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f05_sp - Fluids Lecture 5 Notes 1 Introduction to 3-D Wings...

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Fluids – Lecture 5 Notes 1. Introduction to 3-D Wings 2. 2-D and 3-D Coeﬃcients Reading: Anderson 5.1 Introduction to 3-D Wings A 2-D airfoil can be considered as a wing of infinite span, with each spanwise location identical. In contrast, on a 3-D finite-span wing, the presence of wingtips introduces spanwise ﬂow variations, a number of important new physical effects. Spanwise ﬂow. An upward-lifting wing must on average have a pressure difference between its upper and lower surfaces. Outside of the wingtips, this pressure difference must disappear. Consequently, ﬂuid particles which approach the wintip above the wing are subjected to a spanwise pressure gradient which causes them to curve towards the wing center. Fluid particles which approach below the wing will curve away from the wing center. Particles close to the tip will tend to ﬂow around the tip edge, from the lower to the upper surface. ∆− p V upper−surface streamline lower−surface streamline reduced upper pressure increased lower pressure Top View Front View ∆− p − ( pressure gradient ) − ( pressure gradient ) Trailing vortices. The ﬂow curling around the tip forms a tip vortex , which then trails down- stream, and can be easily made visible with smoke visualization. Downwash. The velocity field associated with the two trailing vortices is mostly downward (opposite to lift direction) directly behind the wing, and upward outside the tip vortices.

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f05_sp - Fluids Lecture 5 Notes 1 Introduction to 3-D Wings...

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