Elizaldo Domingues dos Santos

Constructal Design of Complex Assembly of Fins

Constructal design is a method that conducts the designer toward flow (e.g., heat flux) architectures that have greater global performance. This numerical work uses this method to seek for the best geometry of a complex assembly of fins, i.e., an assembly where there is a cavity between the two branches of the T-Y-assembly of fins and two additional extended surfaces. The global thermal resistance of the assembly is minimized four times by geometric optimization subject to the following constraints: the total volume, the volume of fin material, the volume of the cavity, and the volume of the two additional extended surfaces. Larger amount of fin material improves the performance of the assembly of fins. The three times optimized global thermal resistance of the complex assembly of fins performs 32% better than the best T-Y-configuration under the same thermal and geometric conditions. The three times minimized global thermal resistance of the complex assembly of fins was correlated by power laws as a function of its corresponding optimal configurations.

Constructal design applied to the elastic buckling of thin plates with holes

Elastic buckling is an instability phenomenon that can occur if a slender and thin plate is subjected to axial compression. An important characteristic of the buckling is that the instability may occur at a stress level that is substantially lower than the material yield strength. Besides, the presence of holes in structural plate elements is common. However these perforations cause a redistribution in plate membrane stresses, significantly altering their stability. In this paper the Bejan’s Constructal Design was employed to optimize the geometry of simply supported, rectangular, thin perforated plates subjected to the elastic buckling. Three different centered hole shapes were considered: elliptical, rectangular and diamond. The objective function was to maximize the critical buckling load. The degree of freedom H/L (ratio between width and length of the plate) was kept constant, while H0/L0 (ratio between the characteristic dimensions of the holes) was optimized for several hole volume fractions (ϕ). A numerical model employing the Lanczos method and based on the finite element method was used. The results showed that, for lower values of ϕ the optimum geometry is the diamond hole. For intermediate and higher values of ϕ, the elliptical and rectangular hole, respectively, led to the best performance.

STUDY ABOUT BUCKLING PHENOMENON IN PERFORATED THIN STEEL PLATES EMPLOYING COMPUTATIONAL MODELING AND CONSTRUCTAL DESIGN METHOD

PERFORATED STEEL THIN PLATES ARE COMMONLY USED IN STRUCTURAL ENGI-NEERING. DUE TO THEIR GEOMETRIC CHARACTERISTICS, THESE PANELS CAN SUFFER THE UNDESIRED BUCKLING PHENOMENON. IN THIS CONTEXT, THE PRESENT WORK ASSOCIATES THE COMPUTATIONAL MODELING AND THE CONSTRUCTAL DESIGN METHOD TO EVALUATE THE INFLUENCE OF THE GEOMETRIC CONFIGURATION IN THE PLATE BUCKLING BEHAVIOR, USING THE EXHAUSTIVE SEARCH METHOD TO DETERMINE WHICH GEOMETRIES CONDUCT TO SUPERIOR MECHANICAL BEHAVIOR. TO DO SO, NUMERICAL MODELS ARE EMPLOYED TO SOLVE ELASTIC AND ELASTO-PLASTIC BUCKLING OF PLATES HAVING A CENTERED PERFORATION. DIFFERENT HOLE TYPES (LONGITUDINAL OBLONG, TRANSVERSAL OBLONG, ELLIPTICAL, RECTANGULAR, DIAMOND, LONGITUDINAL HEXAGONAL, OR TRANSVERSAL HEXAGONAL) WITH DIFFERENT SHAPES (VARIATION OF CHARACTERISTICS DIMENSIONS OF EACH HOLE TYPE) ARE ANALYZED. LIMIT CURVES TO AVOID BUCKLING WERE OBTAINED, AS WELL AS THE DEFINITION OF THE GEOMETRIES THAT CAN IMPROVE UP TO 107% THE PLATE PERFORMANCE.

Constructal Design of Double-T Shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing

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.

Numerical analysis including pressure drop in oscillating water column device

Abstract The wave energy conversion into electricity has been increasingly studied in the last years. There are several proposed converters. Among them, the oscillatingwater column (OWC) device has been widespread evaluated in literature. In this context, the main goal of this work was to perform a comparison between two kinds of physical constraints in the chimney of the OWC device, aiming to represent numerically the pressure drop imposed by the turbine on the air flow inside the OWC. To do so, the conservation equations of mass,momentumand one equation for the transport of volumetric fraction were solved with the finite volume method (FVM). To tackle thewater-air interaction, the multiphase model volume of fluid (VOF)was used. Initially, an asymmetric constraint inserted in chimney duct was reproduced and investigated. Subsequently, a second strategywas proposed,where a symmetric physical constraint with an elliptical shapewas analyzed. Itwas thus possible to establish a strategy to reproduce the pressure drop in OWC devices caused by the presence of the turbine, as well as to generate its characteristic curve.

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.

Constructal Design of a Triangular Fin Inserted in a Cavity with Mixed Convection Lid-Driven Flow

The present work applies Constructal Design to study numerically a fin-cavity system under mixed convection flow. The system is composed of a heat triangular fin inserted in a squared cavity. The flow is driven by the superior wall (lid) displacement. The main purpose is to study the effect of the fin geometry and area ratio (φ) over the dimensionless convective heat transfer coefficient (Nusselt number). The effect of Rayleigh (RaH) and Reynolds (ReH) numbers over the thermal performance and optimal geometries is also evaluated. For all cases the Prandtl number is constant (Pr = 0.71). The conservation equations of mass, momentum and energy are solved numerically with a code based in the Finite Volume Method (FVM). Results showed that the thermal performance increased with the increase of Reynolds and Rayleigh numbers and with the decrease of fin area ratio (φ). Otimal geometries for the triangular fin are compared to optimal rectangular fins, for RaH = 105 results showed a better performance (up to 8%) of the triangular fin for low Reynolds numbers (ReH < 200), while rectangular fins performed better than triangular ones for the highest magnitudes of ReH numbers. In general, results showed that different conditions change the optimal shape of a flow system, always evolving to architectures that facilitate the access to the flows that flow through it.

Estudio Numérico de Flujos Turbulentos Isotérmicos en Canales y Flujos Laminares con Convección Mixta en Cavidades

A numerical study about three-dimensional steady state turbulent channel flows and laminar transient cavity flows with mixed convection heat transfer has been done. The solution of the conservation equations is obtained by means of Finite Element Method and Taylor-Galerkin explicit scheme. Large Eddy Simulation is employed for the treatment of turbulence. For the isothermal case, flows with Re = 3300 were simulated using the Smagorinsky and Dynamical subgrid models. The latter model allowed improving the average velocity profiles as well as turbulence statistics. The transient velocity and temperature fields were compared with results of the literature, leading to a deviation lower than 6%.

Constructal Design Associated with Genetic Algorithm to Maximize the Performance of H-Shaped Isothermal Cavities

The constructal design method associated with the genetic algorithm is used to optimize the geometry of a H-shaped cavity that intrudes into a solid conducting wall. The objective is to minimize the maximum excess temperature between the solid and the cavity. Internal heat generation is distributed uniformly throughout the solid wall. The cavity surface is isothermal, while the solid wall has adiabatic conditions on the outer surface. There are six degrees of freedom which are free to vary. The H-cavity is optimized completely, i.e. it is optimized with respect to all its degrees of freedom. The ratio between the volume of the H-shaped cavity and the total volume (ϕ) is a problem constraint, which is evaluated here. Numerical results show that the optimal H-shaped configuration is the one that distributes better the hot spots in agreement with the optimal imperfections principle. The H-shaped cavity has its worst performance when the ratio between its height and length is set equal to two. The performance improves as this ratio is larger or smaller than two. An important finding is that the dimensionless maximum excess temperature calculated for the best H-shaped cavity with ratio between the height and the length of the cavity equal to 0.1 is approximately only 30% of the maximum excess temperature calculated for the elemental C-shaped cavity under the same thermal conditions.

A Netlogo and Matlab Hybrid Approach for Constructal Design of the Double-T Shaped Cavity by Means of Simulated Annealing

This paper describes the use of the NetLogo environment to perform the Constructal Design of a Double-T shaped Cavity with the stochastic algorithm Simulated Annealing. The algorithm is used in the geometric optimization of a heat transfer problem, which consists in a solid body with an internal uniform heat generation, which is cooled by a cavity that is maintained at a minimal temperature. The other surfaces are kept with an adiabatic condition. The objective is to minimize the maximum excess of temperature in the solid domain through geometric optimization of the isothermal double-T shaped cavity.