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The driven cavity turbulent flow with porous walls: Energy transfer, dissipation, and time-space correlations

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Abstract

The energy transfer and dissipation as well as the turbulent structures in a lid-driven cavity flow with porous walls are investigated via the lattice Boltzmann method, with direct numerical simulation (DNS) for an isothermal incompressible flow for which the Reynolds number (Re) is 50 000. A generalized Navier-Stokes equation with the Brinkman-Forchheimer-extended Darcy model is implemented, in which the presence of permeable walls is taken into account. This study focuses on the modulations of the flow field due to porous walls, by comparing with the results from the cavity flow bounded with smooth walls. Firstly, we derived the exact expression of the kinetic energy dissipation rate in a cavity to study the budget balance of the induced and dissipated kinetic energy. By decomposing the total kinetic energy dissipation into the componential contributions of the viscous and porous medium layer, we found that the kinetic energy dissipated in the thin porous layer occupies 37% of the total driven lid-induced kinetic energy in the present parameters. Then we found that the time-averaged kinetic energy, turbulent kinetic energy (TKE), as well as the strength of the large-scale energy-containing eddy, and secondary eddies are significantly attenuated. Furthermore, it is found that the momentum and kinetic energy transfer near the corners are vastly decreased. Finally, the space-time velocity correlation functions are also provided to examine the decorrelation property of small eddies by means of convection and distortion motions in the cavity turbulent field.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Wen-wu Yang, Bo-fu Wang, Quan Zhou & Yu-hong Dong

Authors
  1. Wen-wu Yang
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  2. Bo-fu Wang
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  3. Quan Zhou
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  4. Yu-hong Dong
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Corresponding author

Correspondence to Yu-hong Dong.

Additional information

Projects supported by the Natural Science Foundation of China (Grant Nos. 91852111, 92052201, 12172207 and 11972220), the Program of the Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-09-E00018).

Biography: Wen-wu Yang (1990-), Male, Ph. D. Candidate

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Yang, Ww., Wang, Bf., Zhou, Q. et al. The driven cavity turbulent flow with porous walls: Energy transfer, dissipation, and time-space correlations. J Hydrodyn 33, 712–724 (2021). https://doi.org/10.1007/s42241-021-0072-2

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  • DOI: https://doi.org/10.1007/s42241-021-0072-2

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