An Explicit Model for Concentration Distribution using Biquadratic-Log-Wake Law in an Open Channel Flow

The log-wake law with biquadratic boundary correction for the vertical velocity distribution which was changed from cubic boundary correction by Guo for the pipe data is applied to turbulent flow in open-channels. The biquadraticlog- wake law is tested with experimental data from Coleman, Lyn, Wang and Qian and Kironoto and Graf. It shows that the biquadratic-log-wake law matches well with flume data. A new mathematical model for vertical concentration distribution using the biquadratic-log-wake law is proposed and tested with the existing laboratory data. This study reflect the fact that sediment suspension has significant effects on both von Karman constant and Coles’ wake strength

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

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

An explicit expression for velocity profile in presence of secondary current and sediment in an open channel turbulent flow

The present study revisits the determination of vertical distribution of streamwise velocity in an open channel turbulent flow considering the effect of secondary current in the presence of sediment together with a concentration dependent settling velocity and von Karman constant κs. The work mainly modifies a previous study that introduced a lot of assumptions to obtain an analytical solution of the velocity distribution. The present study overcomes those assumptions in the model and though not fully analytical, attempts to present a semi-analytical solution that is explicit and in the form of a convergent series. Homotopy analysis method is used for this purpose and it is validated with numerical solution as well as with available laboratory data from the literature. How the secondary current and concentration dependent κs influence the velocity profile, is also discussed.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

International Conference on Computational and Applied Mathematics

This book features original research papers presented at the International Conference on Computational and Applied Mathematics, held at the Indian Institute of Technology Kharagpur, India during November 23–25, 2018. This book covers various topics under applied mathematics, ranging from modeling of fluid flow, numerical techniques to physical problems, electrokinetic transport phenomenon, graph theory and optimization, stochastic modelling and machine learning. It introduces the mathematical modeling of complicated scientific problems, discusses micro- and nanoscale transport phenomena, recent development in sophisticated numerical algorithms with applications, and gives an in-depth analysis of complicated real-world problems. With contributions from internationally acclaimed academic researchers and experienced practitioners and covering interdisciplinary applications, this book is a valuable resource for researchers and students in fields of mathematics, statistics, engineering, and health care