The instantaneous structure of secondary flows in turbulent boundary layers

Abstract

Secondary flows can develop in turbulent boundary layers that grow over surfaces with spanwise inhomogeneities. In this article, we demonstrate the formation of secondary flows in both experimental and numerical tests and dissect the instantaneous structure and topology of these secondary motions. We show that the formation of secondary flows is not very sensitive to the Reynolds number range investigated, and direct numerical simulations and experiments produce similar results in the mean flow as well as the dispersive and turbulent stress distributions. The numerical methods capture time-resolved features of the instantaneous flow and provide insight into the near-wall flow structures, that were previously obscured in the experimental measurements. Proper orthogonal decomposition was shown to capture the essence of the secondary flows in relatively few modes and to be useful as a filter to analyse the instantaneous flow patterns. The secondary flows are found to create extended regions of high Reynolds stress away from the wall that comprise predominantly sweeps similar to what one would expect to see near the wall and which are comparable in magnitude to the near-wall stress. Analysis of the instantaneous flow patterns reveals that the secondary flows are the result of a non-homogeneous distribution of mid-size vortices.

Rearrangement of secondary flow over spanwise heterogeneous roughness

“…while the distribution for h = 0 is in good agreement with the studies of ridge-type roughness(Hwang & Lee 2018;Vanderwel et al 2019). The Reynolds stress v w at different elevation of the smooth stripes h. Brown solid lines mark the isolines for the streamwise mean velocity distribution with isolevels corresponding toFigure 4.…”

Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers

“…Similar additional vortices were also observed by Vanderwel & Ganapathisubramani (2015) but it was speculated that these could have been caused by the presence of small pins on the top of the LEGO brick roughness. However, in a more recent study by Vanderwel et al (2019) along with the DNS of Hwang & Lee (2018), these were reported to exist even for a smooth flat ridge, identical to the HS4-HS6 cases. The results are similar from both the present experiment and the DNS, and these new structures are shown to grow stronger for wider ridges, while a weakening of the previous large-scale vortices is observed.…”

“…However, in spite of their impact on the primary flow, the secondary motions are shown to be relatively weak in comparison to the mean flow. In fact, the secondary flows were demonstrated to be simply the result of superimposition of stronger instantaneous vortices, which only occur in a small fraction of the total time, and are unevenly distributed in the cross-plane (Kevin et al 2017;Vanderwel et al 2019).…”

Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges

“…The spatial domain for the computation was selected such that y 1 was midway between two ridges, y N y = y 1 + s, z 1 corresponds to the ridge top elevation and z N z is the free-surface level. The width of the spatial domain used for the POD computation was set to s (as in Vanderwel et al 2019) to allow a consistent comparison between obtained POD mode patterns for the different experiments. Following the POD snapshot method (e.g.…”

“…A number of experimental and numerical studies have explored open-channel, closed-channel and boundary-layer flows over streamwise ridges with different cross-sectional shapes (e.g. Nezu & Nakagawa 1993;Wang & Cheng 2006;Vanderwel & Ganapathisubramani 2015;Hwang & Lee 2018;Medjnoun, Vanderwel & Ganapathisubramani 2018;Vanderwel et al 2019;Zampiron et al 2020), alternating streamwise strips of different surface roughness (e.g. Nezu & Nakagawa 1993;Wang & Cheng 2006;Willingham et al 2014;Anderson et al 2015;Bai, Kevin & Monty 2018;Chung, Monty & Hutchins 2018;Wangsawijaya et al 2018) and converging/diverging riblet patterns (e.g.…”