Flow past finite cylinders of constant curvature

Wake visualization experiments were conducted on a finite curved cylinder whose plane of curvature is aligned with the free stream. The stagnation face of the cylinder is oriented concave or convex to the flow at $230\leqslant Re_{D}\leqslant 916$, where $Re_{D}$ is the cylinder Reynolds number and the curvature is constant and ranges from a straight cylinder to a quarter-ring. While the magnitude of the local angle of incidence to the flow is the same for both orientations, the contrast in their wakes demonstrates a violation of a common approximation known as the ‘independence principle’ for curved cylinders. Vortex shedding always occurred for the convex-oriented cylinder for the Reynolds-number range investigated, along most of the cylinder span, at a constant vortex shedding angle. In contrast, a concave-oriented cylinder could exhibit multiple concurrent wake regimes along its span: two shedding regimes (oblique, normal) and two non-shedding regimes. The occurrence of these wake regimes depended on the curvature, aspect ratio and Reynolds number. In some cases, vortex shedding was entirely suppressed, particularly at higher curvatures. In the laminar wake regime, increasing the curvature or decreasing the aspect ratio restricts vortex shedding to smaller regions along the span of the cylinder. Furthermore, the local angle of incidence where vortex shedding occurs is self-similar across cylinders of the same aspect ratio and varying curvature. After the wake transitions to turbulence, the vortex shedding extends along most of the cylinder span. The difference in the wakes between the concave and convex orientations is attributed to the spanwise flow induced by the finite end conditions, which reduces the generation of spanwise vorticity and increases the incidence of non-shedding and obliquely shedding wakes for the concave cylinder.

Conservation laws and conserved quantities for the two-dimensional laminar wake

A systematic and unified method is presented for the derivation of the conserved quantities for the laminar classical wake and the wake of a self-propelled body. The multiplier method for the derivation of conservation laws is applied to the far downstream wake equations expressed in terms of the velocity components which gives rise to a second-order system of two partial differential equations, and in terms of the stream function which results in one third-order partial differential equation. Once the corresponding conservation laws are obtained, they are integrated across the wake and upon imposing the boundary conditions and the condition that the drag on a self-propelled body is zero, the conserved quantities for the classical wake and the wake of a self-propelled body are derived. In addition, this method results in the discovery of a new laminar wake which may have physical significance.

Test section streaks originating from imperfections in a zither located upstream of a contraction

Defining a link between wind-tunnel settling chamber screens, flow quality and test section boundary-layer spanwise variation is necessary for accurate transition prediction. The aim of this work is to begin establishing this link. The computed, steady, laminar wake of a zither (screen model) with imperfect wire spacing is tracked through a contraction and into a model test section. The contraction converts the zither wake into streamwise vorticity which then creates spanwise variation (streaks) in the test-section boundary layer. The magnitude of the spanwise variation is sensitive to the zither open-area ratio and imperfections, but the observed wavelength is relatively insensitive to the zither wire spacing. Increased spanwise variation is attributed to large wavelength variation of drag across the zither, and not the coalescence of jets phenomena. The linear stability of the streaks is predicted using the parabolized stability equations with the $\text{e}^{N}$ method. A standard deviation of zither wire position error of 38.1 ${\rm\mu}$m (15 % of wire diameter) for a zither of 50 % open-area ratio is found to suppress Tollmien–Schlichting wave growth significantly.

On the Response of Planar Wakes to Asymmetric Initial Conditions

This work reports an experimental investigation on the response of a planar wake generated by a profiled flat plate to various upstream flow conditions. A tripping wire was placed on the upper side of the flat plate just downstream of the leading edge of the plate that resulted in asymmetric separating shear layers at the trailing edge. The near wake asymmetry is compared to the symmetrical case at two different Reynolds numbers. Two asymmetric initial conditions resulted, namely, laminar boundary layer on the lower side and a turbulent boundary layer on the upper side, and a turbulent boundary layer on the lower side and tripped turbulent boundary layer on the upper surface. The near wake dynamics were investigated under the effects of the degree of asymmetry using hot-wire anemometry and flow visualizations. The measurements showed when one of the two boundary layers was tripped, the wake shifted towards the tripped side and wake spreading was found to be larger than in the case of the symmetrical wake with the effect being more pronounced in the asymmetric laminar wake. Self-similarity of the asymmetrical wakes was established by properly selecting appropriate similarity variables however, the similarity of the wake was less evident in the tripped laminar boundary layer case. Convection velocity, Uc, of the Von Karman large eddies, estimated using processed flow visualization images seemed to increase with increased Reynolds number and with increased upstream momentum thickness. In the symmetric laminar wake, Uc/U∞ increases from 0.2 and reached an asymptotic value of about 0.85 further downstream. In the presence of perturbation, Uc/U∞ attained a constant value of about 0.83 further downstream compared to the symmetric case. For the turbulent wake, however, asymmetry of the turbulence levels was found to increase the convection speed compared to both the laminar wake and the symmetric turbulent wake reaching a constant value nearly at the same downstream position for both the symmetric and asymmetric turbulent wake.