侧壁效应对Rayleigh-Bénard对流影响的数值模拟研究

Effect of sidewall thermal conductivity on Rayleigh-Bénard convection:a numerical study

Rayleigh-Bénard(RB)对流的研究中通常使用侧壁绝热的温度边界条件,然而实际的对流换热设备中侧壁存在导热性且会对系统传热和流动特性产生影响。为探究侧壁导热性对RB对流的影响,本文采用侧壁等温假设,即侧壁温度为上下壁面温度的平均值,使用二维和三维直接数值模拟的方法研究了侧壁恒温的RB对流。流体工质为普朗特数Pr=5.3的水,二维和三维方腔宽高比Γ为1。将侧壁等温的计算结果与经典的侧壁绝热的RB对流结果进行比较,研究表明:侧壁等温时,二维和三维系统中均存在上下壁面Nu不相等的情形,该特性发生在有限的Ra值区间内,且与系统内的流动结构密切相关;侧壁恒温时,系统的传热效率要高于侧壁绝热情况下的传热效率,这是由于侧壁恒温条件下,一部分热量可以直接通过侧壁来传递,从而绕开温度边界层。当采用恒温边界条件时,流场的强度减弱,从而系统的Re要小于侧壁绝热条件下对应的Re。

In the study of Rayleigh-Bénard (RB) convection, it is usually assumed that sidewalls are adiabatic. However, this is not always the case in real heat exchangers. Consequently, the flow structures and heat transfer will be inevitably affected by non-adiabatic walls. The effect of the thermal conductivity of sidewalls on RB convection is investigated by two-and three-dimensional direct numerical simulations with the sidewall temperature being set to the mean of the top and bottom temperatures. The working fluid is water with the Prandtl number Pr = 5.3 and the aspect ratio Γ of the simulation box is fixed to Γ = 1. The results are further compared with those of traditional RB convection with adiabatic sidewalls. It is found that in a certain range of the Rayleigh number Ra, the Nusselt numbers Nu of the top and bottom plates are not equal, which is closely related to the flow structures. The global heat transport is higher for the isothermal sidewall case than that of the adiabatic sidewall case. This is because, in the former case, part of the heat can be transferred directly through sidewalls instead of being absorbed by the thermal boundary layer. For the isothermal sidewall case, the global Reynolds number is smaller than that of the adiabatic sidewall case due to lower turbulence insensity.