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 = R root rho.omega/mu, the shear wave number or Stokes number, k = omega.R/c, known as the reduced frequency, sigma = root mu.C-rho/lambda, the square root of the Prandtl number and gamma = C-rho/C-nu,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 < (sigma)over dot < 1.1 and 1.0 < gamma < 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. (C) 2000 Academic Press.