# Ch1_2 - Cambridge University Engineering Department 4A12...

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Cambridge University Engineering Department 4A12: Turbulence Lecture Notes Dr. E. Mastorakos Hopkinson Lab E-mail: [email protected] http://www.eng.cam.ac.uk/ em257 1

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Chapter 1 Introduction 1.1 Aims The main aims of this course are: 1. To introduce some fundamental physical aspects of turbulence. 2. To describe the phenomenology of some turbulent ﬂows. 3. To allow the student make simple estimates of the order of magnitude of certain quan- tities in turbulent ﬂows. 1.2 Introduction Turbulent ﬂows are found everywhere and we all have some intuitive feeling as to what constitutes a turbulent ﬂow. A good way to describe the various facets of turbulent motion is to consider it as a “ syndrome ”, with some special characteristics (Stewart, 1969, NSF Film). These include disorder , vorticity ,and mixing . Tennekes and Lumley [1] in the Introduction to their book, mention irregularity , difusivity , vorticity ﬂuctuations , dissipation and large Reynolds numbers as a few of the key features of the nature of turbulence. Turbulence is created through instabilities of laminar ﬂows at large Re , e.g. laminar pipe ﬂow becomes turbulent at about Re = Ud/ν = 2000 and a boundary layer at a = 600 ( δ is the displacement thickness). Most turbulent ﬂows involve velocity shear; if shear or any other production mechanism such as buoyancy are absent, then turbulence decays. We will discuss later the rate of this decay and on how to estimate the velocity ﬂuctuations. There is no general approach to the solution of turbulent ﬂows, but one of the most prominent methods is to analyze the equations of motion or experimental data in a statistical manner. Often, the time-averaged values of the main quantities (±rst-order moments) is the only thing we are interested in from an engineering point of view. However, there are many situations where we are also interested in relatively rare events, e.g. a high temperature excursion from the mean in a ﬂame or a high-concentration parcel of ﬂuid in a pollutant plume, where we would like to be in a position to estimate the full range of possible values. This we achieve with probability densities and by considering higher moments. Statistical 2
studies have also allowed us to throw some light to the structure of the motion, through quantities like two-point correlations that tell us how big are the various “eddies” that comprise the turbulent ﬂow. Only a hint on these aspects of turbulence will be given in this course. Our main target will be to be able to make useful estimates about various quantities such as the mean velocity, the intensity of the turbulent ﬂuctuations, the rate of mixing etc. These estimates will necessarily be approximate and we will resort often to hand-waving, order of magnitude analysis. We will be borrowing freely results from experiments, so our treatment includes a phenomenological component.

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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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Ch1_2 - Cambridge University Engineering Department 4A12...

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