Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation

Snehasis Kundu

Physica A: Statistical Mechanics and its Applications, 2018, vol. 506, issue C, 135-155

Abstract: In this study vertical distribution of sediment particles in steady uniform turbulent open channel flow over erodible bed is investigated using fractional advection–diffusion equation (fADE). Unlike previous investigations on fADE to investigate the suspension distribution, in this study the modified Atangana–Baleanu–Caputo fractional derivative with a non-singular and non-local kernel is employed. The proposed fADE is solved and an analytical model for finding vertical suspension distribution is obtained. The model is validated against experimental as well as field measurements of Missouri River, Mississippi River and Rio Grande conveyance channel and is compared with the Rouse equation and other fractional model found in literature. A quantitative error analysis shows that the proposed model is able to predict the vertical distribution of particles more appropriately than previous models. The validation results shows that the fractional model can be equally applied to all size of particles with an appropriate choice of the order of the fractional derivative α. It is also found that besides particle diameter, parameter α depends on the mass density of particle and shear velocity of the flow. To predict this parameter, a multivariate regression is carried out and a relation is proposed for easy application of the model. From the results for sand and plastic particles, it is found that the parameter α is more sensitive to mass density than the particle diameter. The rationality of the dependence of α on particle and flow characteristics has been justified physically.

Keywords: Suspension concentration distribution; Open channel flow; Turbulent flow; Fractional advection–diffusion equation; Rouse equation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:506:y:2018:i:c:p:135-155

DOI: 10.1016/j.physa.2018.04.009

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