Experimental study of the flow in the wake of a stationary sphere immersed in a turbulent boundary layer

Abstract

In many applications, finite-sized particles are immersed in a turbulent boundary layer (TBL) and it is of interest to study wall effects on the instantaneous shedding of turbulence structures and associated mean velocity and Reynolds stress distributions. Here, 3D flow field dynamics in the wake of a prototypical, small sphere (D + = 50, 692 < Re D < 959) placed in the TBL's outer, logarithmic, and buffer layer, were measured using time-resolved tomo-PIV. Increasing wall proximity increasingly tilted the mean recirculating wake away from the wall implying a negative lift force. Mean velocity deficit recovery scaled with the mean wake length with minor effects of wall proximity. Farthest from the wall, streamwise Reynolds normal stresses encircled the mean wake as an axisymmetric tubular "shell," while transverse and wall-normal stresses extended off its tip as axisymmetric tapered cones. Wall proximity removed axisymmetry and attenuated values near the wall. Reynolds shear stresses were distributed as antisymmetric lobes extending off the mean wake displaying increasing values with reducing sphere-wall gap. Instantaneous snapshots revealed a wake densely populated by "archlike" vortices with shedding frequencies lower than for a sphere in uniform flow except in the buffer layer. Tilting of the wake away from the wall resulted from self-induced motion of shed hairpinlike vortices whose symmetry plane was increasingly wall-normal oriented with reduced sphere-wall gap.

Three-dimensional flow field measurements in the wake of a tethered sphere crossing the onset of vortex induced vibrations

“…2010), and the data quality was assessed by evaluating the residual of the continuity equation for an incompressible fluid, ( values exceeded 0.87, see also van Hout et al. 2018).…”

“…This is not expected to remove any relevant large-scale flow structures in the sphere wake. Spatial velocity gradients were based on the locally fitted quadratic regression (Elsinga et al 2010), and the data quality was assessed by evaluating the residual of the continuity equation for an incompressible fluid, ∂U i /∂x i = 0 (R 2 values exceeded 0.87, see also van Hout et al 2018).…”

Three-dimensional tracking of finite-size spheres in a turbulent boundary layer

“…The mean lift forces simulated for spheres with 1.78 ≤ d + /2 ≤ 12.47 centered at a wall-normal location y + = 17.31 from the wall at Re τ = 178.12 were negative in all cases. In this context, tomographic PIV performed by van Hout et al (2018) also suggested a negative lift contribution on a tethered sphere with d + /2 = 25 centered at y + = 43 above the wall at Re τ = 352 due to the sphere wake tilting away from the wall. Under both studies, the gaps between the wall and the bottom sphere were 4.84 ≤ y + ≤ 18.…”

Time-resolved sphere and fluid motions in turbulent boundary layers

“…The mean lift forces simulated for spheres with 1.78 ≤ d + /2 ≤ 12.47 centered at a wallnormal location y + = 17.31 from the wall at friction Reynolds number, Re τ = 178.12 were negative in all cases. Tomographic PIV performed by van Hout et al (2018) at Re τ = 352 downstream of a tethered sphere with d + /2 = 25 centered at y + = 43 above the wall also suggested a negative lift contribution due to the sphere wake tilting away from the wall. By contrast, Hall (1988), who measured the mean lift force acting on a stationary particle lying on the wall in a turbulent boundary layer using a force transducer, reported a positive lift contribution.…”