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Applied Mathematics and Mechanics

, Volume 32, Issue 12, pp 1565–1576 | Cite as

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

  • Li Xu (徐 丽)Email author
  • Pei-fen Weng (翁培奋)
Article

Abstract

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing the period boundary condition, the computation regions of flows are discretized by using the structured chimera grids composed of a fine rotor grid and a cylindrical background grid. In the background grid, the mesh cells located in the wake regions are refined after the solution reaches the approximate convergence. Considering the interpolation characteristic of the WENO scheme, three layers of the hole boundary and the interpolation boundary are searched. The performance of the schemes is investigated in a transonic flow and a subsonic flow around the hovering rotor. The results reveal that the present approach has great capabilities in capturing the vortex wake with high resolution, and the WENO scheme has much lower numerical dissipation in comparison with the MUSCL scheme.

Key words

hovering rotor vortex wake Navier-Stokes equation chimera grid weighted essentially non-oscillatory (WENO) scheme 

Chinese Library Classification

V211.3 

2010 Mathematics Subject Classification

76M12 76N15 

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References

  1. [1]
    Egolf, T. A. Recent rotor wake simulation and modeling studies at United Technologies Corporation. AIAA Paper, 2000-115 (2000)Google Scholar
  2. [2]
    He, C. and Zhao, J. Modeling rotor wake dynamics with viscous vortex particle method. AIAA Journal, 47(4), 902–915 (2009)CrossRefGoogle Scholar
  3. [3]
    Harris, R. E., Sheta, E. F., and Habchi, S. D. An efficient adaptive Cartesian vorticity transport solver for rotorcraft flowfield analysis. AIAA Paper, 2010-1072 (2010)Google Scholar
  4. [4]
    Wagner, S. On the numerical prediction of rotor wakes using linear and non-linear methods. AIAA Paper, 2000-0111 (2000)Google Scholar
  5. [5]
    Dietz, M., Keler, M., Kramer, E., and Wagner, S. Tip vortex conservation on a helicopter main rotor using vortex-adapted chimera grids. AIAA Journal, 45(8), 2062–2074 (2007)CrossRefGoogle Scholar
  6. [6]
    Caradonna, F. X., Directorate, A., Aviation, U. S., and Command, M. Developments and challenges in rotorcraft aerodynamics. AIAA Paper, 2000-0109 (2000)Google Scholar
  7. [7]
    Hariharan, N. and Sankar, L. N. High-order essentially nonoscillatory schemes for rotary-wing wake computations. Journal of Aircraft, 41(2), 258–267 (2004)CrossRefGoogle Scholar
  8. [8]
    Hariharan, N. High order accurate numerical convection of vortices across overset interfaces. AIAA Paper, 2005-1263 (2005)Google Scholar
  9. [9]
    Usta, E., Wake, B. E., Egolf, T. A., and Sankar, L. N. Application of a symmetric total variation diminishing scheme to aerodynamics and aeroacoustics of rotors. American Helicopter Society 57th Annual Forum, Washington, D. C. (2001)Google Scholar
  10. [10]
    Kim, H., Williams, M., and Lyrintzis, A. Improved method for rotor wake capturing. Journal of Aircraft, 39(5), 794–803 (2002)CrossRefGoogle Scholar
  11. [11]
    Borges, R., Carmona, M., Costa, B., and Don, W. S. An improved weighted essentially nonoscillatory scheme for hyperbolic conservation laws. Journal of Computational Physics, 227(6), 3191–3211 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  12. [12]
    Liu, X. D., Osher, S., and Chan, T. Weighted essentially non-oscillatory schemes. Journal of Computational Physics, 115(1), 200–212 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  13. [13]
    Jiang, G. S. and Shu, C. W. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126(1), 202–228 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    Yoon, S. and Jameson, A. Lower-upper symmetric Gauss-Seidel method for the Euler and Navier-Stokes equations. AIAA Journal, 26(9), 1025–1026 (1988)CrossRefGoogle Scholar
  15. [15]
    Chen, R. and Wang, Z. Fast, block lower-upper symmetric Gauss-Seidel scheme for arbitrary grids. AIAA Journal, 38(12), 2238–2245 (2000)CrossRefGoogle Scholar
  16. [16]
    Baldwin, B. S. and Lomax, H. Thin layer approximation and algebraic model for separated turbulent flow. AIAA Paper, 78-0257 (1978)Google Scholar
  17. [17]
    Roe, P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2), 357–372 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  18. [18]
    Chen, X., Zha, G. C., and Yang, M. T. Numerical simulation of 3-D wing flutter with fully coupled fluid-structural interaction. Computers and Fluids, 36(5), 856–867 (2007)CrossRefzbMATHGoogle Scholar
  19. [19]
    Harten, A. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3), 357–393 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  20. [20]
    Xu, L., Yang, A. M., Guang, P., and Weng, P. F. Numerical experiments using one high-resolution scheme for unsteady inviscid compressible flows. Acta Aerodynamica Sinica, 27(5), 602–607 (2009)Google Scholar
  21. [21]
    Titarev, V. A. and Toro, E. F. WENO schemes based on upwind and centred TVD fluxes. Computers and Fluids, 34(6), 705–720 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  22. [22]
    Caradonna, F. X. and Tung, C. Experimental and analytical studies of a model helicopter rotor in hover. NASA TM, 81232 (1981)Google Scholar
  23. [23]
    Strawn, R. C. and Barth, T. J. A finite-volume Euler solver for computing rotary-wing aerodynamics on unstructured meshes. Journal of the American Helicopter Society, 38, 61–67 (1993)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsShanghai University of Electric PowerShanghaiP. R. China
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China

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