Franck Plouraboué (IMFT)

Wave propagation within networks arises in many fluid mechanical contexts ---such as water distribution networks, vascular system, complex hydraulic networks,—but also mechanical ones (assembled beams, floating structures, flexible tree’s vibrations), and others…

Considering water-hammer as the main wave of interest for this talk, this presentation first introduces their physical/mechanical origin : liquid quasi-incompressibility and Fluid-Structure-Interaction (FSI), as well as their relevance : security issues, body pulse pressure waves.

Then, recent advances in water-hammer modeling and understanding will be provided covering the asymptotic derivation of 1D FSI coupled pressure/stress waves, as well as their continuity conditions at network’s nodes. Quasi-analytical solutions will be discussed in simple configurations first, and later-on, in networks mapped onto metric graphs. In this context, the use of quantum graph eigenfunctions, as well as the so -called secularity condition for the mode selection will be detailed. Finally long-wavelength corrections for the improvement of 1D models will also be discussed within the asymptotic analysis of pressure wave scattering at network’s singularities. Many of the presented concepts and methods are relevant to acoustic and solid mechanics where the various wave’s Degree-of-Freedom can be coupled in networks. Some applications will be presented as well as perspectives related to the interest of these concepts in several questions chasing network’s properties from wave’s propagation information.