Yuan Chao, Zhang Hong-Na, Chen Li-Xia, Zhao Jun-Long, Li Xiao-Bin, Li Feng-Chen
School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510006, China.
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China.
Entropy (Basel). 2020 Jan 3;22(1):64. doi: 10.3390/e22010064.
The cross-slot geometry plays an important role in the study of nonlinear effects of viscoelastic fluids. The flow of viscoelastic fluid in a micro cross-slot with a high channel aspect ratio (, the ratio of channel depth to width) can be divided into three types, which are symmetric flow, steady-state asymmetric flow and time-dependent flow under the inlet condition with a constant velocity. However, the flow pattern of a viscoelastic fluid in the cross-slot when a stimulation is applied at inlets has been rarely reported. In this paper, the response of cross-slot flow under an external sinusoidal stimulation is studied by numerical simulations of a two-dimensional model representing the geometry with a maximum limit of . For the cases under constant inlet velocity conditions, three different flow patterns occur successively with the increase of Weissenberg number (). For the cases under sinusoidal varying inlet velocity conditions, when the stimulation frequency is far away from the natural frequency of a viscoelastic fluid, the frequency spectrum of velocity fluctuation field shows the characteristics of a fundamental frequency and several harmonics. However, the harmonic frequency disappears when the stimulation frequency is close to the natural frequency of the viscoelastic fluid. Besides, the flow pattern shows spatial symmetry and changes with time. In conclusion, the external stimulation has an effect on the flow pattern of viscoelastic fluid in the 2D micro cross-slot channel, and a resonance occurs when the stimulation frequency is close to the natural frequency of the fluid.
十字槽几何形状在粘弹性流体非线性效应的研究中起着重要作用。在具有高通道纵横比（通道深度与宽度之比）的微十字槽中，粘弹性流体的流动在入口速度恒定的条件下可分为三种类型，即对称流、稳态非对称流和时变流。然而，当在入口处施加激励时，粘弹性流体在十字槽中的流动模式鲜有报道。本文通过对一个二维模型进行数值模拟，研究了外部正弦激励下十字槽流动的响应，该模型表示的几何形状的最大尺寸为 。对于入口速度恒定的情况，随着魏森贝格数（ ）的增加，依次出现三种不同的流动模式。对于入口速度正弦变化的情况，当激励频率远离粘弹性流体的固有频率时，速度波动场的频谱呈现基频和若干谐波的特征。然而，当激励频率接近粘弹性流体的固有频率时，谐波频率消失。此外，流动模式呈现空间对称性并随时间变化。总之，外部激励对二维微十字槽通道中粘弹性流体的流动模式有影响，当激励频率接近流体的固有频率时会发生共振。
