Analysis of flapping motion of reattaching shear layer behind a two-dimensional backward-facing step

Abstract

An experimental investigation was carried out on the flapping motion of a turbulent reattaching shear layer downstream of a two-dimensional backward-facing step. The Reynolds number was 2.0 × 104, based on the free-stream velocity and the step height. The aim of this study is to analyze the flapping motion, which is featured unsteadiness of the reattaching shear layer, and its interaction with the recirculation region. High-resolution planar particle image velocimetry was used to measure the separated and reattaching shear layer in a horizontal-vertical plane. The velocity vector fields have shown the reattaching shear layer considerably flaps upwards and downwards as much in scale as approximately one step height from the middle part of recirculation region to the reattachment area. As a result, the recirculation region varies in size and the reattachment point shifts upstream and downstream. By applying singular value decomposition and proper orthogonal decomposition, the flapping motion is decomposed into multiple spatial modes, each of which represents interactions between the reattaching shear layer and recirculation region. In particular, the unsteady movement of the reattachment point is highly correlated with the flapping motion, and so is the maximum reverse flow. As a result, the flapping motion contributes substantial parts of the Reynolds shear stress and turbulent kinetic energy within the shear layer in the latter half of the reattachment length.

Internal flows of ventilated partial cavitation

“…Figure 10 illustrates the trend of the reattachment length (X r ) of BF S flow upon change in Re h . As shown in the figure, for BF S , Boiko et al (2011); , Etheridge and Kemp (1978); , Kostas et al (2002); , Scarano et al (1999); •, Nadge and Govardhan (2014); +, Ma and Schröder (2017); ×, Jovic and Driver (1995); , X r of external recirculation region of OC from Qin et al (2019); , TBC length from the present study. Note that the X r of single phase flows are marked with filled symbols, and the data points corresponding to VPC studies of ours and Qin et al (2019) are marked with hollow symbols.…”

“…To provide a better comparison between the flow structures, we introduce the velocity ratio of the forward flow and the reverse flow along the same velocity profile at each streamwise location. It should be noted that the maximum of this ratio (r F R,max ) yields 0.15 for OC internal flows and 0.14 for turbulent BF S flow (Ma and Schröder, 2017). Moreover, the unsteady behaviors of OC internal flow resemble those of turbulent BF S flow.…”

“…In addition, both flow fields show a maximum reverse flow velocity occurring at the center of the circulation vortex, i.e., the internal flow circulation vortex of OC ( Fig. 5a) and the recirculation vortex of turbulent BF S flow (Ma and Schröder, 2017). To provide a better comparison between the flow structures, we introduce the velocity ratio of the forward flow and the reverse flow along the same velocity profile at each streamwise location.…”

Periodic forcing of a large turbulent separation bubble

“…1984; Driver, Seegmiller & Marvin 1987; Hudy et al. 2003; Ma & Schröder 2017). Geometry-induced TSBs differ from pressure-induced TSBs inasmuch as the separation point is fixed in the former case but may fluctuate in the latter.…”

Dynamics of a supersonic transitional flow over a backward-facing step

“…The expected K-H instability was not observed by Tinney and Ukeiley [8] due to the short residence time of flow in the shear layer. However, experimental work of Duncan Jr [9] shows that there exists a critical step height as a function of unit Reynolds number, beyond which the traveling and shedding of the K-H vortices is the main incentive of the transition process, see also [10]. The classical transition path consist of the roll-up of the shear layer, the convection of quasi-periodic K-H vortices, flapping motion of the reattachment and separation bubble, as well as the vortex breakdown to turbulence [11].…”