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Use of tensor polynomials for constructing an equation for turbulence scale in semiempirical models

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Abstract

Thek-kl-model of turbulence based on the equation of second two-point moments (pointsA andB) of the fluctuating velocity field is presented. The second and third moments entering into this equation are expressed using polynomials whose terms are products of the tensor components characterizing a given turbulent motion and scalar functions of the distanceAB. ForAB=0 the equation obtained gives thek-turbulence energy balance equation and, on being integrated overAB from 0 to ∞, the transport equation for thekl-quantity (l is the integral turbulence scale). The model is used for calculating mixing layers, plane and circular jets, the wake behind a cylinder, tube and channel flows, and the boundary layer on a plate. The results of all the calculations agree well with the experimental data for a single set of empirical coefficients.

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Authors
  1. N. I. Akatnov
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St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 51–64, July–August, 1994.

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Akatnov, N.I. Use of tensor polynomials for constructing an equation for turbulence scale in semiempirical models. Fluid Dyn 29, 479–490 (1994). https://doi.org/10.1007/BF02319069

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