Liércio André Isoldi

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

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.

Constructal Design of Y-Shaped Conductive Pathways for Cooling a Heat-Generating Body

This paper applies constructal design to obtain numerically the configuration that facilitates the access of the heat that flows through Y-shaped pathways of a high-conductivity material embedded within a square-shaped heat-generating medium of low-conductivity to cooling this finite-size volume. The objective is to minimize the maximal excess of temperature of the whole system, i.e., the hot spots, independent of where they are located. The total volume and the volume of the material of high thermal conductivity are fixed. Results show that there is no universal optimal geometry for the Y-shaped pathways for every value of high conductivity investigated here. For small values of high thermal conductivity material the best shape presented a well defined format of Y. However, for larger values of high thermal conductivity the best geometry tends to a V-shaped (i.e., the length of stem is suppressed and the bifurcated branches penetrates deeply the heat-generating body towards the superior corners). A comparison between the Y-shaped pathway configuration with a simpler I-shaped blade and with X-shaped configuration was also performed. For constant values of area fraction occupied with a high-conductivity material and the ratio between the high thermal conductivity material and low conductivity of the heat-generating body (φ = 0.1 and = 100) the Y-shaped pathways performed 46% and 13% better when compared to I-shaped and X-shaped pathway configuration, respectively. The best thermal performance is obtained when the highest temperatures (hot spots) are better distributed in the temperature field, i.e., according to the constructal principle of optimal distribution of imperfections.

Numerical Approach of the Main Physical Operational Principle of Several Wave Energy Converters: Oscillating Water Column, Overtopping and Submerged Plate

In this work it is numerically studied the wave flow inside a tank and the main operational physical principle of three different wave energy converters (WEC): oscillating water column (OWC), overtopping and submerged plate. The wave energy converters are evaluated in laboratory and real scales. For all studied cases 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. Several results showed the accuracy of the numerical approach for estimation of the physical phenomenon of wave flow inside tanks, as well as, its interaction with the studied devices. For the cases with geometrical optimization, Constructal Design is employed for geometrical evaluation of the devices. Results presented several theoretical recommendations about the influence of geometrical parameters (such as ratios between heights and lengths of OWC chamber and ramp of overtopping device and the distance from the plate to the seabed of wave tank) over the available power take off (PTO) in the OWC and submerged plate devices and over the amount of water stored in the reservoir of the overtopping device. Results showed the importance of geometric shapes over the devices performance. Moreover, it is evaluated the influence of several wave parameters (such as wave period and relative depths) over the fluid dynamic performance of the devices and geometrical parameters of the devices. It is noticed the non-occurrence of universal optimal shapes.

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

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.

Design of Cooling Cavities by the Application of the Constructal Design

This paper develops a numerical study about the geometry of isothermal cavities in solid bodies with internal heat generation. The solid is constituted of a isotropic material, with low thermal conductivity, and adiabatic external surfaces. The cavity is used to dissipate the internally generated heat. An evolutionary algorithm is proposed, based on Constructal Theory, that builds a cavity able to maximize the heat transfer between the solid body and the ambient. Initial solid geometry (a squared fin) is divided into smaller squared elements (regions) that will be remove in order to build the cavity. First element is removed from the bottom center of the geometry and other elements are, at every step, removed so that minimize the hot spots in the solid domain. At every stage of the building process, thermal diffusion equation is numerically solved by the finite element method (FEM). The cavity construction must be flexible so that it freely progresses (evolves) in direction to the hot spots. Results show that the smaller the elements (resolution) used in the cavity construction the lower will be the maximum temperature. Besides that, present results are compare with similar works for cavities C, H, X e Y, presented in literature, showing that current methodology is very efficient in minimizing maximum solid internal temperature.

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

Numerical Analysis of the Oscillating Water Column (OWC) Wave Energy Converter (WEC) Considering Different Incident Wave Height

The ocean wave energy conversion into electricity has been increasingly researched in the last years. There are several proposed converters, among them the Oscillating Water Column (OWC) device has been widely studied. The present paper presents a two-dimensional numerical investigation about the fluid dynamics behavior of an OWC Wave Energy Converter (WEC) into electrical energy. The main goal of this work was to numerically analyze the optimized geometric shape obtained in previous work under incident waves with different heights. To do so, the OWC geometric shape was kept constant while the incident wave height was varied. For the numerical solution it was used the Computational Fluid Dynamic (CFD) commercial code FLUENT®, based on the Finite Volume Method (FVM). The multiphasic Volume of Fluid (VOF) model was applied to tackle with the water-air interaction. The computational domain is represented by the OWC device coupled with the wave tank. This work allowed to check the influence of the incident wave height on the hydropneumatic power and the amplification factor of the OWC converter. It was possible to identify that the amplification factor increases as the wave period increases, thereby improving the OWC performance. It is worth to highlight that in the real phenomenon the incident waves on the OWC device have periods, lengths and height variables.