Turbulent kinetic energy transport in a corner formed by a solid wall and a free surface

Abstract

High-resolution DPIV and LDV measurements were made in a turbulent mixed- boundary corner, i.e. a turbulent boundary layer generated by horizontal flow of water along a vertical wall in the vicinity of a horizontal free surface. This work is an extension of an earlier numerical/experimental study which established the existence of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak, slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. The objective of the current investigation, then, was to understand the combined effects of a horizontal, shear-free, free surface and a vertical, rigid, no-slip boundary on turbulent kinetic energy transport. The context of this work is providing physical insights and quantitative data for advancing the state of the art in free-surface turbulence modelling. Experiments were conducted in a large free-surface water tunnel at momentum-thickness Reynolds numbers, Reθ, of 670 for the DPIV studies, and 1150 for the LDV measurements. A high-resolution, two-correlation DPIV program was used to generate ensembles of vector fields in planes parallel to the free surface. These data were further processed to obtain profiles of turbulent kinetic energy transport terms, such as production and dissipation. In addition, profiles of streamwise and surface-normal velocity were made (as functions of distance from the wall) using two-component LDV. Key findings of this study include the fact that both turbulent kinetic energy production and dissipation are dramatically reduced close to the free surface. Far from the wall, this results in an increase in surface-parallel uctuations very close to the free surface. The degree of this anisotropy and the spatial scales over which it exists are critical data for improved free-surface turbulence models.

Large-eddy simulations of ducts with a free surface

“…This issue will be discussed later based on the Reynolds-stress budget data. A difference between the results of the present work and those of Hsu et al (2000) is that the recovery of u u occurs across almost all the surface, except at the lower-wall bisector where ∂ u /∂y is equal to zero and ∂ u /∂z values are almost constant in the region 0.8 < z/D < 1. Previous studies of Perot & Moin (1995) and Walker et al (1996) revealed significant differences between shear-free boundary layers near solid walls and free surfaces, such as the higher tangential Reynolds stress and lower dissipation near a free surface.…”

“…All terms contribute to the budgets of v v and w w . Hsu et al (2000), observed that both TKE production and dissipation are dramatically reduced in the near-corner region, close to the free surface. Far from the wall, this results in an increase of the surface-parallel fluctuations very close to the free surface.…”

“…One is the use of the Fr = 0 approximation, which is least accurate in the corner region. However, the experiments of Grega et al (1995) and Hsu et al (2000) were conducted at a low reference Froude number, so that waves and surface deformations are not expected to have a significant effect on the interaction of the free surface with the turbulence-driven secondary flows developed near the corner. The second, and perhaps most significant, factor relates to the method used in the experimental studies to determine the skin friction.…”

“…The existence of mean secondary flows in the corner (similar to those that occur in the closed ducts) adds complexity to the problem. Studies of turbulent flows in the corner formed by a vertical solid wall and a free surface have been performed, among others, by Grega et al (1995), Longo, Huang & Stern (1998), Sreedhar & Stern (1998), Hsu et al (2000) and Grega, Hsu & Wei (2002). Grega et al (1995) carried out numerical simulations in conjuction with experimental flow visualization and single-component laser-Doppler anemometry (LDA) velocity measurements.…”

Modelling vortex-induced fluid–structure interaction

“…In particular, Shah et al (1999Shah et al ( , 2000 have used highly resolved digital particle image velocimetry (DPIV) data to compute terms in the vorticity transport equation, along with turbulent strain rates in a turbulent tip vortex shed from a half D-wing. Hsu et al (2000) presented turbulent kinetic energy transport quantities obtained from DPIV measurements in a turbulent boundary layer.…”