Evolution of flat plate wakes in sink flow

Authors: Parsheh, M., Dahlkild, A. A.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 626   241-262
Year: 2009


Evolution of planar wakes in sink flow has been studied both analytically and experimentally. A similarity solution is derived for such wakes which considers simultaneous presence of both laminar and turbulent stresses in the wake. This solution utilizes an additional Reynolds stress term which accounts for the fluctuations similar to those in wall bounded flows. In this solution, it is shown that the total stress, the sum of laminar and Reynolds shear stresses, becomes self-similar. To investigate the accuracy of the analytical results, the wake of a flat plate located at the centreline of a planar contraction is studied using hot-wire anemometry. Wakes of both tapered and blunt edges are considered. The length of the plates and the flow acceleration number, K = 6.25 ×10 ?6, are chosen such that the boundary layer profiles at the plate edge approach the self-similar laminar solution of Pohlhausen (1921). A short plate in which the boundary layer at the edge does not fully relaminarize is also considered. The development of the turbulent diffusivity used in the analysis is determined empirically for each experimental case. We have shown that the obtained similarity solutions, accounting also for the initial conditions in each case, generally agree well with the experimental results even in the near field. The results also show that the mean velocity of the transitional wake behind a tapered edge becomes self-similar almost immediately downstream of the edge.