Large-scale structures in turbulent and reverse-transitional sink flow boundary layers

Abstract

Aspects of large-scale organized structures in sink flow turbulent and reverse-transitional boundary layers are studied experimentally using hot-wire anemometry. Each of the present sink flow boundary layers is in a state of ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (The Structure of Turbulent Shear Flow, 1st and 2nd edns, 1956, 1976, Cambridge University Press) and Rotta (Progr. Aeronaut. Sci., vol. 2, 1962, pp. 1–220) and conforms to the notion of ‘pure wall-flow’ (Coles,J. Aerosp. Sci., vol. 24, 1957, pp. 495–506), at least for the turbulent cases. It is found that the characteristic inclination angle of the structure undergoes a systematic decrease with the increase in strength of the streamwise favourable pressure gradient. Detectable wall-normal extent of the structure is found to be typically half of the boundary layer thickness. Streamwise extent of the structure shows marked increase as the favourable pressure gradient is made progressively severe. Proposals for the typical eddy forms in sink flow turbulent and reverse-transitional flows are presented, and the possibility of structural self-organization (i.e. individual hairpin vortices forming streamwise coherent hairpin packets) in these flows is also discussed. It is further indicated that these structural ideas may be used to explain, from a structural viewpoint, the phenomenon ofsoftrelaminarization or reverse transition of turbulent boundary layers when subjected to strong streamwise favourable pressure gradients. Taylor's ‘frozen turbulence’ hypothesis is experimentally shown to be valid for flows in the present study even though large streamwise accelerations are involved, the flow being even reverse transitional in some cases. Possible conditions, which are required to be satisfied for the safe use of Taylor's hypothesis in pressure-gradient-driven flows, are also outlined. Measured convection velocities are found to be fairly close to the local mean velocities (typically 90% or more) suggesting that the structure gets convected downstream almost along with the mean flow.

Effect of mean and fluctuating pressure gradients on boundary layer turbulence

“…Consequently, the outer layer frequently consists of extended regions of low turbulence. The shallow inclinations are in line with previous studies (e.g Piomelli et al 2000;Dixit & Ramesh 2010). and, as discussed later, are predominantly caused by the larger ∂U/∂y and ∂U/∂x relative to the vortex self-induction.…”

“…The vortical structures extend to smaller distances away from the wall and their inclination angles decrease. Jang, Sung & Krogstad (2011) use DNS to reveal that the streamwise velocity correlation contours are aligned at shallower angles with the wall, while measurements of Dixit & Ramesh (2010) show that these inclination angles decrease systematically as K increases. For very mild FPG (K ∼ 0.08 × 10 −6 ), Harun et al (2013) find that the outer-layer large-scale structures are weaker than those in ZPG boundary layers.…”

Numerical simulations of sink-flow boundary layers over rough surfaces

“…The sink flow is the simplest accelerating boundary layer and has been studied numerically 24 and experimentally; [31][32][33][34] in this type of flows, K and the Reynolds number remain constant, resulting in statistical similarity in the flow direction. Therefore, a sink flow is substantially less expensive computationally, compared to spatially developing accelerating flows.…”

Investigation of Coherence behind a Single Foamed Tube

“…Hutchins et al [22,23] used two-point span-wise correlation to obtain statistical information regarding the width and spacing of the coherent structures. In literature, a number of studies can be found in which two-point correlation is used to obtain the shape of the structures inside the wake region [24,25].…”