具有非Boussinesq效应的热对流稳定性和非线性演化

Thermal convection is a flow widely existed in nature and engineering applications. Study on the onset and evolution mechanism of thermal convection has important scientific significance and great theoretical value in guiding engineering applications. Theoretical model for thermal convection is commonly based on Boussinesq approximation. However, thermal convection with large temperature difference in nature and engineering applications no longer obey the Boussinesq approximation, and so called non-Oberbeck-Boussinesq (NOB) effects exist. There are a few available research work on this issue. NOB effects can generally be divided into two categories, one is that the flow is still impressible while physical parameters change with temperature; the other is that the assumption of incompressible flow does not hold. The mechanisms of flow are much more complex due to the compressibility. By methods of direct numerical simulation and global stability analysis, this project is mainly to study onset, stability and nonlinear evolution of thermal convection with two kinds of NOB effects, explore the effects of NOB and coupled mechanisms of compressibility, thermal force and shearing of convection. In addition, instability and evolution of thermal convection are studied with system rotation effect. At high Rayleigh’s numbers, affects of NOB on heat transfer and flow structures are also investigated.

热对流是自然界和工程应用中广泛存在的流动，研究其形成与演化机制具有重要的科学意义，并对工程应用有重要的理论指导价值。常规的热对流理论模型多基于Boussinesq近似，然而自然界和工程应用中的很多大温差热对流并不满足Boussinesq近似，存在非Boussinesq效应，相应的研究还很少。非Boussinesq效应有两类，一是必需考虑物性参数随温度的变化，但不可压缩流动的假设依然成立，二是不可压缩流动假设不再成立，还需要考虑流体可压缩性的影响，流动机理更加复杂。本项目主要采用直接数值模拟和整体稳定性分析的方法，分别研究两类非Boussinesq效应下的热对流形成、稳定性及非线性演化规律，探讨非Boussinesq效应的影响，揭示可压缩效应与热力、对流剪切的耦合作用机制，并研究耦合系统旋转效应的热对流失稳与演化特性；在较高的瑞利数下，研究非Boussinesq效应对传热与流动结构的影响。

浮力驱动的湍流热对流现象广泛存在于自然界中。当对流温差较大时，存在非Boussinesq(NOB)效应，NOB效应分为不可压缩近似下的NOB-I效应和考虑弱可压缩性的NOB-II效应。本项目主要研究了两类NOB效应下热对流的形成、流动稳定性及非线性演化规律。具体包括：（1）结合线性稳定性分析和直接数值模拟，研究了密度极值导致的NOB-I效应对圆筒Rayleigh-Bénard（RB）对流和方腔RB对流的影响，发现圆筒RB对流中两类轴对称对流解的稳定性特征定性不同，获得了圆筒和方腔RB对流中的若干普适规律；（2）通过数值模拟，研究了NOB-II效应对二维方腔RB对流中流动反转的影响，发现了流动反转的新形式，与传统的流动反转在大尺度动力学行为上存在本质的不同，阐释了具有NOB-II效应时流动反转的动力学机制；（3）结合数值模拟和稳定性分析，揭示了含NOB-II效应的方腔RB对流的稳定性和非线性演化特性，发现NOB-II效应对线性稳定性和非线性演化的影响敏感地依赖于系统尺寸；（4）使用小马赫数方程数值研究了具有NOB-II效应的二维侧加热对流，发现靠近热板的速度边界层和温度边界层都变薄，中心温度有所提高，但是整体输运量对NOB-II效应很不敏感；（5）基于完全可压缩方程，通过线性稳定性分析研究了快速旋转球环中可压缩流体的对流失稳过程，发现其失稳过程对Prandtl数(Pr)和密度分层强度很敏感，得到了新的失稳模态，并证明了密度分层较强时滞弹性近似可能会失效。