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Flow, Turbulence and Combustion

, Volume 90, Issue 1, pp 29–68 | Cite as

Immersed Boundaries in Large Eddy Simulation of Compressible Flows

  • Cindy Merlin
  • Pascale DomingoEmail author
  • Luc Vervisch
Article

Abstract

Methods to immerse walls in a structured mesh are examined in the context of fully compressible solutions of the Navier–Stokes equations. The ghost cell approach is tested along with compressible conservative immersed boundaries in canonical flow configurations; the reflexion of pressure waves on walls arbitrarily inclined on a cartesian mesh is studied, and mass conservation issues examined in both a channel flow inclined at various angles and flow past a cylinder. Then, results from Large Eddy Simulation of a flow past a rectangular cylinder and a transonic cavity flow are compared against experiments, using either a multi-block mesh conforming to the wall or immersed boundaries. Different strategies to account for unresolved transport by velocity fluctuations in LES are also compared. It is found that immersed boundaries allow for reproducing most of the coupling between flow instabilities and pressure-signal properties observed in the transonic cavity flow. To conclude, the complex geometry of a trapped vortex combustor, including a cavity, is simulated and results compared against experiments.

Keywords

Large Eddy Simulation Compressible flow Immersed boundaries 

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References

  1. 1.
    Balaras, E.: Modeling complex boundaries using an external force field on fixed Cartesian grids in Large Eddy Simulations. Comput. Fluids 33, 375–404 (2004)zbMATHCrossRefGoogle Scholar
  2. 2.
    Berthelsen, P., Faltinsen, O.: A local directional ghost cell approach for incompressible viscous flow problems with irregular boundaries. J. Comput. Phys. 227(9), 4354–4397 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Beyer, R.P., Leveque, R.J.: Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Math. 29, 332–364 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Burg, J.: Maximum entropy spectral analysis. Ph.D. thesis, Stanford University (1975)Google Scholar
  5. 5.
    Burguburu, J.: Experimental study of flame stability in an aeronautical combustion chamber using trapped burned gases. Ph.D. thesis, National Institute of Applied Sciences Rouen (2012)Google Scholar
  6. 6.
    Capizzano, F.: A turbulent wall model for immersed boundary methods. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Orlando (2010)Google Scholar
  7. 7.
    Chen, J.H., Pritchard, W.G., Tavener, S.J.: Bifurcation for flow past a cylinder between parallel planes. J. Fluid Mech. 284, 23 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Choi, J.I., Oberoi, R.C., Edwards, J.R., Rosati, J.A.: An immersed boundary method for complex incompressible flows. J. Comput. Phys. 224, 757–784 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    de Tullio, M.D., Palma, P.D., Iaccarino, G., Pascazio, G., Napolitano, M.: An immersed boundary method for compressible flows using local grid refinement. J. Comput. Phys. 225(2), 2098–2117 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Domingo, P., Vervisch, L., Deynante, D.: Large Eddy Simulation of a lifted methane jet flame in a vitiated coflow. Combust. Flame 152, 415–432 (2008)CrossRefGoogle Scholar
  11. 11.
    Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., Poinsot, T.: Large Eddy Simulation of the shock/turbulence interaction. J. Comput. Phys. 152, 517–549 (1999)zbMATHCrossRefGoogle Scholar
  12. 12.
    Ducros, F., Laporte, F., Soulères, T., Guinot, V., Moinat, P., Caruelle, B.: High-order fluxes for conservative skew-symmetric-like schemes in stuctures meshes: application to compressible flows. J. Comput. Phys. 161, 114–139 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Fadlun, E.A., Verzicco, R., Orlandi, P., Mohd-Yusof, J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Forestier, N., Geffroy, P., Jacquin, L.: Etude expérimentale des propriétés instationnaires d’une couche de mélange compressible sur une cavité: cas d’une cavité ouverte peu profonde. Rt 22/00153 dafe, ONERA (in French) (2003)Google Scholar
  15. 15.
    Forestier, N., Jacquin, L., Geffroy, P.: The mixing layer over a deep cavity at high-subsonic speed. J. Fluid Mech. 475, 101–145 (2003)zbMATHCrossRefGoogle Scholar
  16. 16.
    Ghias, R., Mittal, R., Lund, T.S.: A non-body conformal grid method for simulation of compressible flows with complex immersed boundaries. AIAA Paper (2004)Google Scholar
  17. 17.
    Ghias, R., Mittal, R., Dong, H.: A sharp interface immersed boundary method for compressible viscous flows. J. Comput. Phys. 225, 528–553 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Ghosal, S., Lund, T.S., Moin, P., Akselvoll, K.: A dynamic localization model for large eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Gloerfelt, X.: Bruit rayonné par un écoulement affleurant une cavité: simulation aéroacoustique directe et application de méthodes intégrales. Ph.D. thesis, Ecole Centrale de Lyon (2001)Google Scholar
  20. 20.
    Gloerfelt, X.: Cavity noise. In: VKI Lectures: Aerodynamic Noise from Wall-Bounded Flows. Von Karman Institute (2009)Google Scholar
  21. 21.
    Goldstein, D., Handler, R., Sirovich, L.: Modeling a no-slip boundary condition with an external force field. J. Comput. Phys. 105, 354–366 (1993)zbMATHCrossRefGoogle Scholar
  22. 22.
    Gottlieb, S., Shu, C.: Total variation diminishing runge-kutta schemes. Math. Comput. 67(221), 73–85 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Grigoriadis, D.G.E., Bratzis, J.G., Goulas, A.: LES of the flow past a rectangular cylinder using the immersed boundary concept. Int. J. Numer. Methods Fluids 41, 615–632 (2003)zbMATHCrossRefGoogle Scholar
  24. 24.
    Grigoriadis, D.G.E., Bartzis, J.G., Goulas, A.: Efficient treatment of complex geometries for Large Eddy Simulations of turbulent flows. Comput. Fluids 33, 201–222 (2004)zbMATHCrossRefGoogle Scholar
  25. 25.
    Hu, X., Khoo, B., Adams, N., Huang, F.: A conservative interface method for compressible flows. J. Comput. Phys. 219(2), 553–578 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Iaccarino, G., Verzicco, R.: Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56(3), 331–347 (2003)CrossRefGoogle Scholar
  27. 27.
    Jameson, A., Schmidt, W., Turkel, E.: Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes. AIAA Paper 1259, 1981 (1981)Google Scholar
  28. 28.
    Kim, J., Kim, D., Haecheon, C.: An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–150 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Kirkpatrick, M.P., Armfield, S.W., Kent, J.H.: A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional cartesian grid. J. Comput. Phys. 184(1), 1–36 (2003)zbMATHCrossRefGoogle Scholar
  30. 30.
    Klein, M., Sadiki, A., Janicka, J.: A digital filter based generation of inflow data for spatially developing direct numerical or Large Eddy Simulation. J. Comput. Phys. 186, 652–665 (2003)zbMATHCrossRefGoogle Scholar
  31. 31.
    Lai, M.C., Peskin, C.S.: An immersed boundary method with formal second order accuracy and reduced numerical viscosity. J. Comput. Phys. 160, 705–719 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Laizet, S., Lardeau, S., Lamballais, E.: Direct numerical simulation of a mixing layer downstream a thick plate. Phys. Fluids 22(1), 015,104 (2003)Google Scholar
  33. 33.
    Lamarque, N., Porta, M., Nicoud, F., Poinsot, T.: On the stability and dissipation of wall boundary conditions for compressible flows. Int. J. Numer. Methods Fluids 62(10), 1134–1154 (2010)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Lamballais, E., Silvestrini, J.: Direct numerical simulation of interactions between a mixing layer and a wake around a cylinder. J. Turbulence 3, Article Number 028 (2002). doi: 10.1088/1468-5248/3/1/028 (2002)
  35. 35.
    Larchevêque, L., Sagaut, P., Mary, I., Labbé, O.: Large-Eddy Simulation of a compressible flow past a deep cavity. Phys. Fluids. 15(1), 193–210 (2003)CrossRefGoogle Scholar
  36. 36.
    Larchevêque, L., Sagaut, P., Lê, T.H., Comte, P.: Large eddy simulation of a compresible flow in a three dimensional open cavity at high Reynolds number. J. Fluid Mech. 516, 265–301 (2004)zbMATHCrossRefGoogle Scholar
  37. 37.
    Larchevêque, L., Sagaut, P., Labbé, O.: Large-Eddy Simulation of a subsonic cavity flow including asymmetric three-dimensional effects. J. Fluid Mech. 577, 105–126 (2007)zbMATHCrossRefGoogle Scholar
  38. 38.
    Lodato, G., Domingo, P., Vervisch, L.: Three-dimensional boundary conditions for direct and Large-Eddy Simulation of compressible viscous flows. J. Comput. Phys. 227(10), 5105–5143 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Lodato, G., Vervisch, L., Domingo, P.: A compresssible wall-adapting similarity mixed model for Large-Eddy Simulation of the impinging round jet. Phys. Fluids 21, 035,102 (2009)CrossRefGoogle Scholar
  40. 40.
    Lyn, D.A., Einavv, S., Rodi, W., Park, J.H.: A laser-doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. J. Fluid Mech. 304, 285–319 (1995)CrossRefGoogle Scholar
  41. 41.
    Majumdar, S., Iaccarino, G., Durbin, P.: RANS solver with adaptive structured boundary non-conforming grids. In: Annual Research Briefs, pp. 353–366 (2001)Google Scholar
  42. 42.
    Marple, S.L.: Digital Spectral Analysis with Applications. Prentice Hall (1987)Google Scholar
  43. 43.
    McLean, I., Gartshore, I.: Spanwise correlation of pressure on a rigid square section cylinder. J. Wind Eng. 41, 779–808 (1992)Google Scholar
  44. 44.
    Meneveau, C., Lund, T., Cabot, W.: A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385 (1996)zbMATHCrossRefGoogle Scholar
  45. 45.
    Meyer, M., Devesa, A., Hickel, S., Adams, N.A.: A conservative immersed interface method for Large-Eddy Simulation of incompressible flows. J. Comput. Phys. 229, 6300–6317 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  46. 46.
    Mittal, R., Balanchadar, S.: Effect of intrinsic three-dimensionality on the lift and drag of nominaly two-dimensional cylinders. Phys. Fluids. 7(8), 1841 (1995)CrossRefGoogle Scholar
  47. 47.
    Mittal, R., Dong, H., Bozkurttas, M., Najjar, F., Vargas, A., Von Loebbecke, A.: A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227(10), 4825–4852 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Mohd-Yusof, J.: Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries. In: Annual Research Briefs, pp. 317–327 (1997)Google Scholar
  49. 49.
    Moin, P., Squires, K., Cabot, W., Lee, C.: A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids. A 3(11), 2746–2757 (1991)zbMATHCrossRefGoogle Scholar
  50. 50.
    Murakami, S., Izuka S. ans Ooka, R.: Cfd analysis of turbulent flow past square cylinder using dynamic LES. J. Fluids Struct. 13, 1097–1112 (1999)CrossRefGoogle Scholar
  51. 51.
    Nicoud, F.: Defining wave amplitude in characteristic boundary conditions. J. Comput. Phys. 149, 418–422 (1999)zbMATHCrossRefGoogle Scholar
  52. 52.
    Palma, P.D., de Tullio, M.D., Pascazio, G., Napolitano, M.: An immersed boundary method for compressible viscous flows. Comput. Fluids 35(7), 693–702 (2006)zbMATHCrossRefGoogle Scholar
  53. 53.
    Peskin, C.S.: The fluid dynamics of heart valves: experimental, theoretical and computational methods. Annu. Rev. Fluid. Mech. 14, 135–259 (1982)CrossRefGoogle Scholar
  54. 54.
    Poinsot, T., Lele, S.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  55. 55.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer (2000)Google Scholar
  56. 56.
    Sagaut, P., Garnier, E., Tromeur, E., Larchevêque, L., Labourasse, E.: Turbulent inflow conditions for Large-Eddy Simulation of supersonic and subsonic wall flows. AIAA J. 42, 469–477 (2004)CrossRefGoogle Scholar
  57. 57.
    Sagaut, P., Deck, S., Larchevêque, L.: Numerical simulation data: from validation to physical analysis. In: Congrès Francophone de Technique Laser. CFTL 2008, Futuroscope (2008)Google Scholar
  58. 58.
    Samtaney, R., Pullin, D.I., Kosovic, B.: Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13, 1415–1430 (2001)CrossRefGoogle Scholar
  59. 59.
    Schlichting, H., Gersten, K.: Boundary Layer Theory. Springer, Berlin (2003)Google Scholar
  60. 60.
    Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather Rev. 91(3), 99–164 (1963)CrossRefGoogle Scholar
  61. 61.
    Subramanian, V., Domingo, P., Vervisch, L.: Large-Eddy Simulation of forced ignition of an annular bluff-body burner. Combust. Flame 157(3), 579–601 (2010)CrossRefGoogle Scholar
  62. 62.
    Swanson, R., Turkel, E.: On central-difference and upwind schemes. J. Comput. Phys. 101(2), 292–306 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Tatsumi, S., Martinelli, L., Jameson, A.: Flux-limited schemes for the compressible Navier–Stokes equations. AIAA J. 33(2), 252–261 (1995)zbMATHCrossRefGoogle Scholar
  64. 64.
    Thornber, B., Drikakis, D.: Implicit Large-Eddy Simulation of a deep cavity using high-resolution methods. AIAA J. 46(10), 2634–2645 (2008)CrossRefGoogle Scholar
  65. 65.
    Tseng, Y.H., Ferziger, J.H.: LES of 3D turbulent wavy bounadry flow: validation of a ghost-cell immersed boundary method. In: Proc. 3rd International Symposium on Turbulence and Shear Flow Phenomena. Sendai, Japan (2003)Google Scholar
  66. 66.
    Tyagi, M., Acharya, S.: Large Eddy Simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary method. Int. J. Numer. Methods Fluids 48, 691–722 (2005)zbMATHCrossRefGoogle Scholar
  67. 67.
    Verzicco, R., Mohd-Yusof, J., Orlandi, P., Haworth, D.: LES in complex geometries using boundary body forces. AIAA 38, 427–433 (2000)CrossRefGoogle Scholar
  68. 68.
    Voke, P.R.: Flow past a square cylinder test case LES2, vol. Direct and Large Eddy Simulation II. ERCOFTAC Series (1997)Google Scholar
  69. 69.
    Vreman, A.W.: An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications, Phys. Fluids 16(10), 3670–3681 (2004)CrossRefGoogle Scholar
  70. 70.
    Ye, T., Mittal, R., Udaykumar, H.S., Shyy, W.: An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156, 209–240 (1999)zbMATHCrossRefGoogle Scholar
  71. 71.
    Yoshizawa, A.: Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 2152–2164 (1986)zbMATHCrossRefGoogle Scholar
  72. 72.
    Zang, Y., Street, R.L., Koseff, J.R.: A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5(12), 3186–3196 (1993)CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.CORIA - CNRS & INSA de RouenSaint-Etienne-du-RouvrayFrance

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