A thermodynamically consistent model for hydraulic transients in metallic pipes undergoing elasto-viscoplastic deformations

Abstract

This work presents an extension of the fluid transient analysis to include the elasto-viscoplastic behavior of the pipe material. A previously developed quasi-2D flow model is employed as a basic framework, and the pipe’s elasto-viscoplastic behavior is added by considering constitutive equations formulated via an internal variables theory. The resulting governing equations form a non-linear hyperbolic system of partial differential equations whose approximated solutions are obtained by employing the method of characteristics followed by the Newton–Raphson method. The model is thermodynamically consistent, a feature that is consistently detailed in this work to uphold the application of energy-based theoretical analyses of the phenomenon. Taking as reference the transient responses obtained from an experimental installation that simulates an accident, the present approach is found to be fully consistent and valuable for simulating fast hydraulic transients in metallic materials experiencing plastic deformation. By comparing the pressure fluctuations of models with and without elasto-viscoplasticity, more attenuation and dispersion of the pressure responses are found when such behavior is considered. The elasto-viscoplasticity effect on the pressure responses is better understood when the connection between the viscoplastic mechanisms and energy dissipation is exposed. During the fluid transient, the pipe dissipates meaningful amounts of energy that cause a significant alteration in the whole fluid–pipe dynamics. Another numerical example, based on a hypothetical water hammer flow that causes plastic deformation in the pipeline, is also addressed. Such a case puts in evidence that not only the anelastic behavior of the pipe must be taken into account but also that an accurate description of the fluid friction may be significant to portray realistically fluid transient responses. At last, an assessment of the pipe integrity by means of a scalar damage variable theory is carried out to emphasize the application prospects of the present research.