Riblets in the viscous sublayer [Elektronische Ressource] : optimal shape design of microstructures / vorgelegt von Elfriede Friedmann

Inaugural - Dissertationzur Erlangung der Doktorwur¨ de derNaturwissenschaftlich - MathematischenGesamtfakulta¨t derRuprecht - Karls - Universit¨at Heidelbergvorgelegt vonDiplom MathematikerinElfriede Friedmannaus Temeschburg/Rum¨anienTag der mundlic¨ hen Prufung:¨ 10.11.2005ThemaRiblets in the viscous sublayerOptimal Shape Design of MicrostructuresGutachter Prof. Dr. Dr. h.c.mult Willi J¨agerProf. Dr. Rolf RannacherAbstractPreviousresearchhasestablishedthatasmoothsurfacehasnotnecessarilyminimaldrag:Many experiments by different laboratories, e.g. NASA and DLR Berlin, indicate that anextra surface layer with tiny grooves aligned in the stream-wise direction can be used toreduce the drag. The aim of this project is to find the optimal shape of such microstruc-tures on surfaces of submerged bodies. We assume that these microstructures remainin the viscous sublayer where the flow equations are the 3D incompressible, steady stateNavier-StokesequationswithaCouettein-andoutflowdeterminatedthroughtwobound-ary conditions, the no-slip condition on the lower boundary and the friction condition onthe upper one. The objective function of our optimization problem is the tangentialdrag force, which we want to minimize. Solving this problem is difficult because of therough boundary, which causes a big amount of data. We apply homogenization theoryand replace the rough boundary by a smooth one, where the right boundary conditionshave been determined.