On water hammer waves

Water hammer waves, i.e., low-frequency, low-Mach number propagation of finite-amplitude pressure waves in pipe flow, are investigated by means of the wave equation proposed in Di Nucci et al., 2024a, 2024b. The wave equation, resembling a linear damped wave equation, comes from the turbulent-viscosity model based on the quasi-incompressible Reynolds Averaged Navier-Stokes equations. Changes in temperature due to entropy production are neglected, and adiabatic conditions are imposed. Additional insights on the assumptions used to derive the wave equation are also provided. Focusing on the one-dimensional propagation of pressure waves in liquid-filled pipes (without cavitation), analytical solution of the wave equation is tested against experimental data available from the literature. The impact of the simplifying assumptions on the quantitative outcomes appears to be small; therefore a good level of accuracy in replicating water hammer wave characteristics (including damping, smoothing, and maximum pressure peak) is achieved. Results show that the Reynolds number has minimal influence on water hammer wave propagation, i.e., the vorticity field has no remarkable effect on flow behavior. Deeper attention is given to entropy production, and to the role played by the dimensionless number which is identified as predominant in water hammer wave propagation. Damping properties are also determined.