A Computational Investigation of Symmetric and Asymmetric Turbulent Wakes

Abstract

The near wake of a flat plate with a circular trailing edge is investigated via direct numerical simulations (DNS). The computations are performed with a high-order accurate finite difference method. Many earlier experimental investigations have used thin plates with turbulent boundary layers to create the wake. This results in large θ/D values (θ is the boundary layer momentum thickness towards the end of the plate and D is the thickness of the plate). Here the emphasis is on relatively thick plates with blunt trailing edges resulting in θ/D values less than one. The Reynolds numbers based on the plate length and D are 1.275 x 10 6 and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case). The value of θ/D based on the turbulent boundary layer is about 0.24 in both cases. The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient. Results including wake velocity statistics, streamwise variations of wake thickness and maximum defect velocity, and velocity spectra and flow visualization in the wake for both cases are provided and compared. Unlike the far wake where the wake thickness varies as the inverse of the maximum defect velocity (u d ) in the streamwise direction, here it varies as C - u d / u ∞ , where C is a constant, from x/D ≈ 6.5 onwards until the end of resolved region of the grid (x/D = 10.0) in both cases. It was found that for streamwise and cross-stream normal intensities (total), the rate of decay obtained on the turbulent side for the asymmetric case was consistent with that obtained in the symmetric case; a generally lower decay rate was obtained on the laminar side for the asymmetric case. These and other similarities/differences in the two cases and, the potential for near wake profile-similarity of velocity statistics are discussed here.