Skip to main content
Log in

Lattice Boltzmann simulation of a fluid flow around a triangular unit of three isothermal cylinders

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the Bhatnagar–Gross–Krook model are used to simulate two-dimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Mittal and S. Balachandar, “Direct Numerical Simulation of Flow Past Elliptic Cylinders,” J. Comput. Phys. 124, 351–367 (1996).

    Article  ADS  MATH  Google Scholar 

  2. B. Sharman, F. S. Lien, L. Davidson, and C. Norberg, “Numerical Predictions of Low Reynolds Number Flows over Two Tandem Circular Cylinders,” Int. J. Numer. Methods Fluids 47, 423–447 (2005).

    Article  ADS  MATH  Google Scholar 

  3. D. Arumuga Perumal, G. V. S. Kumar, and A. K. Dass, “Lattice Boltzmann Simulation of Viscous Flow Past Elliptical Cylinder,” J. CFD Lett. 4, 127–139 (2012).

    Google Scholar 

  4. K. Shintani, A. Umemura, and A. Takano, “Low-Reynolds-Number Flow Past an Elliptic Cylinder,” J. Fluid Mech. 136, 277–289 (1983).

    Article  ADS  MATH  Google Scholar 

  5. F. J. Higuera and J. Jimenez, “Boltzmann Approach to Lattice Gas Simulation,” Europhys. Lett. 9, 663–668 (1989).

    Article  ADS  Google Scholar 

  6. F. Massaioli, R. Benzi, and S. Succi, “Exponential Tails in Two-Dimensional Rayleigh–Be’nard Convection,” Europhys. Lett. 21, 305–310 (1993).

    Article  ADS  Google Scholar 

  7. Y. Chen, H. Ohashi, and M. A. Akiyama, “Thermal Lattice Bhatnagar–Gross–Krook Model without Nonlinear Deviations in Macro Dynamic Equations,” Phys. Rev. E 50, 2776–2783 (1994).

    Article  ADS  Google Scholar 

  8. P. Pavlo, G. Vahala, L. Vahala, and M. Soe, “Linear-Stability Analysis of Thermo-Lattice Boltzmann Models,” J. Comput. Phys. 139, 79–91 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. B. Crouse, M. Krafczyk, S. Kuhner, et al., “Indoor Air Flow Analysis Based on Lattice Boltzmann Methods,” Energy Build 34, 941–949 (2002).

    Article  Google Scholar 

  10. A. D’Orazio, M. Corcione, and G. P. Cielata, “Application to Natural Convection Enclosed Flows of a Lattice Boltzmann BGK Model Coupled with a General Purpose Thermal Boundary Condition,” Int. J. Thermal Sci. 43, 575–586 (2004).

    Article  Google Scholar 

  11. A. Korichi and L. Oufer, “Numerical Heat Transfer in a Rectangular Channel with Mounted Obstacles on the Upper and Lower Walls,” Int. J. Thermal Sci. 44, 644–655 (2005).

    Article  Google Scholar 

  12. G. Juncu, “A Numerical Study of Momentum and Forced Convection Heat Transfer Around Two Tandem Circular Cylinders at Low Reynolds Numbers. Pt 2. Forced Convection Heat Transfer,” Int. J. Heat Mass Transfer 50, 3799–3808 (2007).

    Article  MATH  Google Scholar 

  13. M. Farhadi, K. Sedighi, and M. M. Madani, “Convective Cooling of Tandem Heated Squares in a Channel,” J. Mech. Eng. Sci. 223, 965–978 (2009).

    Article  Google Scholar 

  14. M. Mohammadi Pirouz, M. Farhadi, K. Sedighi, et al., “Lattice Boltzmann Simulation of Conjugate Heat Transfer in a Rectangular Channel with Wall-Mounted Obstacles,” J. Sci. Iranica B 18, 213–222 (2011).

    Article  Google Scholar 

  15. B. Chopard and P. O. Luthi, “Lattice Boltzmann Computations and Applications to Physics,” Theoret. Comput. Phys. 217, 115–130 (1999).

    MathSciNet  MATH  Google Scholar 

  16. R. R. Nourgaliev, T. N. Dinh, T. G. Theofanous, and D. Joseph, “The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications,” Int. J. Multiphase Flow 29, 117–169 (2003).

    Article  MATH  Google Scholar 

  17. D. Yu, R. Mei, L. S. Luo, and W. Shyy, “Viscous Flow Computations with the Method of Lattice Boltzmann Equation,” Progr. Aerospace Sci. 39, 329–367 (2003).

    Article  ADS  Google Scholar 

  18. A. A. Mohammad, Applied Lattice Boltzmann Method for Transport Phenomena Momentum Heat Mass Transfer (Univ. Calgary Press, Calgary, 2007).

    Google Scholar 

  19. D. M. Aghajani, M. Farhadi, and K. Sedighi, “Effect of Heater Location on Heat Transfer and Entropy Generation in the Cavity Using the Lattice Boltzmann Method,” Heat Transfer Res. 40, 521–536 (2009).

    Article  Google Scholar 

  20. A. Mezrhab, M. Jami, C. Abid, et al., “Lattice Boltzmann Modeling of Natural Convection in an Inclined Square Enclosure with Partitions Attached to its Cold Wall,” Int. J. Heat Fluid Flow 27, 456–465 (2006).

    Article  Google Scholar 

  21. X. He and L. S. Luo, “Lattice Boltzmann Model for the Incompressible Navier–Stokes Equations,” J. Statist. Phys. 88, 927–944 (1997).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. N. Thürey and U. Rüde, “Stable Free Surface Flows with the Lattice Boltzmann Method on Adaptively Coarsened Grids,” Comput. Visual. Sci. 12, 247–263 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  23. Z. L. Guo, Ch. Zheng, and B. C. Shi, “An Extrapolation Method for Boundary Conditions in Lattice Boltzmann Method,” Phys. Fluids 14 (6), 2007–2010 (2002).

    Article  ADS  MATH  Google Scholar 

  24. J. Park, K. Kwon, and H. Choi, “Numerical Solutions of Flow Past a Circular Cylinder at Reynolds Number up to 160,” KSME Int. J. 12, 1200 (1998).

    Google Scholar 

  25. D. Sucker and H. Brauer, “Fluiddynamikbei der Angestromten Zilindern,” Wärmeund Stoffübertrag 8, 149 (1975).

    Article  ADS  Google Scholar 

  26. W. A. Khan, J. R. Culham, and M. M. Yovanovich, “Fluid Flow Around and Heat Transfer from Elliptical Cylinders: Analytical Approach,” J. Thermophys. Heat Transfer 19, 178–185 (2005).

    Article  Google Scholar 

  27. J. Hoffman, “Efficient Computation of Mean Drag for the Subcritical Flow Past a Circular Cylinder using General Galerkin G2,” Int. J. Numer. Methods Fluids 59 (11), 1241–1258 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. C. Von Wieselsberger, “Neuere Festellungen über die Gesetze des Flüssigkeits un Luftwiderstands,” Phys. Z. 22, 321–328 (1921).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Alinejad.

Additional information

Original Russian Text © J. Alinejad.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 1, pp. 136–145, January–February, 2016. Original article submitted January 10, 2013; revision submitted January 24, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alinejad, J. Lattice Boltzmann simulation of a fluid flow around a triangular unit of three isothermal cylinders. J Appl Mech Tech Phy 57, 117–126 (2016). https://doi.org/10.1134/S0021894416010132

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894416010132

Keywords

Navigation