The perturbation of a turbulent boundary layer by a two-dimensional hill

Abstract

Turbulent boundary layers over flat walls in the presence of a hill are frequently found in nature and industry. Some examples are the air flows over hills and desert dunes, but also water flows over aquatic dunes inside closed conduits. The perturbation of a two-dimensional boundary layer by a hill introduces new scales in the problem, changing the way in which velocities and stresses are distributed along the flow. When in the presence of sediment transport, the stress distribution along the hill is strongly related to bed instabilities. This paper presents an experimental study on the perturbation of a fully-developed turbulent boundary layer by a two-dimensional hill. Water flows were imposed over a hill fixed on the bottom wall of a closed conduit and the flow field was measured by Particle Image Velocimetry. From the flow measurements, mean and fluctuation fields were computed. The general behaviors of velocities and stresses are compared to published asymptotic analyses and the surface shear stress is analyzed in terms of instabilities of a granular bed.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. Accepted Manuscript for the Journal of the Brazilian Society of Mechanical Sciences and Engineering, v. 35, p. 337-346, 201

Turbulent channel flow perturbed by triangular ripples

“…Franklin and Ayek [19] studied the perturbation of a fully developed turbulent boundary layer by a two-dimensional triangular hill. In their experiments, water flows were imposed over a triangular ripple with sharp edges fixed to the bottom wall of a closed-conduit channel.…”

“…The authors found that at the leading edge of the ripple the xy component of turbulent stresses increases to around eight times the value over the plane bed, while the viscous stress remains of the same order of magnitude, indicating that the inner regions of the perturbed flow are not in local equilibrium for the triangular ripple with sharp edges. Franklin and Ayek [19] proposed that the absence of local equilibrium is due to the relatively large ratio between the vertical and longitudinal scales of the flow. However, it could be due to the sharp leading edge, which probably shed vortices for Reynolds numbers above some threshold.…”

“…Two ripple configurations were employed: one single asymmetric triangular ripple, and two consecutive asymmetric triangular ripples, all of them having the same geometry. Unlike in [19], the ripples have slightly rounded edges to represent better the ripples found in nature. In the arrangement used here, water flows are imposed in a closed conduit with a rectangular cross section and either one or two ripples fixed to the bottom wall.…”

Estudo experimental de um escoamento turbulento em um canal perturbado por uma forma triangular

“…Na indústria, os principais exemplos estão relacionados aos escoamentos sobre rugas no interior de dutos e tubos, como ocorre em oleodutos, em linhas de dragagem e em dutos de esgoto. Existem muitos estudos sobre o assunto (Jackson e Hunt, 1975;Hunt e outros, 1988;Weng e outros, 1991;Belcher e Hunt, 1998;Franklin e Ayek, 2013).…”

“…Para modelar uma perturbação triangular bidimensional, uma pequena forma de fundo de geometria triangular foi fixada na placa de PVC na seção de testes. A forma triangular teve as mesmas escalas das rugas aquáticas (Franklin, 2010(Franklin, , 2011Franklin e Ayek, 2013). A figura 3.5 apresenta um esquema do perfil triangular fixado na placa PVC e suas dimensões em milímetros.…”