Global Field Invariants and Local Vortex Axis Invariants Analysis for Flow Prediction

Abstract

Flow prediction is the ultimative task of each aerodynamicist. The knowledge about the flow structure, in particular it’s vortical structures and their temporal development would allow to design more efficient technical applications or flow control systems. The goal of this paper is to analyze the global flow field and the flow along local vortex axes by applying topological criteria with the objective to get more information about the structural stability of the flow field for flow prediction. The analysis is performed on a numerical calculated dataset of a pitching delta wing flow. In the global field approach vortical flow regions are detected, whereas the invariants of the involved vector fields are analyzed and visualized. The topological flow structure change is shown by temporal development of the invariants in relation to the evolution of the dominant vortices. For the local flow topological analysis, vortex axis identification and calculation methods have been utilized to destinate the vortex axes of the dominant vortices. Here, a new vortex axis detection scheme has been applied. A local analysis of the flow field invariants on the vortex axes allows us to visualize their development in time. The resulting curves in the phase space of tensor invariants embody stability information that indicates changes of topological flow structures. The analysis of these phase space curves can be used as a prediction methodology for topological flow structure change. In a further step surfaces of invariants of the vorticity vector field are presented in relation to the development of the velocity field. This gives significant insight into the development of the vortex breakdown phenomenon and reveals the interdependency of different vector fields. This can serve as a fundamental building block in methods for controlling flow structures.