# Reynolds-Averaged, Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

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## Abstract

A lean premixed propane/air bluff-body stabilized flame (Volvo test rig) is calculated using the Scale-Adaptive Simulation turbulence model (SAS) and Large-Eddy simulations (LES) as well as the conventional Reynolds-averaged approach (RAS). RAS and SAS are closed by the standard *k*-*𝜖* and the *k*-*ω* Shear Stress Transport (SST) turbulence models, respectively. The conventional Smagorinsky and the *k*-equation sub-grid scales models are used for the LES closure. Effects of the sub-grid scalar flux modeling using the classical gradient hypothesis and Clark’s tensor diffusivity closures both for the inert and reactive LES flows are discussed. The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction. It assumes that molecular mixing and the subsequent combustion occur in the ’fine structures’ (smaller dissipative eddies, which are close to the Kolmogorov scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the ’fine structures’ are evaluated using different turbulence models (RAS, SAS and LES). The finite-rate chemical kinetics is taken into account by treating the ’fine structures’ as constant pressure and adiabatic homogeneous reactors, calculated as a system of ordinary-differential equations (ODEs) described by a Perfectly Stirred Reactor (PSR) concept. Several further enhancements to model the PSRs are proposed, including a new Livermore Solver (LSODA) for integrating stiff ODEs and a new correction to calculate the PSR time scales. All models have been implemented as a stand-alone application \(\text {edcPisoFoam}\) based on the OpenFOAM technology. Additionally, several RAS calculations were performed using the Turbulence Flame Speed Closure model in Ansys Fluent to assess effects of the heat losses by modeling the conjugate heat transfer between the bluff-body and the reactive flow. Effects of the turbulence Schmidt number on RAS results are discussed as well. Numerical results are compared with available experimental data. Reasonable consistency between experimental data and numerical results provided by RAS, SAS and LES is observed. In general, there is satisfactory agreement between present LES-EDC simulations, numerical results by other authors and measurements without any major modification to the EDC closure constants, which gives a quite reasonable indication on the adequacy and accuracy of the method and its further application for turbulent premixed combustion simulations.

## Keywords

URANS Eddy dissipation concept Large eddy simulation LSODA Scale adaptive simulation Lean premixed bluff-body combustion Heat transfer Volvo test rig edcPisoFoam## Notes

### Acknowledgements

We are grateful to the Norwegian Meta center for Computational Science (NOTUR) for providing the uninterrupted HPC computational resources and useful technical support. Comments and recommendations for three anonymous and very skilled reviewers of the Journal have increased considerably the quality of the paper.

### Funding Information

Except for the computer allowance acknowledged above, this study has not received any funding.

### Compliance with Ethical Standards

### Conflict of interests

The authors declare that they have no conflict of interest.

## References

- 1.Weller, H.G., Tabor, G., Jasak, H., Fureby, C.: Tensorial approach to computational continuum mechanics using object-oriented techniques. A. Comp. Phys.
**12**(6), 620–631 (1998)CrossRefGoogle Scholar - 2.Lysenko, D.A., Ertesvåg, I.S., Rian, K.E.: Modeling of turbulent separated flows using OpenFOAM. Comput. Fluids
**80**, 408–422 (2013)CrossRefzbMATHGoogle Scholar - 3.Lilleberg, B., Christ, D., Ertesvåg, I.S., Rian, K.E., Kneer, R.: Numerical simulation with an extinction database for use with the Eddy Dissipation Concept for turbulent combustion. Flow Turbul. Combust.
**91**, 319–346 (2013)CrossRefGoogle Scholar - 4.Lysenko, D.A., Ertesvåg, I.S., Rian, K.E.: Numerical simulation of non-premixed turbulent combustion using the eddy dissipation concept and comparing with the steady laminar flamelet model. Flow Turbul. Combust.
**93**, 577–605 (2014)CrossRefGoogle Scholar - 5.Lysenko, D.A., Ertesvåg, I.S., Rian, K.E.: Numerical simulations of the sandia flame d using the eddy dissipation concept. Flow Turbul. Combust.
**93**, 665–687 (2014)CrossRefGoogle Scholar - 6.Barlow, R.S., Frank, J.H.: Effects of turbulence on species mass fractions in methane/air jet flames. Proc Combust. Inst.
**27**, 1087–1095 (1998)CrossRefGoogle Scholar - 7.Dunn, M.J., Masri, A.R., Bilger, R.W.: A new piloted premixed jet burner to study strong finite-rate chemistry effects. Combust. Flame
**151**(1-2), 46–60 (2007)CrossRefGoogle Scholar - 8.Dunn, M.J., Masri, A.R., Bilger, R.W., Barlow, R.S., Wang, G.H.: The compositional structure of highly turbulent piloted premixed flames issuing into a hot coflow. Proc. Combust. Inst.
**32**(2), 1779–1786 (2009)CrossRefGoogle Scholar - 9.Barlow, R.S., Fiechtner, G.J., Carter, C.D., Chen, J.-Y.: Experiments on the scalar structure of turbulent CO/H2/N2 jet flames. Combust. Flame
**120**, 549–569 (2000)CrossRefGoogle Scholar - 10.Dally, B.B., Masri, A.R., Barlow, R.S., Fiechtner, G.J.: Instantaneous and mean compositional structure of bluff-body stabilised nonpremixed flames. Combust. Flame
**114**, 119–148 (1998)CrossRefGoogle Scholar - 11.Launder, B., Spalding, D.: The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng.
**3**(2), 269–289 (1974)CrossRefzbMATHGoogle Scholar - 12.Gran, I.R., Magnussen, B.F.: A numerical study of a bluff-body stabilized diffusion flame. Part 2. Influence of combustion modeling and finite-rate chemistry. Combust. Sci. Technol.
**119**, 191–217 (1996)CrossRefGoogle Scholar - 13.Bowman, C.T., Hanson, R.K., Davidson, D.F., Gardiner, W.C., Lissianski, V., Smith, G.P., Golden, D.M., Frenklach, M., Goldenberg, M.: GRI-Mech. http://www.me.berkeley.edu/gri-mech/. Accessed February 2013 (2008)
- 14.Menter, F.R., Egorov, Y.: The Scale-Adaptive Simulation method for unsteady turbulent flow predictions. Part 1, Theory and model description. Flow Turbul. Combust.
**85**, 113–138 (2010)CrossRefzbMATHGoogle Scholar - 15.Ertesvåg, I.S., Magnussen, B.F.: The eddy dissipation turbulence energy cascade model. Combust. Sci. Technol.
**159**, 213–235 (2000)CrossRefGoogle Scholar - 16.Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, 2nd rev. ed. Springer-Verlag, Berlin (1996)CrossRefzbMATHGoogle Scholar
- 17.Radhakrishnan, K., Hindmarsh, A.C.: Description and use of LSODE, the Livermore solver for ordinary differential equations, Lawrence Livermore national laboratory report, UCRL-ID-113855 (1993)Google Scholar
- 18.Sjunnesson, A., Olovsson, S., Sjöblom, B.: Validation rig – a tool for flame studies, VOLVO Aero AB S-461 81. Trollhättan, Sweden (1991)Google Scholar
- 19.Sjunnesson, A., Nelson, C., Max, E.: LDA measurements of velocities and turbulence in a bluff body stabilized flame, Laser Anemometry 3, ASME (1991)Google Scholar
- 20.Sjunnesson, A., Henriksson, P., Löfström, C.: CARS measurements and visualization of reacting flows in a bluff body stabilized flame. AIAA 92–3650 (1992)Google Scholar
- 21.Jones, W.P., Marquis, A.J., Wang, F.: Large eddy simulation of a premixed propane turbulent bluff body flame using the Eulerian stochastic field method. Fuel
**140**, 514–525 (2015)CrossRefGoogle Scholar - 22.Ma, T., Gao, Y., Kempf, A.M., Chakraborty, N.: Validation and implementation of algebraic LES modelling of scalar dissipation rate for reaction rate closure in turbulent premixed combustion. Combust. Flame
**161**, 3134–3153 (2014)CrossRefGoogle Scholar - 23.Manickam, B., Franke, J., Muppala, S.P.R., Dinkelacker, F.: Large-eddy simulation of triangular-stabilized lean premixed turbulent flames: quality and error assessment. Flow Turbul. Combust.
**88**, 563–596 (2012)CrossRefzbMATHGoogle Scholar - 24.Sabelnikov, V., Fureby, C.: LES combustion modeling for high Re flames using a multi-phase analogy. Combust. Flame
**160**, 83–96 (2013)CrossRefGoogle Scholar - 25.Peters, N.: Turbulent combustion. Cambridge University Press, Cambridge (2000)CrossRefzbMATHGoogle Scholar
- 26.Magnussen, B.F., Hjertager, B.H: On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Proc. Combust. Inst.
**16**, 719–729 (1976)CrossRefGoogle Scholar - 27.Magnussen, B.F.: Modeling of NOx and soot formation by the Eddy Dissipation Concept. Int.Flame Research Foundation, 1st topic Oriented Technical Meeting., 17-19. Holland, Amsterdam (1989)Google Scholar
- 28.Menter, F.R., Egorov, Y.: Formulation of the Scale-Adaptive Simulation (SAS) model during the DESIDER Project. In: Haase, W., Braza, M., Revell, A. (eds.) Notes on Num. Fluid Mech Multidisc Design, 103, Springer (2009)Google Scholar
- 29.Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust.
**62**, 183–200 (1999)CrossRefzbMATHGoogle Scholar - 30.Menter, F., Esch, T.: Elements of industrial heat transfer prediction. In: 16th Brazilian Congress of Mechanical Engineering (COBEM) (2001)Google Scholar
- 31.Menter, F.R., Kuntz, M., Langtry, R.: Ten years of industrial experience with the SST turbulence model. Turbulence Heat and Mass Transfer
**4**, 625–632 (2003)Google Scholar - 32.Yoshizawa, A.: Statistical theory for compressible shear flows, with the application to subgrid modelling. Phys. Fluids
**29**(2152), 1416–1429 (1986)Google Scholar - 33.Smagorinsky, J.S.: General circulation experiments with primitive equations. Mon. Weather Rev.
**91**(3), 99–164 (1963)CrossRefGoogle Scholar - 34.Sagaut, P.: Large Eddy Simulation for Incompressible Flows, 3rd ed. Springer, Berlin (2006)zbMATHGoogle Scholar
- 35.Magnussen, B.F.: The Eddy Dissipation Concept a bridge between science and technology. In: ECCOMAS Thermal Conference on Computational Combustion, Lisbon (2005)Google Scholar
- 36.Butz, D., Gao, Y., Kempf, A.M., Chakraborty, N.: Large eddy simulation of a turbulent premixed swirl flame using an algebraic scalar dissipation rate closure. Combust. Flame
**162**, 3180–3196 (2015)CrossRefGoogle Scholar - 37.Westbrook, C.K., Dryer, F.L.: Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combust. Sci. Technol.
**27**, 31–43 (1981)CrossRefGoogle Scholar - 38.Westbrook, C.K., Dryer, F.L.: Chemical kinetic modeling of hydrocarbon combustion. Prog. Energy Combust. Sci.
**10**, 1–57 (1984)CrossRefGoogle Scholar - 39.http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html, Update on 2014-10-04
- 40.Zimont, V.L., Lipatnikov, A.N.: A numerical model of premixed turbulent combustion of gases. Chem. Phys. Rep.
**14**, 993–1025 (1995)Google Scholar - 41.Karpov, V.P., Lipatnikov, A.N., Zimont, V.L.: A test of an engineering model of premixed turbulent combustion. Proc. Combust. Inst.
**26**, 249–257 (1996)CrossRefGoogle Scholar - 42.Warnatz, J., Maas, U., Dibble, R.W.: Combustion, 4th ed. Springer, Berlin (2006)zbMATHGoogle Scholar
- 43.ANSYS FLUENT R13. Theory guide. Tech. rep., Ansys Inc (2013)Google Scholar
- 44.Cheng, P.: Dynamics of a radiating gas with application to flow over a wavy wall. AIAA J.
**4**(2), 238–245 (1966)CrossRefGoogle Scholar - 45.Smith, T.F., Shen, Z.F., Friedman, J.N.: Evaluation of coefficients for the weighted sum of gray gases model. ASME J. Heat Transfer
**104**(4), 602–608 (1982)CrossRefGoogle Scholar - 46.Dunkle, R.V.: Geometric mean beam lengths for radiant heat transfer calculations. ASME J. Heat Transfer
**86**(1), 75–80 (1964)CrossRefGoogle Scholar - 47.Vandoormaal, J.P., Raithby, G.D.: Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer
**7**, 147–163 (1984)zbMATHGoogle Scholar - 48.Issa, R.: Solution of the implicitly discretized fluid flow equations by operator splitting. J. Comput. Phys.
**62**, 40–65 (1986)MathSciNetCrossRefzbMATHGoogle Scholar - 49.Waterson, N.P., Deconinck, H.: Design principles for bounded higher-order convection schemes – a unified approach. J. Comput. Phys.
**224**, 182–207 (2007)MathSciNetCrossRefzbMATHGoogle Scholar - 50.Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys.
**49**, 357–393 (1983)MathSciNetCrossRefzbMATHGoogle Scholar - 51.Jasak, H., Weller, H.G., Gosman, A.D.: High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Meth. Fluids
**31**, 431–449 (1999)CrossRefzbMATHGoogle Scholar - 52.Geurts, B.: Elements of direct and large-eddy simulation. R.T.Edwards, Philadelphia (2004)Google Scholar
- 53.Rhie, C., Chow, W.: Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J.
**21**, 1525–32 (1983)CrossRefzbMATHGoogle Scholar - 54.Lysenko, D.A., Ertesvåg, I.S., Rian, K.E.: Large-eddy simulation of the flow over a circular cylinder at Reynolds number 3900 using the OpenFOAM toolbox. Flow Turbul. Combust.
**89**, 491–518 (2012)CrossRefGoogle Scholar - 55.Lysenko, D.A., Ertesvåg, I.S., Rian, K.E.: Large-eddy simulation of the flow over a circular cylinder at Reynolds number 2 × 10
^{4}. Flow Turbul. Combust.**92**, 673–698 (2014)CrossRefGoogle Scholar - 56.Sanquer, S., Bruel, P., Deshaies, B.: Some specific characteristics of turbulence in the reactive wakes of bluff bodies. AIAA J.
**36**(6), 994–1001 (1998)CrossRefGoogle Scholar - 57.Hasse, C., Sohm, V., Wetzel, M., Durst, B.: Hybrid URANS/LES turbulence simulation of vortex shedding behind a triangular flameholder. Flow Turbul. Combust.
**83**, 1–20 (2009)CrossRefzbMATHGoogle Scholar - 58.Shanbhogue, S.J., Husain, S., Lieuwen, T.: Lean blowoff of bluff body stabilized flames: scaling and dynamics, Prog. Energy Combust. Sci.
**35**, 98–120 (2009)Google Scholar - 59.Welch, P.: The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust.
**15**(6), 70–73 (1967)CrossRefGoogle Scholar - 60.Cao, Y., Tamura, T.: Large-eddy simulations of flow past a square cylinder using structured and unstructured grids. Comput. Fluids
**137**, 36–54 (2016)MathSciNetCrossRefGoogle Scholar - 61.Yasari, E., Verma, S., Lipatnikov, A.N.: RANS simulations of statistically stationary premixed turbulent combustion using flame speed closure model. Flow Turbul. Combust.
**94**, 381–414 (2015)CrossRefGoogle Scholar - 62.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 - 63.Sathiah, P., Lipatnikov, A.: Effects of flame development on stationary premixed turbulent combustion. Proc. Comb. Inst.
**31**, 3115–3122 (2007)CrossRefGoogle Scholar - 64.Baudoin, E., Bai, R.Yu., Nogenmyr, K.J., Bai, X.S., Fureby, C.: Comparison of LES models applied to a bluff body stabilized flame. AIAA 2009–1178 (2009)Google Scholar
- 65.Allauddin, U., Klein, M., Pfitzner, M., Chakraborty, N.: A priori and a posteriori analyses of algebraic flame surface density modeling in the context of Large Eddy Simulation of turbulent premixed combustion. Numer Heat Transfer, Part A: Appl.
**71**(2), 153–171 (2017)CrossRefGoogle Scholar - 66.Klein, M., Chakraborty, N., Pfitzner, M.: Analysis of the combined modelling of sub-grid transport and filtered flame propagation for premixed turbulent combustion. Flow Turbul. Combust.
**96**, 921–938 (2016)CrossRefGoogle Scholar - 67.Clark, R.A., Ferziger, J.H., Reynolds, W.C.: Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech.
**91**, 1–16 (1979)CrossRefzbMATHGoogle Scholar - 68.O’Malley, R.E.: Singular perturbation methods for ordinary differential equations. Springer-Verlag, New York (1991)CrossRefzbMATHGoogle Scholar
- 69.Shampine, L.F., Reichelt, M.W.: The MATLAB ODE Suite, SIAM. J. Sci. Comput.
**18**, 1–22 (1997)MathSciNetzbMATHGoogle Scholar - 70.Robertson, H.H.: The Solution of a set of reaction rate equations. In: Walsh, J. (ed.) Numerical Analysis: an Introduction, pp. 178-182. Academic Press, London (1966)Google Scholar
- 71.Gobbert, M.K.: Robertson’s example for stiff differential equations. Arizona State University, Technical report (1996)Google Scholar