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Sound Attenuation in Tubes due to Visco-Thermal Effects

The propagation of periodic axial sound waves in gases contained in circular cylindrical structures is a function of four parameters: s=Rρ·ω/μ, the shear wave number or Stokes number, k=ω·R/c, known as the reduced frequency, σ=μ·Cp/λ, the square root of the Prandtl number and γ=Cp/Cv, the ratio of specific heats. The complete Kirchhoff solution of the sound propagation in tubes problem obtained in 1868 was expressed in terms of these parameters by Tijdeman [1]. In previous works [1, 2] the complex propagation constant was obtained by solving this expression. The results were presented for a limited range in reference [1] and for a broader range in reference [2] but in both cases only for a single fluid, air. In this work the results of a computer code to solve for this propagation constant are presented. The code was used to find the propagation constants (attenuation and phase-shift coefficients) in the range 5<s<5000, 0·01<k<6, 0·8<σ<1·1 and 1·0<γ<1·7. This range of conditions covers most conditions of interest. The data was then used to fit an equation to express the attenuation and phase-shift coefficients in terms of simpler polynomial-type expressions as a function of these four parameters. A set of tables to obtain the values of the attenuation and phase shift coefficients for values of these four non-dimensional parameters in the above range is also presented. Sound attenuation measurements using superheated R134a refrigerant agrees reasonably well with the computed attenuation in the plane wave region.