Stability lecture 2

Stability lecture 2 - Lecture 2 Introduction A classic...

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Lecture 2 Introduction A classic problem – Reynolds Experiment (1883). Constant Head Tank Introduced dye into inlet of pipe. Key parameter in interpretation of experiment was Reynolds number. u - avg. velocity ρ - density µ - viscosity D - diameter Re uD = Dimensionless group. 1. R e 13,000 < He got laminar flow, lamina – level in Latin. 2. - Critical Reynolds number Re ~13,000 c Intermittent Turbulence. Local instabilities If let go for a while you get turbulent patch. Called Turb. Slug.
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3. R e 13,000 > Turbulent pg 61 in Van Dyke Dye spreads out. The experiment has been repeated many times. Re c - depends on flow conditions, especially at the inlet, and ambient vibrations. Schiller (1922) similar apparatus got about 20,000. Ekman (1910) got about 40,000 smooth pipe, low vibrations. Nonlinear effects are important. Turbulence can’t be maintained below 2,000. Above 2,000 it depends on nonlinearities. It appears unstable if disturbances are large enough. Theoretical Approaches Basic idea behind theoretical approaches is called Reynolds Suppostion. If we have a laminar flow that is a solution to the Navier-Stokes equations and represents a
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This note was uploaded on 06/07/2011 for the course EOC 6934 taught by Professor Staff during the Fall '08 term at University of Florida.

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Stability lecture 2 - Lecture 2 Introduction A classic...

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