Study On Natural Convection In Cavity With Porous Medium By Lattice Boltzmann Method

The phenomenon of natural convection heat transfer in cavity filled with porous medium are ubiquitous in natural and engineering applications,for example,the process of the heat exchange and collection in the solar wall system,the heat dissipation of electronic components and the matching problem with buried pipe of heat exchanger in the soil source heat pump system.Due to the randomness of the pore structure and the complexity of the fluid-solid interface in porous cavity,which prevents people from exploring the law of natural convection heat transfer inside the pore,therefore,it is very important to find a reasonable and efficient research method.In recent years,with the advantages of clear physical background,easy boundary treatment and high numerical accuracy,lattice Boltzmann method(LBM)has been successfully applied to the study of fluid flow and heat transfer in porous media with complex geometric structures and the simulation result works well.LBM is used to simulate problems of the natural convection heat transfer in porous cavity at the mesoscopic scale,based on the theoretical analysis,the corresponding mathematical model and physical model are established,the distribution of streamlines,isotherms and the value of average or local N usselt number at the hot wall in the porous cavity is analyzed.First,this paper discusses the natural convection heat transfer in a vertical porous cavity with six different types of partially thermally active walls,included Top-Middle,Middle-Middle,Bottom-Middle,Middle-Top,Bottom-Bottom and Bottom-Top respectively,and analyses the influence of heat transfer characteristics of natural convection in the vertical porous cavity with six different heating and cooling zones.The results reveal that: The location of partially thermally active walls has a significant influence on the flo w pattern and heat transfer in the cavity,the case of Bottom-Top with bottom heating and top cooling provides a higher heat transfer rate compared to other cases of partial heating,and better than the fully heated wall of the cavity.Second,this paper presents the analysis of natural convection heat transfer in a vertical porous cavity with rough walls,which have three ways of the distribution of wall roughness element,CASE A,CASE B and Smooth.The roughness of the wall is changed by changing the number n and the height A of the roughness element,set them with n=2?4?6 and A=0.5?1?1.5.Then,the paper conducts a detailed discussion aboat the effect of Darcy number and Rayleigh number on convective flow heat transfer with porosity.The results show that: When n=6?Ra=106,comparing with case Smooth,the average N usselt number at the hot wall in case A is reduced by 11.87%,and the average Nusselt number at the hot wall in case B is reduced by 19.80%;When A=1.5?Ra=106,comparing with case Smooth,the average N usselt number at the hot wall in case A is reduced by 9.50%,and the average N usselt number at the hot wall in case B is reduced by 20.40%.Under the same parameters,the average N usselt reduction at the hot wall in case B is approximately two times bigger than that of case A compared with case Smooth.Third,the paper discusses the natural convection heat transfer in inclined porous cavity with a hot square obstacle and studies the problem of fluid-solid coupling heat transfer,with the size of the hot square obstacle is 0.4,0.5 and 0.6 respectively,and analyzes the distribution characteristics of streamlines and isotherms.Because of the lower precision and slower convergence rate of LBGK model,the MRT-LBM model is established to analyze the effect of Ra* number(Ra*=Da·Ra)and angle of inclination ? on natural convection heat transfer.The results show that the average Nusselt number presents a distribution features of “M” type at the hot wall with the increasing of inclination angle,and when ?=90°,the average Nusselt number curve is symmetrical at the angle and obtains the minimum value,while the average N usselt number curve achieves the least value at the angle with ?=-90°and ?=270°.The average Nusselt number curve obtains the maximum value at different inclination angle with different porosity and Ra number.Date obtained in the presented numerical study has been used to derive a power exponential function expression between Ra* number and the average Nusselt number at the hot wall by the utilization of curve fitting method.Finally,the paper summarizes the research details and prospects the next research work.