E-proceedings of the 38 th IAHR World Congress September 1-6, 2019, Panama City, Panama doi:10.3850/38WC092019-1818 3386 UNSTEADY FRICTION IN A RAPID FILLING PIPELINE WITH TRAPPED AIR LING ZHOU (1) , ALAIN ELONG (2) & BRYAN KARNEY (3) (1) College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China; Visiting Professor, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada. M5S 1A4. E-mail: zlhhu@163.com (corresponding author) (2) College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China. E-mail: alainjoel.elong@yahoo.fr (3) Department of Civil Engineering, University of Toronto, Toronto, ON, Canada. M5S 1A4. E-mail: karney@ecf.utoronto.ca ABSTRACT 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. Keywords: Transient flow; air-water interaction; entrapped air pocket; unsteady friction; methods of characteristics 1 INTRODUCTION Air pockets are often entrapped in pipeline systems, whether power or pump stations, urban supply or sewer systems. Previous publications (Martin 1976, Zhou et al 2011a) suggest that entrapped air can exacerbate the resulting pressure oscillations. In particular, a sudden pressurization transient may induce abnormally high pressures, which can easily induce geysers or otherwise damage pipelines (Wright et al. 2010; Zhou et al. 2004). Several researchers have considered the numerical simulation of transient events in water pipelines containing air pockets. A pioneering contribution associated with air compression was published by Martin (1976) who investigated the effect of entrapped air pockets on pressure oscillations using a rigid column approach. Zhou et al. (2002) elaborated on Martin’s model with greater consideration of the filling water column, the air phase model and the rate of energy loss. Lee and Martin (1999) included the influence of compressibility and solved the governing equations by Method of Characteristics (MOC), thus establishing an elastic model approach. Liu et al. (2011), Zhou et al. (2011, 2013a, 2018a) proposed the “rigid plug” and “virtual plug” method within an elastic model in order to avoid the interpolation error produced by the MOC while numerically tracking the air-water interface. However, the pressure oscillation patterns during rapid filling predicted by the above one-dimensional (1D) models tend to only accurately reproduce the first pressure peak, while producing greater error in subsequent peaks. Indeed, all these models (including the current work) tend to embed several important modelling assumptions, of which three are key: (1) assuming a well-defined air-water interface that neglects dynamic air-water interactions, (2) only considering steady-flow friction factors and (3) using a constant polytropic exponent for an ideal gas to represent the air phase. In order to account for the thermal processes potentially influencing an entrapped air pocket during rapid filling, Zhou et al. (2018b) recently introduced a three-dimensional (3D) computational fluid dynamics (CFD) approach based on a volume of fluid (VOF) formulation to simulate air-water interactions in a rapidly filling pipeline. The free air-water interactions, wall shear stress and boundary layer, thermal conduction and convection in three different media (air, liquid water, and the pipe wall), are all considered. Experimental results, confirm that this 3D CFD model, although computationally quite expensive, could accurately simulate transient flow through this more complete representation of the associated physical processes. This CFD investigation also has an important implication for the current work: specifically, this work implies that the