Skip to main content
Log in

Flow Simulation Around Cambered Airfoil by Using Conformal Mapping and Intermediate Domain in Lattice Boltzmann Method

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

In this paper the developed interpolation lattice Boltzmann method is used for simulation of unsteady fluid flow. It combines the desirable features of the lattice Boltzmann and the Joukowski transformation methods. This approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system. Simulation of unsteady flow around a cambered airfoil in a non-uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long-term periodic flow phenomena. The developed solver is also coupled with a fast adaptive grid generator. In addition, the new approach retains all the advantages of the standard lattice Boltzmann method. The Strouhal number, the pressure, the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations. Numerical studies for various test cases illustrate the strength of this new approach.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Poozesh, A.: Analysis of IncompressibleViscous Flow on Non-uniform Grid Using Lattice Boltzmann Method, [Dissertation]. Toosi University of Technology, K. N (2012)

    Google Scholar 

  2. N. Cao, S. Chen ,S. Jin and D. Martinez , Physical symmetry and lattice symmetry in Lattice Boltzmann method, Phys. Rev. E, 55, pR21, 1997

  3. Mei, R., Shyy, W.: on the finite difference-based lattice Boltzmann method in curvilinear coordinates. J. Comp. Phys. 134, p306 (1997)

    Article  Google Scholar 

  4. Nannelli, F., Succi, S.: The lattice Boltzmann equation on irregular lattice. J. Stat. Phys. 68, p401 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Amati, G., Succi, S., Benzi, R.: Turbulent channel flow simulation using a coarse-gained extension of the lattice Boltzmann method. Fluid Dyn. Res. 19, p289 (1997)

    Article  ADS  Google Scholar 

  6. Fillipova, O., Hanel, D.: Grid refinement for lattice-BGK models. J. Comput. Phys. 147, 219 (1998)

    Article  ADS  MATH  Google Scholar 

  7. Mei, R., Luo, L.-S., Shyy, W.: An accurate curved boundary treatment in the lattice Boltzmann method. J. Comp. Phys. 155, p307 (1999)

    Article  ADS  MATH  Google Scholar 

  8. He, X., Luo, L.S., Dembo, M.: Some progress in lattice Boltzmann method, Part 1. Non-uniform mesh grids. J. Comput. Phys. 129, 357 (1996)

    Article  ADS  MATH  Google Scholar 

  9. He, X., Doolen, G.: Lattice Boltzmann method on curvilinear coordinate system: flow around a circular cylinder. J. Comput. Phys. 134, 306 (1997)

    Article  ADS  MATH  Google Scholar 

  10. X. He and G. D. Doolen, Lattice Boltzmann method on a curvilinear coordinate system: Vortex shedding behind a circular cylinder, Phys. Rev.E56, Number 1.July 1997

  11. He, X.: Error Analysis for the Interpolation-Supplemented Lattice-Boltzmann Equation Scheme. International Journal of Modern Physics C 8(4), 737–745 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  12. Lu et al: Large eddy simulations of a stirred tank using the lattice Boltzmann method on a nonuniform grid. J Comput Phys 181, 675–704 (2002)

    Article  ADS  MATH  Google Scholar 

  13. McNamara, G., Zanetti, G.: Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett. 61, 2332 (1988)

    Article  ADS  Google Scholar 

  14. Higuera, F., Succi, S.: Simulating the Flow past a Cylinder with a Lattice Boltzmann Equation. Europhys. Lett. 8(6), 517 (1989)

    Article  ADS  Google Scholar 

  15. Higuera, F., Succi, S., Benzi, R.: Lattice Gas Dynamics with Enhanced Collisions. Europhys. Lett. 9(4), 345 (1989)

    Article  ADS  Google Scholar 

  16. Zarghami, A., Biscarini, Ch., Succi, S., Ubertini, S.: Hydrodynamics in Porous Media: A Finite Volume Lattice Boltzmann Study. Journal of Scientific Computing 59(1), 80–103 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Imamura, T., Suzuki, K., Nakamura, T., Yoshida, M.: Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method. Journal of Computational Physics 202, 645–663 (2005)

    Article  ADS  MATH  Google Scholar 

  18. T. Imamura, K. Suzuki, T. Nakamura, M. Yoshida, Flow Simulation Around an Airfoil by LatticeBoltzmann Method on Generalized Coordinates, AIAA JOURNAL, Vol. 43, No. 9, September 2005

  19. J. Katz, A.Plotkin, Low-Speed Aerodynamics, Cambridge University Press, 2001

  20. Ziegler, D.P.: Boundary conditions for lattice Boltzmann simulations. J. Stat. Phys. 71, p1171 (1993)

    Article  ADS  Google Scholar 

  21. 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. Journal of Computational Physics 218, 460–478 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Mirzaei, M., Poozesh, A.: Simulation of fluid flow in a body-fitted grid system using the lattice Boltzmann method. Phys. Rev. E 87, 063312 (2013)

    Article  ADS  Google Scholar 

  23. Lee, T., Lin, C.-L.: A characteristic Galerkin method for discrete Boltzmann equation. J. Comput. Phys. 171, 336 (2001)

    Article  ADS  MATH  Google Scholar 

  24. Klaus A. Hoffmann and Steve T. Chiang, “Computational fluid Dynamics for engineers”, Engineering Education System, 2000

  25. M. H. Hekmat, M. Mirzaei, Development of Discrete Adjoint Approach Based on the Lattice Boltzmann Method ,Advances in Mechanical Engineering, Volume 2014 (2014) , Article ID 230854, 16 pages

  26. Gopinath, A.K., Jameson, A.: Application of the Time Spectral Method to PeriodicUnsteady Vortex Shedding, 44th AIAA Aerospace Sciences Meeting and Exhibit, January 9–12. Reno, Nevada (2006)

    Google Scholar 

  27. X. P. Chen, Application of lattice Boltzmann method to turbulent flow around two dimension airfoil, engineering of application computational fluid mechanics,Vol 6, No. 4, pp 572-(589) 2012

Download references

Acknowledgements

The authors are thankful to the parallel computational lab of Centre of Excellent for Design and Simulation of Space Systems of K.N.Toosi University of Technology for its supports.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amin Poozesh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Poozesh, A., Mirzaei, M. Flow Simulation Around Cambered Airfoil by Using Conformal Mapping and Intermediate Domain in Lattice Boltzmann Method. J Stat Phys 166, 354–367 (2017). https://doi.org/10.1007/s10955-016-1657-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-016-1657-y

Keywords

Navigation