Flow Topology for Evaluation of Aerodynamic Configurations

Classification of fluid flows is an essential part of Fluid Dynamics. Flows are typically characterized and distinguished by their properties and the associated equations. A classical example is the distinction between incompressible and compressible flows. Another approach is to analyze the flow field itself by looking for elementary brick stones describing the main spatial characteristics of the field in particular by reconstruction of streamlines with only a few elements. These locally distributed brick stones are building a kind of a map of the flow, the so-called Flow Topology. In the first part of this lecture an introduction into the research field of Flow Topology is given. The mathematical background is explained, in particular the critical point theory will be addressed and discussed. Thereafter it will be shown that there is a strong connection between large scale flow field structures, for example vortices, and some dominant flow topological elements in the flow field. A further essential point is the strong connection between flow maps of different flow fields. Their temporal interrelation is giving hints to the reason for temporal structure change. In the second part of this lecture the possibility to apply analysis techniques from Flow Topology research to evaluate the flow around aerodynamics configurations is addressed. Based on the analytical background some derived flow field analysis techniques will be explained. Further, first insights into application principles which help to understand spatial and temporal flow behavior will be given. Additionally, illustrative aerodynamic applications will be shown, practical advices will be discussed and also a glance on future research directions will be given, here, pointing out the relation to field decomposition methods (POD) and AI research