Effect of Free-Stream Turbulence on Turbulent Boundary Layers

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Johns Hopkins University
Direct numerical simulations (DNS) are performed to study turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from DNS of homogeneous isotropic turbulence. When free-stream turbulence buffets a zero-pressure-gradient turbulent boundary layers, the skin friction coefficient is elevated relative to its value in the canonical flow configuration. The change can be explained in terms of an increase in the power input into the production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream disturbances being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the log layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn increases turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall. Due to the enhanced Reynolds stresses by the free-stream forcing, the wall-normal heat flux is also increased, which has the dual effect of distorting the base temperature profile and enhancing the production of scalar variance; both contribute to the increase in the wall heat-transfer rate. These changes are accompanied by modification of the spectra of the thermal field in the outer region of the boundary layer, where large-scale thermal structures are formed in response to the large-scale velocity motions. In the near-wall region, the outer hydrodynamic field modulates and then strengthens not only the hydrodynamic but also thermal structures relative to the unforced flow. The configuration of the forced boundary layer on the concave curve introduces additional complications because the fluid is subjected to a centrifugal instability as well as streamwise pressure gradients. Absent free-stream disturbances, adverse pressure gradient near the onset of curvature leads to sharp decrease in skin friction, by more than 70% its initial value, and intermittent separation. Over the curve, the spanwise and wall-normal Reynolds stresses intensify and the radial distance between their peaks increases, which is indicative of growing Görtler vortex structures. The forced boundary layer is buffeted by free-stream turbulence with 10% intensity. The change in boundary-layer thickness modifies the apparent curvature, and its near-wall distortion reduces the probability of separation. The forcing also enlarges and strengthens the Görtler vortices: The peak spanwise and wall-normal Reynolds stresses part farther, the associated shear-stress correlation increases and so does the streamwise stress. Sustained by centrifugal effects and intensified by free-stream turbulence, these large-scale structures directly influence the near-wall region: Free-stream fluid is `seen' more often deep within the buffer layer, and large-scale, outer-flow motions strongly correlate with near-wall disturbances. Intense, persistent roll motions above the curved wall thus directly send the free-stream turbulence towards the buffer layer. Such mechanism will diminish under weaker curvature, which is consistent with flat-plate boundary layers.
Turbulent boundary layer, Free-stream turbulence, Direct numerical simulations, Concave curve