Vortex control in channel flows using translational invariant cost functionals

The use of translation invariant cost functionals for the reduction of vortices in the context of shape optimization of fluid flow domain is investigated. Analytical expressions for the shape design sensitivity involving different cost functionals are derived. Channel flow problems with a bump and an obstacle as possible control boundaries are taken as test examples. Numerical results are provided in various graphical forms for relatively low Reynolds numbers. Striking differences are found for the optimal shapes corresponding to the different cost functionals, which constitute different quantification of a vortex. Copyright Springer Science+Business Media, LLC 2012