Turbulent bulk viscosity

The Reynolds decomposition is used to derive a new set of mean-flow equations for linear viscous fluids, with low compressibility (fluids in the liquid state). Additional shear and normal stresses are related to the velocity turbulent fluctuations in order to interpret the considerable energy dissipation in processes which are accompanied by rapid changes in liquid density, at least within the frame of the local thermodynamic equilibrium (LTE) approximation. A constitutive equation for the normal turbulent stresses, which involves the turbulent bulk viscosity, is given. A closure equation for the turbulent bulk viscosity is suggested. In the field of hydraulic engineering, the model is applied to investigate the classical problem of 1D finite amplitude pressure waves propagation in liquid-filled pipes (water hammer phenomenon). Available experimental pressure data are used to calibrate the model parameters and to demonstrate the capability of the proposed theoretical model in reproducing the experimental trials. The model results are discussed with attention paid to the role played by the turbulent bulk viscosity on the energy dissipation processes.