Vorticity and Energy Dynamics for Flow Control

Abstract

Minimization of viscous drag is the most important goal in the design process of modern civil aircraft. In numerical optimization processes either local surface or global flow field methods can be used to improve aircraft shapes. On the one hand insights from vortex dynamics lead to an analytical description of wall bounded vorticity flux which allows to identify promising surface flow quantities which could be manipulated in order to reduce overall drag. Derived relations reveal the connection between surface forces acting on an aircraft and its geometrical shape contour, but also the pressure and viscous flow related fluxes. Here, in particular, the boundary vorticity flux, formulated in the most general form by using surface quantities is considered. On the other hand flow field energy relations deliver insight into the transport of vorticity, energy and work of viscous drag. In particular, the Helmholtz decomposition of the velocity field allows to identify the interaction energy of potential and vortical flow field components, which is directly related to the work of viscous drag manifested in the flow field. This leads to the Josephson-Anderson (J-A) relation which allows to combine local surface flow quantities stemming from vortex dynamics with global energy flow field relations. This relation can be extended by precisely defined source terms of wall shear stress, enabling the identification of relevant shape optimization terms. Eventually, this work investigates sources of wall-shear stress using elements of the boundary vorticity flux relations and their impact on the global interaction energy field, and eventually on drag. As an application example the flow around an extruded 2D airfoil is investigated for which the potential flow field can be determined analytically. In addition, steady RANS simulation are performed, providing viscous flow solution as foundation for the analysis of the extended J-A relation. Furthermore, geometrical shape changing flow control elements are mounted on the ex�truded airfoil in order to demonstrate the impact of surface shape and curvature change on drag power transport in the energy interaction field.