Weakly nonlinear acoustic oscillations in gas columns in the presence of temperature gradients

Guillaume Penelet (1) , Tristan Chareyre , Joël Gilbert (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans

This study deals with the description of nonlinear propagation of guided acoustic waves in the presence of temperature gradients. Nonlinear propagation of guided acoustic waves has been extensively studied in the past decades. It is nowadays well-established that, in the frame of weakly nonlinear acoustics, it is possible to derive a Burgers equation describing nonlinear and lossy propagation in tubes, with possible account of the variation of the tube's cross-section. However, the effect of a temperature gradient on non linear propagation has not been studied a lot. This topic may be worth studying in the field of thermoacoustics, where both high amplitude acoustic waves and steep temperature gradients are present. In this study, the appropriate Burgers equation is first derived, describing the propagation of a single wave in a tube submitted to a linear temperature gradient. This equation can be solved using a frequency domain numerical model, which allows to quantify the impact of temperature gradients in specific cases. The case a weak temperature gradient along a waveguide exhibiting variable cross section, and the case of a strong temperature gradient along a straight duct closed at both ends will be treated in this study.

Mots clés: nonlinear acoustics; thermoacoustics

Domaines: Acoustique [physics.class-ph]

Guillaume Penelet, Tristan Chareyre, Joël Gilbert. Weakly nonlinear acoustic oscillations in gas columns in the presence of temperature gradients. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810884⟩