Direct numerical simulation (DNS) is performed to study turbulent heat transfer in Poiseuille-Rayleigh-Bénard (PRB) flows with low Prandtl numbers in this article. The mesh is Cartesian and a highly accurate finite difference sixth-order compact scheme is chosen to discretize the incompressible Navier–Stokes equations to perform DNS. Liquids with a fixed Richardson number of 0.25 and four different Prandtl number (Pr = 0.025, 0.05, 0.1, 0.71) are simulated and compared with Poiseuille flow to investigate the influence of Prandtl number and buoyancy on –PRB flows. Constant fluid properties and Boussinesq approximation are assumed. The obtained results are discussed and analysed in an extensive way in this study. Specifically, buoyancy initiate large scale circulation and the scale shrinks with the increasing of Prandtl number. Velocity fluctuations become stronger with PRB flow which indicate that buoyancy can strongly enhance the turbulent intensity. ${\mathrm{Re}}_{\tau }$ is increased in the cases of low Pr. Moreover, when Pr decreases, temperature distributions are found to be more homogeneous and mixing of the fluids is more sufficient in the middle of the channel. Additionally, the scale of the large-scale structures is enlarged in mixed convection compared with forced convection. This can be observed in the temperature field of low-Prandtl-number fluids. It is also observed that Reynolds analogy cannot be used to predict the thermal field under mixed convection or forced convection with low Prandtl number. The research results can be used for the R&D of Gen IV nuclear fast reactors.

本文通过直接数值模拟（DNS）来研究Poiseuille-Rayleigh-Bénard（PRB）流中具有低Prandtl数的湍流传热。网格是笛卡尔坐标系，并且选择了一个高精度的有限差分六阶紧致格式来离散不可压缩的Navier–Stokes方程来执行DNS。模拟固定Richardson数为0.25且有四个不同的Prandtl数（Pr = 0.025、0.05、0.1、0.71）的液体，并将其与Poiseuille流量进行比较，以研究Prandtl数和浮力对–PRB流量的影响。假定流体特性为常数，并且采用Boussinesq近似。在这项研究中，对获得的结果进行了广泛的讨论和分析。具体来说，浮力会引发大规模的环流，并且随着Prandtl数的增加，规模会缩小。${\mathrm{关于}}_{\tau }$Pr低的情况下会增加。而且，当Pr降低时，发现温度分布更加均匀，并且在通道的中间流体的混合更加充分。另外，与强制对流相比，在混合对流中大型结构的规模扩大了。这可以在低普朗特数流体的温度场中观察到。还可以观察到，雷诺兹类比不能用于预测低Prandtl数的混合对流或强制对流下的热场。研究结果可用于第四代核快堆的研发。