A one-dimensional mathematical model is suggested for nonstationary incompressible flow in a cylindrical tube under the action of a sonic wave propagating in it. Within the framework of this model, a problem of determining the acoustic energy density at the beginning of the tube from the given volumetric flow rate of the fluid in the tube is posed. This problem relates to the class of inverse problems associated with the restoration of the dependence of the right-hand sides of parabolic equations on time. A computational algorithm is proposed for solving the problem posed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. P. Mason (Ed.), Physical Acoustics [Russian translation], Vol. 2, Mir, Moscow (1969).
A. I. Ivanovskii, Theoretical and Experimental Study of Flows Caused by Sound [in Russian], Gidrometeoizdat, Moscow (1959).
L. K. Zarembo and V. A. Krasil′nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).
O. V. Rudenko and S. I. Soluyan, Theoretical Principles of Nonlinear Acoustics [in Russian], Nauka, Moscow (1975).
V. A. Krasil′nikov and V. V. Krylov, Introduction to Physical Acoustics [in Russian], Nauka, Moscow (1984).
C. Eckart, Vortices and streams caused by sound waves, Phys. Rev., 71, No. 1, 68–76 (1948).
O. V. Rudenko and S. I. Soluyan, Concerning the theory of nonstationary acoustic wind, Akust. Zh., 17, No. 1, 122–127 (1971).
O. V. Rudenko and A. A. Sukhorukov, Nonstationary Eckart flows and pumping of liquid in an ultrasonic field, Akust. Zh., 44, No. 5, 653–658 (1998).
M. K. Aktas and B. Farouk, Numerical simulation of acoustic streaming generated by finite-amplitude resonant oscillations in an enclosure, J. Acoust. Soc. Am., 116, 2822–2831 (2004)
V. Daru, D. Baltean-Carles, C. Weisman, P. Debesse, and G. Gandikota, Two-dimensional numerical simulations of nonlinear acoustic streaming in standing waves, Wave Motion, 50, 955–963 (2013).
L. G. Loitsyanskii, Mechanics of Liquids and Gases [in Russian], Nauka, Moscow (1987).
A. A. Samarskii and P. N. Vabishchevich, Numerical Methods of Solving Inverse Problems of Mathematical Physics [in Russian], Izd. LKI, Moscow (2009).
V. T. Borukhov and G. M. Zayats, Identification of a time-dependent source term in nonlinear hyperbolic or parabolic heat equation, Int. J. Heat Mass Transf., 91, 1106–1113 (2015).
Kh. M. Gamzaev, Modeling nonstationary nonlinear-viscous liquid flows through a pipeline, J. Eng. Phys. Thermophys., 88, No. 2, 480–485 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 92, No. 1, pp. 167–173, January–February, 2019.
Rights and permissions
About this article
Cite this article
Gamzaev, K.M. An Inverse Problem of Acoustic Flow. J Eng Phys Thermophy 92, 162–168 (2019). https://doi.org/10.1007/s10891-019-01918-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-019-01918-6