Regime transitions in stratified shear flows: the link between horizontal and inclined ducts
Regime transitions in stratified shear flows: the link between horizontal and inclined ducts
复制标题
分层剪切流中的状态转变：水平和倾斜管道之间的联系
DOI：
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发表时间：
2020
影响因子：
3.7
通讯作者：
H. Clercx
中科院分区：
文献类型：
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作者：
M. Duran‐Matute;S. J. Kaptein;H. Clercx
本文给出了层流分层斜管(SID)流动的二维速度场和密度场的解析解，其中沿流道动量方程中扩散占主导地位，而密度输运方程中扩散占主导地位。由于控制方程中的领先平衡，我们将这种近似称为动量平流和密度平流的流体静力/引力/粘性(HGV-A)近似。该解析解适用于长管极限内两层结构的层流流动。在HGV-A近似下，无因次体积通量由以下公式给出：$Fr^*={{Re}}_g/(Ak)$，它是一个控制参数，其中${Re}_g$是重力雷诺数，$A$是管道的展宽比，而$K是由解析解得到的依赖于管道倾角的几何参数。这一解析解与实验室实验的结果进行了验证，使我们能够对SID流动的动力学和特性有新的了解。最重要的是，在水平和倾斜管道中，恒定值$Fr^*都描述了日益湍动的流动状态之间的转变：从层流到界面波，再到间歇湍流和持续湍流。
Abstract We present the analytical solution for the two-dimensional velocity and density fields within an approximation for laminar stratified inclined duct (SID) flows where diffusion dominates over inertia in the along-channel momentum equation but is negligible in the density transport equation. We refer to this approximation as the hydrostatic/gravitational/viscous in momentum and advective in density (HGV-A) approximation due to the leading balances in the governing equations. The analytical solution is valid for laminar flows in a two-layer configuration in the limit of long ducts. The non-dimensional volume flux within the HGV-A approximation is given by $Fr^* ={{Re}}_g/(AK)$, which is a control parameter with ${{Re}}_g$ the gravitational Reynolds number, $A$ the aspect ratio of the duct and $K$ a geometrical parameter that depends on the tilt of the duct and is obtained from the analytical solution. This analytical solution was validated against results from laboratory experiments, and allows us to gain new insight into the dynamics and properties of SID flows. Most importantly, constant values of $Fr^*$ describe, in both horizontal and inclined ducts, the transitions between increasingly turbulent flow regimes: from laminar flow, to interfacial waves, to intermittent turbulence and sustained turbulence.