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SLIDE 1

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❘❡❛❧ ❋❧♦✇s

❙❖❊✷✶✺✻✿ ❋❧✉✐❞s ▲❡❝t✉r❡ ✶✵

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SLIDE 2

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❘❡❝❛♣

Pr❡✈✐♦✉s ❧❡❝t✉r❡ ④ ❞✬❆❧❡♠❜❡rt✬s ♣❛r❛❞♦① ④ ❞r❛❣ ❢♦r❝❡ ♦♥ ❛ ❜♦❞② ✐♥ ✐❞❡❛❧ ✌♦✇ ✐s ③❡r♦✳ ❈♦✉♥t❡r✲✐♥t✉✐t✐✈❡ ✭❛♥❞ ✇r♦♥❣✮✳ ❲❤②❄ ❉r❛❣ ❢♦r❝❡s ❛r✐s❡ ❜❡❝❛✉s❡ ✌✉✐❞s ❛r❡ ♥♦t ✐❞❡❛❧✳ ❚✇♦ ♠❛✐♥ ❞✐☛❡r❡♥❝❡s ❜❡t✇❡❡♥ ✐❞❡❛❧ ❛♥❞ r❡❛❧ ✌♦✇s ✿

✎ ■❞❡❛❧ ✌♦✇ ❤❛s ✗ ❂ ✵✳ ❘❡❛❧ ✌✉✐❞s ❤❛✈❡ ✗ ✻❂ ✵ ✎ ■❞❡❛❧ ✌♦✇ ❝❛♥ ❜❡ ♥♦♥✲③❡r♦ ♥❡①t t♦ ❛ ✇❛❧❧✳ ❘❡❛❧ ✌✉✐❞s ❞♦

♥♦t ❜❡❤❛✈❡ t❤✐s ✇❛②✳

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SLIDE 3

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❉r❛❣ ♦♥ ❛♥ ♦❜❥❡❝t ❛r✐s❡s ❢r♦♠ t✇♦ s♦✉r❝❡s ✿ ♣r❡ss✉r❡ ❢♦r❝❡s ❛♥❞ ✈✐s❝♦✉s str❡ss✳ ■❞❡❛❧ ✌♦✇ s♦❧✉t✐♦♥ ✐s s②♠♠❡tr✐❝ ✭❢r♦♥t ✰ ❜❛❝❦✮ ④ t❤✉s s②♠♠❡tr✐❝ ♣r❡ss✉r❡ ❞✐str✐❜✉t✐♦♥ ④ ③❡r♦ ❞r❛❣✳ ❘❡❛❧ ✌♦✇ ✐s ♥♦t s②♠♠❡tr✐❝✳ ■❞❡❛❧ ✌♦✇ s♦❧✉t✐♦♥ ❤❛s ✗ ❂ ✵ ④ ③❡r♦ ✈✐s❝♦✉s str❡ss ④ ③❡r♦ ❞r❛❣✳ ❘❡❛❧ ✌✉✐❞s ❤❛✈❡ ♥♦♥✲③❡r♦ ✈✐s❝♦✉s str❡ss❡s✳ ❍♦✇❡✈❡r ♣♦t❡♥t✐❛❧ ✌♦✇ ♠❡t❤♦❞ ❝❛♥ st✐❧❧ ❜❡ ✉s❡❢✉❧ ④ ✐❢ ✇❡ ❛❧❧♦✇ ❢♦r t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳

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SLIDE 4

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❇♦✉♥❞❛r② ❧❛②❡rs

❇♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s ❢♦r ❛ r❡❛❧ ✌✉✐❞ ✿ ❈❧♦s❡ t♦ ❛ ✇❛❧❧✱ ✉ ❂ ✵✳ ■❢ t❤❡ ✇❛❧❧ ✐s ♠♦✈✐♥❣✱ ✉ ❂ ❱ ✇❛❧❧

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SLIDE 5

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❙✐♥❝❡ ✉ ❂ ✵ ❛t t❤❡ ✇❛❧❧✱ ❛♥❞ ✉ ✻❂ ✵ ❛✇❛② ❢r♦♠ t❤❡ ✇❛❧❧✱ t❤❡r❡ ♠✉st ❜❡ ❛ r❡❣✐♦♥ ✇❤❡r❡ t❤❡ ✌♦✇ ❛❞❥✉sts ❢r♦♠ ✉ ❂ ✵ ✦ ✉ ✻❂ ✵✳ ❚❤✐s r❡❣✐♦♥ ✐s ❝❛❧❧❡❞ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❖✈❡r❛❧❧✱ ✐❢ ❘❡ ✐s ❧❛r❣❡ ✦ ✗ s♠❛❧❧ ✭r❡❧❛t✐✈❡❧②✮ ④ ✈✐s❝♦s✐t② ✉♥✐♠♣♦rt❛♥t ④ ✌♦✇ ❝❛♥ ❜❡ ♠♦❞❡❧❧❡❞ ❛s ✐❞❡❛❧✳ ■♥ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✱ ✉ ✐s s♠❛❧❧ ✭✦ ✵✮✱ s♦ ❘❡ ✐s s♠❛❧❧ ✦ ✈✐s❝♦s✐t② ✐s ✐♠♣♦rt❛♥t ④ ✌♦✇ ♠✉st ❜❡ tr❡❛t❡❞ s❡♣❛r❛t❡❧②✳

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SLIDE 6

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❊❣✳ ✌♦✇ ❛r♦✉♥❞ ❛♥ ♦❜❥❡❝t ④ ♣♦t❡♥t✐❛❧ ✌♦✇ ❡①❝❡♣t ✐♥ ❜♦✉♥❞❛r② ❧❛②❡r ❛♥❞ ✇❛❦❡✳

Potential Flow Potential Flow Wake Boundary layer Separation

❆s ❝♦♥❞✐t✐♦♥s ✐♥ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❝❤❛♥❣❡✱ s♦ ❞♦❡s t❤❡ ❞r❛❣ ❢♦r❝❡✳ ❚♦ ❛♥❛❧②s❡ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✱ ✇❡ ✇♦✉❧❞ ♥❡❡❞ t♦ s♦❧✈❡ t❤❡ ◆❛✈✐❡r✲❙t♦❦❡s ❡q✉❛t✐♦♥s✳ ❚♦ ❛♥❛❧②s❡ t❤❡ ✇❛❦❡✱ ✇❡ ♠❛② ♥❡❡❞ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧❧✐♥❣✳

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SLIDE 7

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮

❚✉r❜✉❧❡♥❝❡ ✐s ❞✐✍❝✉❧t t♦ ❞❡☞♥❡ ♣r❡❝✐s❡❧② ④ ❡❛s✐❡r t♦ ❞✐s❝✉ss ✐ts ♣r♦♣❡rt✐❡s ✿

✎ st❛t❡ ♦❢ ✌✉✐❞ ♠♦t✐♦♥ ❝❤❛r❛❝t❡r✐s❡❞ ❜② ❝♦♠♣❧❡①✱ ❝❤❛♦t✐❝

♠♦t✐♦♥

✎ q✉❛s✐✲r❛♥❞♦♠ ♠♦t✐♦♥s ✎ ♦❢t❡♥ ❞❡s❝r✐❜❡❞ ✐♥ t❡r♠s ♦❢ t✉r❜✉❧❡♥t ❡❞❞✐❡s ♦❢ ❞✐☛❡r❡♥t

s❝❛❧❡s ✐♥ t❤❡ ✌♦✇

✎ ✈♦rt✐❝✐t② r❡♣r❡s❡♥ts str❡♥❣t❤ ♦❢ ❡❞❞✐❡s

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SLIDE 8

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❲❤❡r❡ ❞♦❡s ✐t ♦❝❝✉r❄

✎ ❲❛❧❧ t✉r❜✉❧❡♥❝❡ ✿ ✇❛❧❧s ✭t✉r❜✉❧❡♥t ❜✳❧✳✮✱ ♣✐♣❡s ❡t❝ ✎ ❋r❡❡ t✉r❜✉❧❡♥❝❡ ✿ ✇❛❦❡s✱ ❥❡ts

■♥❞✐✈✐❞✉❛❧ ❡❞❞✐❡s ✐♥t❡r❛❝t ✰ t❡♥❞ t♦ ❜r❡❛❦ ✉♣✳ ❊♥❡r❣② ✐♥ t✉r❜✉❧❡♥❝❡ ✿

✶ st❛rts ♦☛ ✐♥ ❧❛r❣❡ s❝❛❧❡ ❡❞❞✐❡s ✷ ✐s tr❛♥s♠✐tt❡❞ t♦ s♠❛❧❧❡r ❛♥❞ s♠❛❧❧❡r ❡❞❞✐❡s ✸ ✳ ✳ ✳ ✉♥t✐❧ ✐t ❡♥❞s ✉♣ ✐♥ t❤❡ s♠❛❧❧❡st ♣♦ss✐❜❧❡ ❡❞❞✐❡s

❚❤❡ s♠❛❧❧❡st ❡❞❞✐❡s ❛r❡ t❤♦s❡ ❞♦♠✐♥❛t❡❞ ❜② ✈✐s❝♦✉s ❡☛❡❝ts ✿ t❤❡✐r ❡♥❡r❣② ✐s ❞✐ss✐♣❛t❡❞ ❛s ❤❡❛t✳ ❚❤✐s ♣❛tt❡r♥ ✐s ❦♥♦✇♥ ❛s t❤❡ t✉r❜✉❧❡♥t ❝❛s❝❛❞❡✳

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SLIDE 9

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

■♥❞✐✈✐❞✉❛❧ ❡❞❞✐❡s ♦❜❡② ◆❙ ❡q✉❛t✐♦♥s ✭♦♥❡ s♦❧✉t✐♦♥ t❡❝❤♥✐q✉❡ ✐s t♦ ❝♦♠♣✉t❡ t❤❡♠ ④ ❉✐r❡❝t ◆✉♠❡r✐❝❛❧ ❙✐♠✉❧❛t✐♦♥✱ ❉◆❙✮✳ ❍♦✇❡✈❡r t❤✐s ✐s ✉♥r❡❛❧✐st✐❝ ❢♦r ❛♥② r❡❛s♦♥❛❜❧② t✉r❜✉❧❡♥t ✌♦✇✳ ■♥st❡❛❞ ✇❡ ❝♦♠♣✉t❡ ✭✉s✐♥❣ ❈❋❉✮ ❛♥ ❛✈❡r❛❣❡ ✌♦✇✱ ♣❧✉s ❛ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧ ❢♦r t❤❡ t✉r❜✉❧❡♥t ✌✉❝t✉❛t✐♦♥s ❛r♦✉♥❞ t❤✐s ❛✈❡r❛❣❡✳ ▼♦st ❝♦♠♠♦♥ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧ ✐s t❤❡ ❦ ✎ ♠♦❞❡❧✳

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SLIDE 10

❘❡❛❧ ❋❧♦✇s ❘❡❝❛♣ ❇♦✉♥❞❛r② ❧❛②❡rs ❚✉r❜✉❧❡♥❝❡ ✭❝♦♥t✮ ❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

❙♦❧✉t✐♦♥ str❛t❡❣✐❡s

✎ ❋r❡❡ str❡❛♠ ✌♦✇ ❛t ❤✐❣❤ ❘❡

✎ ♣♦t❡♥t✐❛❧ ✌♦✇ t❤❡♦r② ♣❧✉s ❜♦✉♥❞❛r② ❧❛②❡r t❤❡♦r② ✎ ❡❣✳ str❡❛♠❧✐♥✐♥❣✱ ❛❡r♦❢♦✐❧s✱ t♦r♥❛❞♦❡s

✎ ▲♦✇ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✌♦✇

✎ ◆❛✈✐❡r✲❙t♦❦❡s ❡q✉❛t✐♦♥s ✭❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥✮

✎ ◆❡❛r✲✇❛❧❧ ✌♦✇s ✭❜♦✉♥❞❛r② ❧❛②❡rs✮

✎ ◆❛✈✐❡r✲❙t♦❦❡s ❡q✉❛t✐♦♥s ✭❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥✮

✎ ❚✉r❜✉❧❡♥t ✌♦✇s

✎ ❈❋❉ ✰ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧❧✐♥❣