• Energy Research

The present study aims to evaluate the difference in the fluid-dynamic behavior of an overtopping wave energy converter under the incidence of irregular waves based on a realistic sea state when compared to the incidence of regular waves, representative of this sea state. Thus, the sea data of three regions from the Rio Grande do Sul coast, Brazil, were considered. Fluent software was employed for the computational modeling, which is based on the finite volume method (FVM). The numerical generation of waves occurred through the imposition of the velocity boundary conditions using transient discrete values through the WaveMIMO methodology. The volume of fluid (VOF) multiphase model was applied to treat the water–air interaction. The results for the water amount accumulated in the device reservoir showed that the fluid-dynamic behavior of the overtopping converter has significant differences when comparing the two proposed approaches. Differences up to 240% were found for the water mass accumulated in the overtopping device reservoir, showing evidence that the results can be overestimated when the overtopping device is analyzed under the incidence of the representative regular waves. Furthermore, for all studied cases, it was possible to approximate the water volume accumulated over time in the overtopping reservoir through a first-degree polynomial function.

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.

Abstract Current work aims to study the geometry of an overtopping wave energy converter in real scale using Constructal Design. Problem studied here is submitted to two constraints (areas of wave tank and overtopping ramp) and two degrees of freedom: ratio between the height and length of ramp (H1/L1) (or ramp slope, β) and distance between the bottom of wave tank and the device (S). The effect of H1/L1 and S over dimensionless device available power (Pd) is evaluated for three different ramp area fractions (ϕ) and two different monochromatic waves. Conservation equations of mass, momentum and one equation for the transport of water volume fraction are solved with the finite volume method. To tackle with water-air mixture, multiphase model Volume of Fluid is used. Results showed the applicability of Constructal Design for improvement of device performance. For fixed magnitudes of S, the highest magnitudes of Pd are achieved for the lowest possible ratio of H1/L1. For smaller construction areas of the ramp, intermediate magnitudes of S led to the highest magnitudes of Pd, i.e., the sinking of device does not led necessarily to the best performance. Moreover, optimal shapes are not universal (the same) for the two wave conditions studied.

The growing global demand for energy and the costly taxes on electric energy demonstrate the importance of seeking new techniques to improve energy efficiency in industrial facilities. Refrigeration units demand a large amount of electricity due to the high power needs of the components of the system. One strategy to reduce the electric energy consumption in these facilities is pressure condensation control. The objective here was to develop a logical control model where the physical quantities in the thermodynamic process can be monitored and used to determine the optimum point of the condensation pressure and the mass flow rate of the air in the evaporative condenser. The algorithm developed was validated through experiments and was posteriorly implemented in an ammonia industrial system of refrigeration over a period of sixteen months (480 days). The results showed that the operation of the evaporative condenser with a controlled air mass flow rate by logical modeling achieved a reduction of 7.5% in the consumption of electric energy, leading to a significant reduction in the operational cost of the refrigeration plant.

Abstract This study investigates numerically the design of heated semi-elliptical blocks assembled inside of forced convective channel flows. The Constructal Design method, associated with the exhaustive search, was used to determine the restrictions, the degrees of freedom, the performance indicators, and the modality to sweep the search space of solutions. The degrees of freedom were defined as the ratios between the vertical and horizontal lengths of the semi-elliptical blocks, while the blocks and channel reference areas represented the constraints. The air flow (Pr = 0.72) is assumed as two-dimensional, incompressible, laminar, and steady-state. The fluid dynamic and thermal performances are evaluated for different Reynolds numbers (ReH =10, 50, and 100). The multi-objective assessment of the problem was carried out using the Technique for Order Preference by Similarity to Ideal Solution method. Conservation equations of mass, momentum, and energy are solved numerically using the Finite Volume Method. The results indicated important gains on the thermal and fluid dynamic performances of nearly 76% and 1275%, respectively when the best and worst shapes were compared in the first optimization level. It is worth mentioning that, in the multi-objective viewpoint, the employed method above-cited correctly indicated the best configurations and the gain of performance in comparison with the pressure drop minimization and the heat transfer rate maximization.

Abstract Present work performs a numerical study about the energy removal in a heated tubular array submitted to an external flow. Taking into account that a large variety of tubular arrangements can exists, in this work it is developed a tubular array that does not use any kind of initial predefined arrangement. Using the principles of Constructal Theory (or Law) and a positioning function dependent on the velocity and temperature fields, it is calculated, in a deterministic way, the location where each tube should be positioned. Pressure drop is not taken in to account in this first algorithm implementation as a performance indicator. In order to validate the proposed methodology, the Constructal Array is compared with standard aligned and staggered arrangements suggested in literature. The minimum distance between tubes (p) is considered as a degree of freedom. Four variations are studied: p = 1D, p = 1.25D, p = 1.5D and p = 2D, where D is the tube diameter. It is considered here the simulation of a transient, incompressible and laminar flow of a Newtonian fluid in a two-dimensional domain with forced convection and Prandtl number equal to 0.71. Results are computed when the flow reaches to the steady state condition. It is evaluated three values for Reynolds number: ReD = 10, 50 and 100. Thermal analysis of the formed patterns has shown that best thermal performance was not obtained with p = 1D, neither with p = 2D, i.e., tube distance has an influence on its formation and, consequently, on the heat transfer exchange. In all performed analyzes, Constructal arrays configuration showed higher energy removal (up to 71%) than the aligned and staggered arrangements, which highlights the capacity of proposed method. Constructal Array for p = 1.5D showed the most homogeneous distribution and proved to be the most effective in 4 of the six studied cases.

Abstract This work applies Constructal design to study numerically the geometry of cavities bathed by a fluid with constant heat transfer coefficient that are intruded into a cylindrical solid body. The objective is to minimize the maximum excess of temperature between the solid body and the ambient by morphing the cavity geometry. Internal heat generating is distributed uniformly into the solid body which has adiabatic conditions on the outer surfaces. The total volume and the volume of the cavities are fixed. The cavities are rectangular with variable aspect ratio. The optimized geometry and performance are reported as functions of the ratio between the volume of the cavities and the total volume, the number of cavities and the dimensionless parameter that accounts for the convective heat transfer, λ . The main results indicate that for fixed number of cavities, ϕ c , and dimensionless parameter λ , there is an optimal number of cavities, N o , that minimizes the maximum excess of temperature and this optimal number of cavities in general increases as ϕ c and λ increases.

Given the increasing global energy demand, the present study aimed to analyze the influence of bathymetry on the generation and propagation of realistic irregular waves and to geometrically optimize a wave energy converter (WEC) device of the oscillating water column (OWC) type. In essence, the OWC WEC can be defined as a partially submerged structure that is open to the sea below the free water surface (hydropneumatic chamber) and connected to a duct that is open to the atmosphere (in which the turbine is installed); its operational principle is based on the compression and decompression of air inside the hydropneumatic chamber due to incident waves, which causes an alternating air flow that drives the turbine and enables electricity generation. The computational fluid dynamics software package Fluent was used to numerically reproduce the OWC WEC according to its operational principles, with a simplification that allowed its available power to be determined, i.e., without considering the turbine. The volume of fluid (VOF) multiphase model was employed to treat the interface between the phases. The WaveMIMO methodology was used to generate realistic irregular waves mimicking those that occur on the coast of Tramandaí, Rio Grande do Sul, Brazil. The constructal design method, along with an exhaustive search technique, was employed. The degree of freedom H1/L (the ratio between the height and length of the hydropneumatic chamber of the OWC) was varied to maximize the available power in the device. The results showed that realistic irregular waves were adequately generated within both wave channels, with and without bathymetry, and that wave propagation in both computational domains was not significantly influenced by the wave channel bathymetry. Regarding the geometric evaluation, the optimal geometry found, H1/Lo = 0.1985, which maximized the available hydropneumatic power, i.e., the one that yielded a power of 25.44 W, was 2.28 times more efficient than the worst case found, which had H1/L = 2.2789.

A numerical study was performed in the present work about an Overtopping Device Wave Energy Converter (OTD-WEC) with one and two ramps incorporated in a real breakwater. The Constructal Design method was applied to evaluate the effects on the average dimensionless overtopping flow of the degrees of freedom of the device with one and two ramps. In addition, a comparison was carried out among the different geometry configurations of the OTD-WEC to determine which one presents the best hydrodynamic performance. The work used the JONSWAP spectrum and the multiphase Volume of Fluid model. It also solved the conservation equations for mass, momentum, and an equation for the transport of the volume fraction using the Finite Volume Method. Results showed that a device with a two-ramps configuration presented an average dimensionless overtopping flow 6.48% higher than those obtained for the one ramp. Present results obtained using Constructal Design theoretical recommendations about the influence of a complex configuration with four degrees of freedom over the performance of an OTD-WEC integrated into the east breakwater of the city of São José do Norte, State of Rio Grande do Sul (RS), Brazil.