Unsteady draining of reservoirs over weirs and through constrictions
Unsteady draining of reservoirs over weirs and through constrictions
复制标题
水库通过堰和狭窄处排水不稳定
作者：
Edward W. G. Skevington;A. Hogg
重力驱动的流体从水库的部分崩溃后，其限制大坝，或其限制锁的部分开放，使用非线性浅水方程组，耦合到流出条件，其中的排水模拟为流动收缩，宽顶堰。由此产生的不稳定运动揭示了系统的排水，在排水上施加了强烈的和相对较快的振荡。振荡在流出物和储层的不可渗透的后壁之间传播。这种动力学研究利用三种方法：速端技术产生准解析解，渐近分析在相对较晚的时间后，启动和数值积分的控制方程。速端图变换是用来找到精确的解决方案，在早期，揭示了从最初的静态条件下的流体排水，但反复产生的间隔期间，有恒定的深度和速度的区域相邻的边界。采用一种新的修正的多尺度渐近分析方法来确定极限排水率和波浪结构。结果表明，当障碍物的高度有限时，多余高度随t^{-2}$的变化而衰减，速度场随t^{-3}$的变化而衰减，并呈现出一种趋于恒定且相对较快的相速度的波动结构。在纯收缩的情况下，所有的流体最终都从水库中排出，运动调整到自相似状态，在这种状态下，速度场衰减为t^{-1}。围绕这个状态的振荡具有指数增长的周期。数值模拟与一种新的实现边界条件，他们确认速端解决方案，并提供数据的渐近结果。
The gravitationally driven flow of fluid from a reservoir following the partial collapse of its confining dam, or the partial opening of its confining lock, is modelled using the nonlinear shallow water equations, coupled to outflow conditions, in which the drainage is modelled as flow over a constricted, broad-crested weir. The resulting unsteady motion reveals systematic draining, on which strong and relatively rapid oscillations are imposed. The oscillations propagate between the outflow and the impermeable back wall of the reservoir. This dynamics is investigated utilising three methods: hodograph techniques to yield quasi-analytical solutions, asymptotic analysis at relatively late times after initiation and numerical integration of the governing equations. The hodograph transformation is used to find exact solutions at early times, revealing that from initially quiescent conditions the fluid drains and yet repeatedly generates intervals during which there are regions of constant depth and velocity adjacent to the boundaries. A novel modified multiscale asymptotic analysis designed for late times is employed to determine the limiting rate of draining and wave structure. It is shown that the excess height drains as $t^{-2}$ and, when the obstacle has finite height, the velocity field decays as $t^{-3}$ , and exhibits a wave structure that tends towards a constant and relatively rapid phase speed. In the case of a pure constriction, for which all the fluid ultimately drains out of the reservoir, the motion adjusts to a self-similar state in which the velocity field decays as $t^{-1}$ . Oscillations around this state have an exponentially increasing period. Numerical simulations with a novel implementation of boundary conditions are performed; they confirm the hodograph solution and provide data for the asymptotic results.