Modeling of low Mach number unsteady turbulent pipe flows

Under adiabatic conditions, and neglecting temperature variations due to entropy production, we present a set of Reynolds Averaged Navier–Stokes (RANS) equations for fluids of low compressibility, i.e., fluids in the liquid state. In the low Mach number limit, we specialize the RANS equations to the one-dimensional unsteady pipe flow, and we deduce the dimensionless number that plays a predominant role in the flow behavior. We reduce the system of equations to a linear damped wave equation, and use its analytical solution to investigate the propagation of large amplitude pressure waves in liquid-filled pipes (water hammer phenomenon). We test the model reliability by comparing the analytical solution of the proposed model against experimental data available in the literature.