Eccentricity effect on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Bifurcation phenomena and the existence of dual solutions in natural convection in eccentric annulus are numerically investigated using the lattice Boltzmann method (LBM). Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. Different scenarios for the onset and evolution of pitchfork bifurcation are tracked. To validate the LBM code, the occurrence of various instabilities and bifurcation phenomena in concentric annulus is analyzed for different relevant parameters, such as the Rayleigh number Ra, Prandtl number Pr and radius ratio R. The numerical results obtained by LBM are found to be highly consistent with other published works. Then, bifurcation phenomena in eccentric annulus are analyzed. Isotherms, streamlines and bifurcation diagrams are presented for vertical, horizontal and diagonal eccentricities. The results show that the eccentricity is a crucial factor for the instability and existence of bifurcation of natural convection in eccentric annulus.