Henry M. Tufo
Mathematics and Computer Science Division
Argonne National Laboratory, Argonne, IL
These images illustrate the generation of hairpin vortices in the wake of a hemispherical roughness element placed in a laminar boundary layer. This flow was studied experimentally by Acalar and Smith (JFM, 175 , 1987). The Reynolds number is Re=700, based upon the hemisphere radius, R, and the free-stream velocity. The boundary layer thickness is 1.2R. The vortices are identified using the definition of a vortex developed by Jeong and Hussain in (JFM, 285 , 1995). The shading indicates the pressure distribution on the vortex surfaces, with white corresponding to high pressure.
A standing horseshoe vortex is seen upstream of the hemisphere. Above a Reynolds number of roughly 450, the region about 2R downstream of the hemisphere destabilizes, transitioning the from a steady to a steady-periodic state and yielding a sequence of interlacing hairpin vortices. As they progress downstream, the hairpin tails stretch and move towards the wall while the heads lift away. Careful inspection of this and other views reveal the bridging of the tails, seen in the upper image as a white vertical bar appearing about 3 diameters downstream of the hemisphere. The bridge and head appear to lift off as a ring-vortex near the exit of the lower figure. The formation of new vortices on either side of the main hairpin can be seen in the last third of the upper figure. This type of spreading has been observed by several researchers, including Bart Singer and the group of C. Smith.
This simulation employed 1021 elements of order 13, (2.2 million gridpoints) and was computed on the 512-node Intel Paragon at Caltech. Simulation time for a single shedding cycle is about 3 hours.
Last update: January 23, 1999 (pff)