. It was also observed that φ1 = 0.1 led to a better fluid dynamics performance with a ratio between the best and the worst performance for fluid dynamics case of 25.2 times. For φ1 = 0.3, the best thermal performance is achieved, where the optimal case has a performance 65.75% higher than that reached for the worst case.

scholarly journals TWO-DIMENSIONAL GEOMETRIC OPTIMIZATION OF AN OSCILLATING WATER COLUMN CONVERTER IN LABORATORY SCALE

2012 ◽  
Vol 11 (1-2) ◽  
pp. 30
Author(s):  
M. N. Gomes ◽  
C. D. Nascimento ◽  
B. L. Bonafini ◽  
E. D. Santos ◽  
L. A. Isoldi ◽  
...  
Keyword(s):  
Water Column ◽  
Geometric Optimization ◽  
Degree Of Freedom ◽  
Laboratory Scale ◽  
Computational Domain ◽  
Two Dimensional ◽  
Regular Wave ◽  
Oscillating Water Column ◽  
Worst Case ◽  
Constructal Design

The present paper presents a two-dimensional numerical study about the geometric optimization of an ocean Wave Energy Converter (WEC) into electrical energy that has as operational principal the Oscillating Water Column (OWC). To do so, the Constructal Design fundamentals were employed to vary the degree of freedom H1/L (ratio between height and length of the OWC chamber), while the other degree of freedom H2/l (ration between height and length of chimney) was kept constant. The OWC chamber area (φ1) and the total OWC area (φ2) are also kept fixed, being the problem constraints. In this study was adopted a regular wave with laboratory scale dimensions. The main goal was to optimize the device’s geometry aiming to maximize the absorbed power when it is subjected to a defined wave climate. For the numerical solution it was used the Computational Fluid Dynamic (CFD) commercial code FLUENT®, which is based on the Finite Volume Method (FVM). The multiphasic Volume of Fluid (VOF) model was applied to treat the water-air interaction. The computational domain was represented by an OWC device coupled into a wave tank. Thereby, it was possible to analyze the WEC subjected to regular wave incidence. An optimal geometry was obtained for (H1/L)o=0.84, being this one approximately ten times more efficient then the worst case (H1/L = 0.14), showing the applicability of Constructal Design in this kind of engineering problem.

scholarly journals Computational Modeling and Constructal Design Theory Applied to the Geometric Optimization of Thin Steel Plates with Stiffeners Subjected to Uniform Transverse Load

Metals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 220 ◽  
Author(s):  
Grégori Troina ◽  
Marcelo Cunha ◽  
Vinícius Pinto ◽  
Luiz Rocha ◽  
Elizaldo dos Santos ◽  
...  
Keyword(s):  
Computational Modeling ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Geometric Optimization ◽  
Steel Plates ◽  
Transverse Load ◽  
Constructal Design ◽  
Thin Steel ◽  
Reference Plate

Stiffened thin steel plates are structures widely employed in aeronautical, civil, naval, and offshore engineering. Considering a practical application where a transverse uniform load acts on a simply supported stiffened steel plate, an approach associating computational modeling, Constructal Design method, and Exhaustive Search technique was employed aiming to minimize the central deflections of these plates. To do so, a non-stiffened plate was adopted as reference from which all studied stiffened plate’s geometries were originated by the transformation of a certain amount of steel of its thickness into longitudinal and transverse stiffeners. Different values for the stiffeners volume fraction (φ) were analyzed, representing the ratio between the volume of the stiffeners’ material and the total volume of the reference plate. Besides, the number of longitudinal (Nls) and transverse (Nts) stiffeners and the aspect ratio of stiffeners shape (hs/ts, being hs and ts, respectively, the height and thickness of stiffeners) were considered as degrees of freedom. The optimized plates were determined for all studied φ values and showed a deflection reduction of over 90% in comparison with the reference plate. Lastly, the influence of the φ parameter regarding the optimized plates was evaluated defining a configuration with the best structural performance among all analyzed cases.

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