Structural Ensemble Dynamics Based Rayleigh-Bénard Convection Similarity Solutions And Heat Transfer Scaling

Rayleigh-Benard(RB)Convection is a teperature-difference driven system,which fluid filled in a closed cell,heated on the bottom,cooled on the top,with adiabatic no-slip side wall.The system has simple boundary condictions,however,the quantitative relation of nondi-mensional heat transfer efficiency Nusselt number(Nu),flow intensity Reynolds number(Re)with temperature difference Rayleigh number(Ra)and fluid property Prandtl number(Pr)and aspect-ratio(r)is quite complicated.The study of convection system's heat transfer mecha-nism has a great scientific value for human society activities,such as environment,atmosphere and geophysics.For a long time,the research on RB Convection has been based on GL theory established by Grossmann and Lohse,which simpifies RB system into boundary layer and bulk region,and deduces the global physics quantities.Thus the influence of complicated factor on global heat transfer coefficient cannot be accurately described.This thesis applies Structured Ensemble Dynamics(SED)established by Professor Zhensu She,combines homotopy analy-sis and theory of wall jet,studies the coupled mechanism of each regions' flow structure and contributions to the global heat transfer of turbulent RB convection,and establishes a two-dimensional self-similarity model.This thesis provides the LSC and Corner-Rolls' kinetic similarity solution model.We complete 40 Direct Numerical Simulation(DNS)cases for different Ra and Pr in three dimension(Ra=107?5 × 109,Pr=0.08?50)and two dimension(Ra=5 × 107?1 ×1010,Pr=0.01?104).Based on the physical character,we divides the fields into Large Scale Circulation,Corner-Roll,Oblique Impinging Jet Reattachment Region,Aderverse Pressure Gradient Shear Region and Plume Emission Region.Based on flow's geomoetric similarity,a homotopy geometric similarity variable is constructed,for moderate Ra and Pr.With con-sidering Reynolds averaged stream function equation,a unique character Reynolds number is obtained by the solution's parameter.With SED theory,a multi-layer function is constructed to describe the behavior of large scale structure on near-wall region.We extend Castaing's Mixing Zone Theory[1]to corner flow,with the empirical corner-roll scale rcr?Ra-0.085,we accurately provide the Ra scaling of corner-roll's characteristic Re with Recr?Ra0.25 and heat transfer Nu with Nucr?Ra1/3.Secondly,We propose a "wall jet" mechanism of LSC-induced oblique jet reattachment and obtain a similarity solution.The maximum velocity and characteristic height with lo-cal momentum rate as character normalizing quantity is found to fulfill self-similarity rela-tion.Through separation variable method,heat transfer coefficient of wall jet decay expo-nentially Nuimp=Numaxexp(-x#)is deduced.By propose the heat transfer balance near the reattachment point with corner-roll scale's Ra-scaling,the Nu number scaling is found to be Numax?Ra0.2925.Based on symmetry analysis of Structrual Ensemble Dynamics(SED),an analytical expression of streamwise velocity and temperature profile's streamwise variation in adverse pressure gradient shear region and the distribution of temperature in Plume Emission Region are obtained.With the turbulent Prandtl number's universality of streamwise and Ra effect,a heat flux relation with friction and ratio of momentum and thermal transport eddies scale is deduced.By considering the mechanism of plume emission,we found that the heat transfer scaling in this region is Nu?Ra0.369.With the spatial occupation as the weight and the local Nu scaling mention before,we obtain the quantitative relation of global Nu and Ra,and extend this relation to predict other geometric cases'heat transfer.Thirdly,we employ SED theory to analysis the streamwise velocity and temperature to characterize Pr effect.We confirm that the inner two-layer structure of streamwise velocity stress length function is independent to Pr.With decreasing of Pr,the effect of pressure gradient weaken and the eddies's characteristic scale become smaller while the thickness of viscous sublayer thicker.For temperature profile,temperature length fulfill three-layer structure.With increasing Pr,conduct sublayer and buffer layer become thicker.With analysis of parameter of SED,we obtain the thermal Karman coefficient's streamwise and Pr effect,which consist with the DNS result.In conclustion,this thesis extends SED theory into turbulent RB convection and poses similarity solutions for two-dimensional large scale separation flow,provides a similarity the-ory to accurately depict local mean velocity and heat flux.