Instabilities and turbulence in a forced turbulent convex wall jet

Abstract

The outer part of a turbulent wall jet streaming over a convex surface satisfies the centrifugal instability criterion. This gives rise to streamwise vortices that convect and grow with the wall jet. These vortices are highly unsteady, which causes the turbulence characteristics of a convex wall jet to be much stronger than that of a plane wall jet. Particle image velocimetry based investigations have been carried out in this work to understand the source of this unsteadiness. A cylinder with steady spanwise heterogeneities at the nozzle lip has been used to restrict the unsteadiness of the naturally occurring streamwise vortices such that ensemble averaging techniques can be applied. The analysis reveals that the turbulent stresses are spanwise periodic; radial and azimuthal fluctuations are highest in the upwash regions, and spanwise fluctuations are highest in the downwash regions between the counter-rotating vortices. The spanwise wavelength of the vortices increases by merging, but the merging process does not restore the spanwise uniformity of the Reynolds stresses. A Proper Orthogonal Decomposition (POD) analysis in the cross-stream plane suggests the existence of instabilities that extract energy from the mean flow to sustain these fluctuations. Secondary flows produced by steadier streamwise vortices generate inflection points in the spanwise and radial directions that trigger such secondary instabilities. POD analysis in the streamwise plane reveals the presence of a traveling wave that gives rise to the spanwise meandering of the vortices. The local Strouhal number of this traveling wave, defined using the local spanwise wavelength and jet maximum velocity, is a constant value of 1. Instability waves with similar characteristics have also been observed in other centrifugally unstable flows.