Modelling the attenuation of laminar fluid transients in piping systems

The damping of laminar fluid transients in piping systems is studied numerically using a two-dimensional water hammer model. The numerical scheme is based on the classical fourth order Runge–Kutta method for time integration and central difference expressions for the spatial terms. The results of the present method show that the damping of transients in piping systems is governed by a non-dimensional parameter representing the ratio of the Joukowsky pressure force to the viscous force. In terms of time scales, this non-dimensional parameter represents the ratio of the viscous diffusion time scale to the pipe period. For small values of this parameter, the damping of the fluid transient becomes more pronounced while for large values, the fluid transient is subjected to insignificant damping. Moreover, the non-dimensional parameter is shown to influence other important transient phenomena such as line packing, instantaneous wall shear stress values and the Richardson annular effect.