Este estudo numérico consiste em avaliar a forma geométrica de um arranjo triangular de cilindros submetidos a escoamentos transientes, bi-dimensionais, incompressíveis, laminares e com convecção mista por meios do Constructal Design. As simulações foram realizadas para escoamentos com números de Reynolds e Prandtl, de 100 e 0,71, respectivamente, avaliando-se três diferentes números de Richardson: Ri = 0,1; 1,0; e 10,0. This numerical study is to evaluate the geometric shape of a triangular arrangement of cylinders subjected to transient flows, two-dimensional, incompressible, laminar and mixed convection by means of Constructal Design. The simulations were performed for Reynolds and Prandtl numbers, 100 and 0.71, respectively, evaluating three different numbers of Richardson: Ri = 0.1; 1.0; and 10.0. The mass conservation equations, momentum and energy were solved using the finite volume method (FVM -English: Finite Volume Method). The area occupied by the cylinder is a geometric constraint problem. The main objective is to evaluate the influence of Ri in the effect of the ratio S T /D (cross step on the diameter) on the drag coefficient (C D ) and the Nusselt number (Nu D ) between the cylinders and the surrounding flow, and obtain the optimal geometry of the multi-objective problem. In all cases studied the ratio S L /D (on the longitudinal pitch diameter) was fixed S L /D = 1.5. It was estimated that the variation of the driving mechanism of the flow (caused by the variation of Richardson number) have affected the C D magnitudes and Nu D .Keywords: Arrange of Cylinders, Geometrical Optimization, Mixed Convection INTRODUÇÃOSistemas térmicos em problemas que envolvem interações entre um escoamento de fluido e superfícies são amplamente estudados e empregados em diversas áreas da engenharia. Os escoamentos externos sobre cilindros, em especial, representam de forma simplificada diversos problemas de engenharia como pontes, torres, conversores de energia eólica, condensadores,

The present study consists on the numerical evaluation of a triangular arrangement of circular cylinders submitted to transient, two-dimensional, incompressible, laminar and mixed convective flows. The geometrical evaluation is performed by means of Constructal Design. For all simulations it is considered Reynolds and Prandtl numbers of Re D = 100 and Pr = 0.71. Moreover, three different values of Richardson number are investigated: Ri = 0.1 (which represents flows dominated by forced convective), 1.0 (which represents an equilibrium between forced and natural driven forces) and 10.0 (which represents flows with dominance of natural convective). The conservation equations of mass, momentum and energy are solved with the use of Finite Volume Method (FVM). The buoyancy forces are tackled with the Boussinesq approximation. The area occupied by the triangular arrangement of cylinders is a geometric constraint of the problem and the cylinders have the same diameter. The main purpose is to evaluate the effect of Richardson number over the drag coefficient (C D) and Nusselt number (Nu D) between the cylinders and the surrounding flow, as well as, over the optimal ratio S T /D (ratio between transversal pitch and the cylinder) for two different values of the ratio S L /D = 1.5 and 2.5 (ratio between longitudinal pitch and the cylinders diameter). Results showed that the effect of S T /D over drag coefficient and Nusselt number is strongly affected by the magnitude of Richardson number. Concerning the Nusselt number, for Ri = 0.1 the optimal geometry which maximizes the Nu D is reached for the highest magnitude of S T /D, while for Ri = 10.0 an intermediate optimal ratio of S T /D maximizes the Nu D. The Richardson magnitudes also have large influence over the fluid dynamic and thermal behavior of fluid flow for all evaluated geometries. An increase in the ratio S L /D improved the heat exchange of the flow, but decreased the fluid dynamic performance.

The present study consists on the numerical evaluation of a triangular arrangement of circular cylinders submitted to transient, two-dimensional, incompressible, laminar and mixed convective flows. The geometrical evaluation is performed by means of Constructal Design. For all simulations it is considered Reynolds and Prandtl numbers of ReD = 100 and Pr = 0.71. Moreover, three different values of Richardson number are investigated: Ri = 0.1 (which represents flows dominated by forced convective), 1.0 (which represents an equilibrium between forced and natural driven forces) and 10.0 (which represents flows with dominance of natural convective). The conservation equations of mass, momentum and energy are solved with the use of Finite Volume Method (FVM). The buoyancy forces are tackled with the Boussinesq approximation. The area occupied by the triangular arrangement of cylinders is a geometric constraint of the problem and the cylinders have the same diameter. The main purpose is to evaluate the effect of Richardson number over the drag coefficient (CD) and Nusselt number (NuD) between the cylinders and the surrounding flow, as well as, over the optimal ratio ST/D (ratio between transversal pitch and the cylinder) for two different values of the ratio SL/D = 1.5 and 2.5 (ratio between longitudinal pitch and the cylinders diameter). Results showed that the effect of ST/D over drag coefficient and Nusselt number is strongly affected by the magnitude of Richardson number. Concerning the Nusselt number, for Ri = 0.1 the optimal geometry which maximizes the NuD is reached for the highest magnitude of ST/D, while for Ri = 10.0 an intermediate optimal ratio of ST/D maximizes the NuD. The Richardson magnitudes also have large influence over the fluid dynamic and thermal behavior of fluid flow for all evaluated geometries. An increase in the ratio SL/D improved the heat exchange of the flow, but decreased the fluid dynamic performance.