1.4067!turbulence-tot

1.4067!turbulence-tot - Introduction to Turbulence by Hkan...

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Introduction to Turbulence by Håkan Gustavsson Division of Fluid Mechanics Luleå University of Technology
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Foreword The intention with these pages is to present the student with the basic theoretical concepts of turbulence and derive exact relations from the governing equations. The idea is to show that despite the complexity of turbulent flows, some general properties can be educed from the equations. Hopefully, this will remove some of the mystique that has surrounded turbulence as a topic in undergraduate courses. The material is used as lecture notes in the course MTM 162 (Advanced Fluid Mechanics) given in the last year of undergraduate studies at Ltu. Luleå, October 2006 Håkan Gustavsson Division of Fluid Mechanics
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Contents Page 1. Introduction 1 2. Reynolds’ decomposition 3 3. Equations for the mean flow 4 3.1 Continuity 4 3.2 Momentum 4 3.3 Kinetic energy 6 4. Equations for the turbulent fluctuations 7 4.1 Momentum 7 4.2 Kinetic energy 8 5. Turbulent channel flow 9 5.1 Momentum equation 9 5.2 Turbulence production 13 5.3 Mean velocity profile 14 6. Kolmogorov microscales 16 7. Turbulence structure 17 References 18
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1 1. Introduction Turbulence is generally considered one of the unresolved phenomena of physics. This means that there is not one model that describes the appearance and maintenance of turbulence in all situations where it appears. Because of the technical importance of turbulence, models based on correlations of particular experimental data have been developed to a large extent. The task to develop a general turbulence model is challenging since turbulence appears almost everywhere: Flows in rivers, oceans and the atmosphere are large scale examples. Flows in pipes, pumps, turbines, combustion processes, in the wake of cars, airplanes and trains are some technical examples. Even the blood flow in the aorta is occasionally turbulent. In fact, one can say that turbulence is the general flow type on medium and large scales whereas laminar flows appear on small scales, and where the viscosity is high. For example, the flow of lubricating oils in bearings is laminar. Before we discuss the technical aspects of turbulence it is necessary to state its main kinematic characteristics. In the list below, some flows may have one or two features but turbulence has all three. Irregularity. Observing structures in the flow from a smoke stack, or measuring the velocity in a pipe flow, show that any particular pattern never repeats itself. This randomness suggests that a statistical treatment of turbulence is worthwhile. In fact, statistical quantities such as mean values, correlations etc. are generally repeatable and make statistical theories attractive. Mixing. A case of randomness is the deflection of a water surface due to wind. However, in this flow fluid particles stay largely in one place which they do not in a stirred cup of coffee.
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This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.

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1.4067!turbulence-tot - Introduction to Turbulence by Hkan...

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