Transient Interface Shape of a Two-Layer Liquid in an Abruptly Rotating Cylinder
Transient Interface Shape of a Two-Layer Liquid in an Abruptly Rotating Cylinder
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突然旋转圆柱体中两层液体的瞬态界面形状
DOI：
10.1115/1.2910142
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
J. Hyun
中科院分区：
文献类型：
--
作者：
T. Lim;Sangmin Choi;J. Hyun
描述了突然旋转的圆柱体中两层液体界面的瞬时形状。下层的密度高于上层的密度，但粘度可以取任意值。整体埃克曼数远小于1，圆柱体纵横比为0（1）。经典的Wedemeyer模型，其中涉及的自旋从静止的均匀流体，扩展到处理两层液体系统。如果上层流体具有较高的粘度，则界面在小的和中等的时间在中心（外围）上升（下沉）。在中心达到最大高度后，界面趋于抛物线形状特征的最终状态刚体旋转。如果下层流体具有较高的粘度，则界面在小的和中间的时间在中心（外围）下沉（上升）。中心处的变形达到最小高度，之后界面接近终态抛物线。粗调过程在自旋加速时间尺度E[sub n][sup [minus]1/2][Omega][sup [minus]1]上完成，其中E[sub n]和[Omega]分别表示两个层的埃克曼数的较低值和圆柱形容器的角速度。这些解释与前面提出的物理解释是一致的。通过转台实验对瞬态界面形状进行了描述。界面形态的模型预测与实验室测量结果符合良好。«少
A description is made of the transient shape of interface of a two-layer liquid in an abruptly rotating circular cylinder. The density of the lower layer is higher than that of the upper layer, but the viscosities may assume arbitrary values. The overall Ekman number is much smaller than unity, and the cylinder aspect ratio is 0(1). The classical Wedemeyer model, which deals with the spin-up from rest of a homogeneous fluid, is extended to tackle the two-layer liquid system. If the upper layer fluid is of higher viscosity, the interface, at small and intermediate times, rises (sinks) in the center (periphery). After reaching a maximum height at the center, the interface tends to the parabolic shape characteristic of the final-state rigid-body rotation. If the lower-layer fluid is of higher viscosity, the interface, at small and intermediate times, sinks (rises) in the center (periphery). The deformation at the center reaches a minimum height, after which the interface approaches the final-state parabola. The gross adjustment process is accomplished over the spin-up time scale, E[sub n][sup [minus]1/2][Omega][sup [minus]1], where E[sub n] and [Omega] denote the lower value of the Ekman numbers of the two layers and the angular velocity of the cylindricalmore » container, respectively. These depictions are consistent with the physical explanations offered earlier. A turntable experiment is performed to portray the transient interface shape. The model predictions of the interface form are in satisfactory agreement with the laboratory measurements.« less