Self-Similarity in Turbulent Wall-Wake Flow Downstream of a Wall-Mounted Vertical Cylinder

Flow past vertical bluff bodies is a key consideration in numerous theoretical and practical applications, thus attracting the interests of many researchers. For instance, when a bluff body is present in a fluid flow, it results in a wake, which is a flow zone downstream of the body with distinct features as compared to the plane boundary layer flow. Considering the fact that there are different types of vertical bluff such as bridge piers, wake flows experience an effect from the bottom wall surface hence resulting in a wall-wake flow. Unfortunately, most of the current investigations on the behavioral characteristics of wall-wake flow downstream of a mounted vertical cylinder have emphasized more on the general flow structure and vortex shedding. Therefore, significant efforts have been recently focused on understanding the flow velocity and turbulence characteristics by majorly considering self-similarity in their vertical profiles.

Recently, Professor Roberto Gaudio at Università della Calabria in collaboration with Professor Subhasish Dey, Dr. Debshri Swargiary and Professor Sankar Sarkar at Indian Institute of Technology Kharagpur and Professor Hongwei Fang at Tsinghua University investigated experimentally the turbulent wall-wake flow characteristics downstream a wall-mounted vertical cylinder. The authors utilized the Vectrino plus probe to determine the three-dimensional flow velocities. It was placed at different longitudinal distances both downstream of and upstream to the wall-mounted cylinder along asymmetric vertical lines.  Furthermore, from a self-similarity point of view, they analyzed the Reynolds shear stress, third-order moments, turbulence intensities and vertical profiles. Their work is published in Journal of Hydraulic Engineering.

The research team observed that the wall-wake flow incorporated fluid agitation effects that resulted in the damping of the velocity profiles. Consequently, the agitation significantly influenced the turbulence intensity profiles and the Reynolds shear stress effects in the wall-wake flow. As a result, the turbulence intensity profiles and the Reynolds shear stress exhibited maximum positive and negative values respectively in their individual profiles. However, the decrease in the downstream distance and reduction in the effects of the cylinder on the wake flow lead to the disappearance of the maximum values. Furthermore, a decrease in the traversing distance of the eddies in the wake-flow was noted in the middle layer of flow while an increase of the same was seen in the near wall and outer flow zones. This was attributed to the severe fluid agitation in the outer layer to improve the Reynolds shear stress and decrease the vertical gradient of the streamwise velocity.

The study has successfully advanced the understanding of the features of a time-averaged turbulent wall-wake flow downstream of a wall-mounted vertical cylinder by clarifying the self-similarity in turbulence and velocity quantities. For instance, the deficits in Reynolds shear stress, streamwise velocity, third order moments and turbulence intensities exhibited self-similarities in their vertical profiles when scaled by their corresponding maximum deficit values. In addition, further scaling resulted in the similarities in the vertical profiles of the deficits in mixing length and turbulent length.

Therefore, Professor Roberto Gaudio and the research team are optimistic that the findings in their study will be of great importance in the validation of the numerical simulations of the wall-wake flow downstream of and upstream to a vertical cylinder.