Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Abstract

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

Analysis of Combined Natural Convection and Radiation Heat Transfer Using a Similarity Solution

“…As it is presented in the Table 3 by reduction of Pr * (lower radiation parameter), thickness of momentum boundary layer increases and also the maximum value of velocity inside the boundary layer increases. Similar conclusions are reported by Luo et al (2014). For N R value equal to 0.5 the momentum boundary thickness is enhanced by 46% and maximum velocity inside the boundary layer increases by 41% at Pr =1.…”

Study on Bifurcation and Dual Solutions in Natural Convection in a Horizontal Annulus with Rotating Inner Cylinder Using Thermal Immersed Boundary-Lattice Boltzmann Method

“…It has been found by many researchers that the bifurcation phenomenon appears in the natural convection in a horizontal annulus [ 7 , 11 , 12 , 31 ]. Different initial conditions will lead to different structures of convection.…”

“…Wu et al discussed the accuracy of thermal IB-LBM [ 30 ]. Recently, the thermal lattice Boltzmann method with curving boundary treatment becomes popular in simulating natural convection in a horizontal annulus [ 11 , 12 , 31 , 32 ].…”