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Unformatted text preview: 1 FACE8 Turbulence and Mixing FACE8 2006 Turbulence and Mixing 2 FACE8 Turbulence and Mixing Recommended reading Frank M. White (1991): Viscous fluid flow, McGraw Hill International Editions, Mechanical Engineering Series. ISBN0071009957 H. Schlichting and K. Gersten (2002). Boundary layer theory, 8th revised and enlarged edition, Springer Verlag. ISBN 3540662707 Also previous editions are recommended (published by McGraw Hill)! Munson, Young and Okiishi. Fundamentals of Fluid Mechanics General fluidmechanics books normally have a chapter on boundary layers A. Walz (1966). Strmungs und Temperaturgrenzschichten, 1st edition, Braun Also in english G.M. Homsy et al (2000). Multimedia Fluid Mechanics, Cambridge University Press. ISBN 0521787483 Ber & Chigier (1972). Combustion aerodynamics. Applied Science Publ. ISBN 0 85334 513 9 3 FACE8 Turbulence and Mixing Structure of lecture 2 8.158.30 Introduction 8.309.00 Boundary layers 9.009.15 Break 9.159.45 Boundary layers 9.4510.30 Problem solving session 10.3010.45 Break 10.4511.15 Problem solving session 11.1511.30 Presentation of results 11.3012.00 BL+free shear flows 4 FACE8 Turbulence and Mixing Fundamentals of boundary layers 2 2 1 y u x p y u v x u u t u + = + + The boundary layer The governing (Prandtls) equations = y p = + y v x u 5 FACE8 Turbulence and Mixing Some general observations of turbulent flows and fluids ... I n g e n e r a l By introducing some userdefined reference variables we can nondimensionalise the above Density (mass), length and velocity (time) ] / [ ] [ 3 2 1 m N x x v x p Dt Dv s x v k k i i i i i + = = 6 FACE8 Turbulence and Mixing General thoughts contd... W e g e t And reintroduce into our governing equations L tU t U p p U v v L x x i i i i = = = = * 2 * * * ; ; ; ] [ ] [ * * * 2 * * * * * * + = = k k i i i i i x x v UL x p Dt Dv x v 7 FACE8 Turbulence and Mixing General thoughts contd... O r F o r R e we get the Euler equations for ideal fluids No friction Balance between inertia and pressure forces But... This gives slip velocity on boundaries, and empirical observations contradict this (at least for continua, with Kn<0.02) So we need a different treatment of the near wall areas to adhere to the noslip principle ] [ Re 1 * * * 2 * * * * + = k k i i i x x v x p Dt Dv 8 FACE8 Turbulence and Mixing Inside the boundary layer Point P: u=0 (noslip) Point Q: u=0.99U Balance between inertial and pressure forces Balance between inertial, pressure and viscous forces n u = n 9 FACE8 Turbulence and Mixing How fast does a laminar boundary layer grow?...
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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
 Staff
 Mechanical Engineering

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