One-dimensional ultrasound propagation in stratified gas

• Autorzy: Leble S. , Solovchuk M.
• Języki publikacji: EN

Abstrakty

EN

The system of hydrodynamic-type equations is derived by two-sided distribution function for a stratified gas in gravity field and applied to the problem of ultrasound. The theory is based on the generalized Gross-Jackson kinetic equation, the solution of which is built by means of locally equilibrium distribution function with different local parameters for molecules moving "up" and "down". The problem of propagation of the sound wave from an oscillating plane is explored. The linearized version of the obtained system is studied and compared with other results and experiments for a wide range of Knudsen numbers (Kn). The discrepancy with experiment in attenuation behavior at big Kn range forced us to use generalized kinetic description leading to the Alexeev-Boltzmann equation. Its use essentially improves the results.

Słowa kluczowe

EN

ultrasound; fluid mechanics; rarefied gas dynamics; kinetic theory

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2009
• Tom: Vol. 34, No. 2
• Strony: 215--229
• Opis fizyczny: Bibliogr 20 poz., rys.

Twórcy

autor

Leble S.

autor

Solovchuk M.

• Gdańsk University of Technology, Faculty of Technical Physics and Applied Mathematics, G. Narutowicza 11/12, 80-952 Gdańsk-Wrzeszcz, Poland,

Bibliografia

• [1] Nguyen N.T., Wereley S.T., Fundamentals and Applications of Microfluidics, 2nd ed, Artech House, 2006.
• [2] Leble S., Vereshchagin D., Shchekin A., Boundary regime propagation in Stratified Gas with Arbitrary Knudsen Number, Journ. Applied Math. and Tech. Phys, N5, 70–79 (1993).
• [3] Vereshchagin D.A., Leble S.B., Piecewise continuous partition function and acoustics in stratified gas, Nonlinear Acoustics in Perspective, R. Wei [Ed.], 142–146 (1996).
• [4] Chen X., Rao H., Spiegel E.A., Continuum description of rarefied gas dynamics: II. The propagation of ultrasound, Phys. Rev. E, 64, 046309 (2001).
• [5] Alexeev B.V., Generalized Boltzmann Physical Kinetics, Elsevier, 2004.
• [6] Curtiss C.F., The classical Boltzmann equation of a gas of diatomic molecules, J. Chem. Phys. 75, 376–378 (1981).
• [7] Chetverushkin B.N., Kinetic schemes and quasi-gasdynamic system, MAKS Press, Moscow 2004.
• [8] Vereshchagin D.A., Leble S.B., Solovchuk M.A., Piecewise continuous distribution function method in the theory of wave disturbances of inhomogeneous gas, Physics Letters A, 348, 326–334 (2006).
• [9] Lees L., Kinetic theory description of rarefied gas flow, J. Soc. Industr. and Appl. Math., 13, 1, 278–311 (1965).
• [10] Leble S.B., Solovchuk M.A., Three-dimensional fluid equations from distribution function with discontinuity in velocity space, Mathematical modeling, 18, 4, 118–128 (2006).
• [11] Meyer E., Sessler G., Schallausbreirung in Gasen bei hohen Frequenzen und sehr niedriegen Drucken, Z. Physik, 149, 15–39 (1957).
• [12] Schotter R., Rarefied gas acoustics in the noble gases, Phys. Fluids, 8, 1163–1168 (1974).
• [13] Gross E.P., Jackson E.A., Kinetic models and linearized Boltzmann equation, Phys. Fluids, 2, 4, 432–441 (1959).
• [14] Leble S.B., Solovchuk M.A., WESPAC-IX, Western Pacific Acoustics Conference, ArXive:physics/0607161, http://eprintweb.org/S/authors/All/S/M_Solovchuk
• [15] Vereshchagin D.A., Leble S.B., Piecewise continuous distribution function method: Fluid equations and wave disturbances at stratified gas, J. of Atmospheric and Solar-Terrestrial Phys., 68, 1321–1329 (2006).
• [16] Marques W. Jr., Dispersion and absorption of sound in monatomic gases: An extended kinetic description, J. Acoust. Soc. Am., 106, 3282–3288 (1999).
• [17] Struchtrup H., Torrilhon M., Regularization of Grad’s 13 moment equations: Derivation and linear analysis, Phys. Fluids, 15, 9, 2668–2680 (2003).
• [18] Sharipov F., Marques W. Jr., Kremer G.M., Free molecular sound propagation, J. Acoust. Soc. Am., 112, 2, 395–401 (2002).
• [19] Alexeev B.V., Physical principles of the generalized Boltzmann kinetic theory, UFN, 170, 649–679 (2000).
• [20] Wójcik J., Nonlinear reflection and transmission of plane acoustic waves, Archives of Acoustics, 29, 4, 607–632 (2004).