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Flow, Turbulence and Combustion

, Volume 93, Issue 4, pp 637–663 | Cite as

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

  • Umair Ahmed
  • Robert Prosser
  • Alistair J. Revell
Article

Abstract

Flame turbulence interaction is one of the leading order terms in the scalar dissipation \(\left (\widetilde {\varepsilon }_{c}\right )\) transport equation [35] and is thus an important phenomenon in premixed turbulent combustion. Swaminathan and Grout [36] and Chakraborty and Swaminathan [15, 16] have shown that the effect of strain rate on the transport of \(\widetilde {\varepsilon }_{c}\) is dominated by the interaction between the fluctuating scalar gradients and the fluctuating strain rate, denoted here by \(\overline {\rho }\widetilde {\Delta }_{c}= \overline {\rho {\alpha }\nabla c^{\prime \prime }S_{ij}^{\prime \prime }\nabla c^{\prime \prime }}\); this represents the flame turbulence interaction. In order to obtain an accurate representation of this phenomenon, a new evolution equation for \(\widetilde {\Delta }_{c}\) has been proposed. This equation gives a detailed insight into flame turbulence interaction and provides an alternative approach to model the important physics represented by \(\widetilde {\Delta }_{c}\). The \(\widetilde {\Delta }_{c}\) evolution equation is derived in detail and an order of magnitude analysis is carried out to determine the leading order terms in the \(\widetilde {\Delta }_{c}\) evolution equation. The leading order terms are then studied using a Direct Numerical Simulation (DNS) of premixed turbulent flames in the corrugated flamelet regime. It is found that the behaviour of \(\widetilde {\Delta }_{c}\) is determined by the competition between the source terms (pressure gradient and the reaction rate), diffusion/dissipation processes, turbulent strain rate and the dilatation rate. Closures for the leading order terms in \(\widetilde {\Delta }_{c}\) evolution equation have been proposed and compared with the DNS data.

Keywords

Flame turbulence interaction Scalar turbulence interaction Premixed turbulent combustion Scalar dissipation 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Umair Ahmed
    • 1
  • Robert Prosser
    • 1
  • Alistair J. Revell
    • 1
  1. 1.Modelling & Simulation Centre, School of MACEUniversity of ManchesterManchesterUK

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