Evolution equations for the decomposed components of displacement speed in a reactive scalar field

R. Yu, T. Nilsson, C. Fureby, A. N. Lipatnikov

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The study of a turbulent premixed flame often involves analysing quantities conditioned to different iso-surfaces of a reactive scalar field. Under the influence of turbulence, such a surface is deformed and translated. To track the surface motion, the displacement speed of the scalar field respective to the local flow velocity is widely used and this quantity is currently receiving growing attention. Inspired by the apparent benefits from a simple decomposition of into contributions due to (i) curvature, (ii) normal diffusion and (iii) chemical reaction, this work aims at deriving and exploring new evolution equations for these three contributions averaged over the reaction surface. Together with a previously obtained-evolution equation, the three new equations are presented in a form that emphasizes the decomposition of into three terms. This set of equations is also supplemented with a curvature-evolution equation, hence providing a new perspective to link the flame topology and its propagation characteristics. Using two direct numerical simulation databases obtained from constant-density and variable-density reaction waves, all the derived equations and the term-wise decomposition relations are demonstrated to hold numerically. Comparison of the simulated results indicates that the thermal expansion weakly affects the key terms in the considered evolution equations. Thermal expansion can cause variations in the averaged and its decomposed parts through multiple routes more than introducing a dilatation term. The flow plays a major role to influence the key terms in all equations except the curvature one, due to a cancellation between negatively and positively curved surface elements.

TidskriftJournal of Fluid Mechanics
StatusPublished - 2021

Bibliografisk information

Funding Information:
R.Y., T.N., C.F. gratefully acknowledge the financial support by the Swedish Research Council (VR). A.L. gratefully acknowledges the financial support by CERC. The simulations were performed using the computer facilities provided by the Swedish National Infrastructure for Computing (SNIC) at PDC and HPC2N.

Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.

Copyright 2021 Elsevier B.V., All rights reserved.

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