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Two-dimensional distribution of stream-wise mean velocity in turbulent flow with effect of suspended sediment concentration

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Abstract

The present study aims to develop a two-dimensional model for stream-wise mean velocity distribution in a steady, uniform, sediment-laden open-channel turbulent flow considering all the flow velocity components. The derivation starts from the Reynolds-averaged Navier-Stokes (RANS) equation and unlike most of the researchers incorporates the effect of sediment presence in suspension through modified density and viscosity of the sediment-mixed fluid. The resulting partial differential equation is solved numerically using the finite difference method. The model is valid for wide or narrow open channels, and it includes the dip-phenomenon, which is the reason for maximum velocity below the free surface in the case of a narrow open channel. Results show that the cross-sectional velocity contours shift towards the boundary wall with an increase in sediment concentration in the flow and for the case of transverse velocity distribution, the effect of sediment concentration is mainly observed in the main flow region. It is also observed that for smaller aspect ratio, only one circular vortex exists in the secondary circulation and as the aspect ratio increases, the number of circular vortexes also increases. The distribution of velocity along the transverse direction shows a periodic variation due to periodic assumptions in vertical and transverse velocity components, which are appropriate for realistic flow conditions. The model has been validated for centreline velocity distribution along vertical direction by comparing it with relevant data sets for both sediment-mixed fluid and clear fluid. Due to the lack of cross-sectional and transverse velocity distribution data for sediment-mixed fluid in the literature, the model has been verified with clear water laboratory data and also with existing models for clear water flow. Good agreement in all the cases shows the efficiency of the proposed model.

Article highlights

  • A model is formed to study the 2D distribution of stream-wise velocity in an open-channel sediment-laden turbulent flow.

  • The effect of concentration on the transverse and cross-sectional velocity profiles is shown.

  • Velocity profiles are validated with experimental data, which shows good agreement.

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Availability of data and material

All experimental data have been taken from published papers.

Code availability

MATLAB has been used for coding.

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Authors and Affiliations

  1. Department of Mathematics, NIT Jamshedpur, Jharkand, 8311014, India

    Snehasis Kundu

  2. Department of Mathematics, IIT Kharagpur, Kharagpur, 721302, India

    Sumit Sen, Shiv Mohan & Koeli Ghoshal

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  1. Snehasis Kundu
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  2. Sumit Sen
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  3. Shiv Mohan
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  4. Koeli Ghoshal
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All authors’ have actively participated in developing the model and performing the solution.

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Correspondence to Koeli Ghoshal.

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Kundu, S., Sen, S., Mohan, S. et al. Two-dimensional distribution of stream-wise mean velocity in turbulent flow with effect of suspended sediment concentration. Environ Fluid Mech 22, 133–158 (2022). https://doi.org/10.1007/s10652-022-09834-9

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  • DOI: https://doi.org/10.1007/s10652-022-09834-9

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