Axisymmetric Weakly Compressible Transient Pipe Flow and Water Hammer Control

摘要

The transient flow in a long cylindrical pipe caused by the motion of a valve is a subject of significant interest in wide engineering applications. Despite the partial success of existing theoretical models in explaining certain transient flow phenomena, they can hardly predict the evolution of strong water hammer, in particular the one downstream the valve caused by its closing (reversed water hammer). We attack this important problem by a new theory based on the unsteady axisymmetric and compressible Navier-Stokes equations, so that the viscous effect and inevitable coupling between the pressure wave and vortical wave can be fully taken into account. The weak compressibility of water naturally permits applying perturbation approach, of which the leading-order transient solution is found to be in excellent agreement with the result of direction simulation of the original N-S equation. We establish a simple connection between the valve motion and adjacent pressure in reversed water hammer, which enables the optimization of the valve motion to minimize the strength of the water hammer. Extension of the present laminar theory to turbulent flow with cavitation is being investigated and will be reported elsewhere.