论文标题
使用Oldroyd-B模型表征三维冯·卡曼漩涡流中的弹性湍流
Characterizing elastic turbulence in the three-dimensional von Karman swirling flow using the Oldroyd-B model
论文作者
论文摘要
我们使用Oldroyd-B模型介绍了两个平行板之间von Karman旋转流的完整三维数值研究，并表征了弹性湍流的发作和发展。我们用次级流强度量化流量状态，这是速度波动的平均强度的度量，然后将订单参数定义为次级流强度的时间平均值。该顺序参数显示了从层流到可见的流动的亚临界过渡，该流量在弱混沌流和弹性湍流之间切换。到Biscable流的过渡发生在关键的Weissenberg Number $ \ Mathrm {Wi_c} = 12 $。高于$ \ mathrm {wi_c} $，在弹性湍流状态下，我们观察到速度波动和流动电阻的强烈增加，我们将其定义为在流体上执行的总工作。在湍流状态下启动模拟并随后将$ \ mathrm {Wi} $降低到其临界值以下时，我们观察到顺序参数和流动电阻的滞后行为，这是亚临界过渡的共同特征。在实验中也发现了滞后。此外，我们发现速度波动的空间和时间功率光谱中的幂律缩放，这是弹性湍流的特征。我们的模拟中幂律指数的最大值为$α_t= 3.41 $的时间指数，空间指数的$α_s= 3.17 $，它们非常接近实验中获得的值。
We present the full three-dimensional numerical investigation of the von Karman swirling flow between two parallel plates using the Oldroyd-B model and characterize the onset and development of elastic turbulence. We quantify the flow state with the secondary-flow strength, a measure of the average strength of the velocity fluctuations, and then define an order parameter as the time average of the secondary-flow strength. The order parameter displays a subcritical transition from the laminar to a bistable flow that switches between weakly chaotic flow and elastic turbulence. The transition to the bistable flow occurs at the critical Weissenberg number $\mathrm{Wi_c}=12$. Above $\mathrm{Wi_c}$, in the elastic turbulent state, we observe a strong increase in velocity fluctuations and flow resistance, which we define as the total work performed on the fluid. Upon starting simulations in the turbulent state and subsequently lowering $\mathrm{Wi}$ below its critical value, we observe hysteretic behavior in the order parameter and the flow resistance, which is a common feature of a subcritical transition. Hysteresis has also been found in experiments. Additionally, we find power-law scaling in the spatial and temporal power spectra of the velocity fluctuations, characteristic for elastic turbulence. The maximum values of the power-law exponents in our simulations are $α_t= 3.41$ for the temporal exponent and $α_s= 3.17$ for the spatial exponent, which are remarkably close to the values obtained in experiments.
