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Two-Dimensional Simulation of the Navier-Stokes Equations for Laminar and Turbulent Flow around a Heated Square Cylinder with Forced Convection

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Document pages: 22 pages

Abstract: Few studies jointly investigate thermal and turbulent effects. In general, thesesubjects are treated separately. The purpose of this paper is to use the ImmersedBoundary Method (IBM) coupled with the Virtual Physical Model(VPM) to investigate incompressible two-dimensional Newtonian flowaround a heated square cylinder at constant temperature on its surface withforced convection and turbulence. The VPM model dynamically evaluates theforce that the fluid exerts on the immersed surface and the thermal exchangebetween both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . Forsimulations of turbulence the Smagorinsky and Spalart-Allmaras models areused. The first model uses the Large Eddy Simulation (LES) methodology andis based on the local equilibrium hypothesis for small scales associated withthe Boussinesq hypothesis, such that the energy injected into the spectrum ofthe turbulence balances the energy dissipated by convective effects. Thesecond model uses the concept Unsteady Reynolds Averaged Navier-StokesEquations (URANS), with only one transport equation for turbulent viscosity,being calibrated in pressure gradient layers. The goal of this work is to analysethe combination of the heat-transfer phenomena with the turbulence for thethermo-fluid-structure interaction in a square cylinder. For this, it was developeda C C++ code that requires low computational costs in regards to memoryand computer facilities. It is observed that, with the increase of the Reynoldsnumber, an increase of the drag coefficient occurs, as well as reinforcesthe influence of the pressure distribution downstream of the cylinder, which isstrongly influenced by the formation and detachment of vortices on the upperand lower sides of the square cylinder.

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