Modelling of pulsating inverted conical flames: a numerical instability analysis

Abstract

The study of combustion-thermoacoustic instabilities is a topic of interest in the development of engines. However, the modelling of these systems involves a high computational burden. This paper focuses on a simpler class of systems that still features such instabilities: inverted conical flames anchored on a central bluff-body. Here these flames are modelled by solving species mass, momentum and energy transport equations, coupled with a skeletal methane/air chemical kinetic mechanism. The aim is to characterise the dynamic behaviour of inverted conical flames, both due to their natural dynamics and to external incoming velocity fluctuations. The main contribution is the detailed model of the flames, including the smallest scales. The analysis of the impact of the mesh adaption on the flame response shows a trade-off between model accuracy and computational burden that can be adjusted by changing the temperature gradient threshold. The flame response analysis in terms of the temperature and OH mass fraction gives a detailed characterisation of the flame front behaviour in its different scales, both in time and space. The analysis of the flame front dynamic response employing a spectral analysis shows that these have a natural frequency of 35 Hz, and this frequency interacts with the flame response due to incoming velocity excitations. More specifically, when forcing the flame with low frequencies ($f\le 125$ Hz) the flame responds only to the forcing and some harmonics, whereas when forcing between $125<f\le 172$ Hz the flame response comprises both the natural and forced behaviour. Forcing beyond 200 Hz shows the natural flame response only.

Keywords:

• Laminar premixed flame
• thermo-acoustic instability
• flame transfer function
• flame frequency response
• computational fluid dynamics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant Agreement nr 766264. This work was performed while L. F. Figueira da Silva was on leave from the Institut Prime at the Centre national de la recherche scientifique (CNRS, France). The authors also gratefully acknowledge the support provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, under the Research Grant No. 403904/2016-1.