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.