Fluid transients in viscoelastic pipes via an internal variable constitutive theory

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

“…where 𝐾 is the fluid bulk modulus and 𝜀 𝜃 is the pipe circumferential strain, and 𝜌 0 designates the mass density of the fluid in undisturbed state from which variations in 𝜌 are measured [33].…”

“…In the present elasto-viscoplasticity theory, if Odqvist's creep law with an initial yield stress 𝜎 𝑦 is assumed [27], then the pseudo-potential of dissipation Φ(𝛔, 𝐵 𝛽 ) can be introduced as [39,40]:…”

“…In effect, these properties of Φ make the inequality in Eq. ( 44) obey a classical result from convex analysis, which can be expressed in a compact form as [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]:…”

An analysis of fluid–structure interaction coupling mechanisms in liquid-filled viscoelastic pipes subject to fast transients

“…This approach applies to laminar and turbulent flows. Invoking the classic parabolic laminar velocity profile, the material constants of the model result in (see Appendix A of Andrade et al, 2023a):…”

“…The core region is characterized by a constant turbulent kinematic viscosity η c while in the annulus, with a thickness equal to δ = 0.2R, the turbulent kinematic viscosity varies linearly from the value η w at the wall (r = R), to the value η c at the interface of these regions. Within this framework, a fully developed velocity profile is achieved, and then, the material constants associated with the interaction forces in the core and annulus regions are (see Appendix A of Andrade et al (2023a)):…”