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On Using Lagrangian Mechanics Methods to Analyze the Energy Balance in Compressed Gas Vortex Flows

On Using Lagrangian Mechanics Methods to Analyze the Energy Balance in Compressed Gas Vortex Flows The paper proposes to describe the dynamics of perturbations of compressible ideal gas flows in the formalism of Lagrangian mechanics. The key point is the choice of generalized coordinates that most naturally describe the system dynamics. The proposed choice of main variables leads to the Lagrange equations, which correspond to the displacement field equation and convective wave equation for the scalar potential. This approach yields the acoustic energy balance equation via the first variations of the variables for the flows with nonzero vorticity. The results can be used for energy analysis of the sound emission for flows with localized vortices, jet flows, and duct flows. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acoustical Physics Springer Journals

On Using Lagrangian Mechanics Methods to Analyze the Energy Balance in Compressed Gas Vortex Flows

Acoustical Physics , Volume 67 (1) – Mar 10, 2021

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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021. ISSN 1063-7710, Acoustical Physics, 2021, Vol. 67, No. 1, pp. 83–90. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Akusticheskii Zhurnal, 2021, Vol. 67, No. 1, pp. 98–106.
ISSN
1063-7710
eISSN
1562-6865
DOI
10.1134/S1063771021010012
Publisher site
See Article on Publisher Site

Abstract

The paper proposes to describe the dynamics of perturbations of compressible ideal gas flows in the formalism of Lagrangian mechanics. The key point is the choice of generalized coordinates that most naturally describe the system dynamics. The proposed choice of main variables leads to the Lagrange equations, which correspond to the displacement field equation and convective wave equation for the scalar potential. This approach yields the acoustic energy balance equation via the first variations of the variables for the flows with nonzero vorticity. The results can be used for energy analysis of the sound emission for flows with localized vortices, jet flows, and duct flows.

Journal

Acoustical PhysicsSpringer Journals

Published: Mar 10, 2021

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