A Passive Nonlinear Three-Port Junction Model For Fluid Mechanics and Acoustics

Wind instruments can be seen as a main bore along which lateral holes are connected by the means of a three-port cavity called a junction. Here, we introduce a passive and physically interpretable model of a junction allowing for the connection of 3 resonators. It is build on a set of geometrical, fluid mechanical and thermodynamic hypotheses and uses a lumped parameter approach. The cavity is approximated by a 2D cartesian volume in which the volumetric mass density is homogeneous. From these hypotheses, we build a fluid mechanical macroscopic model, the passivity of which is guaranteed by the use of the port-Hamiltonian framework. The junction model is interpreted using a nonlinear equivalent electrical circuits and a state-space representation. From this base model, we build five different versions ranging from fluid mechanics to linear acoustics by the means of a shift method, preserving nonlinearities, and approximations (mass convection, behaviour law of the fluid).