标题： 非牛顿流体的湍流管道流动 显示英文标题

标题： Turbulent Pipe Flow of Thixotropic Fluids

摘要： 具有内部微观结构的复杂材料，如悬浮液和乳液，表现出时间依赖的流变性，其特征是粘弹性与触变性。 在许多大规模应用中，如湍流管道流动，弹性响应发生的时间尺度远小于触变性，因此这些流动是纯粹的触变性。 触变性湍流的基本动力学尚不明确，特别是微观结构状态、流变性和湍流结构之间的相互作用。 为解决这一问题，我们对一种模型触变性（Moore）流体在一系列触变粘度数$\Lambda$的充分发展湍流管道流动进行了直接数值模拟（DNS），从相对于涡旋翻转时间较慢（$\Lambda\ll 1$）到较快（$\Lambda\gg 1$）的触变动力学。 在拉格朗日框架中对DNS结果的分析显示，正如预期的那样，在慢速和快速动力学极限下，这些时间依赖的流动表现为时间不变的纯粘性（广义牛顿型）类似物。 对于中间动力学（$\Lambda\sim 1$），流变性由触变衰减记忆核在拉格朗日剪切历史分布上的\emph{路径积分}所决定，后者通过一个简单的随机模型来模拟径向非平稳的管道流动。 基于这种有效粘度闭合的DNS计算与完全触变性模型在$\Lambda=1$上表现出极好的一致性（误差在2.4%以内），表明纯粘性（广义牛顿型）类似物在任意$\Lambda\in[0,\infty^+)$值和跨非线性流变模型的情况下仍然存在。 这些结果揭示了微观结构、流变性和湍流之间的反馈机制，并为触变性湍流的结构提供了基本见解。 显示英文摘要

摘要： Complex materials with internal microstructure such as suspensions and emulsions exhibit time-dependent rheology characterized by viscoelasticity and thixotropy. In many large-scale applications such as turbulent pipe flow, the elastic response occurs on a much shorter timescale than the thixotropy, hence these flows are purely thixotropic. The fundamental dynamics of thixotropic turbulence is poorly understood, particularly the interplay between microstructural state, rheology, and turbulence structure. To address this gap, we conduct direct numerical simulations (DNS) of fully developed turbulent pipe flow of a model thixotropic (Moore) fluid over a range of thixoviscous numbers $\Lambda$ from slow ($\Lambda\ll 1$) to fast ($\Lambda\gg 1$) thixotropic kinetics relative to the eddy turnover time. Analysis of DNS results in the Lagrangian frame shows that, as expected, in the limits of slow and fast kinetics, these time-dependent flows behave as time-independent purely viscous (generalized Newtonian) analogues. For intermediate kinetics ($\Lambda\sim 1$), the rheology is governed by a \emph{path integral} of the thixotropic fading memory kernel over the distribution of Lagrangian shear history, the latter of which is modelled via a simple stochastic model for the radially non-stationary pipe flow. DNS computations based on this effective viscosity closure exhibit excellent agreement (within 2.4\% error) with the fully thixotropic model for $\Lambda=1$, indicating that the purely viscous (generalized Newtonian) analogue persists for arbitrary values of $\Lambda\in[0,\infty^+)$ and across nonlinear rheology models. These results uncover the feedback mechanisms between microstructure, rheology, and turbulence and offer fundamental insights into the structure of thixotropic turbulence.