The feedback effect caused by bed load on a turbulent liquid flow

Abstract

Experiments on the effects due solely to a mobile granular layer on a liquid flow are presented (feedback effect). Nonintrusive measurements were performed in a closed conduit channel of rectangular cross section where grains were transported as bed load by a turbulent water flow. The water velocity profiles were measured over fixed and mobile granular beds of same granulometry by Particle Image Velocimetry. The spatial resolution of the measurements allowed the experimental quantification of the feedback effect. The present findings are of importance for predicting the bed-load transport rate and the pressure drop in activities related to the conveyance of grains.Comment: Accepted Manuscript for the Journal of the Brazilian Society of Mechanical Sciences and Engineering, v. 36, p. 725-736, 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s40430-013-0122-

Barchan Dunes Cruising Dune‐Size Obstacles

“…The cross-sectional mean velocities of water U were within 0.226 m/s and 0.312 m/s, corresponding to Reynolds numbers based on the channel height (Panton, 2010), Re = ρU2δ/μ, within 1.13 × 10 4 and 1.55 × 10 4 , respectively, and to Stokes numbers (Andreotti et al, 2013) St t = Udρ s /(18μ) within 6.3 and 35.5, where ρ is the density and μ the dynamic viscosity of the fluid. The shear velocities on the channel walls u * (base flow) were computed from velocity profiles measured in previous works with a two-dimensional particle image velocimetry device (Alvarez & Franklin, 2018;Cúñez et al, 2018;Franklin et al, 2014), and were found to follow the Blasius correlation (Schlichting, 2000), from which we found 0.0133 m/s ≤ u * ≤ 0.0168 m/s. This corresponds to Reynolds numbers at the grain scale, Re * = ρu * d/μ, within 3 and 8 and to Shields numbers, θ = 𝐴𝐴 ( 𝜌𝜌𝜌𝜌 2 * ) ∕((𝜌𝜌𝑠𝑠 − 𝜌𝜌)𝑔𝑔𝑔𝑔) , within 0.060 and 0.086.…”

Transporte de grãos por leito móvel em um escoamento turbulento

“…Those upper and lower bounds were fixed to allow bed load and, at the same time, avoid the fast formation of ripples on the granular bed. The water flow profiles presented in Franklin et al (2014a) were assumed to be valid for the present experiments and are used here.…”

“…For example, the water stream is responsible for the solid discharge, which, by its turn, modifies the morphology of the bed by erosion and sedimentation processes (Franklin, 2012). Other example is the modification of the fluid flow by momentum transfers from the fluid to the moving grains, and from the latter to the fixed part of the bed, known as feedback effect (Franklin et al, 2014a).…”

“…Recently, Franklin et al (2014a) measured the velocity profiles of turbulent water flows over fixed and mobile granular beds of same granulometry using PIV. They quantified the perturbation caused solely by bed load on the turbulent stream, known as feedback effect.…”