Simulation of Natural Convection in Eccentric Annulus: A Combined Lattice Boltzmann and Smoothed Profile Approach

In the present study, a hybrid method of thermal lattice Boltzmann and smoothed profile methods have been applied to simulate free convection in an eccentric annulus with a constant temperature wall. Smoothed profile method employs an Eulerian approach to consider the fluid-solid interaction without using an extra mesh for capturing solid boundary. As a result of this property, the combination of this method and Lattive Boltzmann method can be considered as an efficient method to simulate free convection in complex geometries like annulus. In order to investigate the effect of inner cylinder position on the natural convection, the inner cylinder was placed in different horizontal, vertical and diagonal positions. Influences of the Rayleigh number (103 ≤ Ra ≤ 10^5), eccentricity (-0.75 ≤ e ≤ 0.75)) and the radial ratio (Ro /Ri=2, 2.6 and 3.2) on the streamlines, isotherms and Nusselt number were studied. It was found that the Nusselt number has a positive relationship with Rayleigh number and radial ratio. Also, it can be confirmed that Nusselt number in the case with the negative eccentricity (e=−0.75) was larger than the others. It was found that a very good agreement exists between the present results and those from the open literature.