Iso-scalar surfaces, mixing and reaction in turbulent flows

César Dopazo; Jesús Martín; Juan Hierro

doi:10.1016/j.crme.2006.07.004

Iso-scalar surfaces, mixing and reaction in turbulent flows
[Surfaces iso-scalaires, mélange, et réaction dans des écoulements]

César Dopazo ¹ ; Jesús Martín ¹ ; Juan Hierro ^1,²

¹ Centro Politécnico Superior, Área de Mecánica de Fluidos, Universidad de Zaragoza, Maria de Luna, 3, 50018 Zaragoza, Spain
² Mechanical Engineering Department, The Johns Hopkins University, 3400 North Charles St. Baltimore, MD 21218, USA

Comptes Rendus. Mécanique, Observation, analysis and modelling in complex fluid media, Volume 334 (2006) no. 8-9, pp. 483-492.

Abstract (VO)
Résumé

Turbulent scalar mixing with chemical reaction is investigated in terms of the local geometrical features of the iso-scalar surfaces—‘scalar field topologies’—, using Direct Numerical Simulation data. Two scalars with identical initial distribution, one inert and the other obeying a prescribed Arrhenius-like chemical reaction, evolve in homogeneous isotropic turbulence with a mesh size 256³. The two local principal curvatures, $k_{1}$ and $k_{2}$ , of the iso-scalar surface at each point are straightforwardly obtained from the curvature tensor, $n_{i, j}$ , whose elements are the spatial derivatives of the unit vector normal to the iso-surface. The scalar diffusive flux is decomposed into a ‘flat-front’ contribution plus a curvature induced molecular transport. Expressions for the normal propagating velocity relative to the fluid of iso-surfaces, of both the inert and the reactive scalar fields, are provided making use of the previous decomposition. The ‘flat-front’ and the curvature induced contributions to the diffusive fluxes, beside to the chemical reaction rate, are correlated with the principal curvatures. Results, including the joint statistics of the principal curvatures and their correlations with the scalar dissipation, are also presented.

Le mélange turbulent de scalaires en présence de réaction chimique est considéré en termes de caractéristiques géométriques locales de surfaces iso-scalaires— « topologies de champs scalaires »—, à partir de données de simulations numériques directes. Deux scalaires de distributions initiales identiques, un inerte et l'autre obeissant à une réaction chimique prescrite du type Arrhenius, évoluent dans une turbulence homogène et isotrope sur une grille 256³. Les deux courbures principales, $k_{1}$ et $k_{2}$ , des surfaces iso-scalaires en chaque point sont obtenus directement à partir du tenseur de courbure, $n_{i, j}$ , dont les éléments sont les dérivées spatiales du vecteur unitaire normal à l'iso-surface. Le flux diffusif du scalaire est décomposé en une contribution ‘front-plat’ et un transport moléculaire induit par la courbure. Les expressions pour la vitesse de propagation normale par rapport au fluide des iso-surfaces, des champs scalaires réactif et inerte, sont données en utilisant la décomposition précédente. Le ‘front-plat’ et les contributions induites par effet de courbure aux flux diffusifs, à côté du taux de réaction chimique, sont corrélés aux courbures principales. Des résulats incluant les statistiques conjointes des courbures principales et leurs corrélations avec la dissipation scalaire sont aussi présentées.

Publié le : 2006-08-01

DOI : 10.1016/j.crme.2006.07.004

Keywords: Turbulence, Turbulent reacting flows, Scalar mixing, Direct Numerical Simulation, Curvature
Mots-clés : Turbulence, Écoulements turbulents réactifs, Mélange d'un scalaire, Simulations Numériques Directes, Courbure

Affiliations des auteurs :

César Dopazo ¹ ; Jesús Martín ¹ ; Juan Hierro ^{1, 2}

¹ Centro Politécnico Superior, Área de Mecánica de Fluidos, Universidad de Zaragoza, Maria de Luna, 3, 50018 Zaragoza, Spain
² Mechanical Engineering Department, The Johns Hopkins University, 3400 North Charles St. Baltimore, MD 21218, USA

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     title = {Iso-scalar surfaces, mixing and reaction in turbulent flows},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {483--492},
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César Dopazo; Jesús Martín; Juan Hierro. Iso-scalar surfaces, mixing and reaction in turbulent flows. Comptes Rendus. Mécanique, Observation, analysis and modelling in complex fluid media, Volume 334 (2006) no. 8-9, pp. 483-492. doi : 10.1016/j.crme.2006.07.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.07.004/

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Mengzhen Cheng; Haiou Wang; Kun Luo; Jianren Fan A direct numerical simulation study on the structures and turbulence–flame interactions of a laboratory-scale lean premixed jet flame in cross-flow, Journal of Fluid Mechanics, Volume 957 (2023) | DOI:10.1017/jfm.2023.78
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Marius M. Neamtu-Halic; Dominik Krug; Jean-Paul Mollicone; Maarten Van Reeuwijk; George Haller; Markus Holzner Connecting the time evolution of the turbulence interface to coherent structures, Journal of Fluid Mechanics, Volume 898 (2020), p. 24 (Id/No a3) | DOI:10.1017/jfm.2020.414 | Zbl:1460.76509
Cesar Dopazo; Luis Cifuentes; Juan Hierro; Jesus Martin Micro-scale Mixing in Turbulent Constant Density Reacting Flows and Premixed Combustion, Flow, Turbulence and Combustion, Volume 96 (2016) no. 2, p. 547 | DOI:10.1007/s10494-015-9663-8
Luis Cifuentes; Cesar Dopazo; Jesus Martin; Carmen Jimenez Local flow topologies and scalar structures in a turbulent premixed flame, Physics of Fluids, Volume 26 (2014) no. 6 | DOI:10.1063/1.4884555
Marc Wolf; M. Holzner; B. Lüthi; D. Krug; W. Kinzelbach; A. Tsinober Effects of mean shear on the local turbulent entrainment process, Journal of Fluid Mechanics, Volume 731 (2013), pp. 95-116 | DOI:10.1017/jfm.2013.365 | Zbl:1294.76168
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