Laminar to turbulent flow transition inside the boundary layer adjacent to isothermal wall of natural convection flow in a cubical cavity

Abstract

We investigate three-dimensional natural convection flow in an air-filled, differentially heated cubical cavity. The vertical wall on the left is heated and the vertical wall on the right is cooled, with the remaining four walls being adiabatic. We performed direct numerical simulations of the natural convection flow using discrete unified gas-kinetic scheme (DUGKS), with an improved implementation of boundary conditions. Thin boundary layers are developed along the two isothermal walls. The laminar to turbulent flow transition inside the boundary layers is studied in this paper. The simulations are conducted at three Rayleigh numbers of 1.5×109,1.0×1010,1.0×1011 using nonuniform grids with resolution up to 3203. The Prandtl number is fixed at 0.71. We provide a detailed analysis of the transition from laminar to turbulent flow inside the vertical boundary layers and its influence on the rate of heat transfer. Time traces of temperature and velocity, time-averaged flow field, statistics of fluctuation fields are presented to illustrate distinct behaviors in the laminar and turbulent thermal boundary layer, as well as to determine the transition location at different Ra numbers. The average Nusselt numbers for different Ra numbers are compiled and compared to previous results. A guideline of the resolution requirement is suggested based on the Ra scaling of laminar thermal boundary layer.