Comparative analysis of unsteady friction models for pipe flows in light of the second law of thermodynamics

摘要

An analysis of six distinct unsteady friction models for one-dimensional pipe flows was done aiming to verify not only the ability to correctly describe the water-hammer phenomenon features but also whether they satisfy the local form of the classical second law of thermodynamics. These models belong to three different categories and are named herein, by the authors, as Schohl-UZ, Brunone-1991, Brunone-VB, VitkovskATIN SMALL LETTER Y WITH ACUTE, Vardy-Brown, and Pezzinga. To achieve this objective, these models were implemented numerically in the context of the method of characteristics, by employing second-order numerical approximations of the source terms. Numerical simulations were carried out for a reservoir-tube-valve system in which fast hydraulic transients were generated by valve slam. The estimated head histories were compared with that of experimental data available in the literature and the classic thermodynamic inequality was verified numerically. It was observed that the Schohl-UZ, Vardy-Brown, and Pezzinga models do not satisfy the classic inequality, for both laminar and turbulent flows, despite offering better agreement with experimental data regarding pressure distributions in time and space. Differently from the head results, the wall shear stress and the rate of energy dissipation present sensibility to the grid size. A comparison was also made among the models concerning the wall shear stress results and no common-pattern response was identified among the categories.