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Entropy 2016, 18(9), 318; doi:10.3390/e18090318

Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow

1
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
2
Department of Basic Sciences and Humanities, IIIT Bhubaneswar, Odisha 751003, India
3
Department of Biological & Agricultural Engineering, Texas A&M University, College Station, TX 77843, USA
4
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Antonio M. Scarfone
Received: 31 May 2016 / Revised: 21 August 2016 / Accepted: 23 August 2016 / Published: 30 August 2016
(This article belongs to the Section Statistical Mechanics)
View Full-Text   |   Download PDF [665 KB, uploaded 30 August 2016]   |  

Abstract

In the last few decades, a wide variety of instruments with laser-based techniques have been developed that enable experimentally measuring particle velocity and fluid velocity separately in particle-laden flow. Experiments have revealed that stream-wise particle velocity is different from fluid velocity, and this velocity difference is commonly known as “velocity lag” in the literature. A number of experimental, as well as theoretical investigations have been carried out to formulate deterministic mathematical models of velocity lag, based on several turbulent features. However, a probabilistic study of velocity lag does not seem to have been reported, to the best of our knowledge. The present study therefore focuses on the modeling of velocity lag in open channel turbulent flow laden with sediment using the entropy theory along with a hypothesis on the cumulative distribution function. This function contains a parameter η, which is shown to be a function of specific gravity, particle diameter and shear velocity. The velocity lag model is tested using a wide range of twenty-two experimental runs collected from the literature and is also compared with other models of velocity lag. Then, an error analysis is performed to further evaluate the prediction accuracy of the proposed model, especially in comparison to other models. The model is also able to explain the physical characteristics of velocity lag caused by the interaction between the particles and the fluid. View Full-Text
Keywords: entropy; Shannon entropy; probability distribution; velocity lag; sediment-laden flow entropy; Shannon entropy; probability distribution; velocity lag; sediment-laden flow
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Kumbhakar, M.; Kundu, S.; Ghoshal, K.; Singh, V.P. Entropy-Based Modeling of Velocity Lag in Sediment-Laden Open Channel Turbulent Flow. Entropy 2016, 18, 318.

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