Least Squares Minimization Closure Models for LES of Turbulent Combustion

  • Conrad H. Patton
  • Jack R. Edwards


This work summarizes the development and testing of a new family of chemical closure models for large-eddy simulation (LES) of turbulent combustion using finite-rate chemistry. The goal of this research is to provide a simple, yet effective model that provides a correction to the ‘laminar chemistry’ prediction formed by evaluating chemical production terms using filtered-mean data. The general model takes the form \(\overline {\dot {{\omega }}_{s} (q)} =f(\overline {{q}},{\Delta } ,{\ldots } )\dot {{\omega }}_{s} (\overline {{q}})\), where the enhancement factor, f, accounts for the effects of the subgrid fluctuations on apparent reactivity as expressed at a given mesh level. A form for the enhancement factor is derived by least-squares minimization (LSM) of a ‘reactivity functional’ connecting information at different mesh levels. A modified a priori analysis, in which simultaneous large-eddy simulations are performed on fine and coarse mesh levels, is used to identify candidate modeled forms for the enhancement factor. In the modified a priori analysis, coarse-mesh realizations are constrained by the filtered fine-mesh velocity, allowing eddy structures to be highly correlated. Several LSM variants are described and tested through comparisons with experimental data. The test cases include three experiments conducted at the University of Virginia’s supersonic combustion facility involving non-premixed hydrogen and partially-premixed ethylene combustion as well as a premixed propane-air flame in the Volvo Validation Rig. The results demonstrate the capability of the models to provide a consistent (if modest in some cases) improvement in predictive capability, relative to ‘laminar chemistry’, in a cost-effective manner.


Large eddy simulation Finite-rate chemistry Turbulent combustion 



This work was supported by AFOSR under FA9550-13-1-0049, monitored by Dr. Chiping Li, and by AFRL under FA8650-16-P-270, awarded to Metacomp Technologies. The authors also acknowledge Drs. Amarnatha Potturi (Metacomp Technologies) and Dr. Tarek Echekki (North Carolina State University) for their contributions to this work. Computer time was obtained from NCSU’s High Performance Computing unit and from the DoD’s High Performance Computing Modernization Program.


  1. 1.
    Pierce, C.D.: Progress variable approach for large-eddy simulation of turbulent combustion. PhD. Dissertation, Mechanical Engineering, Stanford University (2001)Google Scholar
  2. 2.
    Ihme, M., Pitsch, H.: Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model. Combust. Flame 155, 70–89 (2008)CrossRefzbMATHGoogle Scholar
  3. 3.
    Larsson, J.: Large eddy simulation of the HyShot II scramjet combustor using a supersonic flamelet model. AIAA Paper 2012-4261 (2012)Google Scholar
  4. 4.
    Pope, S.B.: Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theor. Model. 1, 41–63 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gou, X., Sun, W., Chen, Z., Ju, Y.: A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms. Combust. Flame 157, 1111–1121 (2010)CrossRefGoogle Scholar
  6. 6.
    Candler, G.V., Subbareddy, P.K., Nompelis, I.: Decoupled implicit method for aerothermodynamics and reacting flows. AIAA J. 51, 1245–1254 (2013)CrossRefGoogle Scholar
  7. 7.
    Savard, B., Xuan, Y., Bobbitt, B., Blanquart, G.: A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry. J. Comp. Phys. 295, 740–769 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jaberi, F.A., Colucci, P.J., James, S., Givi, P., Pope, S.B.: Filtered mass density function for large-eddy simulation of turbulent reacting flows. J. Fluid Mech. 401, 85–121 (1999)CrossRefzbMATHGoogle Scholar
  9. 9.
    Valino, L.: A field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow. Flow Turbul. Combust. 60, 157–172 (1998)CrossRefzbMATHGoogle Scholar
  10. 10.
    Dodoulas, A., Navarro-Martinez, S.: Large-eddy simulation of premixed turbulent flames using the probability density function approach. Flow Turbul. Combust. 90, 654–678 (2013)CrossRefGoogle Scholar
  11. 11.
    Koo, H., Donde, P., Raman, V.: A quadrature-based LES/transported probability density function approach for modeling supersonic combustion. Proc. Combust. Inst. 33, 2203–2210 (2011)CrossRefGoogle Scholar
  12. 12.
    Menon, S., McMurtry, P.A., Kerstein, A.R.: A linear eddy subgrid model for turbulent combustion - Application to premixed combustion. AIAA Paper 1993-0107 (1993)Google Scholar
  13. 13.
    Echekki, T., Kerstein, A.R., Dreeben, T.D.: One dimensional turbulence simulation of turbulent jet diffusion flames: model formulation and illustrative applications. Combust. Flame 125, 1083–1105 (2001)CrossRefGoogle Scholar
  14. 14.
    Menon, S., Kerstein, A.: The linear-eddy model. In: Turbulent Combustion Modeling, pp 221–247. Springer, Berlin (2011)Google Scholar
  15. 15.
    Ranjan, R., Murilidharan, B., Nagaoka, Y., Menon, S.: Subgrid-scale modeling of reaction-diffusion and scalar transport in turbulent premixed flames. Combust. Sci. Technol. 188, 1496–1537 (2015)CrossRefGoogle Scholar
  16. 16.
    Berglund, M., Fedina, E., Fureby, C., Tegner, J.: Finite rate chemistry large-eddy simulation of self-ignition in a supersonic combustion ramjet. AIAA J. 48, 540–550 (2010)CrossRefGoogle Scholar
  17. 17.
    Sabelnkov, V., Fureby, C.: Extended LES-PASR model for simulation of turbulent combustion. Prog. Propuls. Phys. 4, 539–568 (2013)CrossRefGoogle Scholar
  18. 18.
    Fedina, E., Fureby, C., Bulat, G., Meier, W.: Assessment of finite-rate chemistry large-eddy simulation combustion models. Flow Turbul. Combust.
  19. 19.
    Potturi, A., Edwards, J.: Investigation of subgrid closure models for finite-rate scramjet combustion. AIAA Paper 2013-2461 (2013)Google Scholar
  20. 20.
    Colin, O., Ducros, F., Veynante, D., Poinsot, T.: A thickened flame model for large eddy simulations of turbulent premixed combustion. Phys. Fluids 12, 1843–1863 (2000)CrossRefzbMATHGoogle Scholar
  21. 21.
    Legier, J., Poinsot, T., Veynante, D.: Dynamically thickened flame LES model for premixed and non-premixed turbulent combustion. In: Proceedings of the Summer Program, Center for Turbulence Research, pp 157–168 (2000)Google Scholar
  22. 22.
    Charlette, F., Meneveau, C., Veynante, D.: A power-law flame-wrinkling model for LES of premixed turbulent combustion Part I: non-dynamic formulation and initial tests. Combust. Flame 131, 159–180 (2002)CrossRefGoogle Scholar
  23. 23.
    Charlette, F., Meneveau, C., Veynante, D.: A power-law flame-wrinkling model for LES of premixed turbulent combustion Part II: dynamic formulation. Combust. Flame 131, 181–197 (2002)CrossRefGoogle Scholar
  24. 24.
    Genin, F., Menon, S.: Simulation of turbulent mixing behind a strut injector in supersonic flow. AIAA J. 48, 526–539 (2010)CrossRefGoogle Scholar
  25. 25.
    Edwards, J., Boles, J., Baurle, R.: Large-eddy/Reynolds-averaged Navier-Stokes simulation of a supersonic reacting wall jet. Combust. Flame 159, 1127–1138 (2012)CrossRefGoogle Scholar
  26. 26.
    Potturi, A., Edwards, J.: Large-eddy Reynolds-averaged Navier-Stokes simulation of cavity-stabilized ethylene combustion. Combust. Flame 162, 1176–1192 (2015)CrossRefGoogle Scholar
  27. 27.
    Fulton, J., Edwards, J., Hassan, H., McDaniel, J., Goyne, C., Rockwell, R., Cutler, A., Johansen, C., Danehy, P.: Large-eddy/Reynolds-averaged Navier-Stokes simulations of reactive flows in a dual-mode scramjet combustor. J. Prop. Power 30, 558–575 (2014)CrossRefGoogle Scholar
  28. 28.
    Fulton, J., Edwards, J., Cutler, A., McDaniel, J., Goyne, C.: Turbulence/chemistry interactions in a ramp-stabilized hydrogen-air diffusion flame. Combust. Flame 174, 152–165 (2016)CrossRefGoogle Scholar
  29. 29.
    Patton, C., Wignall, T., Mirgolbabaei, H., Edwards, J.R., Echekki, T.: LES model assessment for high speed combustion using mesh sequenced realizations. AIAA Paper 2015-4207 (2015)Google Scholar
  30. 30.
    Patton, C.H., Wignall, T.J., Edwards, J.R., Echekki, T.: LES model assessment for high-speed combustion. AIAA Paper 2016-1937 (2016)Google Scholar
  31. 31.
    Patton, C.: Turbulent combustion closure modeling for high speed LES. Ph.D. Dissertation, North Carolina State University. (2017)
  32. 32.
    Gieseking, D., Choi, J., Edwards, J., Hassan, H.: Compressible flow simulations using a new large-eddy simulation/Reynolds-averaged Navier-Stokes model. AIAA J. 49, 2194–2209 (2011)CrossRefGoogle Scholar
  33. 33.
    Lenormand, E., Sagaut, P., Ta Phuoc, L., Compte, P.: Subgrid-scale models for large-eddy simulations of compressible wall-bounded flows. AIAA J. 38, 1340–1350 (2000)CrossRefGoogle Scholar
  34. 34.
    Menter, F.: Two equation eddy viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605 (1994)CrossRefGoogle Scholar
  35. 35.
    Edwards, J.: A low-diffusion flux-splitting scheme for Navier-Stokes calculations. Comput. Fluids 26, 635–659 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Colella, P., Woodward, P.: Piecewise parabolic method for gas-dynamical simulations. J. Comput. Phys. 5, 174–201 (1984)CrossRefzbMATHGoogle Scholar
  38. 38.
    Ducros, F., Ferrand, V., Nicaud, F., Weber, C., Darracq, D., Gachareiu, C., Poinsot, T.: Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152, 517–549 (1999)CrossRefzbMATHGoogle Scholar
  39. 39.
    Burke, M., Chaos, M., Ju, Y., Dryer, F., Klippenstein, S.: Comprehensive H2/O2 kinetic model for high-pressure combustion. In. J. Chem. Kinet. 44, 444–474 (2011)CrossRefGoogle Scholar
  40. 40.
    DesJardin, P., Frankel, S.: Large eddy simulation of a nonpremixed reacting jet: application and assessment of subgrid-scale combustion models. Phys. Fluids 10, 2298–2314 (1998)CrossRefGoogle Scholar
  41. 41.
    Buxton, O., Ganapathisubramani, B.: PIV measurements of convection velocities in a turbulent mixing layer. J. Phys. Conf. Ser. 318, 052038 (2011)CrossRefGoogle Scholar
  42. 42.
    Spina, E., Donovan, J., Smits, A.: On the structure of high Reynolds-number supersonic turbulent boundary layers. J. Fluid Mech. 222, 293–327 (1991)CrossRefGoogle Scholar
  43. 43.
    Ringuette, M., Wu, M., Martin, M.: Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69 (2008)CrossRefzbMATHGoogle Scholar
  44. 44.
    Rockwell, R., Goyne, C., Rice, B., Tatman, B., Smith, C., Kouchi, T., McDaniel, J., Fulton, J., Edwards, J.: Collaborative experimental and computational study of a dual mode scramjet combustor. J. Prop. Power 30, 530–538 (2014)CrossRefGoogle Scholar
  45. 45.
    Cutler, A., Magnotti, G., Cantu, L., Gallo, E., Rockwell, R., Goyne, C.: Dual-pump coherent anti-Stokes Raman apectroscopy measurements in a dual-mode scramjet. J. Prop. Power 30, 539–549 (2014)CrossRefGoogle Scholar
  46. 46.
    Schultz, I., Goldstein, C., Jeffries, C., Hanson, R., Rockwell, R., Goyne, C.: Spatially resolved water measurements in a scramjet combustor using diode laser absorption. J. Prop. Power 30, 1551–1558 (2014)CrossRefGoogle Scholar
  47. 47.
    Cutler, A., Magnotti, G., Cantu, L, Gallo, P., Danehy, P., Rockwell, R., Goyne, C., McDaniel, J.: Dual-pump CARS measurements in the University of Virginia’s dual-mode scramjet Configuration “C”. AIAA Paper 2013-0335 (2013)Google Scholar
  48. 48.
    Luo, Z., Yoo, C., Richardson, E., Chen, J., Law, C., Lu, T.: Chemical explosive mode analysis for a turbulent lifted ethylene jet flame in highly-heated coflow. Combust. Flame 159, 265–274 (2012)CrossRefGoogle Scholar
  49. 49.
    Schultz, I., Goldstein, C., Jeffries, J., Spearrin, R., Hanson, R.: Multispecies mid-infrared absorption measurements in a hydrocarbon-fueled scramjet combustor. J. Prop. Power 30, 1595–1604 (2014)CrossRefGoogle Scholar
  50. 50.
    Sjunnesson, A., Olovsson, S., Sjoblow, B.: Validation rig—a tool for flame studies. International Society for Air-breathing Engines Conference, ISABE-91-7038. Nottingham (1991)Google Scholar
  51. 51.
    Sjunnesson, A., Nelsson, C., Max, E.: LDA measurements of velocities and turbulence in a bluff body stabilized flame. In: Fourth International Conference on Laser Anemometry - Advances and Applications. ASME, Cleveland (1991)Google Scholar
  52. 52.
    Model Validation for Propulsion Workshop:
  53. 53.
    Potturi, A., Patton, C., Edwards, J.: Application of data-driven SGS turbulent combustion models to the Volvo experiment. AIAA Paper 2017-1792 (2017)Google Scholar
  54. 54.
    Ghani, A., Poinsot, T., Gicquel, L., Staffelback, G.: LES of longitudinal and transverse self-excited combustion instabilities in a bluff-body stabilized turbulent premixed flame. Combust. Flame 162, 4075–4083 (2015)CrossRefGoogle Scholar
  55. 55.
    Edwards, J.: Towards unified CFD simulations of real fluid flows. AIAA Paper 2001-2524 (2001)Google Scholar
  56. 56.
    Weiss, J., Smith, W.: Preconditioning applied to variable and constant density flows. AIAA J. 33, 2050–2057 (1995)CrossRefzbMATHGoogle Scholar
  57. 57.
    Normal, M., Semazzi, F., Nair, R.: Conservative cascade interpolation on the sphere: an intercomparison of various non-oscillatory reconstructions. Q. J. R. Meteorol. Soc. 135, 795–805 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA

Personalised recommendations