van Buel Reinier, Stark Holger
Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstrasse 36, 10623, Berlin, Germany.
Sci Rep. 2020 Sep 24;10(1):15704. doi: 10.1038/s41598-020-72402-y.
We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor-Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations, one form of active open-loop control. Slow modulations display rich and complex behavior where elastic turbulence is still present, while it vanishes for fast modulations and a laminar response with the Taylor-Couette base flow is recovered. We find that the transition from the laminar to the turbulent state is supercritical and occurs at a critical Deborah number. In the state diagram of both control parameters, Weissenberg versus Deborah number, we identify the region of elastic turbulence. We also quantify the transition by the flow resistance, for which we derive an analytic expression in the laminar regime within the linear Oldroyd-B model. Finally, we provide an approximation for the transition line in the state diagram introducing an effective critical Weissenberg number in comparison to constant shear. Deviations from the numerical result indicate that the physics behind the observed laminar-to-turbulent transition is more complex under time-modulated shear flow.
我们通过在二维泰勒 - 库埃特几何结构中对Oldroyd - B模型的数值解证明，粘弹性流体中弹性湍流的起始可以通过施加剪切速率调制来控制，这是一种主动开环控制形式。缓慢调制呈现出丰富而复杂的行为，此时弹性湍流仍然存在，而快速调制时弹性湍流消失，恢复为具有泰勒 - 库埃特基流的层流响应。我们发现从层流到湍流状态的转变是超临界的，并且发生在临界德博拉数处。在两个控制参数（魏森贝格数与德博拉数）的状态图中，我们确定了弹性湍流区域。我们还通过流动阻力对转变进行了量化，为此我们在线性Oldroyd - B模型的层流区域中推导了一个解析表达式。最后，与恒定剪切相比，我们通过引入一个有效临界魏森贝格数，给出了状态图中转变线的近似值。与数值结果的偏差表明，在时间调制剪切流下，观察到的层流到湍流转变背后的物理过程更为复杂。
