Secondary instabilities in the wake of an elongated two-dimensional body with a blunt trailing edge

Abstract

The secondary instability in the wake of a two-dimensional blunt body with a chord to thickness ratio of 46.5 was experimentally investigated for Reynolds numbers of 3500, 5200 and 7000 based on the blunt trailing edge height $h$. Planar, stereoscopic and high-speed particle image velocimetry (PIV) measurements were performed to characterise the wake and upstream boundary layer. The same mode B secondary instability that is found in the cylinder wake was found to be present in the wake of the elongated body studied here. The most probable wavelength of the secondary instability, defined as the spanwise distance between adjacent streamwise vortex pairs in the wake, was found to range from $0.7h$ to $0.8h$ by applying a spatial autocorrelation to the spanwise–wall-normal instantaneous fields of the $Q$-criterion. The temporal evolution of the secondary wake vortices was investigated using time-resolved stereoscopic PIV measurements and it was shown that the vortices maintain both their directions of rotation and spanwise positions during the primary vortex shedding cycles. In agreement with previous literature, the secondary instability did not greatly change as the upstream boundary layer transitioned from laminar to turbulent. Moreover, any upstream boundary layer structures were found to rapidly evolve into wake structures just past the blunt trailing edge. The wavelength of the secondary instability was shown to match the spanwise distance between adjacent low-speed zones of streamwise velocity in the wake. These undulating velocity patterns proved to be a viable method for determining the secondary instability wavelength; however, this type of analysis is highly sensitive to the energy content used for data reconstruction when proper orthogonal decomposition is applied beforehand.

The mode B structure of streamwise vortices in the wake of a two-dimensional blunt trailing edge

“…It was shown that the use of POD misrepresents the structure of streamwise vortices when applied to streamwise velocity fields in the wake, and that the near-wake undulations in streamwise velocity only match the streamwise vortices when POD is not applied to the velocity fields beforehand. Considering direct measurements of the streamwise vortices and their temporal behaviour, Gibeau et al (2018) concluded the presence of mode B in the wake for a larger AR, and this was in contrast to the results of Naghib-Lahouti et al (2012, 2014. To our knowledge, no further experimental work regarding the streamwise vortices in the wakes of elongated blunt bodies has been carried out.…”

“…While Gibeau et al (2018) showed that the analysis technique used by Naghib-Lahouti et al (2012, 2014 may have been flawed, the difference in AR between these two studies is too large to draw a conclusion for the lower AR investigated by Naghib-Lahouti et al (2012, 2014 and Ryan et al (2005). The present work seeks to remedy this by utilizing direct measurements of the streamwise vortices, i.e.…”

“…The secondary instabilities in the wake of a nominally two-dimensional BTE, which have been the subject of contradictory studies as of late, are the topic of the present work. These instabilities influence the organization of streamwise vortices in the wake, and recent experimental works have reported different conclusions regarding their scale (Naghib-Lahouti, Doddipatla & Hangan 2012;Naghib-Lahouti, Lavoie & Hangan 2014;Gibeau, Koch & Ghaemi 2018). These works will be further discussed shortly.…”

“…This was possible following the work of Mansy et al (1994) and Wu et al (1996), who showed that the wavelength of the streamwise vortices matches the wavelength of streamwise velocity undulations in the near wake. As was shown by Gibeau et al (2018), this analysis technique coupled with POD has the potential to greatly skew the wavelength results. Gibeau et al (2018) used PIV to study the streamwise vortices in the wake of an elongated blunt body with a much larger AR of 46.5 for 3500 Re(h) 7000.…”

“…As was shown by Gibeau et al (2018), this analysis technique coupled with POD has the potential to greatly skew the wavelength results. Gibeau et al (2018) used PIV to study the streamwise vortices in the wake of an elongated blunt body with a much larger AR of 46.5 for 3500 Re(h) 7000. Their analysis compared direct, time-resolved measurements of the streamwise vortices in the wake to the methods of Naghib-Lahouti et al (2012, 2014).…”