Integrating detailed soot models with combustion models for turbulent flame simulations

The strong competition between turbulent scales of the flow and chemical scales of soot formation processes make the numerical prediction of the soot emission in gas-turbine engines extremely challenging. In this context, precise models for the accurate characterisation of turbulent gas-phase kinetics, as well as for the adequate description of physical and chemical processes of the soot formation are required. To this end, the ESTiMatE project, supported by European Union’s Horizon 2020 programme under the Clean Sky 2 initiative aims to contribute to the development of advanced soot models to accurately predict soot formation and capture the evolution of particle size distribution (PSD) in conditions relevant to gas-turbine engines. Under the ESTiMatE consortium, collaborative research efforts are directed towards the computationally efficient modeling of the turbulent gas-phase chemical kinetics integrated with detailed models describing the evolution of soot PSD. 

At the Technical University of Darmstadt (TUDa), an integrated numerical framework including the Eulerian stochastic field (ESF) method into LES context [1] and the split-based Extended Quadrature based method of moments (S-EQMOM) [2] to account for the evolution of soot particle distribution has been developed, implemented and validated to predict sooting turbulent flames. The main advantage of the S-EQMOM is that the inversion procedure employed yields a system of equations that is solved analytically and has a unique solution, improving the stability of the inversion algorithm and allowing a computationally efficient and robust reconstruction of the soot particle number density function. The numerical framework was used recently to simulate the Delft Adelaide Flame III which is one of the target flames of the International Sooting Flame Workshop (ISF) [3].

Temperature snapshot of the Delft-Adelaide Flame III. (Courtsey:TUDa)
Temperature snapshot of the Delft-Adelaide Flame III. (Courtesy:TUDa)

In the frame of the ESTiMatE project, the research efforts at Barcelona Supercomputing Center (BSC) are dedicated to the development of the Conditional Moment Closure (CMC) to describe turbulent combustion using non-tabulated chemistry methods for LES applications. CMC is based on the concept of solving quantities conditioned to the mixture fraction as a way to reduce scalar fluctuations and obtain accurate estimations of the chemical source terms. The method has been developed in the parallel multiphysics code Alya from BSC and recently validated in a swirl-stabilized diffusion flame [4] from the Cambridge group [5]. The next steps include coupling CMC with the Discrete Sectional Method (DSM) to study soot emissions in aero-engine relevant conditions.

At the Eindhoven University of Technology (TU/e), ESTiMatE researchers are working on the extension of recently investigated FGM-DSM approaches [6] to the turbulent flame simulations under the LES framework of Alya solver. This activity involves close collaboration with BSC with their expertise on LES with Alya. The combination of FGM tabulated chemistry with a presumed PDF-based approach is being developed to account for the subgrid-scale response of soot source terms. The research activities at TU/e are mainly dedicated to the validation of the LES-FGM-DSM framework for the turbulent non-premixed flames characterized in the ISF workshop [7]. In the later stage, the LES-FGM-DSM framework will be applied to the low TRL (Technology Readiness Level) combustor architectures established within the ESTiMatE consortium to facilitate the numerical investigation of the Spatio-temporal evolution of soot along with their PSD.

The simulation activities planned concerning soot modeling within the ESTiMatE exhibit high requirements in terms of computational cost. To address this, preparatory scaling tests have been performed on the different solvers used within the ESTiMatE consortium, and the project is exploring efficient utilisation of High-performance computing (HPC) resources.

Large eddy simulation instantaneous axial velocity and temperature for the Cambridge swirling flame
Large eddy simulation instantaneous axial velocity (left) and temperature (right) for the Cambridge swirling flame [5] computed with CMC. (Courtesy: BSC)


[1] L. Valiño, ‘Field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow’, Flow, Turbul. Combust., 60(2) (1998) 157–172.

[2] S. Salenbauch, C. Hasse, M. Vanni, D. L. Marchisio, ‘A numerically robust method of moments with number density function reconstruction and its application to soot formation, growth and oxidation’, J. Aerosol Sci., 128 (2019) 34–49.

[3] N. H. Qamar, Z. T. Alwahabi, Q. N. Chan, G. J. Nathan, D. Roekaerts, K. D. King, ‘Soot volume fraction in a piloted turbulent jet non-premixed flame of natural gas’, Combust. Flame, 156 (7) (2009) 1339–1347.

[4] E.J. Pérez-Sánchez, D. Mira, O. Lehmkuhl, G. Houzeaux, 'Development of the Conditional Moment Closure with a multi-code approach in the frame of Large Eddy Simulations’, in 10th European Combustion Meeting (2021).

[5] D.E. Cavaliere, J. Kariuki, E. Mastorakos, ‘A comparison of the blow-off behaviour of swirl-stabilized premixed, non-premixed and spray flames’, Flow Turbul. Combust., 91(2) (2013) 347-372.

[6] A. Kalbhor, and J. van Oijen, ‘An assessment of the sectional soot model and FGM tabulated chemistry coupling in laminar flame simulations’, Combust. Flame, 229 (2021) 111381.

[7] J. Zhang, C. R. Shaddix, R. W. Schefer, ‘Design of “model-friendly” turbulent non-premixed jet burners for C2+ hydrocarbon fuels’, Rev. Sci. Inst. 82.7 (2011) 074101.