2017/07/18 by Jeffrey Lin, Carlo Scalo, Lin, Jeffrey +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Quantum, superfluid, helium dynamics #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1707.05876
Submitted manuscript
arxiv created 2017/07/18 · openalex publication_date 2017/07/18 · arxiv updated 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Acoustic wave attenuation due to vibrational and rotational molecular relaxation, under simplifying assumptions of near-thermodynamic equilibrium and absence of molecular dissociations, can be accounted for by specifying a bulk viscosity coefficient μB. In this paper, we propose a simple frequency-dependent bulk viscosity model which, under such assumptions, accurately captures wave attenuation rates from infrasonic to ultrasonic frequencies in Navier--Stokes and lattice Boltzmann simulations. The proposed model can be extended to any gas mixture for which molecular relaxation timescales and attenuation measurements are available. The performance of the model is assessed for air by varying the base temperature, pressure, relative humidity hr, and acoustic frequency. Since the vibrational relaxation timescales of oxygen and nitrogen are a function of humidity, for certain frequencies an intermediate value of hr can be found which maximizes μB. The contribution to bulk viscosity due to rotational relaxation is verified to be a function of temperature, confirming recent findings in the literature. While μB decreases with higher frequencies, its effects on wave attenuation become more significant, as shown via a dimensionless analysis. The proposed bulk viscosity model is designed for frequency-domain linear acoustic formulations but is also extensible to time-domain simulations of narrow-band frequency content flows.