Water hammer is a transient phenomenon that occurs when a flowing fluid is rapidly decelerated, which can be harmful and damaging to a piping system. Three-dimensional computational fluid dynamics (CFD) with three-dimensional geometry is a common tool for studying water hammer, which is more accurate than numerical simulation with one-dimension approximation of the geometry. There are different methods with different accuracy and computational costs for valve closure modelling. This paper presents the result of water hammer 3D simulation with three main technics for modelling an axial valve closure: dynamic mesh, sliding mesh, and immersed solid methods. The variation of the differential pressure variation and the wall shear stress are compared with experimental results. Additionally, the 3D effects of the flow after the valve closure and the computational cost are addressed. The sliding mesh method presents the most physical results compared to the other two methods. The immersed solid method predicts a smaller pressure rise which may be the result of using a source term in the momentum equation instead of modelling the valve movement. The dynamic mesh method adds fluctuations to the primary phenomenon. Moreover, the sliding mesh is less expensive than the dynamic mesh method in terms of computational cost (approximately one-third), which was the primary method for axial valve closure modelling in the literature.

According to the IEC 60041 standard, the pressure-time method (1D PTM) can be employed to determine the flow rate in hydraulic turbines. This method assumes a one-dimensional flow and applies to straight pipes with uniform cross-sections, with specific restrictions on the pipe length, fluid velocity, and distance between the measurement sections from any irregularities in the pipeline. However, challenges arise when applying this method in low-head hydropower plants due to the short lengths, irregularities like bends and developing flows in the intake. The present paper aims to improve the performance of the method in the presence of a bend. To this end, a test rig has been developed and measurements performed, including such geometry. The data are evaluated using the development of a newly proposed approach combining the 1D PTM based on an energy balance formulation and three-dimensional computational fluid dynamics (3D CFD) developed for axis-symmetrical accelerating flows. The updated methodology includes a correction of the experimental pressure measurements used in the 1D PTM to account for the effects of the Dean vortices present after the bend as well as the kinetic energy correction factors which deviate from known values in transient conditions. The results obtained under conditions involving the presence of bends either between or in close proximity to one show a significant improvement compared to the standard one-dimensional pressure-time method.