Propagation and attenuation of sound waves in partially ionised and dissociated plasma flows

• Published in: Journal of fluid mechanics Vol. 1011
• Main Authors: Rapisarda, Claudio, McGilvray, Matthew, di Mare, Luca
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 13.05.2025
• Subjects: JFM Papers; high-speed flow; hypersonic flow
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2025.357

The propagation of sound waves in high-temperature and plasma flows is subject to attenuation phenomena that alter both the wave amplitude and speed. This finite change in acoustic wave properties causes ambiguity in the definition of sound speed travelling through a chemically reactive medium. This paper proposes a novel computational study to address such a dependence of sound-wave propagation on non-equilibrium mechanisms. The methodology presented shows that the equations governing the space and time evolution of a small disturbance around an equilibrium state can be formulated as a generalised eigenvalue problem. The solution to this problem defines the wave structure of the flow and provides a rigorous definition of the speed of sound for a non-equilibrium flow along with its absorption coefficient. The method is applied to a two-temperature plasma evolving downstream of a shock, modelled using Park’s two-temperature model with 11 species for air. The numerical absorption coefficient at low temperatures shows excellent agreement with classical theory. At high temperatures, the model is validated for nitrogen and argon across wide temperature ranges with experimental values, showing that classical absorption theory is insufficient to characterise high-temperature flows due to the effect of finite-rate chemistry and vibrational relaxation. The speed of sound is verified in the frozen and equilibrium limits and its non-equilibrium profile is presented with and without viscous effects. It is furthermore shown that the variation in the speed of sound is driven by the dominating reaction mechanisms that the flow is subject to at different thermodynamic conditions.