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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2012, Volume 53, Issue 4, Pages 57–73
(Mi pmtf1383)
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This article is cited in 2 scientific papers (total in 2 papers)
Critical Reynolds number of the Couette flow of a vibrationally excited diatomic gas energy approach
Yu. N. Grigor'eva, I. V. Ershovb a Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, 630008, Russia
Abstract:
An energy balance equation for plane-parallel flows of a vibrationally excited diatomic gas described by a two-temperature relaxation model is derived within the framework of the nonlinear energy theory of hydrodynamic stability. A variational problem of calculating critical Reynolds numbers $\operatorname{Re}_{cr}$ determining the lower boundary of the possible beginning of the laminar-turbulent transition is considered for this equation. Asymptotic estimates of $\operatorname{Re}_{cr}$ are obtained, which show the characteristic dependences of the critical Reynolds number on the Mach number, bulk viscosity, and relaxation time. A problem for arbitrary wave numbers is solved by the collocation method. In the realistic range of flow parameters for a diatomic gas, the minimum critical Reynolds numbers are reached on modes of streamwise disturbances and increase approximately by a factor of 2.5 as the flow parameters increase.
Keywords:
energy theory, hydrodynamic stability, vibrational relaxation, equations of two-temperature gas dynamics, critical Reynolds number.
Received: 18.10.2011
Citation:
Yu. N. Grigor'ev, I. V. Ershov, “Critical Reynolds number of the Couette flow of a vibrationally excited diatomic gas energy approach”, Prikl. Mekh. Tekh. Fiz., 53:4 (2012), 57–73; J. Appl. Mech. Tech. Phys., 53:4 (2012), 517–531
Linking options:
https://www.mathnet.ru/eng/pmtf1383 https://www.mathnet.ru/eng/pmtf/v53/i4/p57
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