Proper Orthogonal Decomposition (POD) of the flow dynamics for a viscoelastic fluid in a four-roll mill geometry at the Stokes limit
Proper Orthogonal Decomposition (POD) of the flow dynamics for a viscoelastic fluid in a four-roll mill geometry at the Stokes limit
复制标题
DOI：
10.1016/j.jnnfm.2018.12.009
复制
发表时间：
2019-02-01
影响因子：
3.1
通讯作者：
Thomases, Becca
中科院分区：
文献类型：
--
作者：
Gutierrez-Castillo, Paloma;Thomases, Becca
数值模拟的粘弹性流体在斯托克斯极限与四辊轧机的背景力进行了在一定范围内的Weissenberg数（无量纲松弛时间）。对于小的Weissenberg数的流量是稳定的和对称的，但在增加的Weissenberg数（对应于增加的弹性或流动记忆时间），流量变得不稳定，导致各种时间演变到不同的周期性和非周期性的解决方案。这些动力学进行了分析，使用适当的正交分解（POD），提取弹性模式的能量系统的贡献。通过分解捕获的系统的时间行为表明，停滞点的运动驱动不同的流动转变。特别是，一个过渡到一个不对称的状态发生时，伸展停滞点失去其钉扎的背景强迫。当最初被强迫束缚在辊中心的驻点开始移动时，发生向更高频率模态动力学的进一步转变。这些驻点运动的相对频率是决定流动复杂性的一个关键因素，通过捕获系统中大部分能量所需的模式数量来衡量。即使当流动是更复杂的少量的模式是足以捕捉这些流量的时间演变，证明了有用的POD应用于粘弹性流体在零雷诺数。
Numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force were performed at a range of Weissenberg number (non-dimensional relaxation time). For small Weissenberg number the flow is steady and symmetric but upon increasing the Weissenberg number (corresponding to increased elasticity or flow memory time), the flow becomes unstable leading to a variety of temporal evolutions to different periodic and aperiodic solutions. These dynamics were analyzed using a Proper Orthogonal Decomposition (POD) that extracted elastic modes in terms of their contribution to the energy of the system. The temporal behavior of the system, captured by the decomposition, indicates that the motion of the stagnation points drives the different flow transitions. In particular, a transition to an asymmetric state occurs when the extensional stagnation points lose their pinning to the background forcing. A further transition to higher frequency modal dynamics occurs when the stagnation points that were initially tied by the forcing to the centers of the rolls, begin to move. The relative frequencies of the motion of these stagnation points is a critical factor in determining the complexity of the flow, measured by the number of modes needed to capture most of the energy in the system. Even when the flows are more complex a small number of modes is sufficient to capture the time evolution of these flows, demonstrating the usefulness of the POD applied to viscoelastic fluids at zero Reynolds number.