湍流双流体模型基于EMMS原理的改进及应用

Turbulent flow exists widely in engineering and nature, and is one of the most difficult problems in classical physics. Single-fluid turbulence model is one of the main ways to solve the engineering turbulence problems, but it is difficult to describe the character of fluid in computational domain. Spalding regarded turbulent flow as a two-phase flow problem consisted by turbulent fluid and non-turbulent fluid, then proposed the two-fluid model of turbulence and realized the description of different character of fluid in computational domain. However, it is hard to compute the mass, momentum and energy transfer accurately between turbulent fluid and non-turbulent fluid in the two-fluid model of turbulence, influencing the description of character of fluid in computational domain. With the help of split-phase idea in the two-fluid model of turbulence, this project uses the multi-scale analysis method to decompose turbulent flow, and the structure parameters to describe the system state are introduced. Subsequently, the corresponding conservative equations are constructed, and the stability condition of turbulent flow based on the EMMS principle is used to optimize the structure parameters of turbulent flow. Further, the mass, momentum and energy transfer in the two-fluid model of turbulence can be improved, by analyzing the relation between it and the structure parameters of turbulent flow. That is to say, the corresponding EMMS-type formulations of mass, momentum and energy transfer can be established which have some universality and high accuracy, leading to that the engineering turbulent flow can be simulated accurately. Through the research of this project, it will be possible to explore the intrinsic relationship from the structure character of turbulent flow to the mass, momentum and energy transfer between turbulent fluid and non-turbulent fluid, and then provide a scientific basis for improving the accuracy of the two-fluid model of turbulence in simulating the engineering turbulence problems.

湍流广泛存在于工程领域和自然界，是经典物理学最困难问题之一。单流体湍流模型是解决工程湍流问题的一个主要途径，但难以描述计算区域的流体特性。Spalding视湍流为湍流流体和非湍流流体组成的两相流问题，提出湍流双流体模型，实现计算区域不同流体特性的描述。然而，该模型中相间质量、动量和能量交换关系难以准确计算，影响了流体特性的描述。本项目借助湍流双流体模型的分相思想，采用多尺度分析方法分解湍流，引入描述系统状态的结构参数，构建守恒方程，用基于EMMS原理的湍流稳定性条件优化出结构参数。通过分析与结构参数的关系，改进湍流双流体模型已有的质量、动量和能量交换，建立具有普适性和高精度的EMMS型质量、动量和能量交换关系式，实现工程湍流问题高精度模拟。通过本项目研究，将探索出湍流流动结构特征与湍流流体和非湍流流体间质量、动量和能量交换的内在联系，为改进湍流双流体模型模拟工程湍流问题的精度提供科学依据。

湍流广泛存在于工程领域和自然界，是经典物理学中一个有关复杂系统的难题，亟待解决。介科学的EMMS原理认为复杂系统的复杂性物理上都归因于不同主导控制机制在竞争中的协调。因此，EMMS原理给湍流研究带来了新的认识，基于EMMS原理研究湍流流动有望改善当前湍流模拟的精度。本项目主要探讨了如何将EMMS原理用于湍流流动的研究。首先，基于圆管湍流流动问题，数值验证了惯性耗散趋于最大而粘性耗散趋于最小是湍流流动的一对主导控制机制；其次，针对主导控制机制的竞争中协调，在主导控制机制同等重要的认识下，基于气固EMMS模型对其进行了数学公式上的表述；随后，明确了对于任意一个复杂系统，其主导控制机制具有唯一性。在这些工作的基础上，实现了圆管湍流基于EMMS原理的研究。通过上述各方面的工作，解决了将EMMS原理用于湍流流动研究的一些关键的基本问题，如湍流流动主导控制机制的辨识、主导控制机制间竞争中协调的量化、主导控制机制唯一性等。特别地，主导控制机制间竞争中协调数学表述的提出，为将EMMS原理用于任意复杂系统的研究提供了一个可行的数学工具，推动了介科学的进一步发展。