Bulk viscosity and acoustic wave propagation in polyatomic gases and their mixtures are studied in the frame of one-temperature and multi-temperature continuum models developed using the generalized Chapman–Enskog method. Governing equations and constitutive relations for both models are written, and the dispersion equations are derived. In the vibrationally nonequilibrium multi-component gas mixture, wave attenuation mechanisms include viscosity, thermal conductivity, bulk viscosity, diffusion, thermal diffusion, and vibrational relaxation; in the proposed approach these mechanisms are fully coupled contrarily to commonly used models based on the separation of classical Stokes–Kirchhoff attenuation and relaxation. Contributions of rotational and vibrational modes to the bulk viscosity coefficient are evaluated. In the one-temperature approach, artificial separation of rotational and vibrational modes causes great overestimation of bulk viscosity whereas using the effective internal energy relaxation time yields good agreement with experimental data and molecular-dynamic simulations. In the multi-temperature approach, the bulk viscosity is specified only by rotational modes. The developed two-temperature model provides excellent agreement of theoretical and experimental attenuation coefficients in polyatomic gases; both the location and the value of its maximum are predicted correctly. One-temperature dispersion relations do not reproduce the non-monotonic behavior of the attenuation coefficient; large bulk viscosity improves its accuracy only in the very limited frequency range. It is emphasized that implementing large bulk viscosity in the one-temperature Navier–Stokes–Fourier equations may lead to unphysical results.

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Рассматриваются разные стадии релаксации в высокоскоростных и высокотемпературных газах с физико-химическими процессами на основе модельных кинетических уравнений. Выписываются макроскопические уравнения в нулевом приближении модифицированного метода Чепмена Энскога, а также выражения для потоковых членов газодинамических уравнений в терминах интенсивных и экстенсивных параметров. Выводится формула для скорости звука (как скорости распространения малых возмущений) с параметром ae, который в рассматриваемых условиях не является постоянной величиной. Ключевые слова: модельные кинетические уравнения, разные стадии релаксации, экстенсивные и интенсивные параметры.

Model kinetic equations are proposed for the description of ionized monoatomic gas mixture flows. The mixtures are assumed enough rarefied to be treated as ideal gases after multiple ionization steps. The model equations contain the equilibrium distribution functions for the components of the gas mixtures under consideration like it was done in BGK equations and their well-known generalizations. However, in this paper the new forms of the equilibrium distribution functions are used which correspond to the entropy maximum under the constraints of momentum, total energy, nuclei and electrons (both bound and free) conservation. It is shown that the derived model equations allow us to study the local equilibrium flows of the ionized gases and the transport processes of energy, nuclei and electrons in the non-equilibrium conditions.