AERO452 notes 2018 January 18 1-64.pdf

AERO452 notes 2018 January 18 1-64.pdf - Aero 452 Viscous...

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1 Aero 452 Viscous Flows and Heat Transfer Prof. Lee Carlson With contributions by Prof. Sharath S. Girimaji Prof. William S. Saric Prof. Paul Cizmas Prof. Helen L. Reed
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2 Historical Calendar of Fluid Dynamics Leonardo Da Vinci (1500 AD): First scientific observations of turbulence in fluid flow. From his observations he designed the first concepts for what would become the helicopter. (http://en.wikipedia.org/wiki/File:Leonardo_da_Vinci_helicopter.jpg) Euler (1707-1783) Developed first equations of fluid dynamics 𝜕? ? 𝜕? + ? ? 𝜕? ? 𝜕? ? = − 1 ? 𝜕? 𝜕? ? D’Alembert (1717 -1783): Discovered drag force on a body moving at constant velocity through a fluid was nonzero, in contradiction to Euler’s equation. http://visualwikipedia.com/en/D'Alembert's_paradox Claude-Louis Navier (1785-1836) and George Gabriel Stokes (1819-1903): Their separate works were combined to develop the Navier-Stokes equations which govern viscous incompressible fluid flow. 𝜕? ? 𝜕? + ? ? 𝜕? ? 𝜕? ? = − 1 ? 𝜕? 𝜕? ? + ? 𝜕 2 ? ? 𝜕? ? 2 Osborne Reynolds (1842-1912): Most famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow. From these experiments came the dimensionless Reynolds number for dynamic similarity the ratio of inertial forces to viscous forces. Also decomposed turbulent flow parameters into two parts. ? ? = ? ̅ ? + ?′ ? ? ? = ? ̅ ? + ?′ ? Ludwig Prandtl (1875-1953): His research identified the boundary layer and paved the way for Mixing Length Theory. A. N. Kolmogorov (1940s): Developed the famous postulates of turbulence and scaling laws.
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