A derivation of temperature-based energy equation for LES of isochoric turbulent combustion with FDSGS model

Abstract

In this study, with the aim of deriving a temperature-based energy equation and evaluating the fractal dynamic SGS (FDSGS) combustion model under an isochoric condition, modelling of the filtered energy conservation equation in the temperature form is considered and is tested in the contexts of a priori and a posteriori, comparing with a corresponding DNS of turbulent combustion in a constant volume vessel. Conditional averages of various terms in the filtered energy conservation equation in the temperature form show that three unclosed terms, the SGS scalar flux, the SGS pressure-dilatation and the heat release rate, are leading terms. New SGS models for the SGS pressure-dilatation and the heat release rate are proposed and are tested in a priori manner. The zeroth-order models are also compared. The heat release rate models are proposed for reaction zones and post-flame zones separately, since the present analysis revealed a substantial contribution of heat generated in the post-flame zones. In addition to the tests of the SGS models for the energy conservation equation, isochoric treatments for various flame quantities under varying mean pressure and unburnt temperature due to the isochoric condition are also proposed and are tested. LES using the FDSGS combustion model with the new SGS models and isochoric treatments is performed considering the same combustion conditions and configuration as the DNS. The LES with several other SGS combustion models are also performed and are compared. The performed LES show reasonable prediction of flame propagation for any of the SGS combustion models tested, although the prediction by the FDSGS combustion model shows closest to the DNS. Regardless of the SGS combustion models, the peak values of the mean pressure are close to the DNS value, which suggests that the proposed SGS models and isochoric treatments for the energy conservation equation work well.

Keywords:

• Large eddy simulation
• SGS combustion model
• SGS model
• direct numerical simulation
• constant volume vessel

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by a collaborative research program with the research association of Automotive Internal Combustion Engines (AICE), and the Council for Science, Technology and Innovation (CSTI), Cross-Ministerial Strategic Innovation Promotion Program (SIP), Innovative Combustion Technology (Funding agency: JST).