One Dimensional Turbulent Transfer Using Random Square Waves – Scalar/Velocity and Velocity/Velocity Interactions

H. E. Schulz, G. B. Lopes Júnior, A. L. A. Simões and R. J. Lobosco

Chapter 1

"1. Introduction

The mathematical treatment of phenomena that oscillate randomly in space and time, generating the so called “statistical governing equations”, is still a difficult task for scientists and engineers. Turbulence in fluids is an example of such phenomena, which has great influence on the transport of physical proprieties by the fluids, but which statistical quantification is still strongly based on ad hoc models. In turbulent flows, parameters like velocity, temperature and mass concentration oscillate continuously in turbulent fluids, but their detailed behavior, considering all the possible time and space scales, has been considered difficult to be reproduced mathematically since the very beginning of the studies on turbulence. So, statistical equations were proposed and refined by several authors, aiming to describe the evolution of the “mean values” of the different parameters (see a description, for example, in Monin & Yaglom, 1979, 1981). (...)"

Hydrodynamics - Advanced Topics

ISBN 978-953-307-596-9, Hard cover, 442 pages
Publisher: InTech
Publication date: December 2011
Subject: Mechanical Engineering

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Hydrodynamics - Advanced Topics

Edited by: Harry Edmar Schulz, André Luiz Andrade Simões and Raquel Jahara Lobosco

ISBN 978-953-307-596-9, Hard cover, 442 pages
Publisher: InTech
Publication date: December 2011
Subject: Mechanical Engineering

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics.

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STATISTICAL APPROXIMATIONS IN GAS-LIQUID MASS TRANSFER

Harry E. Schulz, André L. A. Simões, Johannes G. Janzen

Abstract: The one-dimensional mass transfer in turbulent flows is considered. The closure problem related to the mean product between concentration and velocity fluctuations is treated by using random square waves. This approximation allows us to represent the statistical variables of turbulent mass transfer as depending on a finite set of basic parameters. The number of equations needed is then limited by the number of basic parameters used. The analysis is applied, in this study, to the interfacial mass transfer at air-water interfaces, generating a closed set of three equations involving three unknown functions. The resulting differential equations are nonlinear. A simplified example is solved.

Key Words: Statistical turbulence, one-dimensional mass transfer, random square waves.

"In 2010, the 6th International Symposium on Gas Transfer at Water Surfaces (GTWS-6) was held at Kyoto University in Kyoto, Japan. The GTWS-6 included 3 invited plenary lectures, 8 keynote lectures, 69 oral and 25 poster presentations from more than 15 countries. Furthermore, we set up a special session supported by the Core Research for Evolutional Science and Technology (CREST). From these presentations, we selected 49 papers for this volume." (excerpt from the preface).