基于环境湍浮力流物理机理的显式代数应力模型研究

Turbulent buoyant flow exists extensively, general turbulent model can hardly simulate such phenomenon accouting for bouyancy, and the implicit solver of the algebraic stress model (ASM) has a large calculation times and may easily lead to numerical singularity. In present study, theoretical analysis, numerical simulation and classic case verification are considered to explore explicit algebraic stress model (EASM) accouting for buoyancy with clearly physical mechanism and stable numerical performance,the main studies include: (1) Deduce explicit algebraic Reynolds stress expression based on the main and basic independent tensors by introduction of the turbulent buoyancy tensor; (2) Derive explicit algebraic active scalar flux expression accounting for bouyancy based on Wikstr?m's nondimensional method in framework of implicit ASM model; (3) Analyze every part contribution of the explicit algebraic Reynolds stress expression and explicit algebraic active scalar flux expression quantitively, and then propose a series of simplified EASM models; (4) Couple the new EASM models into an unstructured 3D model based on SIMPLE algrithm and high accuracy numerical schemes including advective flux,diffusive flux and then verify the precision, efficiency and robustness of the EASM models by using series of experiment data on thermal stratified gravity flow, Calcuation data of heated plane flow by DNS model;(5)At last, a new general simple EASM model accounting for bouyancy is hopeful to be proposed and related sensitive model parameters value will be optimized. Research can not only promote the theory development of universal turbulent buoyant flow model, but also provide a new and effective way to accurately describe the mass transport of the turbulent buoyancy flow, thus has great significance in engineering design, ecological and environmental protection.

针对湍浮力流动广泛存在且一般湍流模型难以有效模拟、隐式代数应力模型求解计算量大且易造成数值奇异等缺陷，本项目拟采用理论分析、数值模拟和实例验证等手段探索物理机理明晰且数值性能稳定的环境湍浮力流显式代数应力模型(EASM)，主要研究内容包括:引入湍浮力张量，构造基本独立张量及其独立不变量，推导计及浮力效应的显式雷诺应力代数式；借鉴Wikstr?m等人思想，推求显式主动标量通量代数式；分析雷诺应力和标量通量代数式各项贡献大小，提出各种简化的EASM模型，并将诸模型集成在基于非结构网格Simple解法和对流扩散高精度离散格式中；结合重力流下潜试验及加热平板流DNS结果，分析EASM模型的精度、效率及鲁棒性，并优化敏感性模型参数取值，提出经济实用的EASM模型。研究成果可从理论上推动通用湍浮力流模型发展，亦可为准确描述湍浮力流物质输运扩散规律提供新的有效途径，对工程设计和生态环境保护具有重要意义。

针对湍浮力流动广泛存在且一般湍流模型难以有效模拟、隐式代数应力模型求解计算量大且易造成数值奇异等缺陷，本项目采用理论分析、数值模拟和实例验证等手段探索物理机理明晰且数值性能稳定的环境湍浮力流显式代数应力模型(EASM)，主要研究内容包括:引入湍浮力张量，构造基本独立张量及其独立不变量，推导计及浮力效应的显式雷诺应力代数式；借鉴Wikström等人思想，推求显式主动标量通量代数式；分析雷诺应力和标量通量代数式各项贡献大小，提出各种简化的EASM模型，并将诸模型集成在基于非结构网格Simple解法和对流扩散高精度离散格式中；结合重力流下潜试验及加热平板流DNS结果，分析EASM模型的精度、效率及鲁棒性，并优化敏感性模型参数取值，提出经济实用的EASM模型。研究成果可从理论上推动通用湍浮力流模型发展，亦可为准确描述湍浮力流物质输运扩散规律提供新的有效途径，对工程设计和生态环境保护具有重要意义。