粘弹性流体Taylor-Couette湍流的直接数值模拟及机理研究

In this project, investigation on turbulent Taylor-Couette flows in a viscoelastic fluid is proposed by using of Direct Numerical Simulation (DNS), aimed to explore the complicated flow physics and energy exchange/transfer mechanism special for this class of fluid flows. This study is mainly focused on the following research issues: development of a high-efficiency, parallelized algorithm required for high-order accurate, stable and reliable calculations of turbulent viscoelastic TC flows, which necessarily guarantees the mathematic properties of the governing equations and conformation tensor; study of the flow dynamics and turbulence features in response to the variations of flow parameter, external forcing and boundary conditions, based on the DNS of some prototype problems; extensive study of the underlying turbulence dynamics and flow physics based on the post-processing of the massive DNS calculations, such as the turbulent transport carried by the fluctuating motions that are subjected to the coupling effects of the fluid inertia and elasticity, and the curvature of flow geometry as well, temporal and spatial characteristics of the turbulence fluctuations and elastic stresses, formation and evolution of the coherent vortices and the resulting influence on the elastic stress distribution, the coupling dynamics of the turbulent and elastic boundary layers and its relevance to the drag enhancement, generation and dissipation of the turbulent kinetic energy, energy cascade and damping in the large- and small-scale motions, storing and releasing processes for the elastic energy, exchange between the kinetic and elastic energy of the fluid motions, energy transfer carried by the coherent vortices, and so on.

本项目着重开展粘弹性流体Taylor-Couette（TC）湍流的直接数值模拟(DNS)及机理研究，探讨这类复杂湍流的特殊流动机理和能量转换机制。研究内容主要包括：综合考虑粘弹性流体TC湍流控制方程和二阶构形张量的数学性质，发展相关的稳定可靠、快速高效的高精度并行算法；通过粘弹性流体TC湍流的DNS计算，研究流动控制参数、外加激励力和边界条件对动力学过程和湍流特性的影响；开展大规模的DNS计算，进行粘弹性流体TC湍流的机理性研究，如流体惯性和弹性效应、以及曲率效应耦合作用下的脉动输运过程、流体脉动和弹性应力的时空特性、拟序涡的生成和演化对弹性应力分布的影响、湍流和弹性应力边界层耦合作用与增阻现象、脉动能量的生成和耗散、大/小尺度运动的能量级串和衰减、弹性势能的积聚和释放、流体动能和弹性势能的相互交换过程、拟序涡的能量输运作用等

在本项目资助下重点开展了粘弹性流体Taylor-Couette (TC)湍流的直接数值模拟(DNS)研究，以及相关的粘弹性流体流固耦合和TC湍流减阻的数值模拟研究，主要进行了如下几个方面的研究：低Re数的弹性-惯性TC湍流转捩问题，以及高Re数下的粘弹性流体TC湍流问题，首次研究了粘弹性流体平板Couette湍流减阻及能量级串问题，拓展研究了粘弹性流体的流固耦合问题和液滴冲击疏水壁面问题、具有超疏水内壁的TC湍流减阻问题、径向加热TC流动的高阶非线性湍流转捩和湍流传热问题等。本项研究取得了以下研究成果：考察了流体惯性和弹性效应相对强弱的变化对TC流动转捩的影响，重现了粘弹性TC流动的多种典型流态，发现了在历经不同路径出现的多态现象；在高Re数的粘弹性TC湍流增阻问题中，发现弹性效应可使TC湍流的生成机制由离心力失稳主导转变成由湍流剪切失稳主导；发现粘弹性平板Couette湍流在近壁区具有典型的湍流减阻特征，而在中心区域则存在弹性势能和湍动能之间巨大能量交换导致的高聚物剧烈拉伸；发现了粘弹性效应对自由来流中柔性丝线摆动的抑制作用，以及对液滴冲击疏水壁面回弹过程的抑制作用；模拟验证了修正的普朗特-冯卡门摩擦律在超疏水TC湍流中的假设；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。