Unsteady Friction in a Rapid Filling Pipeline with Trapped Air

This work investigates the effects of unsteady friction in a rapid filling pipeline with an entrapped air pocket. Existing one-dimensional transient pipe-filling models have primarily considered only steady friction factors, but these same models have tended to underestimate the rate of attenuation of the pressure oscillations. Brunone’s unsteady friction model is combined here with both local inertia and wall friction effects to predict pressure fluctuations using the method of characteristics. Two approaches, Vardy`s analytically deduced shear decay coefficient and the traditional trial and error method, are used to determine the Brunone`s friction coefficient k. Numerical results predicted by the steady friction model, the quasi-steady friction model and the unsteady friction model are compared to each other and to the results obtained from laboratory measurements in a rapidly filling vertical pipe containing an entrapped air pocket. The models that account for unsteady friction are shown to better reproduce measured pressure oscillations.