Water hammer prediction and control: the Green’s function method

Abstract

By Green's function method we show that the water hammer (WH) can be analytically predicted for both laminar and turbulent flows (for the latter, with an eddy viscosity depending solely on the space coordinates), and thus its hazardous effect can be rationally controlled and minimized. To this end, we generalize a laminar water hammer equation of Wang et al. (J. Hydrodynamics, B2, 51, 1995) to include arbitrary initial condition and variable viscosity, and obtain its solution by Green's function method. The predicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.

Study on the Settlement of Tunnel Bottom and Pressure of Rock Mass Based on Curved Beam on Elastic Foundation Theory

“…Optimal flow control of water hammer requires a forecasting model capable of predicting the non-uniform and unsteady water flow in space and time [14]. Analytical solution is still very useful because it helps to reach clear and in-depth physical understanding and also to provide sufficiently simple yet general and accurate tool for practical prediction and control [16]. However, previous analytical studies of water hammer are confined to sudden valve closing and frictionless pipe.…”

On the generalization of Calogero-Ahmed summation formulas

“…In the 1990s, these issues were also dealt with by Wang et al [14]. This group of authors presented an interesting integral-based solution, which was further investigated by Xuan et al [15]. Solutions analogous to Rich's solution were developed by Sobey [16] and Jović [17].…”