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Pore-scale simulation of fluid flow passing over a porously covered square cylinder located at the middle of a channel, using a hybrid MRT-LBM–FVM approach

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Abstract

A comprehensive study was performed to analyze the unsteady laminar flow characteristics around a porously covered, a fully porous, and a solid squared section cylinder located in the middle of a plane channel. In order to simulate fluid flow inside porous media and porous–fluid interface accurately (minimizing modeling error), the porous region was analyzed in pore scale, using LBM. Additionally, to minimize the LBM-related compressibility error through the porous region, a multi-block multiple relaxation time lattice Boltzmann method (MRT-LBM) was used. Also, to decrease CPU time, a Navier–Stokes flow solver, based on finite volume method and SIMPLE algorithm, was coupled with MRT-LBM to simulate flow around the porous obstacle. It should be noted that the flow inside the porous layer is in continuum regime, and hence, the no-slip boundary condition was used to treat the solid walls inside the porous media. In our simulations, we considered variations of porosity and Reynolds number ranging from 0.75 to 0.94 and from 60 to 240, respectively. The effects of porosity and Reynolds number on vortex pattern, mean drag coefficient, amplitude of lift coefficient, and Strouhal number were investigated. Comparison of our results with the ones obtained using Open FOAM, as well as published by others, shows the suitable accuracy of our computations. It is seen that at low Reynolds numbers or at low porosities, where the mean flow does not have large enough momentum to penetrate porous media, the resulting flow field and aerodynamic coefficients are relatively close for three different configurations used. However, as the flow Reynolds number or permeability increases, the mean flow penetrates easier into the porous media and thus provides different shedding characteristics and aerodynamic coefficients for different obstacle shapes.

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References

  1. Williamson C.H.K., Govardhan R.: Vortex-induced vibrations. Ann. Rev. Fluid Mech. 36, 413–455 (2004)

    Article  MathSciNet  Google Scholar 

  2. Bruneau C.H., Mortazavi I.: Passive control of bluff body flow using porous media. Int. J. Numer. Methods Fluids 46, 415–433 (2004)

    Article  MATH  Google Scholar 

  3. Bhattacharyya S., Singh A.K.: Augmentation of heat transfer from a solid cylinder wrapped with a porous layer. Int. J. Heat Mass Transf. 52, 1991–2001 (2009)

    Article  MATH  Google Scholar 

  4. Perng S.W., Wu H.W., Jue T.C.: Numerical investigation of heat transfer enhancement on a porous vortex generator applied to a block-heated channel. Int. J. Heat Mass Transf. 55, 3121–3137 (2012)

    Article  Google Scholar 

  5. Huang P.C., Vafai K.: Passive alteration and control of convective heat transfer utilizing alternate porous cavity-block wafers. Int. J. Heat Fluid Flow 15, 48–61 (1994)

    Article  Google Scholar 

  6. Jue T.C.: Numerical analysis of vortex shedding behind a porous square cylinder. Int. J. Numer. Methods Heat Fluid Flow 14, 649–663 (2004)

    Article  MATH  Google Scholar 

  7. Chen X., Yu P., Winoto S.H.: Numerical analysis for the flow past a porous square cylinder based on the stress-jump interfacial-conditions. Int. J. Numer. Methods Heat Fluid Flow 18, 635–655 (2008)

    Article  Google Scholar 

  8. Bruneau C.H., Mortazavi I.: Numerical modelling and passive flow control using porous media. Comput. Fluids 37, 488–498 (2008)

    Article  MATH  Google Scholar 

  9. Rong F.M., Guo Z.L., Lu J.H., Shi B.C.: Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method. Int. J. Numer. Methods Fluids 65, 1217–1230 (2011)

    Article  Google Scholar 

  10. Wu H.W., Wang W.B.: Unsteady convective heat transfer over a heated square porous cylinder in a channel. Int. J. Heat Mass Transf. 53, 1927–1937 (2010)

    Article  MATH  Google Scholar 

  11. Perng S.W., Wu H.W., Wang R.H., Jue T.C.: Unsteady convection heat transfer for a porous square cylinder varying cylinder-to-channel height ratio. Int. J. Therm. Sci. 50, 2006–2015 (2011)

    Article  Google Scholar 

  12. Liang Y.Y., Chuan H.P., Fu Y.C., Jen C.Y.: Numerical study of heat transfer of a porous-block-mounted heat source subjected to pulsating channel flow. Numer. Heat Transf. Part A Appl. 54, 426–449 (2008)

    Article  Google Scholar 

  13. Cancelliere A., Chang C., Foti E., Rothman D.H., Succi S.: The permeability of a random medium: comparison of simulation with theory. Phys. Fluids A 2, 2085–2088 (1990)

    Article  Google Scholar 

  14. Inamuro T., Yoshino M., Ogino F.: Lattice Boltzmann simulation of flows in a three-dimensional porous structure. Int. J. Numer. Methods Fluids 29, 737–748 (1999)

    Article  MATH  Google Scholar 

  15. Yoshino M., Inamuro T.: Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three-dimensional porous structure. Int. J. Numer. Meth. Fluids 43, 183–198 (2003)

    Article  MATH  Google Scholar 

  16. Wang M., He J., Yu J., Pan N.: Lattice Boltzmann modeling of the effective thermal conductivity for fibrous materials. Int. J. Therm. Sci. 46, 848–855 (2007)

    Article  Google Scholar 

  17. Verma N., Mewes D.: Lattice Boltzmann methods for simulation of micro and macro transport in a packed bed of porous adsorbents under non-isothermal condition. Comput. Math. Appl. 58, 1003–1014 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Javaran E.J, Gandjalikhan Nassab S.A., Jafari S.: Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow. Int. J. Therm. Sci. 49, 1031–1041 (2010)

    Article  Google Scholar 

  19. Li Q., Zhao K., Xuan Y.M.: Simulation of flow and heat transfer with evaporation in a porous wick of a CPL evaporator on pore scale by lattice Boltzmann method. Int. J. Heat Mass Transf. 54, 2890–2901 (2011)

    Article  MATH  Google Scholar 

  20. Albuquerque P., Alemansi D., Chopard B., Leone P.: Coupling a Lattice Boltzmann and Finite Difference Scheme. International Conference on Computational Science. Krakow, Poland (2004)

    Google Scholar 

  21. Christensen A., Graham S.: Multiscale lattice Boltzmann modeling of phonon transport in crystalline semiconductor material. Numer. Heat Transf. B 57, 89–109 (2010)

    Article  Google Scholar 

  22. Joshi H., Agarwal A., Puranik B., Shu C., Agrawal A.: A hybrid FVM–LBM method for single and multi-fluid compressible flow problems. Int. J. Numer. Methods Fluids 62, 403–427 (2010)

    MATH  MathSciNet  Google Scholar 

  23. Luan H.B., Xu H., Chen L., Sun D.L., Tao W.Q.: Numerical illustrations of the coupling between lattice Boltzmann method and finite-type macro-numerical methods. Numer. Heat Transf. B 57, 147–171 (2010)

    Article  Google Scholar 

  24. Luan, H.B., Xu, H., Chen, L., Feng, Y.L., He, Y.L., Tao, W.Q.: Coupling of finite volume method and thermal lattice boltzmann method and its application to natural convection. Int. J. Numer. Meth. Fluids 70, 200–221 (2012)

  25. Chen L., Luan H.B., Feng Y.L., Song C., He Y.L., Tao W.Q.: Coupling between finite volume method and lattice Boltzmann method and its application to fluid flow and mass transport in proton exchange membrane fuel cell. Int. J. Heat Mass Transf. 55, 3834–3848 (2012)

    Article  Google Scholar 

  26. Boomsma B., Poulikakos D., Zwick F.: Metal foams as compact high performance heat exchangers. Mech. Mater. 35, 1161–1176 (2003)

    Article  Google Scholar 

  27. Tadrist L., Miscevic M., Rahli O., Topin F.: About the use of fibrous materials in compact heat exchangers. Exp. Therm. Fluid Sci. 28, 193–199 (2004)

    Article  Google Scholar 

  28. He X., Zou Q., Luo L.S., Dembo M.: Analytic solution and analysis on non-slip boundary condition for the lattice Boltzmann BGK model. J. Stat. Phys. 87, 115–136 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  29. Pan C., Luo L.S., Miller C.T.: An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 35, 898–909 (2006)

    Article  MATH  Google Scholar 

  30. Peng Y., Shu C., Chew Y.T., Niu X.D., Lu X.Y.: Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows. J. Comput. Phys. 218, 460–478 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  31. Xu H., Luan H.B., He Y.L., Tao W.Q.: A lifting relation from macroscopic variables to mesoscopic variables in lattice Boltzmann method: derivation numerical assessments and coupling computations validation. Comput. Fluids J. 54, 92–105 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  32. Breuer M., Bernsdorf J., Zeiser T., Durst F.: Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume. Int. J. Heat Fluid Flow 21, 186–196 (2000)

    Article  Google Scholar 

  33. Bernsdorf J., Durst F., Schafer M.: Comparison of cellular automata and finite volume techniques for simulation of incompressible flows in complex geometries. Int. J. Numer. Method Fluids 29, 251–264 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  34. Yoshino M., Matsuda Y., Shao C.: Comparison of accuracy and efficiency between the lattice Boltzmann method and the finite difference method in viscous/thermal fluid flows. Int. J. Comput. Fluid D 18, 333–345 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  35. Luan H.B., Xu H., Chen L., Sun D.L., He Y.L., Tao W.Q.: Evaluation of the coupling scheme of FVM and LBM for fluid flows around complex geometries. Int. J. Heat Mass Transf. 54, 1975–1985 (2011)

    Article  MATH  Google Scholar 

  36. Pan C.X., Prins J.F., Miller C.T.: A high-performance lattice Boltzmann implementation to model flow in porous media. Comput. Phys. Commun. 158, 89–105 (2004)

    Article  MATH  Google Scholar 

  37. Imamura T., Suzuki K., Nakamura T., Yoshida M.: Acceleration of steady state lattice Boltzmann simulation on non-uniform mesh using local time step method. J. Comput. Phys. 202, 645–663 (2005)

    Article  MATH  Google Scholar 

  38. Mei R., Yu D., Shyy W., Luo L.S.: Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65, 1–14 (2002)

    Article  Google Scholar 

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Authors and Affiliations

  1. Aerospace Engineering Department, Sharif University of Technology, Tehran, Iran

    Mohammad Reza Salimi & Mohammad Taeibi Rahni

  2. Mechanical Engineering, Farab Co., Tehran, Iran

    Freydun Jam

Authors
  1. Mohammad Reza Salimi
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  2. Mohammad Taeibi Rahni
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  3. Freydun Jam
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Correspondence to Mohammad Taeibi Rahni.

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Communicated by Patrick Jenny.

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Salimi, M.R., Taeibi Rahni, M. & Jam, F. Pore-scale simulation of fluid flow passing over a porously covered square cylinder located at the middle of a channel, using a hybrid MRT-LBM–FVM approach. Theor. Comput. Fluid Dyn. 29, 171–191 (2015). https://doi.org/10.1007/s00162-015-0347-8

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  • DOI: https://doi.org/10.1007/s00162-015-0347-8

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