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Continuous adjoint complement to the Blasius equation
Citation Link: https://doi.org/10.15480/882.4116
Publikationstyp
Journal Article
Date Issued
2021-03-15
Sprache
English
Author(s)
Institut
TORE-DOI
TORE-URI
Journal
Volume
33
Issue
3
Article Number
033608
Citation
Physics of Fluids 33 (3): 033608 (2021)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
American Institute of Physics
The 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 .
Subjects
Physics - Fluid Dynamics
Mathematics - Optimization and Control
DDC Class
510: Mathematik
530: Physik
Publication version
publishedVersion
Publisher‘s 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.”
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