A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames
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A‑Priori Validation of Scalar Dissipation Rate Models for Turbulent Non‑Premixed Flames M. P. Sitte1 · C. Turquand d’Auzay2 · A. Giusti3 · E. Mastorakos1 · N. Chakraborty2 Received: 15 June 2020 / Accepted: 9 September 2020 © The Author(s) 2020
Abstract The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of nonpremixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation. Keywords Scalar dissipation rate · Large-eddy simulation · Conditional moment closure · Non-premixed flames
1 Introduction Any combustion process with imperfectly mixed reactants requires mixing at the molecular level of fuel and oxidiser, as well as energy transport from the reacting region to the unburnt reactants, for the flame to develop. In modelling of turbulent non-premixed flames, mixing at the molecular level (also called micro-mixing) is generally related to the energy cascade of a conserved scalar, the mixture fraction 𝜉 , and typically enters into models through the terms representing the dissipation of scalar fluctuations at unresolved scales.
* A. Giusti [email protected] 1
Hopkinson Laboratory, Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
2
School of Engineering, Newcastle University, Newcastle‑Upon‑Tyne NE1 7RU, UK
3
Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 1AL, UK
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Vol.:(0123456789)
Flow, Turbulence and Combustion
The scalar dissipation rate (SDR), defined as N𝜉 = D∇𝜉 ⋅ ∇𝜉 , represents the local rate of mixing (diffusion) at molecular level (Bilger 2004) and therefore it is a key element for the modelling of turbulence effects on reaction rates. In presumed PDF models, the SDR controls the rate at which the variance of the resolved conserved scalar decays in time; the SDR also affects directly the local flame structure in advanced turbulent combustion models such as the conditional moment closure (CMC) (Klimenko and Bilger 1999) as well as flamelet-based approaches (Peters 1984). In models based on transported PDF (Pope 1985) as well as in the Multiple Mapping Conditioning (MMC) (Klimenko and Pope 2003), the micro-mixing effects are included through mixing models (Ren and Pope 2004
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