中文摘要：

采用Boussinesq近似、不可压-理想气体及密度线性差分三种密度处理方法对大温差（？Tmax=1000K）竖直圆柱腔体的定常自然对流进行了模拟.首先,通过模拟一封闭方腔流动并与文献对比,验证了数值模拟方法的有效性.在此基础上,进一步研究了圆柱腔体中表面曲率κ、瑞利数Ra及温差ΔT的影响,特别是这些因素影响下不同密度处理方法对热壁面平均努谢尔特数Nuave数值结果的影响.结果表明,表面曲率κ是影响圆柱腔体自然对流换热的重要因素,且随着κ的不断减小,其Nuave数会逐渐趋近于方腔对流;同时,在温差ΔT和表面曲率κ较大时,基于Boussinesq近似的方法对Nuave的预测存在较大偏差.

英文摘要：

With three density treatment methods, including Boussinesq approximation, incompressible ideal gas and piecewise-linear density, the steady natural convection problem was simulated, which is driven by the large temperature difference inside a vertical cylindrical cavity. Firstly, the validation of numerical method was verified through comparing the result of an enclosed square cavity with the existed literatures. Next, with this method, the influences of surface curvature x, Raleigh Number Ra and the temperature difference AT were investigated. Especially, under the action of those factors, the effect of different density treatment methods was considered on the numerical results about the average Nusselt number Nuave at hot wall. The results showed that the surface curvature was one of the important factors to affect the natural convection of cylindrical cavity. With the decrease of surface curvature, the resultant Nuave will approach to that of square cavity gradually. At the same time, when surface curvature and temperature difference are very large, Boussinesq approximation will bring about the greater relative deviation.