The Effects Of Prandtl Number On Heat Transport And Flow Structures In Rayleigh-Bénard Convection With Roughness

Most of thermal convection phenomena in nature have rough boundaries.The study of Rayleigh-Benard(RB)convection with rough surfaces is of great theoretical value and practical significance for understanding turbulent heat transport and flow structures.In this thesis,we carry out direct numerical simulations(DNS)of turbulent RB convection with rough conducting plates over the Rayleigh number(Ra)range 107?Ra?109 and the Prandtl number(Pr)range 10-2 ?Pr?102.The shape of rough elements used in the simulations is an isosceles right triangle,and the roughness height h can be controlled by changing the number of rough elements.Focusing on the effects of h and Pr on the heat transport and flow structures,there are two main conclusions1)For flow structures,When Pr is small,the flow is very violent,the center of large scale circulation(LSC)will shift with time,and the corner-flow rolls can't exist stably at the diagonal.With the increase of Pr.LSC becomes stable,and corner-flow rolls can be found at the diagonal.When Pr is large enough,plumes become more dominant,LSC and corner-flow rolls disappear.Within the range of 107?Ra?109,Reynolds number(Re)in smooth cases can found that Re-Pr-0.88±0.04.For turbulent thermal convection with roughness,the results show that the effect of the rough elements on the flow includes two aspects.On the one hand,rough elements will limit the size of large-scale circulation(LSC),hence the LSC velocity will be reduced Re is smaller than that of smooth cases when h is small.On the other hand,with the increase of h,the promotion of rough elements on plume generation and secondary vortices become more dominant.Plumes provide energy for the LSC,and the increase in LSC velocity results in Re being larger than smooth cases2)The global heat transport is enhanced at large roughness height h and reduced at small h.The division between the two regimes yields a critical roughness height h,.The relation between hc and Pr can be divided into three regimes.The LSC-controlled regime,thermal boundary layers become thinner with the increase of Pr This makes the boundary layers easier to be disrupted by rough elements,leading to the decrease of hc with Pr.The corner-LSC-competition regime,in this regime the global heat transport is suppressed due to the competition between the corner-flow rolls and the LSC resulting in hc increases with Pr.The plume-controlled regime,the convective flow becomes dominated by plumes.As the rough elements promote more frequent plume emissions,hc decreases with Pr again.Finally,through dimensional analysis.it is concluded that the critical Prandtl number(Prc)Prc-Ra0.26±0.03 is agrees well with the numerical simulation result Prc?Ra0.27±0.03.