Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4116
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dc.contributor.authorKühl, Niklas-
dc.contributor.authorMüller, Peter Marvin-
dc.contributor.authorRung, Thomas-
dc.date.accessioned2020-11-24T16:52:25Z-
dc.date.available2020-11-24T16:52:25Z-
dc.date.issued2021-03-15-
dc.identifier.citationPhysics of Fluids 33 (3): 033608 (2021)de_DE
dc.identifier.issn1089-7666de_DE
dc.identifier.urihttp://hdl.handle.net/11420/7940-
dc.description.abstractThe manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary-layer. The text is structured into three parts. The first part demonstrates, that the adjoint complement can be derived in two ways, either following a first simplify then derive or a first derive and then simplify strategy. The simplification step comprises the classical boundary-layer (b.-l.) approximation and the derivation step transfers the primal flow equation into a companion adjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint b.-l. framework. This leads to similarity parameters, which turn the Partial-Differential-Equation (PDE) problem into a boundary value problem described by a set of Ordinary-Differential-Equations (ODE) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primal Blasius equation, its adjoint complement consists of two ODEs which can be simplified depending on the treatment of advection. It is shown, that the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar b.l. flows. Differences between the primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjoint b.-l. thickness, wall shear stress and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression for the shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutions and numerical results for Navier-Stokes simulations of a flat plate b.-l. at Reynolds numbers between 1E+03 <= ReL <= 1E+05 .en
dc.language.isoende_DE
dc.publisherAmerican Institute of Physicsde_DE
dc.relation.ispartofPhysics of fluidsde_DE
dc.rightsCC BY 4.0de_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subjectPhysics - Fluid Dynamicsde_DE
dc.subjectMathematics - Optimization and Controlde_DE
dc.subject.ddc510: Mathematikde_DE
dc.subject.ddc530: Physikde_DE
dc.titleContinuous adjoint complement to the Blasius equationde_DE
dc.typeArticlede_DE
dc.identifier.doi10.15480/882.4116-
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0114307-
tuhh.oai.showtruede_DE
tuhh.abstract.englishThis manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layerequations for a flat plate boundary layer. The text is structured into three parts. The first part demonstrates that the adjoint complement canbe derived in two ways, following either afirst simplify then deriveor afirst derive and then simplifystrategy. The simplification stepcomprises the classical boundary-layer (BL) approximation, and the derivation step transfers the primal flow equation into a companionadjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint BL framework. This leads to similarityparameters, which turn the partial-differential-equation (PDE) problem into a boundary value problem described by a set of ordinary-differential-equations (ODEs) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primalBlasius equation, its adjoint complement consists of two ODEs, which can be simplified depending on the treatment of advection. It is shownthat the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar BL flows. Differences betweenthe primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjointBL thickness, wall shear stress, and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression forthe shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutionsand numerical results for Navier–Stokes simulations of a flat plate BL at Reynolds numbers between 103 ReL 105. It is seen that thereversal of the inlet and outlet locations and the direction of the flow, inherent to the adjoint formulation of convective kinematics, poses achallenge when investigating real finite length (finiteRe-number) flat plate boundary layer problems. Efforts to bypass related issues arediscussed.de_DE
tuhh.publisher.doi10.1063/5.0037779-
tuhh.publication.instituteFluiddynamik und Schiffstheorie M-8de_DE
tuhh.identifier.doi10.15480/882.4116-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue3de_DE
tuhh.container.volume33de_DE
dc.relation.projectHydrodynamische Widerstandsoptimierung von Schiffsrümpfende_DE
dc.relation.projectWeiterentwicklung von praxistauglichen simulationsbasierten Methoden zur Verbesserung der Leistungsfähigkeit von Schiffen mittels Formoptimierungde_DE
dc.relation.projectModellierung, Simulation und Optimierung mit fluiddynamischen Anwendungende_DE
dc.rights.nationallicensefalsede_DE
dc.identifier.arxiv2011.07583v1de_DE
dc.identifier.scopus2-s2.0-85102771972de_DE
tuhh.container.articlenumber033608de_DE
local.status.inpresstruede_DE
dc.rights.creditline“Copyright (2021) Author(s) Niklas Kühl, Peter Marvin Müller and Thomas Rung; . This article is distributed under a Creative Commons Attribution (CC BY) License.”de_DE
local.type.versionpublishedVersionde_DE
datacite.resourceTypeArticle-
datacite.resourceTypeGeneralJournalArticle-
item.mappedtypeArticle-
item.openairetypeArticle-
item.languageiso639-1en-
item.grantfulltextopen-
item.cerifentitytypePublications-
item.creatorOrcidKühl, Niklas-
item.creatorOrcidMüller, Peter Marvin-
item.creatorOrcidRung, Thomas-
item.creatorGNDKühl, Niklas-
item.creatorGNDMüller, Peter Marvin-
item.creatorGNDRung, Thomas-
item.fulltextWith Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
crisitem.project.funderDeutsche Forschungsgemeinschaft (DFG)-
crisitem.project.funderBundesministerium für Wirtschaft und Klimaschutz (BMWK)-
crisitem.project.funderDeutsche Forschungsgemeinschaft (DFG)-
crisitem.project.funderid501100001659-
crisitem.project.funderid501100006360-
crisitem.project.funderid501100001659-
crisitem.project.funderrorid018mejw64-
crisitem.project.funderrorid02vgg2808-
crisitem.project.funderrorid018mejw64-
crisitem.project.grantnoRU 1575/3-1-
crisitem.project.grantno03SX453B-
crisitem.project.grantnoGRK 2583/1-
crisitem.project.fundingProgramGRK 2583-
crisitem.author.deptFluiddynamik und Schiffstheorie M-8-
crisitem.author.deptFluiddynamik und Schiffstheorie M-8-
crisitem.author.deptFluiddynamik und Schiffstheorie M-8-
crisitem.author.orcid0000-0002-4229-1358-
crisitem.author.orcid0000-0003-0369-1196-
crisitem.author.orcid0000-0002-3454-1804-
crisitem.author.parentorgStudiendekanat Maschinenbau-
crisitem.author.parentorgStudiendekanat Maschinenbau-
crisitem.author.parentorgStudiendekanat Maschinenbau-
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