Effective solution for ultrasound propagation in rectangular pores filled with a rarefied gas

Aim. The aim of the paper is to construct an effective solution in practical application to the problem of ultrasonic wave propagation in rectangular-section pores filled with a rarefied gas. 

Methodology. The solution to unsteady two-dimensional gas dynamics equations in the creeping flow approach is constructed in the form of infinite series of eigenfunctions, in which zero terms of expansions are predefined functions. The Knudsen number, defined as the ratio of the free path length in a gas to the characteristic transverse pore size, is assumed to be less than or on the order of unity. Therefore, boundary conditions taking into account the effects of sliding and temperature jump on the inner surfaces of the pores are used.

Results. A modified solution to the problem of ultrasonic wave propagation in rectangular-section pores filled with a rarefied gas is presented. In contrast to the previously published results, the solution is represented by rapidly converging series of eigenfunctions. Verification by numerical methods shows that only two terms of expansions are needed to ensure a relative accuracy of calculations not exceeding 1%. Approximate relations for eigenvalues and coefficients of two-term expansions convenient for computer calculations are obtained. Several general mathematical results are also presented.

Research implications. The results of the work can be used for engineering assessments of the acoustic characteristics of porous materials operated at low pressures, as well as provide a basis for further theoretical studies of the acoustic properties of porous materials. 

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