Confluence of Wall Shear Stress and its Relation to Vorticity Surface Flux and Flow Separation

Abstract

With regard to the environmental impact of aircraft transportation it is of crucial importance to increase the efficiency of modern aircraft by reducing fuel consumption. From the aerodynamic point of view this translates into a further reduction of viscous forces acting on the surface of an aircraft. Furthermore, its is of equal importance to avoid boundary layer flow separation which induces significant additional drag due to the formation of force inducing vortices. However, due to design constraints, these flow phenomena can be observed in the flow around civil, military or urban air transport vehicles. Hence, flow separation criteria have to be incorporated more deeply into the aircraft shape design process. Thus, it is necessary to have a closer look at these flow physical mechanisms and the associated analytical descriptions. Therefore, in this study a framework is presented, in which the confluence of wall shear stress is connected to the vorticity flux at the surface. In particular, its relation to the aerodynamic forces acting on the surface of an air vehicle is explained and an analysis of the impact of different vorticity surface flux contributors on surface forces is performed. Furthermore, by analyzing vorticity surface flux source terms, a decomposition of the main flux contributors into first and second order terms is conducted which allows to identify the main driver in the force balance. Moreover, it is also demonstrated that the flow separation criteria of Lighthill and Wu can be formulated as the confluence of wall shear stress, demonstrating that this quantity can be identified as an essential parameter in the design process of air vehicle shapes. The analytical considerations are followed by the analysis of CFD results in which the derived relations are investigated and discussed. For two exemplary flow configurations, RANS CFD simulations are performed using the DLR TAU code. It has to be mentioned that only mean quantities of the RANS results are discussed, specialities of turbulence are not investigated here. At first the separating flow around a generic ellipsoid is analyzed, followed by the complex flow around generic aircraft configurations. Focal point is laid on the interconnection between the confluence of wall shear stress and the viscous vorticity flux at the wall and its curvature dependence. Their coincidence manifests in flow separation. However, it reveals also the possibility for flow separation control and, therefore, the control of vortical flows