# Quasi-DNS Dataset of a Piloted Flame with Inhomogeneous Inlet Conditions

## Abstract

A quasi-DNS of the partially premixed turbulent Sydney flame in configuration FJ200-5GP-Lr75-57 has been conducted using detailed molecular diffusion for multi-component mixtures and complex reaction mechanisms. In order to study flame dynamics like regime transition in this flame for the development of new combustion models and to directly compare the quasi-DNS to different LES models, the simulation results are compiled into a data base. Because the simulation was performed with OpenFOAM, we demonstrate the quasi-DNS capabilities of OpenFOAM by performing canonical test cases. They attest that OpenFOAM’s cubic discretization has lower numerical diffusion compared to classical central difference schemes and can reach higher than second order convergence rate in some cases. The quasi-DNS of the Sydney flame is conducted with a self-developed reacting flow solver which is able to accurately compute molecular diffusion coefficients from kinetic gas theory and employs a fast implementation for detailed reaction mechanisms. The computational mesh is shown to be able to resolve the flow as well as the flame front sufficiently for the quasi-DNS. Comparisons with experimental data also show that the simulation can quantitatively reproduce measured time-mean and time-RMS statistics.

## Keywords

Mixed-mode combustion Quasi-DNS Turbulent combustion OpenFOAM## Notes

### Acknowledgements

We thank Assaad Masri for providing valuable information about the burner setup and access to the experimental results, as well as for helpful discussions. This work utilizes resources from the national supercomputer Cray XC40 Hazel Hen at the High Performance Computing Center Stuttgart (HLRS) and the computational resource ForHLR II at KIT funded by the Ministry of Science, Research and the Arts Baden-Württemberg and DFG (“Deutsche Forschungsgemeinschaft”). The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (http://www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer JUWELS at Jülich Supercomputing Centre (JSC) and on the GCS Supercomputer HAZEL HEN at Höchstleistungsrechenzentrum Stuttgart (http://www.hlrs.de).

### Compliance with Ethical Standards

### **Conflict of interests**

The authors declare that they have no conflict of interest.

## References

- 1.Meares, S., Masri, A.R.: A modified piloted burner for stabilizing turbulent flames of inhomogeneous mixtures. Combust. Flame
**161**(2), 484–495 (2014)CrossRefGoogle Scholar - 2.Williams, F.: Recent advances in theoretical descriptions of turbulent diffusion flames. In: Turbulent Mixing in Nonreactive and Reactive Flows, pp 189–208. Springer (1975)Google Scholar
- 3.Williams, F.: Turbulent combustion. In: The Mathematics of Combustion, pp 97–131. SIAM (1985)Google Scholar
- 4.Dahms, R., Felsch, C., Röhl, O., Peters, N.: Detailed chemistry flamelet modeling of mixed-mode combustion in spark-assisted hcci engines. Proc. Combust. Inst.
**33**(2), 3023–3030 (2011)CrossRefGoogle Scholar - 5.Fiorina, B., Mercier, R., Kuenne, G., Ketelheun, A., Avdić, A., Janicka, J., Geyer, D., Dreizler, A., Alenius, E., Duwig, C., et al.: Challenging modeling strategies for les of non-adiabatic turbulent stratified combustion. Combust. Flame
**162**(11), 4264–4282 (2015)CrossRefGoogle Scholar - 6.Hu, B., Rutland, C.J., Shethaji, T.A.: A mixed-mode combustion model for large-eddy simulation of diesel engines. Combust. Sci. Technol.
**182**(9), 1279–1320 (2010)CrossRefGoogle Scholar - 7.Barlow, R., Meares, S., Magnotti, G., Cutcher, H., Masri, A.: Local extinction and near-field structure in piloted turbulent ch 4/air jet flames with inhomogeneous inlets. Combust. Flame
**162**(10), 3516–3540 (2015)CrossRefGoogle Scholar - 8.Olbricht, C., Ketelheun, A., Hahn, F., Janicka, J.: Assessing the predictive capabilities of combustion les as applied to the Sydney flame series. Flow Turb. Combust.
**85**(3–4), 513–547 (2010)zbMATHCrossRefGoogle Scholar - 9.Lipatnikov, A.N.: Stratified turbulent flames: Recent advances in understanding the influence of mixture inhomogeneities on premixed combustion and modeling challenges. Prog. Energy Combust. Sci.
**62**, 87–132 (2017)CrossRefGoogle Scholar - 10.Wang, H., Zhang, P.: A unified view of pilot stabilized turbulent jet flames for model assessment across different combustion regimes. Proc. Combust. Inst.
**36**(2), 1693–1703 (2017)CrossRefGoogle Scholar - 11.Masri, A.: Partial premixing and stratification in turbulent flames. Proc. Combust. Institut.
**35**(2), 1115–1136 (2015)CrossRefGoogle Scholar - 12.Meares, S., Prasad, V., Magnotti, G., Barlow, R., Masri, A.: Stabilization of piloted turbulent flames with inhomogeneous inlets. Proc. Combust. Inst.
**35**(2), 1477–1484 (2015)CrossRefGoogle Scholar - 13.Kleinheinz, K., Kubis, T., Trisjono, P., Bode, M., Pitsch, H.: Computational study of flame characteristics of a turbulent piloted jet burner with inhomogeneous inlets. Proc. Combust. Inst.
**36**(2), 1747–1757 (2017)CrossRefGoogle Scholar - 14.Perry, B.A., Mueller, M.E.: Effect of multiscalar subfilter pdf models in les of turbulent flames with inhomogeneous inlets. Proc. Combust. Inst.
**37**(2), 2287–2295 (2019)CrossRefGoogle Scholar - 15.Perry, B.A., Mueller, M.E., Masri, A.R.: A two mixture fraction flamelet model for large eddy simulation of turbulent flames with inhomogeneous inlets. Proc. Combust. Inst.
**36**(2), 1767–1775 (2017)CrossRefGoogle Scholar - 16.Ji, H., Kwon, M., Kim, S., Kim, Y.: Numerical modeling for multiple combustion modes in turbulent partially premixed jet flames. J. Mech. Sci. Technol.
**32**(11), 5511–5519 (2018)CrossRefGoogle Scholar - 17.Tian, L., Lindstedt, R.: Evaluation of reaction progress variable-mixture fraction statistics in partially premixed flames. Proc. Combust. Inst.
**37**(2), 2241–2248 (2019)CrossRefGoogle Scholar - 18.Weller, H., Tabor, G., Jasak, H., Fureby, C.: OpenFOAM, openCFD ltd. Software available at https://openfoam.org (2017)
- 19.Komen, E., Camilo, L., Shams, A., Geurts, B.J., Koren, B.: A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows. J. Comput. Phys.
**345**, 565–595 (2017)MathSciNetzbMATHCrossRefGoogle Scholar - 20.Komen, E., Shams, A., Camilo, L., Koren, B.: Quasi-DNS capabilities of OpenFOAM for different mesh types. Comput. Fluids
**96**, 87–104 (2014)zbMATHCrossRefGoogle Scholar - 21.Jin, Y., Uth, M., Herwig, H.: Structure of a turbulent flow through plane channels with smooth and rough walls: an analysis based on high resolution DNS results. Comput. Fluids
**107**, 77–88 (2015)zbMATHCrossRefGoogle Scholar - 22.Habchi, C., Antar, G.: Direct numerical simulation of electromagnetically forced flows using OpenFOAM. Comput. Fluids
**116**, 1–9 (2015)MathSciNetzbMATHCrossRefGoogle Scholar - 23.Addad, Y., Zaidi, I., Laurence, D.: Quasi-DNS of natural convection flow in a cylindrical annuli with an optimal polyhedral mesh refinement. Comput. Fluids
**118**, 44–52 (2015)zbMATHCrossRefGoogle Scholar - 24.Lecrivain, G., Rayan, R., Hurtado, A., Hampel, U.: Using quasi-DNS to investigate the deposition of elongated aerosol particles in a wavy channel flow. Comput. Fluids
**124**, 78–85 (2016)MathSciNetzbMATHCrossRefGoogle Scholar - 25.Chu, X., Laurien, E.: Direct numerical simulation of heated turbulent pipe flow at supercritical pressure. J. Nucl. Eng. Rad. Sci.
**2**(3), 031019 (2016)CrossRefGoogle Scholar - 26.Chu, X., Laurien, E.: Flow stratification of supercritical CO2 in a heated horizontal pipe. J. Supercrit. Fluids
**116**, 172–189 (2016)CrossRefGoogle Scholar - 27.Chu, X., Laurien, E., McEligot, D.M.: Direct numerical simulation of strongly heated air flow in a vertical pipe. Int. J. Heat Mass Transf.
**101**, 1163–1176 (2016)CrossRefGoogle Scholar - 28.Zheng, E., Rudman, M., Singh, J., Kuang, S.: Assessing OpenFOAM for DNS of turbulent non-Newtonian flow in a pipe. In: 21st Australasian Fluid Mechanics Conference, vol. 21. Australasian Fluid Mechanics Society (2018)Google Scholar
- 29.Zheng, E., Rudman, M., Singh, J., Kuang, S.: Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM. Applied Mathematical Modelling (2019)Google Scholar
- 30.Bricteux, L., Zeoli, S., Bourgeois, N.: Validation and scalability of an open source parallel flow solver. Concurr. Comput.: Practice Exp.
**29**(21), e4330 (2017)CrossRefGoogle Scholar - 31.Zhong, S., Peng, Z., Li, Y., Li, H., Zhang, F.: Direct numerical simulation of methane turbulent premixed oxy-fuel combustion. Tech. rep., SAE Technical Paper (2017)Google Scholar
- 32.Tufano, G., Stein, O., Kronenburg, A., Frassoldati, A., Faravelli, T., Deng, L., Kempf, A., Vascellari, M., Hasse, C.: Resolved flow simulation of pulverized coal particle devolatilization and ignition in air-and O2/CO2-atmospheres. Fuel
**186**, 285–292 (2016)CrossRefGoogle Scholar - 33.Tufano, G., Stein, O., Kronenburg, A., Gentile, G., Stagni, A., Frassoldati, A., Faravelli, T., Kempf, A., Vascellari, M., Hasse, C.: Fully-resolved simulations of coal particle combustion using a detailed multi-step approach for heterogeneous kinetics. Fuel
**240**, 75–83 (2019)CrossRefGoogle Scholar - 34.Wang, B., Kronenburg, A., Dietzel, D., Stein, O.: Assessment of scaling laws for mixing fields in inter-droplet space. Proc. Combust. Inst.
**36**(2), 2451–2458 (2017)CrossRefGoogle Scholar - 35.Wang, B., Kronenburg, A., Tufano, G.L., Stein, O.T.: Fully resolved DNS of droplet array combustion in turbulent convective flows and modelling for mixing fields in inter-droplet space. Combust. Flame
**189**, 347–366 (2018)CrossRefGoogle Scholar - 36.Vo, S., Kronenburg, A., Stein, O., Cleary, M.: Multiple mapping conditioning for silica nanoparticle nucleation in turbulent flows. Proc. Combust. Inst.
**36**(1), 1089–1097 (2017)CrossRefGoogle Scholar - 37.Zhang, F., Zirwes, T., Habisreuther, P., Bockhorn, H.: Effect of unsteady stretching on the flame local dynamics. Combust. Flame
**175**, 170–179 (2017)CrossRefGoogle Scholar - 38.Vo, S., Kronenburg, A., Stein, O.T., Hawkes, E.R.: Direct numerical simulation of non-premixed syngas combustion using OpenFOAM. In: High Performance Computing in Science and Engineering, vol. 16, pp 245–257. Springer (2016)Google Scholar
- 39.Zhang, F., Bonart, H., Zirwes, T., Habisreuther, P., Bockhorn, H., Zarzalis, N.: Direct numerical simulation of chemically reacting flows with the public domain code OpenFOAM. In: Nagel, W., Kröner, D., Resch, M. (eds.) High Performance Computing in Science and Engineering ’14, pp 221–236. Springer, Berlin (2015)Google Scholar
- 40.Zirwes, T., Zhang, F., Häber, T., Bockhorn, H.: Ignition of combustible mixtures by hot particles at varying relative speeds. Combust. Sci. Technol., 1–18 (2018)Google Scholar
- 41.Goodwin, D., Moffat, H., Speth, R.: Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes. version 2.3.0b (2017). Software available at http://www.cantera.org
- 42.Zirwes, T., Zhang, F., Denev, J., Habisreuther, P., Bockhorn, H.: Automated code generation for maximizing performance of detailed chemistry calculations in OpenFOAM. In: Nagel, W., Kröner, D., Resch, M. (eds.) High Performance Computing in Science and Engineering ’17. Springer, Berlin (2017)Google Scholar
- 43.Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion. RT Edwards, Inc (2005)Google Scholar
- 44.Suite of nonlinear and differential/algebraic equation solvers. http://computation.llnl.gov/casc/sundials
- 45.Barlow, R., Karpetis, A., Frank, J., Chen, J.Y.: Scalar profiles and no formation in laminar opposed-flow partially premixed methane/air flames. Combust. Flame
**127**(3), 2102–2118 (2001)CrossRefGoogle Scholar - 46.Kee, R., Coltrin, M., Glarborg, P.: Chemically Reacting Flow: Theory and Practice. Wiley (2005)Google Scholar
- 47.Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turb. Combust.
**62**(3), 183–200 (1999)zbMATHCrossRefGoogle Scholar - 48.Lu, T., Law, C.: A criterion based on computational singular perturbation for the identification of quasi steady state species: A reduced mechanism for methane oxidation with no chemistry. Combust. Flame
**154**(4), 761–774 (2008)CrossRefGoogle Scholar - 49.Poinsot, T.J., Lelef, S.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys.
**101**(1), 104–129 (1992)MathSciNetzbMATHCrossRefGoogle Scholar - 50.Smith, G., Golden, D., Frenklach, M., Moriarty, N., Eiteneer, B., Goldenberg, M., Bowman, C., Hanson, R., Song, S., Jr., W.G., Lissianski, V., Qin, Z.: Gri 3.0 reaction mechanism. http://www.me.berkeley.edu/gri_mech
- 51.Bilger, R.: Turbulent jet diffusion flames. Prog. Energy Combust. Sci.
**1**(2-3), 87–109 (1976)CrossRefGoogle Scholar - 52.Yamashita, H., Shimada, M., Takeno, T.: A numerical study on flame stability at the transition point of jet diffusion flames. In: Symposium (International) on Combustion, vol. 26, pp 27–34. Elsevier (1996)Google Scholar
- 53.Peters, N.: Turbulent Combustion. Cambridge University Press (2000)Google Scholar
- 54.Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics. Springer Science & Business Media (2012)Google Scholar
- 55.Taylor, G.I., Green, A.E.: Mechanism of the production of small eddies from large ones. Proc. R. S. London Series A-Math. Phys. Sci.
**158**(895), 499–521 (1937)zbMATHCrossRefGoogle Scholar - 56.Abdelsamie, A., Fru, G., Oster, T., Dietzsch, F., Janiga, G., Thévenin, D.: Towards direct numerical simulations of low-mach number turbulent reacting and two-phase flows using immersed boundaries. Comput. Fluids
**131**, 123–141 (2016)MathSciNetzbMATHCrossRefGoogle Scholar - 57.Van Rees, W.M., Leonard, A., Pullin, D., Koumoutsakos, P.: A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers. J. Comput. Phys.
**230**(8), 2794–2805 (2011)MathSciNetzbMATHCrossRefGoogle Scholar - 58.Saad, T., Cline, D., Stoll, R., Sutherland, J.C.: Scalable tools for generating synthetic isotropic turbulence with arbitrary spectra. AIAA J.
**55**(1), 327–331 (2016)CrossRefGoogle Scholar - 59.Comte-Bellot, G., Corrsin, S.: The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech.
**25**(4), 657–682 (1966)CrossRefGoogle Scholar - 60.Lesieur, M.: Turbulence in Fluids (Fluid Mechanics and Its Applications). Springer (2008)Google Scholar
- 61.Zirwes, T., Zhang, F., Denev, J., Habisreuther, P., Bockhorn, H., Trimis, D.: Detailed transport and performance optimization for massively parallel simulations of turbulent combustion with OpenFOAM. In: 13th OpenFOAM Workshop, vol. 13. OpenFOAM Workshop (2018)Google Scholar