Modification of Turbulence in Boundary Layers by Mean and Fluctuating Pressure Gradients

Abstract

In this study we focus on the effect of mean and fluctuating pressure gradients on the structure of boundary layer turbulence. Two dimensional, time-resolved PIV measurements have been performed upstream of and inside an accelerating sink flow for inlet Reynolds number of Reθ = 3071, and acceleration parameter of K=1.1×10−6. The time-resolved data enables us to calculate the planer projection of pressure gradient by integrating the in-plane components of the material acceleration of the fluid (neglecting out-of-plane contribution). We use it to study the effect of boundary layer scale fluctuating pressure gradients ∂p′~/∂x, which are expected to be mostly two-dimensional, on the flow structure. Due to the imposed mean favorable pressure gradient (FPG) within the sink flow, the Reynolds stresses normalized by the local freestream velocity decrease over the entire boundary layer. However, when scaled by the inlet freestream velocity, the stresses increase close to the wall and decrease in the outer part of the boundary layer. This trend is caused by the confinement of the newly generated vortical structures in the near-wall region of the accelerating flow due to combined effects of downward mean flow, and stretching by velocity gradients. Within both the zero pressure gradient (ZPG) and FPG boundary layers, sweeping motions mostly occur during positive fluctuating pressure gradients ∂p′~/∂x>0 as the fluid moving towards the wall is decelerated by the presence of the wall. Vorticity is depleted in the near-wall region, as the wall absorbs −ω′ from the flow by viscous diffusion. On the other hand, ejections occur mostly during periods of favorable fluctuating pressure gradients ∂p′~/∂x<0. During these periods, there is more viscous flux of vorticity −ω′ into the flow, since ∂−ω′/∂y<0 at the wall. Large scale ejection motions associated with ∂p′~/∂x<0 are more likely to transport smaller scale turbulence to the outer region of the boundary layer, while turbulence remains largely confined close to the wall due to the sweeping motions accompanying ∂p′~/∂x>0. During periods of ∂p′~/∂x>0 in the ZPG boundary layer, sweeps tend to increase the momentum in the near-wall region, whereas the adverse pressure gradient decelerates the fluid. These competing effects result in an unstable ω′<0 shear layer which rolls up into coherent vortical structures and increases ω′ω′ near the wall as compared to periods of ∂p′~/∂x<0. Due to the strong mean acceleration of the flow and weaker sweeps in the FPG boundary layer, the formation of an unstable shear layer, and hence vortical structures, is suppressed, decreasing the enstrophy close to the wall as compared to periods of ∂p′~/∂x<0.