Comptes Rendus
no. 1
An objective perspective for classic flow classification criteria
[Une perspective objective pour des critères classiques de classification d'écoulements]
Ramon S. Martins1 ; Anselmo Soeiro Pereira1 ; Gilmar Mompean1  ; Laurent Thais1 ; Roney Leon Thompson2
1 Université de Lille-1 – Sciences et Technologies, Polytech'Lille, and Laboratoire de mécanique de Lille (LML), UMR–CNRS 8107, Cité scientifique, 59655 Villeneuve-d'Ascq cedex, France
2 Laboratório de Mecânica Teórica Aplicada (LMTA), Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, RJ 24210-240, Brazil
Comptes Rendus. Mécanique, Volume 344 (2016) no. 1, pp. 52-59.

Quatre critères classiques utilisés pour la classification des écoulements complexes sont étudiés ici. Ces critères sont utiles pour identifier les régions de l'écoulement liées au cisaillement, à l'extention ou au mouvement de corps rigides. Ces critères habituels, à savoir Q, Δ, λ2 and λcr/λci, utilisent le tenseur taux de rotation du fluide, qui est connu pour varier par rapport au système de référence. Les avantages qu'il y a à utiliser des critères objectifs (invariants par rapport à une transformation générale pour un système de référence) sont discutés dans le present travail. À cet égard, nous construisons des versions des critères classiques en remplaçant la vorticité standard, une quantité non objective, par la vorticité effective, un taux de rotation par rapport à la vitesse angulaire des vecteurs propres du tenseur taux de déformation. Les critères classiques et leurs versions objectives correspondantes sont appliqués pour classifier deux écoulements complexes : l'écoulement ABC transitoire et l'écoulement à travers une contraction brusque 4:1. Les versions objectives de ces critères fournissent des informations plus riches pour la cinématique de l'écoulement.

Four classic criteria used to the classification of complex flows are discussed here. These criteria are useful to identify regions of the flow related to shear, elongation or rigid-body motion. These usual criteria, namely Q, Δ, λ2 and λcr/λci, use the fluid's rate-of-rotation tensor, which is known to vary with respect to a reference frame. The advantages of using objective (invariant with respect to a general transformation on the reference frame) criteria are discussed in the present work. In this connection, we construct versions of classic criteria replacing standard vorticity, a non-objective quantity, by effective vorticity, a rate-of-rotation tensor with respect to the angular velocity of the eigenvectors of the strain-rate tensor. The classic criteria and their corresponding objective versions are applied to classify two complex flows: the transient ABC flow and the flow through the abrupt 4:1 contraction. It is shown that the objective versions of the criteria provide richer information on the kinematics of the flow.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.08.002
Keywords: Objectivity, Flow classification, ABC flow, Contraction, Vortex identification
Mots-clés : Objectivité, Classification d'écoulements, Écoulement ABC, Contraction, Identification de tourbillons

Ramon S. Martins 1 ; Anselmo Soeiro Pereira 1 ; Gilmar Mompean 1 ; Laurent Thais 1 ; Roney Leon Thompson 2

1 Université de Lille-1 – Sciences et Technologies, Polytech'Lille, and Laboratoire de mécanique de Lille (LML), UMR–CNRS 8107, Cité scientifique, 59655 Villeneuve-d'Ascq cedex, France
2 Laboratório de Mecânica Teórica Aplicada (LMTA), Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, RJ 24210-240, Brazil 
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Ramon S. Martins; Anselmo Soeiro Pereira; Gilmar Mompean; Laurent Thais; Roney Leon Thompson. An objective perspective for classic flow classification criteria. Comptes Rendus. Mécanique, Volume 344 (2016) no. 1, pp. 52-59. doi : 10.1016/j.crme.2015.08.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.08.002/

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