Topology of Separated Flows

Participants: Prof.dr.ir P. G. Bakker

Description:

For a long time, it has been believed that the internal structures of flows (e.g. the topology) can only be obtained by accurate numerical simulation or by experiments. Yet, there is another theoretical way of investigating flow patterns. This sort of investigation is called topological investigation of flows and is one of the research subjects of the aerodynamics group.                                                                                                  

Figure 1: The flow patterns in the symmetry plane in front of the cylinder flat plate juncture.

In the past, the difference between topologies (e.g. the qualitative difference between the streamline patterns of Fig.1a and Fig.1b) was explained by a phenomenal study of the singular points (i.e., points where the all the velocity components are vanishing). It has been shown that the notions of elementary singular points and the rules they obey, can easily be used to describe for example the flow above surfaces in planes of symmetry. Further, singular points are important in the description and classification of three-dimensional flow patterns. One of the drawbacks, encountered with this sort of phenomenal studies is the need to identify all the singular points in numerically or experimentally obtained results. Missing a singular point can then be devastating for the final result. 

So, in order to understand the difference between these flow patterns, a systematic approach is needed which enables a systematic investigation of flow patterns. Only recently, it became clear that the presence of singular points (e.g. saddle points, nodes or foci) in, for example, the topology of the symmetry plane or skin friction pattern relies on the qualitative theory of differential equations resulting from a nonlinear dynamical system. The method based on the qualitative theory of differential equations is the key to the systematic investigation of flow patterns.

The two most important successes of the so-called bifurcation approach are on the one hand the ability to systematically identify the different topological structures (Fig.2) and on the other hand to establish a method which describes the evolution from one topology into another.

This second feature is the main reason why we believe that a topological study based on the qualitative theory of differential equations is a suitable approach to obtain a better insight in the topological flow patterns. For example, this theoretical method enabled us to investigate the capturing of a bubble by an upstream moving separation region (Fig.3).

This systematic approach has been used to develop a classification strategy for the description of two- and three-dimensional flow topologies of incompressible flows over flat plates. This approach has also been used to investigate the flow patterns in front of a juncture.

Special attention is presently given to the topological study in relation to the flow patterns over delta wings, combining surface flow visualization with quantitative flow velocity measurements using Particle Image Velocimetry (PIV).