Scalar Dissipation Rate Modeling and its Validation

Abstract

A simple algebraic model for the Favre averaged scalar dissipation rate, c, in high Damkohler number premixed flames is obtained from its transport equation by balancing the leading order terms. Recently proposed models for the dominant terms in the transport equation are revisited and revised. The algebraic model incorporates essential physics of turbulent premixed flames, namely, dilatation rate, its influence on turbulence-scalar interaction, chemical reactions, and dissipation processes. A realizability analysis is carried out to show that the algebraic model is always unconditionally realizable. The model predictions of dissipation rate are compared with the DNS results, and the agreement is good over a range of flame conditions. Application of the Kolmogorov-Petrovski-Piskunov (KPP) theorem along with the above algebraic model gives an expression for the turbulent flame speed. Its prediction compares well with a range of experimental data with no modifications to the model constants.

Keywords:

• Flame speed
• Numerical modeling
• Scalar dissipation rate
• Turbulent premixed flames

The support of EPSRC and Rolls–Royce plc. is acknowledged. HK acknowledges the support of Cambridge Commonwealth Trust. The help of Mr. Shiwaku and Dr. Tanahashi of Tokyo Institute of Technology in DNS data transfer is gratefully acknowledged.