Energy dissipation in unsteady turbulent pipe flows caused by water hammer

Abstract

Energy dissipation and turbulent kinetic energy production and its dissipation in unsteady turbulent pipe flows due to water hammer phenomena are numerically studied. For this purpose, the two-dimensional governing equations of water hammer are solved using the method of characteristics. A k–ω turbulence model which is accurate for two-dimensional boundary layers under adverse and favorable pressure gradients is applied. The numerical results are in good agreement with the experimental data. Through an order of magnitude analysis, two dimensionless parameters have been identified which can be used for the evaluation of viscous and turbulent shear stress terms. The influence of these non-dimensional parameters on pressure oscillations, wall-shear-stress, dissipation rate as well as profiles of velocity, turbulent production and dissipation are investigated. The non-dimensional parameter P, which represents time scale ratio of turbulence diffusion in the radial direction to the pressure wave speed, is used to study the structure and strength of turbulence. It is found that for the case of P≈1, for which the values of the non-dimensional groups are larger, the peaks of turbulence energy production and dissipation move rapidly away from the wall and turbulence structure is significantly changed. For the case of P≫1, for which the values of non-dimensional parameters are smaller, these variations are found to be small.