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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2008, Volume 49, Issue 2, Pages 29–39
(Mi pmtf1880)
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Constraints on the “rapid” part of the pressure-strain rate correlations derived from the spectral presentation
S. R. Bogdanova, T. J. Jongenb a Kareliya State Pedagogical University, Petrozavodsk, 185680, Russia
b Unilever Research Institute, Vlaardingen, 3133, the Netherlands
Abstract:
Based on the exact spectral presentation of the “rapid” part of the pressure-strain rate correlations, semi-empirical approximations used for these correlations within the framework of the second-order closures are analyzed. Simple inequalities relating the values of the model constants, mean velocity parameters, and Reynolds tensor invariants are derived. For certain types of flows, in contrast to conditions of realizability, these inequalities allow verification of the approximations before solving differential equations. It is demonstrated that some models cannot be considered as sufficiently precise ones to describe flows with high degrees of anisotropy. In particular, the condition of non-negative determinacy of the spectral matrix is violated in a considerable region of the physically admissible range of parameters. The boundaries of this region are calculated for an irrotational three-dimensional distortion and for an arbitrary two-dimensional distortion of turbulence in channel flows. Simple constraints on model constants are obtained, which allow these violations to be avoided.
Keywords:
developed turbulence, spectral methods, second-order closures, realizability conditions.
Received: 24.01.2007 Accepted: 25.04.2007
Citation:
S. R. Bogdanov, T. J. Jongen, “Constraints on the “rapid” part of the pressure-strain rate correlations derived from the spectral presentation”, Prikl. Mekh. Tekh. Fiz., 49:2 (2008), 29–39; J. Appl. Mech. Tech. Phys., 49:2 (2008), 179–187
Linking options:
https://www.mathnet.ru/eng/pmtf1880 https://www.mathnet.ru/eng/pmtf/v49/i2/p29
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