Numerical Simulation of the Natural Convection in a Tunnel Whose Floor Has a Variable Sinusoid with a Roof Opening

Abstract

A two-dimensional numerical study of natural convection in a tunnel whose plane is sinusoidal with an opening on the horizontal ceiling is presented. In this work, we study the thermoconvective instabilities of air in a tunnel closed at both ends and heated by the floor. The study was carried out for different cases of geometry by varying the thickness of the sinusoid and the height of the tunnel. In order to create a transverse movement of the air, we heated the floor to the temperature f T and kept the horizontal ceiling at the temperature g T such that g f T T < . This work has a lot of scope of application ranging from geothermal flow to the civil engineering like ventilation in the case of tunnels and thermal comfort of buildings. The Navier Stokes equations that model this problem have been solved using the numerical method with simplifying assumptions such as the Boussinesq hypothesis. And finally an interpretation of the results of the simulations has been made taking into account the variation of the form factors such as the amplitude of the sinusoid for Rayleigh number 4 6 2 10 7 10 a R × ≤ ≤ × and Prendtl number P r = 0.71.