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Instabilités secondaires dans la convection de Rayleigh-Bénard pour des fluides rhéofluidifiants

Author: Thomas VaréChérif NouarChristel MétivierAlain BergeonMarc MedaleAll authors
Publisher: 2019.
Dissertation: Thèse de doctorat : Énergie et mécanique : Université de Lorraine : 2019.
Edition/Format:   Computer file : Document : Thesis/dissertation : English
Summary:
Dans la configuration de Rayleigh-Bénard, on considère une fine couche de fluide placée entre deux parois horizontales, chauffée par le bas et refroidie par le haut. Cette couche peut être le siège d'une instabilité si le gradient thermique est suffisamment important : on passe alors de l'état conductif à l'état convectif et on parle de bifurcation primaire pour qualifier cette première transition. Cette
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Details

Genre/Form: Thèses et écrits académiques
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Thomas Varé; Chérif Nouar; Christel Métivier; Alain Bergeon; Marc Medale; Daniel Henry; Anne Davaille; Université de Lorraine.; École doctorale SIMPPé - Sciences et ingénierie des molécules, des produits, des procédés, et de l'énergie (Lorraine).; Laboratoire d'énergétique et de mécanique théorique et appliquée (Nancy).
OCLC Number: 1129124760
Notes: Titre provenant de l'écran-titre.
Description: 1 online resource
Responsibility: Thomas Varé ; sous la direction de Chérif Nouar et de Christel Métivier.

Abstract:

Dans la configuration de Rayleigh-Bénard, on considère une fine couche de fluide placée entre deux parois horizontales, chauffée par le bas et refroidie par le haut. Cette couche peut être le siège d'une instabilité si le gradient thermique est suffisamment important : on passe alors de l'état conductif à l'état convectif et on parle de bifurcation primaire pour qualifier cette première transition. Cette mise en mouvement du fluide se fait de manière ordonnée : on constate ainsi l'émergence de différents motifs de convection comme des rouleaux, des carrés ou encore des hexagones. Ces structures vont à leur tour subir des instabilités qualifiées de secondaires qui vont limiter la gamme de nombres d'onde stables. On étudie ici théoriquement ces instabilités d'une part à proximité du seuil de la convection grâce à une approche faiblement non linéaire, d'autre part loin des conditions critiques grâce à une approche fortement non linéaire. Le fluide est rhéofluidifiant, ce qui correspond au comportement rhéologique le plus fréquemment rencontré, et est décrit par le modèle de Carreau. À proximité du seuil, on considère deux situations : la première correspond au cas où les plaques ont une conductivité finie, la seconde à celui d'un fluide thermodépendant. Dans chaque cas, l'influence du caractère rhéofluidifiant sur la nature du motif émergeant à la bifurcation primaire et sur les instabilités secondaires est mise en évidence. Pour étudier les motifs de convection loin des conditions critiques, on a recours à une procédure de continuation permettant de déterminer de proche en proche les caractéristiques de l'écoulement comme les champs de vitesse ou de température ainsi que le nombre de Nusselt.

In the Rayleigh-Bénard configuration, we consider a thin layer of fluid confined between two horizontal slabs which is heated from below and cooled from above. This layer undergoes an instability if the thermal gradient is strong enough: a transition from the conductive state to the convective state and called _ primary bifurcation _occurs. Moreover, it happens in an ordered way: we can notice the emergence of various convection patterns such as rolls, squares or hexagons. In their turn, these patterns undergo _ secondary instabilities _ that limit the range of stable wavenumbers. These instabilities are studied theoretically _firstly near the threshold thanks to a weakly nonlinear approach, and secondly far from critical conditions thanks to a strongly nonlinear approach. We consider a shear thinning fluid, the most common rheological behavior, which is described by the Carreau model. Near the threshold, two situations are considered: the first corresponds to finite conductivity plates, the second corresponds to a thermodependent fluid. In each case, the influence of the shear thinning effect on the nature of the pattern emerging at the primary bifurcation and on secondary instabilities is highlighted. To study the convection patterns far from the critical conditions, a continuation procedure is used to determine, step-by-step, the characteristics of the flow, such as the velocity or temperature fields and the Nusselt number.

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<http:\/\/www.worldcat.org\/oclc\/1129124760<\/a>> # Instabilit\u00E9s secondaires dans la convection de Rayleigh-B\u00E9nard pour des fluides rh\u00E9ofluidifiants<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:MediaObject<\/a>, bgn:ComputerFile<\/a>, bgn:Thesis<\/a>, schema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nbgn:inSupportOf<\/a> \"Th\u00E8se de doctorat : \u00C9nergie et m\u00E9canique : Universit\u00E9 de Lorraine : 2019.<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"1129124760<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/bifurcation<\/a>> ; # Bifurcation<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/convection_de_rayleigh_benard<\/a>> ; # Convection de Rayleigh-B\u00E9nard<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/instabilites_hydrodynamiques<\/a>> ; # Instabilit\u00E9s hydrodynamiques<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/instabilites_secondaires<\/a>> ; # Instabilit\u00E9s secondaires<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/rayleigh_benard<\/a>> ; # Rayleigh-B\u00E9nard<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/532.051\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/convection<\/a>> ; # Convection<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/rheologie<\/a>> ; # Rh\u00E9ologie<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/536.25\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/fluides_rheofluidifiants<\/a>> ; # Fluides rh\u00E9ofluidifiants<\/span>\n\u00A0\u00A0\u00A0\nschema:author<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/vare_thomas_1991<\/a>> ; # Thomas Var\u00E9<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/davaille_anne<\/a>> ; # Anne Davaille<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/nouar_cherif<\/a>> ; # Ch\u00E9rif Nouar<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/bergeon_alain_1966<\/a>> ; # Alain Bergeon<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Organization\/ecole_doctorale_simppe_sciences_et_ingenierie_des_molecules_des_produits_des_procedes_et_de_l_energie_lorraine<\/a>> ; # \u00C9cole doctorale SIMPP\u00E9 - Sciences et ing\u00E9nierie des mol\u00E9cules, des produits, des proc\u00E9d\u00E9s, et de l\'\u00E9nergie (Lorraine).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Organization\/laboratoire_d_energetique_et_de_mecanique_theorique_et_appliquee_nancy<\/a>> ; # Laboratoire d\'\u00E9nerg\u00E9tique et de m\u00E9canique th\u00E9orique et appliqu\u00E9e (Nancy).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/metivier_christel_1980<\/a>> ; # Christel M\u00E9tivier<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/henry_daniel_19<\/a>> ; # Daniel Henry<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/medale_marc_19<\/a>> ; # Marc Medale<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Organization\/universite_de_lorraine<\/a>> ; # Universit\u00E9 de Lorraine.<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2019<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Dans la configuration de Rayleigh-B\u00E9nard, on consid\u00E8re une fine couche de fluide plac\u00E9e entre deux parois horizontales, chauff\u00E9e par le bas et refroidie par le haut. Cette couche peut \u00EAtre le si\u00E8ge d\'une instabilit\u00E9 si le gradient thermique est suffisamment important : on passe alors de l\'\u00E9tat conductif \u00E0 l\'\u00E9tat convectif et on parle de bifurcation primaire pour qualifier cette premi\u00E8re transition. Cette mise en mouvement du fluide se fait de mani\u00E8re ordonn\u00E9e : on constate ainsi l\'\u00E9mergence de diff\u00E9rents motifs de convection comme des rouleaux, des carr\u00E9s ou encore des hexagones. Ces structures vont \u00E0 leur tour subir des instabilit\u00E9s qualifi\u00E9es de secondaires qui vont limiter la gamme de nombres d\'onde stables. On \u00E9tudie ici th\u00E9oriquement ces instabilit\u00E9s d\'une part \u00E0 proximit\u00E9 du seuil de la convection gr\u00E2ce \u00E0 une approche faiblement non lin\u00E9aire, d\'autre part loin des conditions critiques gr\u00E2ce \u00E0 une approche fortement non lin\u00E9aire. Le fluide est rh\u00E9ofluidifiant, ce qui correspond au comportement rh\u00E9ologique le plus fr\u00E9quemment rencontr\u00E9, et est d\u00E9crit par le mod\u00E8le de Carreau. \u00C0 proximit\u00E9 du seuil, on consid\u00E8re deux situations : la premi\u00E8re correspond au cas o\u00F9 les plaques ont une conductivit\u00E9 finie, la seconde \u00E0 celui d\'un fluide thermod\u00E9pendant. Dans chaque cas, l\'influence du caract\u00E8re rh\u00E9ofluidifiant sur la nature du motif \u00E9mergeant \u00E0 la bifurcation primaire et sur les instabilit\u00E9s secondaires est mise en \u00E9vidence. Pour \u00E9tudier les motifs de convection loin des conditions critiques, on a recours \u00E0 une proc\u00E9dure de continuation permettant de d\u00E9terminer de proche en proche les caract\u00E9ristiques de l\'\u00E9coulement comme les champs de vitesse ou de temp\u00E9rature ainsi que le nombre de Nusselt.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"In the Rayleigh-B\u00E9nard configuration, we consider a thin layer of fluid confined between two horizontal slabs which is heated from below and cooled from above. This layer undergoes an instability if the thermal gradient is strong enough: a transition from the conductive state to the convective state and called _ primary bifurcation _occurs. Moreover, it happens in an ordered way: we can notice the emergence of various convection patterns such as rolls, squares or hexagons. In their turn, these patterns undergo _ secondary instabilities _ that limit the range of stable wavenumbers. These instabilities are studied theoretically _firstly near the threshold thanks to a weakly nonlinear approach, and secondly far from critical conditions thanks to a strongly nonlinear approach. We consider a shear thinning fluid, the most common rheological behavior, which is described by the Carreau model. Near the threshold, two situations are considered: the first corresponds to finite conductivity plates, the second corresponds to a thermodependent fluid. In each case, the influence of the shear thinning effect on the nature of the pattern emerging at the primary bifurcation and on secondary instabilities is highlighted. To study the convection patterns far from the critical conditions, a continuation procedure is used to determine, step-by-step, the characteristics of the flow, such as the velocity or temperature fields and the Nusselt number.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/9686825240<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Th\u00E8ses et \u00E9crits acad\u00E9miques<\/span>\" ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Instabilit\u00E9s secondaires dans la convection de Rayleigh-B\u00E9nard pour des fluides rh\u00E9ofluidifiants<\/span>\" ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"1129124760<\/span>\" ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/docnum.univ-lorraine.fr\/public\/DDOC_T_2019_0099_VARE.pdf<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.theses.fr\/2019LORR0099\/document<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/1129124760<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/henry_daniel_19<\/a>> # Daniel Henry<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"19..<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Henry<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Daniel<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Daniel Henry<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/medale_marc_19<\/a>> # Marc Medale<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"19..<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Medale<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Marc<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Marc Medale<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/nouar_cherif<\/a>> # Ch\u00E9rif Nouar<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Nouar<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Ch\u00E9rif<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Ch\u00E9rif Nouar<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Person\/vare_thomas_1991<\/a>> # Thomas Var\u00E9<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1991<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Var\u00E9<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Thomas<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Thomas Var\u00E9<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/convection<\/a>> # Convection<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Convection<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/instabilites_secondaires<\/a>> # Instabilit\u00E9s secondaires<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Instabilit\u00E9s secondaires<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Thing\/rayleigh_benard<\/a>> # Rayleigh-B\u00E9nard<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Rayleigh-B\u00E9nard<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/convection_de_rayleigh_benard<\/a>> # Convection de Rayleigh-B\u00E9nard<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Convection de Rayleigh-B\u00E9nard<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/fluides_rheofluidifiants<\/a>> # Fluides rh\u00E9ofluidifiants<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Fluides rh\u00E9ofluidifiants<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/instabilites_hydrodynamiques<\/a>> # Instabilit\u00E9s hydrodynamiques<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Instabilit\u00E9s hydrodynamiques<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/9686825240#Topic\/rheologie<\/a>> # Rh\u00E9ologie<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Rh\u00E9ologie<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.theses.fr\/2019LORR0099\/document<\/a>>\u00A0\u00A0\u00A0\nrdfs:comment<\/a> \"Acc\u00E8s au texte int\u00E9gral<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/1129124760<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/1129124760<\/a>> ; # Instabilit\u00E9s secondaires dans la convection de Rayleigh-B\u00E9nard pour des fluides rh\u00E9ofluidifiants<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2021-02-18<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n