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Calculation of the dissipation coefficient of the mechanical energy of moving fluid in the smooth cylindrical tube in a turbulent flow taking into account the turbulent viscosity

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Abstract

Using a three-layer turbulence model for a cylindrical tube, an analytical calculation of the dissipation coefficient of the mechanical energy of flow in a smooth-walled cylindrical tube was performed, taking into account the turbulent viscosity. To take into account the turbulent viscosity, the turbulence model developed by Y. V. Lapin, O. A. Nekhamkin and M. Kh. Strelets was applied, considering Van Driest’s damping multiplier. Analytical formulas were obtained describing the dependence of the dissipation coefficient of the mechanical energy of the flow on the number Re in the degree and logarithmic velocity distribution in a smooth cylindrical tube. Based on the performed calculations, a plot of the coefficient of dissipation on the number Re is constructed. The obtained results are consistent with the results obtained by other authors and are not inferior to modern, more complex mathematical models and can be used in engineering calculations. This analysis provides simple analytical expressions to determine the coefficient of dissipation concerning turbulent viscosity using a universal velocity profile in a smooth cylindrical tube.

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This research has not received any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Energy Technologies, Cherkasy State Technological University, Cherkasy, Ukraine

    Alla Yovchenko, Sergii Bespalko & Sviatoslav Poliakov

  2. Department of Mechanics, Printing Machines and Technology, Cherkasy State Technological University, Cherkasy, Ukraine

    Tymofii Veretilnyk & Ruslan Kapitan

Authors
  1. Alla Yovchenko
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  2. Sergii Bespalko
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  3. Sviatoslav Poliakov
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  4. Tymofii Veretilnyk
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  5. Ruslan Kapitan
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Correspondence to Ruslan Kapitan.

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Yovchenko, A., Bespalko, S., Poliakov, S. et al. Calculation of the dissipation coefficient of the mechanical energy of moving fluid in the smooth cylindrical tube in a turbulent flow taking into account the turbulent viscosity. Int J Energy Environ Eng 11, 485–496 (2020). https://doi.org/10.1007/s40095-020-00349-x

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