Title: Bulk viscosity model for near-equilibrium acoustic wave attenuation,
Abstract: 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 $\mu_B$. 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 $h_r$, and acoustic frequency. Since the vibrational relaxation
timescales of oxygen and nitrogen are a function of humidity, for certain
frequencies an intermediate value of $h_r$ can be found which maximizes
$\mu_B$. The contribution to bulk viscosity due to rotational relaxation is
verified to be a function of temperature, confirming recent findings in the
literature. While $\mu_B$ 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.