Modelling of High Karlovitz Combustion in Spark-ignition Engines

Principal Investigator:
Karine Truffin

Institut Carnot IFPEN Transports Energie, Energies Nouvelles, Rueil-Malmaison (France)

Local Project ID:

HPC Platform used:

Date published:


The starting points of the present PRACE project was the ANR MACDIL project (Projet-ANR-15-CE22-0014), which addressed modelling issues on highly turbulent and highly diluted combustion in spark-ignition engines.

Nowadays, the car manufacturers rely on CFD tools for designing and optimising spark-ignition engines. However, the current models of turbulent combustion lose their predictivity when they are used to simulate a highly diluted or ultra-lean combustion involving high turbulent intensities. Indeed, the current models are built based on the assumptions of the flamelet regime. Yet, the combustion in a diluted boosted spark-ignition engine shifts from the flamelet regime to the thin reaction zone (TRZ) regime in a Peters diagram [1].

The main goal of the research project was to perform direct numerical simulations (DNS) of premixed C8H18/air statistically flat flame interacting with a turbulent flow field, and to analyse the results in order to develop a combustion model suitable for combustion in the TRZ regime based on the formalism of the coherent flame model (CFM) [2–4].

Method and Results

Numerical setup and conditions

DNS were conducted with the AVBP1code [5]. The computational domain in shown in Figure 1. 

The inlet and outlet boundaries were specified in the direction of the mean flame propagation. The transverse boundaries were periodic. The eddy turnover time of the different simulations were too small compared to the characteristic flame time. Therefore, the chosen strategy was to impose turbulence forcing within the computational domain [6,7]. The present method generated a stochastic time-evolving forcing vector, which was used as a source term in the momentum conservation equation. A stochastic forcing term introduced energy in the largest scales of the domain, which cascaded towards the smallest scales.

Eight simulations were performed. Cases A, B and E corresponds to simulations performed with 3 different values of the Karlovitz number (Ka), from the flamelet to TRZ regime, respectively 3, 21 and 46. Ka=(u'SL0)3/2(ltδL)-1/2, where u', lt, SL0 and  δL are respectively the turbulent flow velocity, the integral length scale of turbulence, the laminar flame speed and the laminar flame thickness. Three other simulations were performed with the same Karlovitz number but with unity Lewis numbers: cases A1, B1 and E1. These simulations were performed with 2-steps mechanisms for iso-octane /air mixture. Indeed, full investigations with a reduced chemistry was out of reach in terms of computational resources. Nevertheless, a case at Ka =21 (B_ARC) was also performed with a reduced analytical mechanism [8], including 18 transported species and 13 species in a quasi-steady state, in order to investigate the impact of the chemical mechanisms on the result. Theses simulations are summarized in Table 1. The last case Bfront aimed at examining the impact of forcing the turbulence only in the fresh gas instead of in the whole domain.

The flame structure

The results allowed to investigate the validity of the flame surface density (FSD) concept in the TRZ regime through the analyses of the flame surface, the flame structure, the characteristics of the flame stretch and of the displacement speed in the TRZ regime, which were considered as key factors in the modelling of highly diluted or ultra-lean turbulent combustion.

Instantaneous snapshots obtained with cases A, B, E, A1, B1 and E1 are shown in Figure 2 for illustration purpose. For all simulations, at least five characteristic flame times (δL/SL) were necessary to reach the statistically steady state, where δL is the laminar flame thickness and SL is the laminar flame speed. Then the statistical analysis and averaging were performed over 5 to 20 flame times depending on the case.

The following observations were obtained:

  • For non-unity Lewis numbers, the flame was significantly thickened in the preheat zone when increasing Ka due to thermo-diffusive effects, while it seemed to become thinner or moderately thickened in the reactive zone as well as in the post-flame region. For unity Lewis numbers, the flame structure was barely affected by the increase of Ka and it remained thinner in the reaction zone as well as in the post-flame region.
  • The displacement speed showed a differentiate dependency on tangential strain rate and curvature.

Impact on modelling proposal

These observations led to focus the modelling study on a specific iso-surface in the reaction zone and to how it was affected by turbulence.  Based on asymptotic theory, an expression for the displacement speed was proposed, as a function of tangential strain rate, curvature and tangential diffusion. Moreover, two effective strain and curvature Markstein lengths correlations were introduced to take into account the Karlovitz value.

Finally, an extension of the CFM model to TRZ regime was proposed through the definition of a new progress variable and using a fine-grained flame surface density. Models were proposed and validated a priori for the mean displacement speed (Figure 3), the mean flame curvature and its square and the mean flame stretch by curvature. A model for the flame tangential strain rate was also proposed.

Related publications:

This study was published in:

E. Suillaud (2021) PhD thesis, Modelling of high Karlovitz combustion in spark-ignition engines. Univ. Paris-Saclay.

E. Suillaud, K. Truffin, O. Colin, D. Veynante, Direct Numerical Simulations of high Karlovitz number premixed flames for the analysis and modeling of the displacement speed, Combustion and Flame, 236 (2022) 111770.

PhD Defense on-line:



[1]     N. Peters, The turbulent burning velocity for large-scale and small-scale turbulence, J. Fluid Mech. 384 (1999) 107–132.

[2]     S.M. Candel, T.J. Poinsot, Flame Stretch and the Balance Equation for the Flame Area, Combustion Science and Technology 70 (1990) 1–15.

[3]     O. Colin, A. Benkenida, C. Angelberger, 3d Modeling of Mixing, Ignition and Combustion Phenomena in Highly Stratified Gasoline Engines, Oil & Gas Science and Technology - Rev. IFP 58 (2003) 47–62.

[4]     S. Richard, O. Colin, O. Vermorel, A. Benkenida, C. Angelberger, D. Veynante, Towards large eddy simulation of combustion in spark ignition engines, Proceedings of the Combustion Institute 31 (2007) 3059–3066.

[5]     V. Moureau, G. Lartigue, Y. Sommerer, C. Angelberger, O. Colin, T. Poinsot, Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids, Journal of Computational Physics 202 (2005) 710–736.

[6]     V. Eswaran, S.B. Pope, An examination of forcing in direct numerical simulations of turbulence, Computers & Fluids 16 (1988) 257–278.

[7]     R. Paoli, K. Shariff, Turbulent Condensation of Droplets, J. Atmos. Sci. 66 (2009) 723–740.

[8]     Lapeyre, C., Selle, L Beda, B. Poinsot, T., ANR IDYLLE Deliverables Report, 2016 (

[9]     E. Suillaud, K. Truffin, O. Colin, D. Veynante, Direct Numerical Simulations of high Karlovitz number premixed flames for the analysis and modeling of the displacement speed, Combustion and Flame, 236 (2022) 111770.

Ongoing Research / Outlook

Ongoing studies are carried out to improve the model when simulated statistically non-planar flames as it is the case during early flame kernel growth and propagation in spark-ignition engines and to take into account the effect of differential diffusion for fuel Lewis number smaller than unity, as hydrogen.

Research Team

Edouard Suillaud1, Karine Truffin1, Olivier Colin1, Denis Veynante2

1 Energies Nouvelles, Rueil-Malmaison, France; Institut Carnot IFPEN Transports Energie
2 CentraleSupelec School, EM2C laboratory, CNRS, Paris-Saclay, France

Scientific Contact

Dr. Karine Truffin
IFP Energies Nouvelles
1 avenue de Bois-Préau
92852 Rueil-Malmaison (France)
e-mail: karine.truffin [@]

NOTE: This simulation project was made possible by PRACE (Partnership for Advanced Computing in Europe) allocating a computing time grant on GCS HPC system JUWELS of the Jülich Supercomputing Centre. GCS is a hosting member of PRACE.

Local project ID: pra102/DNS4ICE

December 2021

Tags: JSC IFPEN Computational and Scientific Engineering Turbulence