scholarly journals GEOMETRIC OPTIMIZATION OF “+”-SHAPED CAVITY USING CONSTRUCTAL THEORY

2017 ◽  
Vol 16 (1) ◽  
pp. 75
Author(s):  
P. A. Avendaño ◽  
J. A. Souza ◽  
D. F. Adamatti ◽  
E. D. dos Santos
Keyword(s):  
Solid Body ◽  
Degrees Of Freedom ◽  
Internal Heat ◽  
Thermal Conditions ◽  
Geometric Optimization ◽  
Optimal Performance ◽  
Constructal Theory ◽  
Maximum Temperature ◽  
Constructal Design ◽  
Better Than

In this work it is applied the Constructal Theory for the study of the geometry of an “+”-shaped isothermal cavity inserted in a conductive solid body. Main goal is to minimize the maximum temperature in the solid. The total volume of the solid and the total volume of the cavity are kept fixed while the dimensions of the cavity geometry vary according to constraints and degrees of freedom defined by the Constructal Design. The solid body has internal heat generation and its external surfaces are insulated. Cavity walls are isothermal with constant temperature Tmin. Obtained results indicate that the optimal performance of “+”-shape cavity is 37.2% better that the optimal performance of “C”-shape cavity and 10.8% better than the “T”-shaped cavity for the same thermal conditions.

Design of Cooling Cavities by the Application of the Constructal Design

2017 ◽  
Vol 372 ◽  
pp. 163-169
Author(s):  
Júlio César Burlamaqui Vianna ◽  
Emanuel da Silva Diaz Estrada ◽  
Liércio André Isoldi ◽  
Elizaldo Domingues dos Santos ◽  
Jeferson Avila Souza
Keyword(s):  
Hot Spots ◽  
Numerical Study ◽  
Internal Heat ◽  
Constructal Theory ◽  
Maximum Temperature ◽  
The Finite Element Method ◽  
Constructal Design ◽  
Solid Geometry ◽  
Building Process ◽  
Solid Bodies

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.

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.

scholarly journals CONSTRUCTAL DESIGN AND SIMULATED ANNEALING EMPLOYED FOR GEOMETRIC OPTIMIZATION OF A Y-SHAPED CAVITY INTRUDED INTO CONDUCTIVE WALL

2015 ◽  
Vol 14 (1) ◽  
pp. 79
Author(s):  
G. V. Gonzales ◽  
E. D. Dos Santos ◽  
L. R. Emmendorfer ◽  
L. A. Isoldi ◽  
E. S. D. Estrada ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Solid Wall ◽  
Internal Heat ◽  
Optimization Methods ◽  
Optimization Method ◽  
Internal Heat Generation ◽  
Geometric Optimization ◽  
Constructal Design ◽  
Optimal Shapes

he problem study here is concerned with the geometrical evaluation of an isothermal Y-shaped cavity intruded into conducting solid wall with internal heat generation. The cavity acts as a sink of the heat generated into the solid. The main purpose here is to minimize the maximal excess of temperature (θmax) in the solid. Constructal Design, which is based on the objective and constraints principle, is employed to evaluate the geometries of Y-shaped cavity. Meanwhile, Simulated Annealing (SA) algorithm is employed as optimization method to seek for the best shapes. To validate the SA methodology, the results obtained with SA are compared with those achieved with Genetic Algorithm (GA) and Exaustive Search (ES) in recent studies of literature. The comparison between the optimization methods (SA, GA and ES) showed that Simulated Annealing is highly effective in the search for the optimal shapes of the studied case.

scholarly journals Constructal design of isothermal X-shaped cavities

2014 ◽  
Vol 18 (2) ◽  
pp. 349-356 ◽  
Author(s):  
G. Lorenzini ◽  
C. Biserni ◽  
F.B. Link ◽  
Dos Santos ◽  
L.A. Isoldi ◽  
...  
Keyword(s):  
Heat Generation ◽  
Solid Body ◽  
Outer Surface ◽  
Area Fraction ◽  
Cavity Volume ◽  
Constructal Design ◽  
Conducting Wall ◽  
And Performance ◽  
Optimal Configurations ◽  
Better Than

This paper applies Constructal design to study the geometry of a X-shaped cavity that penetrates into a solid conducting wall. The objective is to minimize the maximal dimensionless excess of temperature between the solid body and the cavity. There is uniform heat generation on the solid body. The total volume and the cavity volume are fixed, but the geometric lengths and thickness of the X-shaped cavity can vary. The cavity surfaces are isothermal while the solid body has adiabatic conditions on the outer surface. The emerged optimal configurations and performance are reported graphically. When compared to the Y- and C- and H-, the X-shaped cavity performs approximately 53% better than the Y-shaped cavity and 68% better than the C-shaped cavity for the area fraction ? = 0.05, while its performance is 22% inferior to the performance of the H-shaped cavity for the area fraction ? = 0.1. The results indicate that the increase of the complexity of the cavity geometry can facilitate the access of heat currents and improve the performance of the cavities.

scholarly journals CONSTRUCTAL THEORY APPLIED TO THE GEOMETRIC OPTIMIZATION OF ELLIPTICAL CAVITIES INTO A SOLID CONDUCTING WALL

2008 ◽  
Vol 7 (2) ◽  
pp. 81
Author(s):  
L. A. O. Rocha ◽  
C. Biserni ◽  
E. Lorenzini
Keyword(s):  
Solid Wall ◽  
Thermal Conditions ◽  
Geometric Optimization ◽  
Constructal Theory ◽  
Design Parameters ◽  
Cavity Volume ◽  
Cavity Shape ◽  
Elliptical Cavity ◽  
Conducting Wall ◽  
Geometrical Shapes

This work reports, according to Bejan’s Constructal theory, the geometric optimization of an elliptical cavity that intrudes into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The cavity is optimized for two sets of thermal conditions: isothermal cavity and cavity bathed by a steady stream of fluid. The solid conducting wall is isolated on the external perimeter. The total volume and the elliptical cavity volume are fixed while the geometry of the cavity is free to vary. The results show that the optimized geometrical shapes are relatively robust, i.e., insensitive to changes in some of the design parameters: the cavity shape is optimal when penetrates the conducting wall almost completely.

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

2017 ◽  
Vol 370 ◽  
pp. 152-161 ◽  
Author(s):  
Gill Velleda Gonzales ◽  
Elizaldo Domingues dos Santos ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
Antônio José da Silva Neto ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Degrees Of Freedom ◽  
Hybrid Methods ◽  
Transfer Problem ◽  
Geometric Optimization ◽  
Stochastic Methods ◽  
Statistical Tool ◽  
Constructal Design ◽  
Cooling Schedule ◽  
Complete Optimization

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.

Constructal Design of Cavities Inserted Into a Cylindrical Solid Body

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Giulio Lorenzini ◽  
Luiz Alberto Oliveira Rocha ◽  
Cesare Biserni ◽  
Elizaldo Domingues dos Santos ◽  
Liércio André Isoldi
Keyword(s):  
Aspect Ratio ◽  
Solid Body ◽  
Outer Surface ◽  
Hot Spots ◽  
Numerical Optimization ◽  
Internal Heat ◽  
Optimal Distribution ◽  
Constructal Design ◽  
Cylindrical Solid ◽  
And Performance

This paper considers the numerical optimization of the shape of cavities that intrude into a cylindrical solid body. The objective is to minimize the global thermal resistance between the solid body and the cavities. Internal heat generating is distributed uniformly throughout the solid body. The cavities are isothermal, while the solid body has adiabatic conditions on the outer surface. The total volume is fixed. The cavities are rectangular, with fixed volume and variable aspect ratio. The number of cavities of the conducting body, N, is a design parameter. The optimized geometry and performance are reported graphically as functions of the ratio between the volume of the cavities and the total volume, φ0, and N. The paper shows an example of the application of optimal distribution of imperfections principle. The results indicate that the optimal distribution of the hot spots is affected not only by the complexity of the configuration (larger N) but also by the area of cavities fraction φ0.

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.

Constructal Peripheral Cooling of a Rectangular Heat-Generating Area

2006 ◽  
Vol 128 (4) ◽  
pp. 432-440 ◽  
Author(s):  
Alexandre K. da Silva ◽  
Louis Gosselin
Keyword(s):  
Solid Body ◽  
Thermal Performance ◽  
Degrees Of Freedom ◽  
Hot Spot ◽  
Internal Heat ◽  
Numerical Results ◽  
Scale Analysis ◽  
Cooling Channels ◽  
Heated Body ◽  
Spot Temperature

The present paper determines numerically the optimal geometric parameters for the maximal peripheral cooling of a two-dimensional rectangular solid body with internal heat generation. The objective is to maximize the thermal global conductance (i.e., minimize the hot spot temperature on the solid body) by using the minimal cooling space. The flow is conducted around the heated solid body by a sequence of channels of independent width Di, where 1⩽i⩽4. Each configuration is free to morph itself in two directions: (a) the number of cooling channels, and (b) the aspect ratio of the heated body λ. The numerical results show that a number of cooling channels greater than one (i.e., n>1) is profitable in terms of thermal performance when the heated body resembles a square (i.e., λ∼1). However when λ is free to vary, the thermal performance does not necessarily increase with the number of cooling channels. The paper also discusses the importance to allow each configuration to morph itself in multiple directions by comparing the thermal performance of similar configurations with different number of degrees of freedom. Scale analysis is used to verify the results obtained numerically for all the degrees of freedom considered. The numerical results agree with the scaling trends.

Constructal Design Associated to Genetic Algorithm of Asymmetric V-Shaped Pathways

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Emanuel da S. D. Estrada ◽  
Tadeu M. Fagundes ◽  
Liércio A. Isoldi ◽  
Elizaldo D. dos Santos ◽  
Gongnan Xie ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Thermal Resistance ◽  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Geometric Optimization ◽  
Heat Sinks ◽  
Heat Generation Rate ◽  
Conductive Materials ◽  
Constructal Design ◽  
Optimal Shapes

This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.

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