On the Propagation and Attenuation of Turbulent Fluid Transients in Circular Pipes

Abstract

The attenuation of turbulent fluid transients in pipes is numerically investigated in the present study using one-dimensional (1D) and two-dimensional (2D) water hammer models. The method of characteristics (MOC) is used for the integration of the 1D model, while the semidiscretization approach and the fourth-order accurate Runge–Kutta method are used for the integration of the 2D model. The present results for a reservoir–pipe–valve system indicate that the damping of the transient is governed by a nondimensional parameter representing the ratio of the steady-state frictional head to the Joukowsky pressure head. Based on this parameter, the attenuation of the transient could be classified into three main categories. The first category is for values of the nondimensional parameter much smaller than unity, where attenuation of the transient is insignificant and line packing effects are negligible. The second category is for values of the parameter approaching unity, where the attenuation of the transient is significant and line packing results in a pressure rise at the valve that is slightly higher than the Joukowsky pressure rise. The third category is for values of the parameter much greater than unity, such as in long cross-country pipelines, where the transient is damped out within a few cycles and excessive line packing effects would result in a pressure rise at the valve that is significantly larger the Joukowsky pressure rise.