Stability and transition on a Coandă cylinder

Abstract

An experimental stability and transition investigation of a centrifugally unstable wall jet blown from a slot over a circular Coandă cylinder was conducted using flow visualization and particle image velocimetry. Clear and unambiguous observations of spontaneously generated stationary streamwise structures, never observed previously, were analyzed using standard image processing techniques. These structures ultimately exhibited a secondary time-dependent wavy instability that was followed by transition to turbulence. A modified Görtler number, based on the slot height, was used as a basis for comparison to linear stability theory and was directly related to the Reynolds number via geometric scaling. Direct observation of the vortices allowed the identification of an upper limit to the critical Görtler number of 6.3 that bracketed the value of 3.5 from the linear stability theory. The vortical shear layer grew exponentially along the azimuth and was characterized by a Reynolds number dependent growth rate parameter. Extrapolation of the growth rate parameter to zero furnished a critical Görtler number of 3.1 ± 1.25 (95% CI) that compared remarkably well with the linear stability theory. The shear layer separation angle did not vary monotonically with the Reynolds number: as the Reynolds number increased, the thicker boundary layer was more susceptible to separation, and thus, the separation angle, relative to the slot, decreased. However, following transition to turbulence at higher Reynolds numbers (≈400), the high-momentum fluid near the wall, resulting from turbulent mixing, produced a subsequent increase in the separation angle.

Mixing enhancement of a compressible jet over a convex wall

“…Different from the well-studied planar mixing layer, there are not only the Kelvin–Helmholtz type inflectional instability (Neuendorf & Wygnanski 1999; Watanabe & Nagata 2021), but also the Taylor–Görtler type of centrifugal instability (Görtler 1941; Cunff & Zebib 1996; Matsson & John 1998) in the curved jet shear layer. A series of previous studies have shown that this additional centrifugal instability plays an important role in the development of a convex wall jet (Fujisawa & Kobayashi 1987; Neuendorf & Wygnanski 1999; Likhachev, Neuendorf & Wygnanski 2001; Neuendorf, Lourenco & Wygnanski 2004; Han, De Zhou & Wygnanski 2006; Dunaevich & Greenblatt 2020; Pandey & Gregory 2020, 2021). Fujisawa & Kobayashi (1987), Neuendorf & Wygnanski (1999) and Likhachev et al.…”

“…The streamwise vortices induced by the centrifugal effect are considered to be responsible for the mixing enhancement in the curved jet. Dunaevich & Greenblatt (2020) firstly observed the spontaneously generated stationary streamwise structures using flow visualization and particle image velocimetry. These structures ultimately exhibited a secondary time-dependent wavy instability.…”

Small-width wall-attached Coandǎ jets for flow control

“…They include control of circulation in aeronautics (Englar, Smith, Kelley, & Rover, 1994a, 1994b; Nishino, Hahn, & Shariff, 2010; Semaan et al., 2016), wind energy (Djojodihardjo et al., 2013) and drag reduction of bluff bodies (Barros, Borée, Noack, Spohn, & Ruiz, 2016; Geropp & Odenthal, 2000; Haffner, Borée, Spohn, & Castelain, 2020). The flow physics of such jets, on a convex surface, has been extensively investigated in the literature (Dunaevich & Greenblatt, 2020; Gross & Fasel, 2006; Neuendorf, Lourenco, & Wygnanski, 2004; Neuendorf & Wygnanski, 1999) and explained as the result of streamwise Görtler-like vortices. It has to be noted that, for most of the above applications and analyses, the flow is propagating on a convex surface, and the jet has a span width that is several orders of magnitude greater than the jet nozzle length in the streamwise direction.…”

Numerical study of instabilities and compressibility effects on supersonic jet over a convex wall

“…Han, Zhou & Wygnanski (2006) used spanwise heterogeneities at the nozzle lip of a cylinder apparatus to force streamwise vortices, and found that these vortices were subsequently sustained by the centrifugal effects. In the latest work of Dunaevich & Greenblatt (2020), the spontaneously generated stationary streamwise structures were first observed using flow visualization and particle image velocimetry. These structures ultimately exhibited a secondary time-dependent wavy instability.…”