TITLE:
Two-Dimensional Simulation of the Navier-Stokes Equations for Laminar and Turbulent Flow around a Heated Square Cylinder with Forced Convection
AUTHORS:
Rômulo D. C. Santos, Sílvio M. A. Gama, Ramiro G. R. Camacho
KEYWORDS:
Immersed Boundary Method, Virtual Physical Model, Heated Square Cylinder Forced Convection, Turbulence Models
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.3,
March
30,
2018
ABSTRACT: Few studies jointly investigate thermal and turbulent effects. In general, these
subjects are treated separately. The purpose of this paper is to use the Immersed
Boundary Method (IBM) coupled with the Virtual Physical Model
(VPM) to investigate incompressible two-dimensional Newtonian flow
around a heated square cylinder at constant temperature on its surface with
forced convection and turbulence. The VPM model dynamically evaluates the
force that the fluid exerts on the immersed surface and the thermal exchange
between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For
simulations of turbulence the Smagorinsky and Spalart-Allmaras models are
used. The first model uses the Large Eddy Simulation (LES) methodology and
is based on the local equilibrium hypothesis for small scales associated with
the Boussinesq hypothesis, such that the energy injected into the spectrum of
the turbulence balances the energy dissipated by convective effects. The
second model uses the concept Unsteady Reynolds Averaged Navier-Stokes
Equations (URANS), with only one transport equation for turbulent viscosity,
being calibrated in pressure gradient layers. The goal of this work is to analyse
the combination of the heat-transfer phenomena with the turbulence for the
thermo-fluid-structure interaction in a square cylinder. For this, it was developed
a C/C++ code that requires low computational costs in regards to memory
and computer facilities. It is observed that, with the increase of the Reynolds
number, an increase of the drag coefficient occurs, as well as reinforces
the influence of the pressure distribution downstream of the cylinder, which is
strongly influenced by the formation and detachment of vortices on the upper
and lower sides of the square cylinder.