Advertisement

Adaptive Methods for Simulation of Turbulent Combustion

  • John Bell
  • Marcus Day
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 95)

Abstract

Adaptive mesh refinement (AMR) is an effective approach for simulating fluid flow systems that exhibit a large range of numerical resolution requirements. For example, an AMR simulation could dynamically focus maximum numerical resolution near a propagating flame structure, while simultaneously placing coarser computational zones near relatively large flow structures in the exhaust region downstream of the flame. However, since turbulent reacting flow applications already tend to be significantly complex, an AMR implementation might quickly become prohibitively intricate. In this chapter, we discuss basic AMR algorithm design principles that can be applied in a straightforward way to build up extremely efficient multi-stage solution strategies. As an example, we discuss an adaptive projection scheme for low Mach number flows, which was used to analyze flame-turbulence interactions in a full-scale simulation of a turbulent premixed burner experiment using detailed chemistry and transport models.

Keywords

Coarse Grid Adaptive Mesh Turbulent Combustion Composite Solution Composite Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H., Welcome, M.L.: A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142, 1–46 (1998) zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Almgren, A.S., Bell, J.B., Crutchfield, W.Y.: Approximate projection methods: Part I. inviscid analysis. SIAM J. Sci. Comput. 22, 1139–1159 (2000) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Almgren, A.S., Bell, J.B., Szymczak, W.G.: A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM J. Sci. Comput. 17, 358–369 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ascher, U., Petzold, L.R.: Projected implicit Runge Kutta methods for differential algebraic systems. SIAM J. Num. Anal. 28, 1097–1120 (1991) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bell, J., Berger, M., Saltzman, J., Welcome, M.: A three-dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM Journal on Scientific and Statistical Computing 15, 127–138 (1994) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bell, J., Day, M., Kuhl, A.L.: Numerical simulations of shock-induced mixing and combustion. In: 19th ICDERS. Hakone, Japan (July 27 – August 1, 2003) Google Scholar
  7. 7.
    Bell, J.B., Cheng, R.K., Day, M.S., Shepherd, I.G.: Numerical simulation of Lewis number effects on lean premixed turbulent flames. Proc. Combust. Inst. 31, 1309–1317 (2007) CrossRefGoogle Scholar
  8. 8.
    Bell, J.B., Colella, P., Glaz, H.M.: A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85, 257–283 (1989) zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bell, J.B., Day, M.S., Rendleman, C.A., Woosley, S.E., Zingale, M.A.: Adaptive low Mach number simulations of nuclear flame microphysics. J. Comput. Phys. 195, 677–694 (2004) zbMATHCrossRefGoogle Scholar
  10. 10.
    Bell, J.B., Marcus, D.L.: A second-order projection method for variable density flows. J. Comput. Phys. 101, 334–348 (1992) zbMATHCrossRefGoogle Scholar
  11. 11.
    Berger, M.J., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 64–84 (1989) zbMATHCrossRefGoogle Scholar
  12. 12.
    Berger, M.J., Oliger, J.: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53, 484–512 (1984) zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value problems in Differential-Algrebraic Equations. SIAM, Philadelphia, PA (1996) Google Scholar
  14. 14.
    Chan, C.K., Lau, K.S., Chin, W.K., Cheng, R.K.: Freely propagating open premixed turbulent flames stabilized by swirl. Proc. Combust. Inst. 24, 511–518 (1992) Google Scholar
  15. 15.
    Cheng, R.K.: Velocity and scalar characteristics of premixed turbulent flames stabilized by weak swirl. Combust. Flame 101, 1–14 (1991) CrossRefGoogle Scholar
  16. 16.
    Cheng, R.K., Littlejohn, D., Strakey, P.A., Sidwell, T.: Laboratory investigations of a low-swirl injector with h2 and ch4 at gas turbine conditions. Proc. Combust. Inst. 32, 21–46 (2009) Google Scholar
  17. 17.
    Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comp. 22, 745–762 (1968) zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Crutchfield, W.Y.: Load balancing irregular algorithms. Tech. Rep. UCRL-JC-107679, Lawrence Livermore National Laboratory (1991) Google Scholar
  19. 19.
    Day, M.S., Bell, J.B.: Numerical simulation of laminar reacting flows with complex chemistry. Combust. Theory Model. 4, 535–556 (2000) zbMATHCrossRefGoogle Scholar
  20. 20.
    Day, M.S., Bell, J.B., Bremer, P.T., Pascucci, V., Beckner, V.E.: Turbulence effects on cellular burning structures in lean premixed hydrogen flames. Combust. Flame 156, 1035–1045 (2009) CrossRefGoogle Scholar
  21. 21.
    Ern, A., Giovangigli, V.: Multicomponent Transport Algorithms, Lecture Notes in Physics 24, Springer-Verlag, Berlin (1994) zbMATHGoogle Scholar
  22. 22.
    Ern, A., Giovangigli, V.: EGLIB: A General-Purpose Fortran Library for Multicomponent Transport Property Evaluations. J. Comput. Phys. 120, 105–116 (2005) CrossRefMathSciNetGoogle Scholar
  23. 23.
    Frenklach, M., Wang, H., Goldenberg, M., Smith, G.P., Golden, D.M., Bowman, C.T., Hanson, R.K., Gardiner, W.C., Lissianski, V.: GRI-Mech—an optimized detailed chemical reaction mechanism for methane combustion. Tech. Rep. GRI-95/0058, Gas Research Institute (1995). http://www.me.berkeley.edu/gri_mech/
  24. 24.
    Majda, A., Sethian, J.A.: The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Technol. 42, 185–205 (1985) CrossRefGoogle Scholar
  25. 25.
    Mansour, M., Chen, Y.C.: Experimental Thermal Fluid Sci. 32, 1390–1395 (2008) CrossRefGoogle Scholar
  26. 26.
    McMurtry, P., Jou, W.H., Riley, J., Metcalfe, R.: Direct numerical simulations or a reacting mixing layer with chemical heat release. AIAA J. 24, 962–970 (1986) CrossRefGoogle Scholar
  27. 27.
    Najm, H.N., Knio, O.M., Paul, P.H., Wyckoff, P.S.: A study of flame observables in premixed methane-air flames. Combust. Sci. Technol. 140, 369–403 (1998) CrossRefGoogle Scholar
  28. 28.
    Najm, H.N., Wyckoff, P.S.: Premixed flame response to unsteady strain rate and curvature. Combust. Flame 110, 92–112 (1997) CrossRefGoogle Scholar
  29. 29.
    Najm, H.N., Wyckoff, P.S., Knio, O.M.: A semi-implicit numerical scheme for reacting flow. I. Stiff chemistry. J. Comput. Phys. 143, 381–402 (1998) zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Nogenmyr, K., Peterson, P., Bai, X.S., Nauert, A., Olofsson, J., Brackman, C., Seyfried, H., Zetterberg, J., Li, Z.S., Richter, M., Dreizler, A., Linne, M., Alden, M.: Large eddy simulation and experiments of stratified lean premixed methane/air turbulent flames. Proc. Combust. Inst. 31, 1467–1475 (2007) CrossRefGoogle Scholar
  31. 31.
    Pember, R.B., Howell, L.H., Bell, J.B., Colella, P., Crutchfield, W.Y., Fiveland, W.A., Jessee, J.P.: An adaptive projection method for unsteady, low-Mach number combustion. Combust. Sci. Technol. 140, 123–168 (1998) CrossRefGoogle Scholar
  32. 32.
    Peterson, P., Olofsson, J., Brackman, C., Seyfried, H., Zetterberg, J., Richter, M., Alden, M., Linne, M., Cheng, R., Nauert, A., Geyer, D., Dreizler, A.: Simultaneous PIV/OH PLIF, Rayleigh thermometry/OH PLIF and stereo PIV measurements in a low-swirl flame. Appl. Opt 46, 3928–3936 (2007) CrossRefGoogle Scholar
  33. 33.
    Qian, J., Tryggvason, G., Law, C.K.: Front tracking method for the motion of premixed flames. J. Comput. Phys. 144, 52–69 (1988) CrossRefGoogle Scholar
  34. 34.
    Rehm, R.G., Baum, H.R.: The equations of motion for thermally driven buoyant flows. N. B. S. J. Res. 83, 297–308 (1978) zbMATHGoogle Scholar
  35. 35.
    Rendleman, C.A., Beckner, V.E., Lijewski, M., Crutchfield, W.Y., Bell, J.B.: Parallelization of structured, hierarchical adaptive mesh refinement algorithms. Comput. Vis. Sci. 3, 147–157 (2000) zbMATHCrossRefGoogle Scholar
  36. 36.
    Rutland, C., Ferziger, J.: Simulations of flame-vortex interactions. Combust. Flame 84, 343–360 (1991) CrossRefGoogle Scholar
  37. 37.
    Zhang, S., Rutland, C.J.: Premixed flame effects on turbulence and pressure-related terms. Combust. Flame 102, 447–461 (1995) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Center for Computational Sciences and EngineeringLawrence Berkeley National LaboratoryBerkeleyUSA

Personalised recommendations