Time-domain simulation of the acoustic nonlinear response of acoustic liners at high sound pressure level
Résumé
In the aeronautical field, numerical mod-
eling of the acoustic response of liners at high sound
pressure levels is done using impedance boundary con-
ditions. The numerical studies are restricted to clas-
sical locally reacting liners with a known analyti-
cal expression of the impedance. In order to model
numerically the acoustic response of a wider range of
absorbent materials for which no impedance expression
is known, this paper focuses on the numerical model-
ing of the acoustic response of perforated plate lin-
ers at high sound pressure levels in the time domain.
To do so, a porous-based description of the perfo-
rated plate is used to represent the visco-thermal pro-
cesses occurring inside the perforated plate. This is
achieved through the use of the equivalent fluid model
(EFM), which contains two irrational transfer functions
described herein by a generic model that covers the
Johnson–Champoux–Allard–Pride–Lafarge (JCAPL),
the JCAL and JCA models. Nonlinear phenomena
occurring at high sound pressure levels are taken into
account by using Forchheimer’s correction in the time-
domain EFM, which introduces a quadratic nonlinear-
ity in the equations. The formulation of the nonlin-
ear EFM equations in the time domain leads to an
augmented system for which a proof of stability is
given thanks to a Lyapunov functional. An approxi-
mate model is built for numerical simulations from
the nonlinear EFM using a multipole approximation
of the transfer functions. Stability conditions sufficient
for the nonlinear multipole-based approximate EFM
are provided. A numerical scheme using a discontinu-
ous Galerkin method is developed to validate the model
against experiments with perforated plate liners.