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Alternate scales for turbulent boundary layer on transitional rough walls / Noor Afzal in Transactions of the ASME . Journal of fluids engineering, Vol. 130 N° 4 (Avril 2008) 

Public ISBD [article]  in Transactions of the ASME . Journal of fluids engineering > Vol. 130 N° 4 (Avril 2008) . - 16 p. Titre : Alternate scales for turbulent boundary layer on transitional rough walls : universal log laws Type de document : texte imprimé Auteurs : Noor Afzal, Auteur Année de publication : 2009 Article en page(s) : 16 p. Note générale : Fluids engineering Langues : Anglais (eng) Mots-clés : Turbulent  boundary  layer;  nondimensional  roughness  scale;  Reynolds  number Résumé : The present work deals with four new alternate transitional surface roughness scales for description of the turbulent boundary layer. The nondimensional roughness scale ϕ is associated with the transitional roughness wall inner variable ζ=Z+∕ϕ, the roughness friction Reynolds number Rϕ=Rτ∕ϕ, and the roughness Reynolds number Reϕ=Re∕ϕ. The two layer theory for turbulent boundary layers in the variables, mentioned above, is presented by method of matched asymptotic expansions for large Reynolds numbers. The matching in the overlap region is carried out by the Izakson–Millikan–Kolmogorov hypothesis, which gives the velocity profiles and skin friction universal log laws, explicitly independent of surface roughness, having the same constants as the smooth wall case. In these alternate variables, just above the wall roughness level, the mean velocity and Reynolds stresses are universal and do not depend on surface roughness. The extensive experimental data provide very good support to our universal relations. There is no universality of scalings in traditional variables and different expressions are needed for inflectional type roughness, monotonic Colebrook–Moody roughness, k-type roughness, d-type roughness, etc. In traditional variables, the velocity profile and skin friction predictions for the inflectional roughness, k-type roughness, and d-type roughness are supported well by the extensive experimental data. The pressure gradient effect from the matching conditions in the overlap region leads to the universal composite laws, which for weaker pressure gradients yields log laws and for strong adverse pressure gradients provides the half-power laws for universal velocity profiles and in traditional variables the additive terms in the two situations depend on the wall roughness. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/Issue.aspx?issueID=27307 [...] [article] Alternate scales for turbulent boundary layer on transitional rough walls : universal log laws [texte imprimé] / Noor Afzal, Auteur . - 2009 . - 16 p. Fluids engineering Langues : Anglais (eng) in Transactions of the ASME . Journal of fluids engineering > Vol. 130 N° 4 (Avril 2008) . - 16 p. Mots-clés : Turbulent  boundary  layer;  nondimensional  roughness  scale;  Reynolds  number Résumé : The present work deals with four new alternate transitional surface roughness scales for description of the turbulent boundary layer. The nondimensional roughness scale ϕ is associated with the transitional roughness wall inner variable ζ=Z+∕ϕ, the roughness friction Reynolds number Rϕ=Rτ∕ϕ, and the roughness Reynolds number Reϕ=Re∕ϕ. The two layer theory for turbulent boundary layers in the variables, mentioned above, is presented by method of matched asymptotic expansions for large Reynolds numbers. The matching in the overlap region is carried out by the Izakson–Millikan–Kolmogorov hypothesis, which gives the velocity profiles and skin friction universal log laws, explicitly independent of surface roughness, having the same constants as the smooth wall case. In these alternate variables, just above the wall roughness level, the mean velocity and Reynolds stresses are universal and do not depend on surface roughness. The extensive experimental data provide very good support to our universal relations. There is no universality of scalings in traditional variables and different expressions are needed for inflectional type roughness, monotonic Colebrook–Moody roughness, k-type roughness, d-type roughness, etc. In traditional variables, the velocity profile and skin friction predictions for the inflectional roughness, k-type roughness, and d-type roughness are supported well by the extensive experimental data. The pressure gradient effect from the matching conditions in the overlap region leads to the universal composite laws, which for weaker pressure gradients yields log laws and for strong adverse pressure gradients provides the half-power laws for universal velocity profiles and in traditional variables the additive terms in the two situations depend on the wall roughness. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/Issue.aspx?issueID=27307 [...]

Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel / Noor Afzal in Journal of engineering mechanics, Vol. 137 N° 12 (Decembre 2011) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 137 N° 12 (Decembre 2011) . - pp.835-845 Titre : Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel : Universal relations Type de document : texte imprimé Auteurs : Noor Afzal, Auteur ; A. Bushra, Auteur ; Abu Seena, Auteur Année de publication : 2012 Article en page(s) : pp.835-845 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Hydraulic  jump  Bed  roughness  Froude  number  Channels  Turbulent  flow Résumé : The streamwise flow structure of a turbulent hydraulic jump over a rough bed rectangular channel has been investigated. The flow is divided into inner and outer layers, where upstream supercritical flow changes to downstream subcritical flow. The analysis is based on depth averaged Reynolds momentum equations. The molecular viscosity on the rough bed imposes the no slip boundary condition, but close to the wall the turbulent process in inner layer provides certain matching conditions with the outer layer, where molecular viscosity has no dominant role. It is shown that the bed roughness in the inner layer has a passive role in imposing wall shear stress during formation of hydraulic jump in the outer layer. The Belanger’s jump condition of rectangular channel has been extended to account for the implications of the drag attributable to channel bed roughness, kinetic energy correction factor, and coefficient of the Reynolds normal stresses. For depth averaged Reynolds normal stress, an eddy viscosity model containing gradient of depth averaged axial velocity is considered. Analytical solutions for sequent depth ratio, jump length, roller length, and profiles of jump depth and velocity were found to depend upon the upstream Froude number, drag owing to bed roughness, and kinetic energy correction factor. On the basis of dynamical similarity, the roller length and aeration length were proposed to be of the same order as the jump length. An effective upstream Froude number, introduced in the present work, yields universal predictions for sequent depth ratio, jump length, roller length, jump profile, and other hydraulic jump characteristics that are explicitly independent of bed roughness drag. Thus, results for hydraulic jump over a rough bed channel can be directly deduced from classical smooth bed hydraulic jump theory, provided the upstream Froude number is replaced by the effective upstream Froude number. These findings of universality have been supported by experimental data over a rough bed rectangular channel. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.org/emo/resource/1/jenmdt/v137/i12/p835_s1?isAuthorized=no [article] Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel : Universal relations [texte imprimé] / Noor Afzal, Auteur ; A. Bushra, Auteur ; Abu Seena, Auteur . - 2012 . - pp.835-845. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 137 N° 12 (Decembre 2011) . - pp.835-845 Mots-clés : Hydraulic  jump  Bed  roughness  Froude  number  Channels  Turbulent  flow Résumé : The streamwise flow structure of a turbulent hydraulic jump over a rough bed rectangular channel has been investigated. The flow is divided into inner and outer layers, where upstream supercritical flow changes to downstream subcritical flow. The analysis is based on depth averaged Reynolds momentum equations. The molecular viscosity on the rough bed imposes the no slip boundary condition, but close to the wall the turbulent process in inner layer provides certain matching conditions with the outer layer, where molecular viscosity has no dominant role. It is shown that the bed roughness in the inner layer has a passive role in imposing wall shear stress during formation of hydraulic jump in the outer layer. The Belanger’s jump condition of rectangular channel has been extended to account for the implications of the drag attributable to channel bed roughness, kinetic energy correction factor, and coefficient of the Reynolds normal stresses. For depth averaged Reynolds normal stress, an eddy viscosity model containing gradient of depth averaged axial velocity is considered. Analytical solutions for sequent depth ratio, jump length, roller length, and profiles of jump depth and velocity were found to depend upon the upstream Froude number, drag owing to bed roughness, and kinetic energy correction factor. On the basis of dynamical similarity, the roller length and aeration length were proposed to be of the same order as the jump length. An effective upstream Froude number, introduced in the present work, yields universal predictions for sequent depth ratio, jump length, roller length, jump profile, and other hydraulic jump characteristics that are explicitly independent of bed roughness drag. Thus, results for hydraulic jump over a rough bed channel can be directly deduced from classical smooth bed hydraulic jump theory, provided the upstream Froude number is replaced by the effective upstream Froude number. These findings of universality have been supported by experimental data over a rough bed rectangular channel. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.org/emo/resource/1/jenmdt/v137/i12/p835_s1?isAuthorized=no

Hydraulic jump in circular and U-shaped channels / A. Bushra in Journal of hydraulic research, Vol. 44 N°4 (2006) 

Public ISBD [article]  in Journal of hydraulic research > Vol. 44 N°4 (2006) . - 567-576 p. Titre : Hydraulic jump in circular and U-shaped channels Titre original : Ressaut hydraulique dans des canaux de section circulaire et en forme de U Type de document : texte imprimé Auteurs : A. Bushra, Auteur ; Noor Afzal, Auteur Article en page(s) : 567-576 p. Note générale : Hydraulique Langues : Anglais (eng) Mots-clés : Circular  and  U-shaped  channels  Hydraulic  jump  Invariant  relations  Reynolds  normal  stress  model  Canaux  circulaires  et  en  U  Ressaut  hydraulique  Relations  invariables  Modèle  normal  d'effort  de  Reynolds Index. décimale : 627 Ingénierie des cours d'eau naturels, des ports, des rades et des cotes. Installations de navigation, de dragage, de récupération et de sauvetage. Barrages et centrales électriques hydrauliques Résumé : The Reynolds equations of mean turbulent flow in a two-dimensional open channel of arbitrary cross-section have been analyzed. An integral equation for the turbulent hydraulic jump is proposed. In the closure model adopted, the depth-averaged effective normal Reynolds stress is taken proportional to the product of constant eddy viscosity and depth-averaged axial velocity gradient, and the constant of proportionality that is independent of channel geometry. The general theory has been applied to the flows in circular and U-shaped channels. The solutions for sequent depth, hydraulic jump length, roller length and aeration length have been estimated. The comparison of the theory with experimental data of Hager and Stahl for circular and U-shaped channels give very encouraging results. Les équations de Reynolds de l'écoulement turbulent moyen dans un canal ouvert bidimensionnel de section transversale arbitraire ont été analysées. On propose une équation intégrale pour le ressaut hydraulique turbulent. Dans le modèle de fermeture adopté, l'effort normal efficace profondeur fait la moyenne de Reynolds est pris proportionnel au produit de la viscosité constante de remous et profondeur fait la moyenne le gradient axial de vitesse, et la constante de la proportionnalité qui est indépendant de la géométrie de canal. La théorie générale a été appliquée aux écoulements dans des canaux circulaires et en U. Les solutions pour la profondeur sequent, la longueur hydraulique de ressaut, la longueur de rouleau et la longueur d'aération ont été estimées. La comparaison de la théorie avec des données expérimentales de Hager et Stahl pour les canaux circulaires et en U donnent des résultats très encourageants. DEWEY : 627 ISSN : 0022-1686 RAMEAU : Ressaut hydraulique En ligne : afzala@uwindsor.ca [article] Hydraulic jump in circular and U-shaped channels = Ressaut hydraulique dans des canaux de section circulaire et en forme de U [texte imprimé] / A. Bushra, Auteur ; Noor Afzal, Auteur . - 567-576 p. Hydraulique Langues : Anglais (eng) in Journal of hydraulic research > Vol. 44 N°4 (2006) . - 567-576 p. Mots-clés : Circular  and  U-shaped  channels  Hydraulic  jump  Invariant  relations  Reynolds  normal  stress  model  Canaux  circulaires  et  en  U  Ressaut  hydraulique  Relations  invariables  Modèle  normal  d'effort  de  Reynolds Index. décimale : 627 Ingénierie des cours d'eau naturels, des ports, des rades et des cotes. Installations de navigation, de dragage, de récupération et de sauvetage. Barrages et centrales électriques hydrauliques Résumé : The Reynolds equations of mean turbulent flow in a two-dimensional open channel of arbitrary cross-section have been analyzed. An integral equation for the turbulent hydraulic jump is proposed. In the closure model adopted, the depth-averaged effective normal Reynolds stress is taken proportional to the product of constant eddy viscosity and depth-averaged axial velocity gradient, and the constant of proportionality that is independent of channel geometry. The general theory has been applied to the flows in circular and U-shaped channels. The solutions for sequent depth, hydraulic jump length, roller length and aeration length have been estimated. The comparison of the theory with experimental data of Hager and Stahl for circular and U-shaped channels give very encouraging results. Les équations de Reynolds de l'écoulement turbulent moyen dans un canal ouvert bidimensionnel de section transversale arbitraire ont été analysées. On propose une équation intégrale pour le ressaut hydraulique turbulent. Dans le modèle de fermeture adopté, l'effort normal efficace profondeur fait la moyenne de Reynolds est pris proportionnel au produit de la viscosité constante de remous et profondeur fait la moyenne le gradient axial de vitesse, et la constante de la proportionnalité qui est indépendant de la géométrie de canal. La théorie générale a été appliquée aux écoulements dans des canaux circulaires et en U. Les solutions pour la profondeur sequent, la longueur hydraulique de ressaut, la longueur de rouleau et la longueur d'aération ont été estimées. La comparaison de la théorie avec des données expérimentales de Hager et Stahl pour les canaux circulaires et en U donnent des résultats très encourageants. DEWEY : 627 ISSN : 0022-1686 RAMEAU : Ressaut hydraulique En ligne : afzala@uwindsor.ca

Turbulent boundary layer with negligible wall stress / Noor Afzal in Transactions of the ASME . Journal of fluids engineering, Vol. 130 N° 5 (Mai 2008) 

Public ISBD [article]  in Transactions of the ASME . Journal of fluids engineering > Vol. 130 N° 5 (Mai 2008) . - 15 p. Titre : Turbulent boundary layer with negligible wall stress Type de document : texte imprimé Auteurs : Noor Afzal, Auteur Année de publication : 2009 Article en page(s) : 15 p. Note générale : Fluids engineering Langues : Anglais (eng) Mots-clés : Flow  (dynamics);  separation  (technology);  viscosity;  stress;  wakes;  boundary  layer  turbulence;  equations;  pressure  gradient;  boundary  layers;  composite  materials;  shear  (mechanics) Résumé : The turbulent boundary layer subjected to strong adverse pressure gradient near the separation region has been analyzed at large Reynolds numbers by the method of matched asymptotic expansions. The two regions consisting of outer nonlinear wake layer and inner wall layer are analyzed in terms of pressure scaling velocities Up=(νp′∕ρ)1∕3 in the wall region and Uδ=(δp′∕ρ)1∕2 in the outer wake region, where p′ is the streamwise pressure gradient and ρ is the fluid density. In this work, the variables δ, the outer boundary layer thickness, and Uδ, the outer velocity scale, are independent of ν, the molecular kinematic viscosity, which is a better model of fully developed mean turbulent flow. The asymptotic expansions have been matched by Izakson–Millikan–Kolmogorov hypothesis leading to open functional equations. The solution for the velocity distribution gives new composite log-half-power laws, based on the pressure scales, providing a better model of the flow, where the outer composite log-half-power law does not depend on the molecular kinematic viscosity. These new composite laws are better and one may be benefited from their limiting relations that for weak pressure gradient yield the traditional logarithmic laws and for strong adverse pressure gradient yield the half-power laws. During matching of the nonlinear outer layer two cases arise: One where Uδ∕Ue is small and second where Uδ∕Ue of order unity (where Ue is the velocity at the edge of the boundary layer). In the first case, the lowest order nonlinear outer flow under certain conditions shows equilibrium. The outer flow subjected to the constant eddy viscosity closure model is governed by the Falkner–Skan equation subjected to the matching condition of finite slip velocity on the surface. The jet- and wakelike solutions are presented, where the zero velocity slip implying the point of separation, which compares well with Coles traditional wake function. In the second case, higher order terms in the asymptotic solutions for nearly separating flow have been estimated. The proposed composite log-half-power law solution and the limiting half-power law have been well supported by extensive experimental and direct numerical simulation data. For moderate values of the pressure gradient the data show that the proposed composite log-half-power laws are a better model of the flow. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/issue.aspx?journalid=122 [...] [article] Turbulent boundary layer with negligible wall stress [texte imprimé] / Noor Afzal, Auteur . - 2009 . - 15 p. Fluids engineering Langues : Anglais (eng) in Transactions of the ASME . Journal of fluids engineering > Vol. 130 N° 5 (Mai 2008) . - 15 p. Mots-clés : Flow  (dynamics);  separation  (technology);  viscosity;  stress;  wakes;  boundary  layer  turbulence;  equations;  pressure  gradient;  boundary  layers;  composite  materials;  shear  (mechanics) Résumé : The turbulent boundary layer subjected to strong adverse pressure gradient near the separation region has been analyzed at large Reynolds numbers by the method of matched asymptotic expansions. The two regions consisting of outer nonlinear wake layer and inner wall layer are analyzed in terms of pressure scaling velocities Up=(νp′∕ρ)1∕3 in the wall region and Uδ=(δp′∕ρ)1∕2 in the outer wake region, where p′ is the streamwise pressure gradient and ρ is the fluid density. In this work, the variables δ, the outer boundary layer thickness, and Uδ, the outer velocity scale, are independent of ν, the molecular kinematic viscosity, which is a better model of fully developed mean turbulent flow. The asymptotic expansions have been matched by Izakson–Millikan–Kolmogorov hypothesis leading to open functional equations. The solution for the velocity distribution gives new composite log-half-power laws, based on the pressure scales, providing a better model of the flow, where the outer composite log-half-power law does not depend on the molecular kinematic viscosity. These new composite laws are better and one may be benefited from their limiting relations that for weak pressure gradient yield the traditional logarithmic laws and for strong adverse pressure gradient yield the half-power laws. During matching of the nonlinear outer layer two cases arise: One where Uδ∕Ue is small and second where Uδ∕Ue of order unity (where Ue is the velocity at the edge of the boundary layer). In the first case, the lowest order nonlinear outer flow under certain conditions shows equilibrium. The outer flow subjected to the constant eddy viscosity closure model is governed by the Falkner–Skan equation subjected to the matching condition of finite slip velocity on the surface. The jet- and wakelike solutions are presented, where the zero velocity slip implying the point of separation, which compares well with Coles traditional wake function. In the second case, higher order terms in the asymptotic solutions for nearly separating flow have been estimated. The proposed composite log-half-power law solution and the limiting half-power law have been well supported by extensive experimental and direct numerical simulation data. For moderate values of the pressure gradient the data show that the proposed composite log-half-power laws are a better model of the flow. En ligne : http://fluidsengineering.asmedigitalcollection.asme.org/issue.aspx?journalid=122 [...]