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Framework for simulating stationary spherical flames

Ruiz, Fernando and Beardsell, Guillaume and Blanquart, Guillaume (2020) Framework for simulating stationary spherical flames. Proceedings of the Combustion Institute, 38 (2). pp. 2109-2117. ISSN 1540-7489. doi:10.1016/j.proci.2020.06.013.

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Understanding and quantifying the effects of flame stretch rate on the laminar flame speed and flame structure plays an important role from interpreting experimentally-measured laminar burning velocities to characterizing the impact of turbulence on premixed flames. Unfortunately, accounting for these effects often requires an unsteady reacting flow solver and may be computationally expensive. In this work, we propose a mathematical framework to perform simulations of stationary spherical flames. The objective is to maintain the flame at a constant radius (and hence a constant stretch rate) by performing a coordinate change. The governing equations in the new flame-attached frame of reference resemble the original equations for freely-propagating spherical flames. The only difference is the presence of additional source terms whose purpose is to drive the numerical solution to a steady state. These source terms involve one free parameter: the flame stretch rate, which may either be computed in real time or imposed by the user. This parameter controls ultimately the steady state flame radius and the steady state flame speed. That is why, at a given stretch rate, the results of the stationary spherical flame simulations match those of a freely-expanding spherical flame. As an illustration, the dependence of the laminar flame speed on the stretch rate is leveraged to extract Markstein lengths for hydrogen/air mixtures at different equivalence ratios, as well as for hydrocarbon/air mixtures (CH4 and C7H16). Numerical predictions are in good agreement with experimental measurements (within experimental uncertainties). Finally, the proposed methodology is implemented in the chemical kinetic software FlameMaster. The use of a dedicated steady-state solver with a non-uniform optimized mesh leads to significant reductions in the computational cost, highlighting that the proposed methodology is ideally suited for other chemical kinetic software such as Chemkin/Premix and Cantera.

Item Type:Article
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URLURL TypeDescription
Ruiz, Fernando0000-0003-0314-5478
Beardsell, Guillaume0000-0001-7138-488X
Blanquart, Guillaume0000-0002-5074-9728
Additional Information:© 2020 The Combustion Institute. Published by Elsevier Inc. Received 8 November 2019, Revised 25 May 2020, Accepted 10 June 2020, Available online 15 July 2020. This material is based upon work supported by the National Science Foundation under Grant No. 1832548. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Subject Keywords:Laminar flame speed; Markstein length; Stretched flames; Steady-state solver
Issue or Number:2
Record Number:CaltechAUTHORS:20200727-071315792
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Official Citation:Fernando Ruiz, Guillaume Beardsell, Guillaume Blanquart, Framework for simulating stationary spherical flames, Proceedings of the Combustion Institute, Volume 38, Issue 2, 2021, Pages 2109-2117, ISSN 1540-7489, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104577
Deposited By: Tony Diaz
Deposited On:27 Jul 2020 14:55
Last Modified:23 Apr 2021 16:36

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