Laboratoire de Mécanique et Énergétique, Université de Valenciennes, Valenciennes 59313, France.
water hammer wave speed. active surface of the electrochemical probe. diameter of the circular sensor (m). inner pipe diameter. Darcy-Weisbach friction factor. gravitational acceleration. limiting diffusion current. unsteady friction factor. mass transfer coefficient. pipe length. number of electrons involved in the redox reaction. inner pipe radius. wall shear rate (s−1). mean velocity in the cross-section. Vardy's shear decay coefficient. diffusivity. Faraday's constant. concentration of the active ions. Reynolds number, = wall shear stress. quasi-steady wall shear stress. unsteady wall shear stress. density of fluid. kinematic viscosity. dynamic viscosity. friction velocity, = √τw/ρ =(ms−1).
Experimental measurements of the wall shear stress combined to those of the velocity profiles via the electrochemical technique and ultrasonic pulsed Doppler velocimetry, are used to analyse the flow behaviour in transient pipe flow caused by a downstream sudden valve closure. Velocity data are analyzed and the corresponding wall shear stress values are evaluated, leading to a discussion on transient energy dissipation by comparison with results obtained by the electrochemical technique. The Reynolds number of the steady flow based on the pipe diameter is Re=140000. The results show that the quasi-steady approach of representing unsteady friction is valid during the initial phase for relatively large decelerations. For higher decelerations, the unsteady wall shear stress is consistently higher than the quasi-steady values obtained from the velocity profiles. An examination of the range of applicability of the instantaneous-acceleration model shows that the empirical coefficient of unsteady friction is closely linked to the deceleration intensity. This study is made possible owing to the repeatability of different valve closures allowing data to be averaged over numerous tests.
