Stationary vortices and persistent turbulence in Karman grooves

Abstract

The vortex persistence theory of turbulence predicts that the addition of a stationary vortex will reduce the wall fluxes in turbulent flows. To test the theory, the feasibility of holding a vortex sufficiently stationary whilst embedded in a turbulent boundary layer is investigated. Potential flow analysis reveals that the stationarity of the von Karman street of vortices in a wake might be useful for this purpose. In this scheme, the dividing streamline of the stationary vortex street would be replaced by a solid wall having the same wavy shape, which is given by the derived analytical expression for this streamline. An experimental apparatus with just such a wavy wall was built, including a corotating array of vortex generators that are able to accurately position quasi-streamwise vortices near the stationary points of the wavy wall, i.e. in the ‘Karman grooves’. The secondary flow in the cross-plane perpendicular to axes of these vortices corresponds geometrically to that of the vortex street. If the vortices lie exactly upon the geometric stationary points of the Karman grooves, the vortices are observed to be stationary and in the persistent regime of turbulent fluxes. Displacing the vortex generator array only slightly yields different turbulent fluxes. Simple vortex growth measurements provide a graphic demonstration of the difference between persistent and nonpersistent (free) vortices. The experimental set-up was then modified to include a wall heating system and thermocouples to measure the wall heat flux, as a candidate turbulent flux. Experimental results show that the non-dimensional heat transfer coefficient, the Nusselt number, is a function of the Reynolds number with an exponent of ∼0.57 if persistent and ∼0.82 if nonpersistent. The latter is comparable to the flat plate boundary layer heat flux exponent of ∼0.8, for the same Reynolds number range, i.e. 10⁴ through 10⁵, and the transition between the regimes is observed to be a gradual function of vortex location.