### Subproject B06 Maas

# Reduced kinetic models for combustion processes close to walls

## Motivation

The trend towards downsizing e.g. in internal combustion engines leads to questions of heat loss and surface reactions of reacting flows near boundaries. Therefore, flame-wall-interactions (FWI) are in the focus of today’s research. Besides experimental investigations, computations of FWI are performed to study and to improve the combustion processes in these configurations. For the modeling of the chemical kinetics for the computation of combustion processes, reaction mechanisms with hundreds of species are developed. Therefore, and due to the use of the Arrhenius law, even today with modern computational facilities, the detailed simulation of complex combustion processes is very time-consuming due to the high dimension and stiffness of these systems. In order to run simulations in a reasonable CPU time, reduced kinetic models are needed and have been developed recently. The Reaction-Diffusion-Manifold (REDIM), which accounts for both chemical kinetics as well as for diffusion processes, performs a model reduction in a very generic way and is applied and developed in this subproject.

## Objectives

The main objective of this subproject is to generate reduced kinetic models for flames close to walls, especially for the subproject C03 where the generated reduced kinetic models are used. These reduced kinetic models allow time-efficient but nevertheless accurate multi-dimensional computations of complex applications like IC engines or Side-Wall Quenching burners. The reduced kinetic model which was generated in the first funding period is extended and further improved. This comprises the generation of the reduced kinetic models for other fuels and mixture inhomogeneities, the inclusion of pollutant formation and the efficiency enhancement of the REDIM generation. The side-wall quenching burner is, among others, investigated numerically and experimentally in the second funding period. The numerical model system of this burner needs to be at least two-dimensional. For that reason, spatial gradients in two (or three) dimensions occur (in all physical directions). For that reason, multi-dimensional gradient estimates are investigated and implemented in the reduced kinetic model.

## Previous Findings

In the first funding period, a reduced kinetic model for flame-wall-interactions was generated. It has been developed, implemented and demonstrated for the methane-air combustion system. Moreover, the reduced kinetic model accounts not only for the heat loss at the wall but also for heterogeneous wall reactions. An invariant manifold contains all states that are accessed during the combustion process of a certain model system. In the first funding period, a method that allows the reduced kinetic model to expand was developed, which means, that the initial mesh of a manifold does not need to contain all these states because the manifold can enlarge. Moreover, it was shown, that the use of a reduced model equation in physical variables with a constant parametrization matrix can lead to errors during the computation.

## Approach

The REDIM method is the base of the reduced kinetic model for combustion processes close to walls. In order to consider multi-dimensional gradient estimates within the REDIM context, one- as well as multi-dimensional gradient estimates in the state space shall be analyzed. Afterwards, the REDIM for flame-wall-interactions shall be extended, and multi-dimensional gradient estimates are included in the REDIM. Therefore, a more accurate reduced kinetic model, especially for Side Wall Quenching flames, is generated.

In order to develop an algorithm for the construction of REDIMs for Flame-Wall-Interactions, the hierarchically increase of the dimension which has been developed in the first funding period is be used. The dimension of the REDIM can increase in some circumstances which requires a much higher CPU-time wherefore the numeric solution procedure of the REDIM equation needs to be improved.

Moreover, further implementation strategies for the coupling of the reduced kinetic model in the Large Eddy Simulations (LES) shall be developed and the previous implementation strategies need to be extended. In this context, it shall be examined, whether a simultaneous calculation of the REDIM during the LES is possible and reasonable. The gradients that can be obtained in the LES can be used for the generation of the REDIM. The REDIM equation is then integrated and the resulting REDIM is the input for the LES.

## Current Work

Current objectives include the definition of model fuels and reaction mechanisms, which is a recurring process. Furthermore, the investigation and implementation of multi-dimensional gradient estimates and the implementation of reduced kinetic models for inhomogeneous mixtures are part of the ongoing work. Moreover, pollutant formation is considered within the reduced kinetic model because during the flame extinction close to walls pollutant formation can occur, depending on the air-fuel ratio and the model system.

## Cooperations

The main goal of this subproject is the generation of reduced kinetic models for the simplified treatment of the chemical reaction and molecular transport. Therefore, the REDIM method is extended and a continuously exchange and close cooperation with B07 takes place. The developed and constructed reduced kinetic models are provided to C03 for their LES computations. Moreover, the reduced kinetic models are validated with the experimental results of A04. Furthermore, the determination and refinement of the reaction mechanisms will be performed in collaboration with B04.

## Selected Publications

- Schießl, R., Bykov, V., Maas, U., Abdelsamie, A., & Thévenin, D. (2017). Implementing multi-directional molecular diffusion terms into Reaction Diffusion Manifolds (REDIMs). Proceedings of the Combustion Institute, 36(1), 673-679.
- Gubernov, V. V., Bykov, V., & Maas, U. (2017). Hydrogen/air burner-stabilized flames at elevated pressures. Combustion and Flame, 185, 44-52.
- Steinhilber, G., Bykov, V., & Maas, U. (2017). REDIM reduced modeling of flame-wall-interactions: Quenching of a premixed methane/air flame at a cold inert wall. Proceedings of the Combustion Insti-tute, 36(1), 655-661.
- Strassacker, C., Bykov, V., & Maas, U., REDIM reduced modeling of quenching at a cold wall includ-ing heterogeneous wall Reactions, Int J Heat & Fluid Flow, Special issue to NWRF ’17
- Strassacker, C., Bykov, V., Maas, U. Parametrization strategies for manifold based reduced kinetic models, Proc. Comb. Inst.,
- Ganter, S., Strassacker, C., Heinrich, A., Meier, T., Kuenne, G., Maas, U., Janicka, J. Laminar near-wall combustion: Analysis of tabulated chemistry simulations by means of detailed kinetics. Int J Heat & Fluid Flow; Special issue,
- Strassacker, C., Bykov, V., & Maas, U. (2018), REDIM reduced modeling of flame quenching at a cold wall –The influence of detailed transport models and detailed mechanisms, Combust. Sci. Techn.,
- Neagos, A., Bykov, V., & Maas, U. (2017). Adaptive hierarchical construction of Reaction–Diffusion Manifolds for simplified chemical kinetics. Proceedings of the Combustion Institute, 36(1), 663-672.