Numerical calculation of the phase of complex acoustic impedance of air in a cylindrical closed volume

The paper discusses one of the aspects of calibration of the equipment for measuring acoustic pressure in air. To measure complex sensitivity of LS-type microphones during primary pressure calibration (by using a reciprocity or a pistonphone method), it is necessary to theoretically determine the complex acoustic impedance of air within a cylindrical closed volume with absolutely rigid walls. The adiabatic approximation was used as the first step in determining the acoustic impedance of air inside the specified closed volume. However, according to various experimental and theoretical studies, adiabatic approximation is only applicable within a relatively narrow frequency range, while the calibration results can also be affected by other significant factors. Such factors include heat exchange between air inside the cylindrical closed volume and ambient air (through the walls of this volume), as well as reflected waves that appear at high frequencies (depending on how the sound wavelength compares to the length of the closed volume). To study these factors, numerical simulation is proposed. The numerical algorithm is based on the regularized Navier-Stokes equations with quasi-gas-dynamic closure, and accounts for the viscosity, thermal conductivity, and compressibility of air. The phase of the complex acoustic impedance of air in a closed volume with heat-conducting and heat-insulated walls has been characterized. The study results are relevant for both the calibration of measurement microphones at low and infrasound frequencies by using the pressure reciprocity and pistonphone methods, and for studying acoustic processes in liquid and gaseous media using numerical modeling, since these results show the applicability of the model used for numerical calculation. Measurement devices that receive the unit of acoustic pressure in air from the measurement microphones, calibrated by the primary method, are used, for example, to monitor noise from various sources (industrial activity, transport), to monitor noise inside residential and industrial buildings, and to study geophysical phenomena (low-frequency sound oscillations in the atmosphere caused by daily and semi-daily variations in atmospheric pressure, atmospheric currents, tsunamis, volcanic eruptions, etc.).