Numerical simulation of turbulent oscillating flow in porous media

Document Type : Article

Authors

1 - Department of Mechanical Engineering, Tarbiat Modares University, Tehran, P.O. Box 14115-143, Iran. - Department of Mechanical Engineering, University of Mazandaran, Babolsar, P.O. Box 47416-13534, Iran.

2 Department of Mechanical Engineering, Tarbiat Modares University, Tehran, P.O. Box 14115-143, Iran

Abstract

Two macroscopic turbulent models, P-dL and N-K, have been proposed in recent years for simulating turbulent unidirectional flow in porous media. In this paper a modification on N-K model has been proposed for turbulent oscillating flow in porous media. To this purpose, Turbulent oscillating flow in porous media has been simulated in microscale employing a periodic array. The k-ε model was applied to solve turbulent oscillating flow in periodic array. Control volume approach has been used to discretize Navier-Stokes and k-ε equations and the well-established SIMPLE method has been conducted to deal with pressure and velocity coupling. To modify N-K model the effect of different parameters such as frequency and Reynolds number has been investigated and the constants in source terms of turbulent kinetic energy and its dissipation rate has been modified versus Re according to microscale results. In order to validate the new modified constants, the modified N-K model was applied to turbulent oscillating flow in porous media and results were compared to original N-K macroscopic model.

Keywords


References
[1]      Taherzadeh, M. and Saidi, M. S. “Natural circulation in vertical porous annular enclosure with heat generation,” Sci. Iran., vol. 22, no. 1, pp. 208–219, 2015.
[2]      Kardgar, A. and Jafarian, A. “Numerical investigation of oscillating conjugate heat transfer in pulse tubes,” Appl. Therm. Eng., vol. 105, pp. 557–565, 2016.
[3]      Jolls, K. R. and Hanratty, T. J. “Transition to turbulence for flow through a dumped bed of spheres,” Chemical Engineering Science, vol. 21, no. 12. pp. 1185–1190, 1966.
[4]      Dybbs, A. and Edwards, R. V. “A New Look at Porous Media Fluid Mechanics — Darcy to Turbulent,” in Fundamentals of Transport Phenomena in Porous Media, Dordrecht: Springer Netherlands, 1984, pp. 199–256.
[5]      Horton, N. A. and Pokrajac, D. “Onset of turbulence in a regular porous medium: An experimental study,” Phys. Fluids, vol. 21, no. 4, 2009.
[6]      Teruel, F. E.  and Rizwan-uddin, “A new turbulence model for porous media flows. Part I: Constitutive equations and model closure,” Int. J. Heat Mass Transf., vol. 52, no. 19–20, pp. 4264–4272, Sep. 2009.
[7]      Masuoka, T. and Takatsu, Y. “Turbulence model for flow through porous media,” Int. J. Heat Mass Transf., vol. 39, no. 13, pp. 2803–2809, 1996.
[8]      Nield, D. A. “Alternative models of turbulence in a porous medium, and related matters,” J. Fluids Eng. Trans. ASME, vol. 123, no. 4, pp. 928–934, 2001.
[9]      Alvarez, G., Bournet, P. E. and Flick, D. “Two-dimensional simulation of turbulent flow and transfer through stacked spheres,” Int. J. Heat Mass Transf., vol. 46, no. 13, pp. 2459–2469, 2003.
[10]    Antohe, B. V.  and Lage, J. L. “A general two-equation macroscopic turbulence model for incompressible flow in porous media,” Int. J. Heat Mass Transf., vol. 40, no. 13, pp. 3013–3024, 1997.
[11]    Nakayama, A. and Kuwahara, F. “A macroscopic turbulence model for flow in a porous medium,” J. Fluids Eng. Trans. ASME, vol. 121, no. 2, pp. 427–433, 1999.
[12]    Pedras, M. H. J. and De Lemos, M. J. S. “Macroscopic turbulence modeling for incompressible flow through undefromable porous media,” Int. J. Heat Mass Transf., vol. 44, no. 6, pp. 1081–1093, 2001.
[13]    Carvalho, P. H. S.  and de Lemos, M. J. S. “Role of porosity and solid-to-fluid thermal conductivity ratio on turbulent combined heat and mass transfer in a porous cavity,” Int. J. Heat Mass Transf., vol. 132, pp. 221–237, 2019.
[14]    Guo, B., Yu, A., Wright, B. and P. Zulli, “Comparison of Several Turbulence Models Applied To the Simulation of Gas Flow in a Packed Bed,” in 3rd International Conference on CFD in the Minerals and Process Industries, 2003, no. December, pp. 1–5.
[15]    Nouri-Borujerdi, A.  and Seyyed-Hashemi, M. H. “Numerical analysis of thermally developing turbulent flow in partially filled porous pipes,” Sci. Iran. Trans. B, Mech. Eng., vol. 22, no. 3, p. 835, 2015.
[16]    Kazerooni, R. B. and Hannani, S. K.,“Simulation of turbulent flow through porous media employing a v2f model,” in AIP Conference Proceedings, 2007, vol. 963, no. 2, pp. 1257–1260.
[17]    Kim, J. S. and Kang, P. K. “Anomalous transport through free-flow-porous media interface: Pore-scale simulation and predictive modeling,” Adv. Water Resour., vol. 135, p. 103467, Jan. 2020.
[18]    de Lemos M. J. S. and Assato, M. “Turbulence structure and heat transfer in a sudden expansion with a porous insert using linear and non-linear turbulence models,” Int. J. Therm. Sci., vol. 141, pp. 1–13, Jul. 2019.
[19]    Soulaine, C. and Quintard, M. “On the use of a Darcy-Forchheimer like model for a macro-scale description of turbulence in porous media and its application to structured packings,” Int. J. Heat Mass Transf., vol. 74, pp. 88–100, 2014.
[20]    Torabi, M., Torabi, M., Yazdi, M. E. and Peterson, G. P. “Fluid flow, heat transfer and entropy generation analyses of turbulent forced convection through isotropic porous media using RANS models,” Int. J. Heat Mass Transf., vol. 132, pp. 443–461, 2019.
[21]    Kundu, P., Kumar, V. and Mishra, I. M. “Numerical modeling of turbulent flow through isotropic porous media,” Int. J. Heat Mass Transf., vol. 75, pp. 40–57, 2014.
[22]    Chu, X., Yang, G., Pandey, S. and B. Weigand, “Direct numerical simulation of convective heat transfer in porous media,” Int. J. Heat Mass Transf., vol. 133, pp. 11–20, 2019.
[23]    Fu, J., Tang, Y., Li, J., Ma, Y., Chen, W., and Li, H. “Four kinds of the two-equation turbulence model’s research on flow field simulation performance of DPF’s porous media and swirl-type regeneration burner,” Appl. Therm. Eng., vol. 93, pp. 397–404, Jan. 2016.
[24]    Khan F. A. and Straatman, A. G. “Closure of a macroscopic turbulence and non-equilibrium turbulent heat and mass transfer model for a porous media comprised of randomly packed spheres,” Int. J. Heat Mass Transf., vol. 101, pp. 1003–1015, 2016.
[25]    Linsong, J., Hongsheng, L., Shaoyi, S., Maozhao, X., Dan, W., and Minli, B. “Pore-scale simulation of flow and turbulence characteristics in three-dimensional randomly packed beds,” Powder Technol., vol. 338, pp. 197–210, 2018.
[26]    Kuwahara, F., Kameyama, Y., Yamashita, S. and Nakayama, A. “Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array,” J. Porous Media, vol. 1, no. 1, pp. 47–55, 1998.
[27]    Kundu, P., Kumar, V., Hoarau, Y.  and Mishra, I. M. “Numerical simulation and analysis of fluid flow hydrodynamics through a structured array of circular cylinders forming porous medium,” Appl. Math. Model., vol. 40, no. 23–24, pp. 9848–9871, 2016.
[28]    Kim, S. “Numerical investigation on laminar pulsating flow through porous media,” 2008.
[29]    Pathak M. G. and Ghiaasiaan, S. M. “Convective heat transfer and thermal dispersion during laminar pulsating flow in porous media,” Int. J. Therm. Sci., vol. 50, no. 4, pp. 440–448, 2011.
[30]    Kardgar, A., Jafarian, A. and M. Arablu, “An Eulerian-Lagrangian model to study the operating mechanism of Stirling pulse tube refrigerators,” Sci. Iran. Trans. B, Mech. Eng., vol. 23, no. 1, p. 277, 2016.
[31]    Rezaei, M. Jafarian, A. and Kardgar, A. “Numerical investigation of real gas effects on a two-stage pulse tube cryocooler performance,” Int. J. Refrig., vol. 82, pp. 106–118, 2017.
[32]    Nouri-Boroujerdi, A. Rabani, R. and Kermani, M. J. “Effect of porosity variation in determination of stagnant and dispersion thermal conductivities in the resin transfer molding process,” Heat Transf. Res., vol. 43, no. 7, pp. 651–667, 2012.
[33]    Tu, S. W. and Ramaprian , B. R. “Fully developed periodic turbulent pipe flow. Part 1. Main experimental results and comparison with predictions,” J. Fluid Mech., vol. 137, no. 137, pp. 31–58, 1983.
Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 743-756
  • Receive Date: 13 January 2019
  • Revise Date: 12 December 2019
  • Accept Date: 18 January 2020