Numerical modelling of thermoacoustic waves in a rarefied gas confined between coaxial cylinders

• Solution of a linearized and non-stationary kinetic model.
• Macro-characteristics of the gas flow due to thermoacoustic waves.
• Shortcomings of the Navier–Stokes equations in the solution of the problem.
• Influence of curvature effects on the solution of the problem.

Sound waves propagating through a rarefied gas confined between two coaxial cylinders and induced by an unsteady heating of the inner boundary is modelled on the basis of a kinetic model to the linearized and non-stationary Boltzmann equation. The gas flow is considered as fully established so that the dependence of all quantities on time is harmonical. The diffuse scattering of gaseous particles is assumed as the boundary conditions on both cylinders. The solution of the problem depends on three parameters: the Knudsen number, the temperature oscillation frequency and the radius ratio. The deviation of gas properties from their equilibrium values, namely, density, temperature and pressure deviations, and also the bulk velocity and heat flux in the direction of sound propagation are calculated in a wide range of Knudsen number and oscillation frequency in order to cover all the regimes of gas flow, i.e. free molecular, transitional and hydrodynamic regimes. Two values of radius ratio of cylinders are considered to evaluate the curvature effects on the solution of the problem.