Identification for the Coherent Structure in a Backward-Facing Step

Turbulence is regarded as a tangle of vortices with various scales and it’s viewed as essentially a stochastic phenomenon for a long time. Vortex dynamics is usually used to explain many complex turbulence physics. Particularly, coherent vorical structures were evident to be play a dominant role in these separated flows. However, the identification for this kind of vortical structures is still a problem as an accepted definition of a vortex is lacking. As a result, different identification method may pick out different kinds of coherent structures.

Backward-facing step (BFS) flow is fundamental in geometry and design, consequently it’s widely seen in numerous applications in our daily life. In this study, a backward-facing step water flow model is built to generate vortices with Reynold number (based on the step height and mean velocity) of Re_h = 4400. The expansion ratio is 2 : 1, and width to height ratio is set as 10 : 1 to keep flow to be two dimensional as possible.

To provide a global view for the evolution of vortical structures, a synchronous particle image velocimetry (PIV) system was developed. As a result, this system doubled the measurement domain to about 2 × 30cm × 24cm with resolution of 7.35pix / mm. In this backward-facing step model, a section of 12h × 5h transient velocity fields are available, which can show a relatively complete developing process for the coherent vortices. The size of final interrogation area is 20 × 15pixels with resolution of 2.722 × 2.042mm².

A Q method was modified to identify the coherent structures, which is consistent with that in the transient streamlines. A normalization was employed on the velocity matrix before calculation for the Q value. This normalization has greatly enhanced the rotating intensity, thus it’s helpful to present the coherent vortical structures in the shear layer. As a result, a good agreement comes to the identification for the coherent vortex structures between this method and the transient streamlines. This work may contribute to further quantitive analysis for the coherent structures in these flows.