高聚物弹性效应驱动的弹性湍流的直接数值模拟研究

In this project, numerical study of Elastic Turbulence (ET) driven by polymer elasticity is proposed by using of Direct Numerical Simulation (DNS), aimed to reveal the basic physics of complicated fluid motion and turbulent mixing in elastic turbulence. This study is mainly focused on the following research topics: development of a high-efficiency parallelized algorithm for high-order accurate, stable and reliable calculation of elastic turbulence, which guarantees the mathematic properties of ET governing equations and conformation tensor; study of turbulence features subjected to the variation of flow parameter, external forcing and boundary conditions, based on the DNS of typical ET problems; study of passive scalar transport dynamics in ET based on the DNS of scalar transport equation, and study of the effect of turbulent fluid motion on scalar fluctuation and turbulent mixing as well; extensive study of the ET dynamics and physics based on the post-processing of massive DNS calculations, such as the dynamic processes of generation of fluid turbulent kinetic energy, energy exchange between fluid motion and polymer extension, energy transfer between large- and small-scale motions, energy dissipation of small-scale motion, dynamic feature of elastic stress boundary layer and its relevance to drag increase, transport processes of elastic stress and passive scalar, generation and evolution processes of coherent vortices and their influence on elastic stress distribution, temporal and space correlation functions of turbulence fluctuations, effects of coherent vortices on turbulent mixing efficiency, and so on.

本项目着重开展高聚物弹性效应驱动的弹性湍流的直接数值模拟(DNS)研究，探讨这类湍流的复杂流动机理和湍流掺混传热机制。研究内容主要包括：综合考虑弹性湍流控制方程和构型张量的数学性质，发展适用于弹性湍流数值模拟的高精度、稳定可靠的高效并行算法；通过弹性湍流典型问题的DNS计算，研究流动控制参数、外加激励力和边界条件对湍流特性的影响；引入标量输运方程，DNS计算研究弹性湍流中标量输运的动力学过程、湍流特性对标量分布规律和脉动特性的影响，探讨其中的湍流掺混脉动传热机制；开展大规模的DNS计算，进行弹性湍流的机理性研究，如脉动能量的生成、流体和高聚物之间的能量交换、不同尺度运动之间的能量传递、能量的小尺度耗散作用、弹性应力边界层与增阻现象、弹性应力及被动标量的输运过程、拟序涡的生成及演化对弹性应力分布的影响、脉动量的时空相关特性、拟序涡的湍流掺混传热作用；等等。

在本项目资助下重点开展了高聚物弹性效应驱动的弹性湍流的直接数值模拟(DNS)研究，以及相关复杂湍流机理和湍流掺混传热的数值模拟研究，主要进行了如下几个方面的研究：弹性效应作用下的复杂湍流的数值模拟方法研究；Taylor-Couette (TC) 流动中高聚物弹性驱动的弹性湍流特性和非线性流态转换(低Re数)研究；高聚物弹性诱导的TC湍流特性和流动机理(高Re数)研究；径向加热TC流动的高阶非线性湍流转捩和湍流传热机制研究；拓展研究了附着于行波摆动翼型尾端的平板长度对推进性能的影响。本项研究取得了以下研究成果：发展了求解高聚物弹性效应作用下的复杂湍流的高精度三维全隐谱方法、以及相关的高效可靠并行算法；首次通过直接数值模拟TC流动再现了弹性效应驱动的弹性湍流基本特征，尤其是在中心区域精确计算预测了实验观测到的径向速度脉动的频谱特性；首次通过直接数值模TC湍流发现了弹性效应诱导的大尺度Taylor涡破碎和阻力剧增现象，并提出了合理的物理解释：惯性-弹性Görtler失稳机制；在径向加热TC流动中发现了浮力驱动的高阶非线性湍流转捩过程，揭示浮力效应和外柱旋转均导致的湍流传热主导机制由大尺度环流传热转变为小尺度湍流脉动传热；通过流固耦合数值模拟揭示了平板长度对推进性能(包括推力、能耗和推进效率)的影响规律，发现了对应于不同平板长度的三种典型鱼游推进模态：体力占优模态、体力和尾鳍力竞争模态和尾鳍力占优模态，以及不同模态下的动力学特性和流动结构。