Turbulent natural convection in an air-filled isosceles triangular enclosure

Abstract

This paper addresses turbulent natural convection of air confined in an isosceles triangular enclosure representing conventional attic spaces of houses and buildings with pitched roofs and horizontally suspended ceilings. The values to be considered are H = 0.86 m and 2.73 m for the height while the values 1.72 m and 5.46 m were assigned to the width, W, such as the aspect ratio H/ W remains 0.5. The third dimension of the cavity is considered long enough for the flow to be considered 2D. The base wall is heated at 20 °C and the inclined walls are cooled at 0 °C. This combination of factors leads to large Rayleigh numbers equal to 1.58 × 10 9 and 5 × 10 10. Turbulence is modeled by a low-Reynolds-number k– ε model. The system of governing equations, subject to the proper boundary conditions is solved with the finite volume method. Second-order-accurate QUICK and SIMPLE schemes were used for the discretization of the convective terms and the pressure–velocity coupling, respectively. The velocity and temperature distributions were calculated at different locations in the cavity and their mean quantities are presented. The local and average Nusselt numbers and the wall shear stresses are also presented. Since to the knowledge of the authors, no previous results on turbulent thermal convection in this geometry exist, the validation of the numerical code was performed by comparing velocity and temperature profiles against recent experimental measurements, obtained for a square cavity. Satisfactory agreement was observed.