Abstract:

A mathematical model of natural convection outside a heated cylinder in a closed cavity under the influence of surface tension is established by using the lattice Boltzmann method (LBM). Firstly, the model of natural convection and surface tension is verified, and then the heat transfer characteristics of natural convection of heated fluid outside the cylinder under the simultaneous action of surface tension of liquid and solid, and buoyancy force of gravity field are studied. Finally, the simulation results show that with the increase of surface tension (Oh number decreases), the disturbance of natural convection inside and outside the closed cavity will be intensified, the flow pattern will become more complicated, and the heat transfer coefficient of the wall will be improved obviously.When the Ra number is 10⁵ and the surface tension σ=0.076302N/mm (Oh=0.122) is added, the averaged Nusselt number on the left wall of the cavity and the heated cylinder wall are 93.5% and 60.35% higher than those without surface tension In addition, when the surface tension is equal to the buoyancy force of natural convection, the flow fluctuation is more obvious and violent, and in this case the increasing the buoyancy force within a certain range may weaken the heat transfer.

Key words: lattice boltzmann method, natural convection, heating chamber, surface tension, numerical simulation, heat transfer

摘要：

采用格子-玻尔兹曼方法（LBM）构建了考虑表面张力影响下封闭腔体内加热圆柱外自然对流数学模型。在分别对自然对流与表面张力模型模拟验证的基础上，探究了液固表面张力与重力场下浮升力同时作用下加热圆柱外流体自然对流的传热特性。结果表明，在给定Ra数下（10³≤Ra≤10⁶），随着表面张力的增大（Oh数减小），封闭腔体内管外自然对流扰动会加剧，流型会变复杂，壁面换热效率有明显提高。在Ra数为10⁵，长度比（加热圆柱半径和方腔长度之比）为1/10情况下，加入表面张力σ=0.076302N/mm（Oh=0.122），腔体左侧壁面平均努塞尔数和加热圆柱壁面与未加表面张力相比分别提高了93.5%和60.35%。当表面张力大小和自然对流的浮升力相当时，此时的流场波动更加明显剧烈，在一定范围内增大浮升力反而减弱换热。

关键词: 格子Boltzmann方法, 自然对流, 加热腔体, 表面张力, 数值模拟, 传热