Modelling transient pipe flow with cavitation and frequency dependent friction. Part II. Friction and numerical-experimental validation

Modelling of time-depended hydraulic friction is not an easy issue. As numerous studies have shown, wall shear stress in the pipe can be determined as a sum of the quasi-steady and time-dependent expressions. Time-depended expression is an convolution integral of the local acceleration of the liquid and a weighting function. The weighting function, in general, makes allowance for relation of historic velocity changes and unsteady component of wall shear stress. The original weighting function has usually a very complicated structure, and what is more it makes impossible to do an efficient simulation of dynamical runs. In this paper, in order to enable efficient calculation of unsteady component wall shear stress, new weighting functions are presented as a sum of exponential components. To aim this goal in case of turbulent flow, the scaling procedure proposed by Vitkovsky et al. is used. This method makes very easy the estimation of any new turbulent weighting function. Presented approximated weighting functions are compared with the original counterparts, known from literature in case of laminar and turbulent flows. Using the previously discussed models of cavitation flow CSM, CSMG, CSMA, and the BCM with implemented effective weighting function a series of simulation studies has been made, which showed that the introduced changes in models of unsteady flow with cavitation greatly improve the degree of simulation fit in comparison with experimental results.[b]Keywords[/b]: numerical fluid mechanics, transient flow, cavitation, frequency-dependent friction losses, pipeline, waterhamme