Numerical Study On Flow And Heat Transport In Rayleigh Bénard Convection And Plume With Viscoelastic Fluids

Thermal convection is common in natural and has been widely considered as a basic problem for the study of transition mechanisms in fluid dynamics due to its rich scenario of structures and sequences of bifurcations.By means of direct numerical simulation?DNS?,experiments and theoretical analysis,respectively,the characteristics and mechanism of heat transport in turbulent thermal convection with viscoelastic fluids have been unveiled step by step.However,owing to the limited reported studies,the understanding of thermal convection in viscoelastic fluids is still at a preliminary stage,especially the effect on the transition of flow state and coherent structures.In addition,the mechanism is still in constructive and hypothetical stage,which requires more extensive studies to confirm the theories published so far.Based on the idea of changing fluid property,this work is proposed to explore the elastic effect on the stability and mechanism of heat transport in classical nonlinear Rayleigh-Bénard convection?RBC?system.It will lay a foundation and provide important guidance for the future practical application of viscoelastic fluid in thermal convection system.First,a robust solver is developed based on OpenFOAM to simulate high Rayleigh number?Ra?and high Weissenberg number?Wi?problem of thermal convection with viscoelastic fluids,in which the conformation transport equations are solved by adopting log-conformation reformulation method.Two cases related with thermal convection,i.e.,onset and oscillatory convection in parallel plates at low Ra and RBC in an enclosed cell at moderate Ra,are investigated with adopting the developed solver.In order to investigate the elastic effect on the onset and bifurcation of RBC,numerical simulations are conducted in the parallel plates with viscoelastic fluids.The results imply that the elasticity and solution concentration have a weak inhibition effect on the onset due to the insufficient stretching of polymers at small Ra.As Ra increases,the bifurcation to oscillatory flow is delayed by elasticity at small Wi,which results from the inhibition effect when polymers are stretched and absorb energy from fluid flow.Meanwhile,both the amplitude and frequency of oscillation in the oscillatory flow regime are suppressed.As Wi increases,the inhibition effect further suppresses oscillatory convection and even incur the relaminarization phenomenon.Particularly,as Wi further increases,the elastic nonlinearity may make the flow transition irregular or lead to the convection cells travels in horizontal directions.In order to investigate the mechanism of elastic effect acting on flow and heat transport of RBC,numerical simulations are carried out in cavity filled with viscoelastic fluid.The results indicate that the addition of polymers reduces heat transport and the amount of reduction behaves nonmonotonically,which increases firstly but then decreases with Wi.The maximum heat transport reduction?HTR?reaches around 8.7%at the critical Wi.The nonmonotonic behavior of HTR as a function of Wi is then corroborated with the modifications of the period of larger scale circulation and kinetic energy as well as viscous boundary layer thickness.Finally,a standard turbulent kinetic energy?TKE?budget analysis is conducted for whole domain,boundary layer region and bulk region,respectively.It shows that the role change of elastic stress contributions to TKE is mainly responsible for this nonmonotonic behavior of HTR.Then,in order to explore the elastic effect on flow and heat transport of plume,laminar plume and single steady plume with viscoelastic fluids are studied via theoretical analysis and numerical simulations,respectively.For the theoretical analysis,governing equations are derived for laminar plume flow generated from a heated line in viscoelastic fluid,in which similarity variables and single polymer chain model are introduced.The resolved solutions imply that polymers promote the velocity in the centerline-near region,whereas suppress that in the region far from centerline.The equivalent effect of polymers is understood as producing two space-dependent source terms,which can explain the interaction between polymers and fluid flow from the view of energy transport.There exists a critical Wi beyond which the promotion effect in centerline-near region disappears,which results from the competition of stretching and relaxation of polymer chain.For the numerical simulations,a steady single plume in viscoelastic fluids is generated by imposing point heat source at the bottom plate.The results confirm that the heat transport ability is weakened by adding polymers within the here-investigated ranges of Wi and maximum extension length L.The ratio of Nusselt numbers(Nu/Nu_New)shows a power-law scaling relation with L²/Wi,however,the vertical velocity in stem decreases with Wi and L.The distribution of vertical velocity and temperature indicates that plume with viscoelastic fluids is speeded up and widens bigger as compared to that with the Newtonian fluid.As polymer chain travels in the plume,it tends to absorb energy within lower steam whereas release energy within upper stem,which validates some observations in theoretical analysis.In summary,the present studies can give deep insight into the onset,oscillatory convection and coherent structures in thermal convection with viscoelastic fluids and the results are explained by the mechanism of interactions between polymers and fluid flow from different viewpoints.The studies step into these unexplored areas and are therefore useful for the framework of thermal convection in viscoelastic fluids.The research achievement is bound to be of great values for the academic and practical applications.