A Numerical Approach for Natural Convection With Curved Obstacles in an Enclosure Using Lattice Boltzmann Method

Abstract

Abstract The impact of placing curved obstacles on natural convection in enclosures with differentially heated side walls is analyzed in the current study using the lattice Boltzmann method (LBM). A method to choose characteristic velocity based on Knudsen number is implemented which eradicates the need of arbitrarily guessing characteristic velocities to proceed with simulations. In addition, a less computationally intensive probability distribution function for equilibrium temperature is used. For validation, a standard natural convection problem with left wall at high temperature, right wall at low temperature, and top and bottom adiabatic walls is considered. A grid independence test is conducted and the code is validated with existing results for various Rayleigh numbers, which shows a good agreement. The problem is then modified by including circular and elliptical obstacles of adiabatic, hot, and cold nature. A boundary interpolation technique is used to implement the velocity and temperature boundary conditions at the inner boundaries. The streamline patterns and temperature contours show interesting observations such as dependence of location of vortices on the type of obstacle boundary used, and formation of low or high temperature zones around obstacle at high Rayleigh numbers. Results show that the change in the shape of the obstacle contributes to the Nusselt number variations at the high temperature boundary and low Rayleigh numbers.