标题： 格子玻尔兹曼模拟揭示了四辊研磨机中幂律流体流动模式转变中的超临界分叉 显示英文标题

标题： Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill

摘要： 四辊轧机传统上被视为产生简单拉伸流的装置，具有中心停滞点。 我们使用两弛豫时间正则化格子玻尔兹曼（TRT-RLB）模型进行系统研究，揭示了流动物理的意外丰富性，识别出两种此前未报道的超临界分叉模式：一种是四叶形涡旋模式，具有四个对称的反向旋转涡旋，另一种是哑铃形四涡旋模式，其中涡旋从停滞点分离但仍关于停滞点对称。 数值框架代表了TRT-RLB方法首次成功扩展到幂律流体动力学，能够全面映射雷诺数（$1 \leq Re \leq 50$）、幂律指数（$0.7 \leq n \leq 1.3$）和几何构型的流动特性。 四叶形涡旋模式的转变表现出不同的路径，这取决于幂律指数：在相对较小的$n$时，流动直接发生超临界分叉转变为简单拉伸流；而在相对较大的$n$时，它会经历一个中间的哑铃形状态。 在几何参数中，滚筒半径$r$成为控制分叉点和涡旋尺寸的主要因素，而滚筒-容器间隙$\delta$对流动模式的影响极小。 通过停滞点处涡旋尺寸和速度梯度的变化，可以精确表征流动模式之间的转变，为流动模式识别提供定量标准。 这些发现丰富了我们对拉伸装置中分叉现象的基本理解，并为在四辊轧机应用中实现期望的流动模式提供了定量指导。 显示英文摘要

摘要： The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers ($1 \leq Re \leq 50$), power-law indices ($0.7 \leq n \leq 1.3$), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small $n$, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large $n$, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius $r$ emerges as the dominant factor controlling bifurcation points and vortex dimensions, whereas the roller-container gap $\delta$ exerts minimal influence on flow regimes. The transitions between flow modes can be precisely characterized through the evolution of vortex dimensions and velocity gradients at the stagnation point, providing quantitative criteria for flow regime identification. These findings enrich our fundamental understanding of bifurcation phenomena in extensional devices and provide quantitative guidelines for achieving desired flow patterns in four-roll mill applications.