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Unformatted text preview: The First Few Lectures in a First Course on Turbulence Tony Burden’s Lecture Notes, Spring 2007 These lecture notes are intended to make life easier for the lecturer and the stu- dents by reducing the amount of text that is first written on the blackboard and then copied into note books. These notes should be complemented by reading in text books such as “Turbulent Flows” by S.B. Pope. Turbulence is both important in practical engineering work and interesting from a theoretical point of view, but it is not perfectly well understood. When developing an understanding of turbulence it is a good idea to read in several different books. Literature recommendations are included at the end of each chapter in these notes. Chapter 1. Introduction Most naturally occuring fluid flows are turbulent, e.g. ; atmospheric turbulence, the planetary boundary layer, clear-air turbulence and clouds; ocean currents; rivers; the photosphere of the sun; inter-stellar gas clouds; and bush fires. The same is true of most engineering flows, e.g. ; boundary layers on aircraft wings, ships etc.; the wakes of ships, cars, aircraft etc.; chimney plumes; and flow in pipelines and furnaces. Many flows in everyday life and engineering are deliberately made to be turbu- lent, e.g. ; coffee stirring, tea pouring and cocktail shaking; boundary layers on aircraft wings; the chemical process industry including food manufacture; and most combustion processes including car engines. The majority of the pictures of turbulent flow which are used during these lectures have been taken from “An Album of Fluid Motion”, M. van Dyke. Examples — inc. review of previous courses Pipe flow — see Secs 5.2 & 5.4 in ‘Mechanics of Fluids’ by B.S. Massey and Sec. 9.1 in ‘Elementary Fluid Dynamics’ by D.J. Acheson. During the 19th century the engineer Hagen measured the pressure drop in pipe flow and found that it varied with the flow rate according to Δ p ∼ ¯ u (= ¯ u 1 ) for low flow rates but Δ p ∼ ¯ u 2 for high flow rates. (¯ u is the mean flow velocity defined by the flow rate ˙ m = ρ ¯ uA .) Inbetween these two r´ egimes hysterisis could be observed. 1 Nowadays, and in the context of engineering, we would say that the pressure drop behaves according to, Δ p ∼ ¯ u 1 for Re < 2000 Δ p ∼ ¯ u 2 for Re 2000 where Re is the Reynolds number of the flow defined by, Re = ρ ¯ ud μ = ¯ ud ν ....
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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.
- Spring '11