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Time evolution of water surface oscillations in surge tanks

机译：调压罐中水面振荡的时间演变

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Time evolution of water surface oscillations in surge tanks is of importance in pipeline and hydropower engineering, and is often solved graphically or numerically because the associated nonlinear second order ordinary differential equation, with a quadratic damping term, cannot be solved exactly. This research then innovates an accurate approximation based on the Lambert function, Pade approximant, and elliptic integral. Specifically, (i) the characteristic length depends on the pipe-tank geometry, the system resistance, and an unsteady factor; and the characteristic time depends on the pipe-tank geometry, the gravity, and the unsteady factor, but independent of the system resistance; (ii) the surge transit squared velocity is approximated by a Pade approximant of order [2/1], resulting in a simple approximation for the surge tank water surface oscillations in terms of an elliptic integral of the second kind; and (iii) the approximate solution accurately reproduces numerical and laboratory data thereby being applicable in practice.
机译：调压罐中水面振荡的时间演化在管道和水电工程中非常重要，由于无法精确求解带有二次阻尼项的相关联的非线性二阶常微分方程，因此经常以图形或数字方式求解。然后，这项研究基于Lambert函数，Pade近似值和椭圆积分，创新了一种精确的近似值。具体来说，（i）特征长度取决于管箱的几何形状，系统阻力和不稳定因素；特征时间取决于管道箱的几何形状，重力和不稳定因素，但与系统阻力无关； （ii）喘振通过速度的平方近似为[2/1]阶次的Pade近似值，从而以第二种椭圆积分形式简单地近似了喘振罐水面的振荡； （iii）近似解可以准确地再现数值和实验室数据，从而可以在实践中应用。

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