The ESTiMatE project, which is part of the Clean Sky program, is focused on the development of advanced soot models to gain deeper knowledge in soot formation at relevant conditions of the aero engines.
Soot emissions originate from complex multiscale interactions between turbulence, chemical reactions, and particle evolution, which take place over a large range of time and space scales. Therefore, a comprehensive understanding of the processes leading to soot particle formation and its precise prediction in practical combustion systems is crucial. The gas-phase soot precursors, polycyclic aromatic hydrocarbons (PAHs), need to be accounted for to characterise the particle formation and growth. The second fundamental component is the statistical model for the soot particle evolution, as an individual track of soot particles is computationally unrealistic.
A valuable approach is developed and applied by Technical University Darmstadt (TUDa) and integrated into the Computational Fluid Dynamics (CFD) code OpenFOAM. The particle properties are described by the number density function (NDF), whose evolution is tracked by the population balance equation (PBE). The PBE is not directly solved for, but only a small set of its low-order statistical moments. The Quadrature Method of Moments (QMOM) is applied to close the system of equations [1-2]. In the recently developed Split-based Extended Quadrature Method of Moments (S-EQMOM), the moments of sub-NDFs are considered instead of the moments of the entire NDF. The main advantage of the S-EQMOM is that the inversion procedure yields a system of equations that is solved analytically and has a unique solution . This approach greatly improves the stability of the inversion algorithm, allowing a computationally efficient and robust local reconstruction of the soot particle NDF, which is crucial when the model is employed in the LES context.
ESTiMatE researchers at Technical University Darmstadt (TUDa) are applying the developed numerical approach to simulate a model aero-engine combustor, experimentally investigated at DLR [3,4,5]. The model combustor features flow and flame characteristics of a Rich-Burn/Quick-Quench/Lean-Burn (RQL) type aero-engine combustor. Primary air is supplied into the combustion chamber through a central and annular nozzle. The airflows are separated and pass radial swirlers forming a recirculation zone with a turbulent rich primary combustion zone. Gaseous fuel (C2H4) is injected in between both airflows. Secondary air is injected into the chamber through four holes located in the corners of the combustion chamber at an axial position of 80 mm, leading to an RQL-type soot oxidation region. The measurements by Geigle et al. [3–5] provide velocity field information in both cold and reacting conditions as well as temperature and soot volume fraction data at various operating conditions (variations in pressure up to a maximum of 5 bar, equivalence ratio, and cases with and without oxidation air).
Large-Eddy Simulations have been performed with the OpenFOAM solver, extended at the TUDa with an in-house package for the solution of turbulent reacting flows using a tabulated FGM approach . The recently developed Split-based Extended Method of Moments has been applied combined with the tabulated tabulated FGM approach and the artificially thickened flame method [7,8]. An additional transport equation for a lumped PAH species is considered to accurately account for the coupling between the gas and solid phase. Predictions of the velocity evolution and the reaction zone are adequately captured by the model when compared with experimental measurements. The soot statistics predicted by the S-EQMOM are qualitatively in good agreement with the measurements. The time-averaged soot volume fraction is located within the fuel-rich regions and outside the inner recirculation zone, similar to the measurements. Overall, the S-EQMOM model provided a satisfactory agreement with the experiments, yielding a continuous reconstruction of the particle NDF, which is crucial for an accurate prediction of the soot particle oxidation, as well as numerically robustness.
 S. Salenbauch, C. Hasse, M. Vanni and D. L. Marchisio. A numerically robust method of moments with number density function reconstruction and its application to soot formation, growth and oxidation. Journal of Aerosol Science, 128, pp. 34-49, 2019.
 F. Ferraro, C. Russo. R. Schmitz, C. Hasse and M. Sirignano. Experimental and numerical study on the effect of oxymethylene ether-3 (OME3) on soot particle formation. Fuel, 286 (1), p. 119353, 2021.
 K.P Geigle, R. Hadef, M. Stöhr, and W. Meier. Flow field characterization of pressurized sooting swirl flames and relation to soot distributions. Proceedings of the Combustion Institute, 36(3):3917–3924, 2017.
 K.P Geigle, M. Köhler, W. O’Loughlin, and W. Meier. Investigation of soot formation in pressurized swirl flames by laser measurements of temperature, flame structures and soot concentrations. Proceedings of the Combustion Institute, 35(3):3373–3380, 2015.
 K.P. Geigle, W. O’Loughlin, R. Hadef, and W. Meier. Visualization of soot inception in turbulent pressurized flames by simultaneous measurement of laser-induced fluorescence of polycyclic aromatic hydrocarbons and laser-induced incandescence, and correlation to OH distributions. Applied Physics B: Lasers and Optics, 119(4):717–730, 2015.
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 S. Popp, F. Hunger, S. Hartl, D. Messig, B. Coriton, J. H. Frank, F. Fuest, and C. Hasse, “LES flamelet-progress variable modeling and measurements of a turbulent partially-premixed dimethyl ether jet flame,” Combust. Flame, vol. 162, no. 8, pp. 3016–3029, Aug. 2015.
 Ö.H. Cokuslu, C. Hasse, K.P. Geigle, and F. Ferraro, “Soot Prediction in a Model Aero-Engine Combustor using a Quadrature-based Method of Moments,” AIAA 2022-1446. AIAA SCITECH 2022 Forum. January 2022.