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On Mathematical Modeling of Swirling Turbulent Wakes with Varied Total Excess Momentum and Angular Momentum

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Journal of Engineering Thermophysics Aims and scope


The flow in swirling turbulent wakes with varying total excess momentum and angular momentum is described using two second-order mathematical models. The first one includes averaged equations of momenta, turbulence energy balance, and dissipation rate in the far-wake approximation. The closure of the mathematical model relies on Rodi’s algebraic model for Reynolds stresses. The second model is based on simplified representations of the turbulent viscosity coefficients. For small distances, the calculated profiles of averaged motion velocities and turbulence energy are in good agreement with the experimental data of Lavrent’ev Institute of Hydrodynamics of SB RAS. At large distances, numerical experiments have yielded a self-similar solution of problems of dynamics of turbulent wake behind a self-propelled body and momentumless swirling turbulent wake. Group-theoretical analysis of the simplified mathematical model has been done. The model had been reduced to a system of ordinary differential equations, which was solved numerically using asymptotic expansions. The solution obtained was compared with the self-similar solution found by direct numerical integration of the differential equations of the model at large distances from the body, and good agreement was observed. In addition, the problem of asymptotic behavior of swirling turbulent wake behind a sphere with non-zero values of total excess momentum and angular momentum was considered. The group-theoretical analysis has shown the absence of physically meaningful self-similar solutions to the equations of the turbulence model under consideration.

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The formulations of the problems and their computer realization were performed with the financial support of RFBR (project no. 17-01-00332). The numerical experiments were carried out under the IT SB RAS state assignment (AAAA-A17-117022850027-5); the group-theoretical analysis of turbulence models was made under the ICM SB RAS state assignment (AAAA-A18-118011890025-2); the numerical calculations by shooting method were carried out with the financial support of the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional centers for mathematics research and education (Agreement no. 075-02-2020-1534); the discussion of the results of the calculations was made and the article was written under the IT SB RAS state assignment and topics 0316-2018-0001 “Development and Research of New Elements of Computational Technology for Solving Fundamental and Applied Problems of Aero, Hydro, and Wave Dynamics” and 0356-2017-0003 “Comprehensive Analysis of Hydrodynamic Aspects of the Functioning of Natural Systems and Technical Installations in Extreme Conditions” of the ICM SB RAS state assignment.

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Correspondence to G. G. Chernykh, A. G. Demenkov, O. V. Kaptsov or A. V. Schmidt.

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The authors dedicate this work to the blessed memory of V.A. Kostomakha.

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Chernykh, G.G., Demenkov, A.G., Kaptsov, O.V. et al. On Mathematical Modeling of Swirling Turbulent Wakes with Varied Total Excess Momentum and Angular Momentum. J. Engin. Thermophys. 29, 222–233 (2020).

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