Institut für Thermodynamik der Luft- und Raumfahrt der Universität Stuttgart Direktor: Professor Dr.-Ing. B. Weigand

Masterarbeit

Design of an Icing Wind Tunnel for UAVs cand. aer. Joachim Wallisch

Juli 2020

Hiermit versichere ich, dass ich diese Masterarbeit selbstständig mit Unterstützung des

Betreuers / der Betreuer angefertigt und keine anderen als die angegebenen Quellen

und Hilfsmittel verwendet habe.

Die Arbeit oder wesentliche Bestandteile davon sind weder an dieser noch an einer

anderen Bildungseinrichtung bereits zur Erlangung eines Abschlusses eingereicht

worden.

Ich erkläre weiterhin, bei der Erstellung der Arbeit die einschlägigen Bestimmungen

zum Urheberschutz fremder Beiträge entsprechend den Regeln guter

wissenschaftlicher Praxis eingehalten zu haben. Soweit meine Arbeit fremde Beiträge

(z.B. Bilder, Zeichnungen, Textpassagen etc.) enthält, habe ich diese Beiträge als

solche gekennzeichnet (Zitat, Quellenangabe) und eventuell erforderlich gewordene

Zustimmungen der Urheber zur Nutzung dieser Beiträge in meiner Arbeit eingeholt.

Mir ist bekannt, dass ich im Falle einer schuldhaften Verletzung dieser Pflichten die

daraus entstehenden Konsequenzen zu tragen habe.

……………….………………………………. Ort, Datum, Unterschrift

❆❜str❛❝t

❯♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ❛r❡ ❛♥ ❡♠❡r❣✐♥❣ t♦♣✐❝✳ ❚❤❡② s❡❡ ✐♥❝r❡❛s❡❞ ✉s❡ ❛❧❧ ♦✈❡r t❤❡✇♦r❧❞✳ ❚❤❡✐r ✉s❡ ✐♥ ❣❡♦❣r❛♣❤✐❝ ❛r❡❛s ✇✐t❤ ❝♦❧❞ ❝❧✐♠❛t✐❝ ❝♦♥❞✐t✐♦♥s ❝❛✉s❡s ♥❡✇ ❝❤❛❧✲❧❡♥❣❡s✳ ❖♥❡ ♣❛rt✐❝✉❧❛r ❝❤❛❧❧❡♥❣❡ ♦❝❝✉rs ✇❤❡♥ ✐❝❡ ❛❝❝✉♠✉❧❛t❡s ♦♥ t❤❡ ❛✐r❝r❛❢t✳ ■❝❡ ❝❛♥❛❝❝✉♠✉❧❛t❡ ✇❤❡♥ t❤❡ ❛✐r❝r❛❢t ✢✐❡s t❤r♦✉❣❤ ❝❧♦✉❞s ✇✐t❤ s✉♣❡r❝♦♦❧❡❞ ❞r♦♣❧❡ts✳ ❚❤✐s ♣❤❡✲♥♦♠❡♥♦♥ ✐s ❝❛❧❧❡❞ ❛t♠♦s♣❤❡r✐❝ ✐❝✐♥❣✳ ■❝✐♥❣ ❤❛s ❛ ♥❡❣❛t✐✈❡ ✐♥✢✉❡♥❝❡ ♦♥ ♠❛♥② ❝♦♠♣♦♥❡♥ts♦❢ t❤❡ ❛✐r❝r❛❢t✳ ❇❡❝❛✉s❡ ✐❝✐♥❣ ♦♥ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ✐s ♥♦t ✉♥❞❡rst♦♦❞ ❝♦♠♣❧❡t❡❧②✱❢✉rt❤❡r r❡s❡❛r❝❤ ✐s ♥❡❝❡ss❛r②✳ ❋♦r t❤✐s ♣✉r♣♦s❡✱ ❡①♣❡r✐♠❡♥ts ✐♥ s♣❡❝✐❛❧ ✇✐♥❞ t✉♥♥❡❧s ♥❡❡❞t♦ ❜❡ ❞♦♥❡✳ ❚♦ ♦✛❡r s✉❝❤ ❛ ❢❛❝✐❧✐t②✱ t❤✐s t❤❡s✐s ✇❛s ❞♦♥❡ t♦ ❞❡s✐❣♥ ❛ ♥❡✇ ✇✐♥❞ t✉♥♥❡❧ ❢♦r✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ♦♥ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s✳

❚❤❡ t❤❡s✐s st❛rts ✇✐t❤ ❛ s❤♦rt ✐♥tr♦❞✉❝t✐♦♥ ✐♥t♦ t❤❡ t♦♣✐❝✳ ❆❢t❡r✇❛r❞s✱ ❛ ❧✐t❡r❛t✉r❡r❡✈✐❡✇ ✐s ❣✐✈❡♥✳ ❙♦♠❡ ❣❡♥❡r❛❧ ❜❛s✐❝s ❛r❡ ♣r❡s❡♥t❡❞ t❤❛t ❤❡❧♣ t♦ ✉♥❞❡rst❛♥❞ t❤❡ ♦t❤❡rt♦♣✐❝s✳ ❚❤❡ ✇✐❞❡ ❛r❡❛ ♦❢ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ✐s ✐♥tr♦❞✉❝❡❞ ❛♥❞ ❛ ♠♦r❡ ♥❛rr♦✇ ♣❛rt♦❢ t❤❡ s♣❡❝tr✉♠ ✐s s❡❧❡❝t❡❞ t❤❛t ♣❧❛②s ❛♥ ✐♠♣♦rt❛♥t r♦❧❡ ✐♥ t❤✐s t❤❡s✐s✳ ❆ ♣r❡s❡♥t❛t✐♦♥♦❢ t❤❡ t♦♣✐❝ ♦❢ ❛t♠♦s♣❤❡r✐❝ ✐❝✐♥❣ ❢♦❧❧♦✇s✳ ❚❤❡ ♣❤②s✐❝❛❧ ❜❛❝❦❣r♦✉♥❞ ❛♥❞ ♣♦ss✐❜❧❡ ❡✛❡❝ts❛r❡ ♥❛♠❡❞ ❛s ✇❡❧❧ ❛s ♣♦ss✐❜❧❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s✳ ❚❤❡ ❧❛st ♣❛rt ♦❢ t❤✐s ❝❤❛♣t❡r ✐s ❜❛s❡❞♦♥ ✇✐♥❞ t✉♥♥❡❧s✱ t❤❡✐r ❞❡s✐❣♥✱ ❛♥❞ t❤❡ s♣❡❝✐❛❧ ♥❡❡❞s ♦❢ ✇✐♥❞ t✉♥♥❡❧s ❢♦r ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts✳

❚❤❡ t❤✐r❞ ❝❤❛♣t❡r ❝♦♥t❛✐♥s t❤❡ r❡q✉✐r❡♠❡♥ts ❛♥❞ ❡q✉❛t✐♦♥s t❤❛t ✇❡r❡ ✉s❡❞ ❞✉r✐♥❣ t❤❡❞❡s✐❣♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ ❛❧❧ r❡❧❛t❡❞ ❝♦♥s✐❞❡r❛t✐♦♥s✳ ❚❤✐s ❛❧s♦ ✐♥❝❧✉❞❡s t❤❡ ❜❡❤❛✈✐♦r♦❢ ❞r♦♣❧❡ts ✐♥ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ ❢♦✉♥❞❛t✐♦♥❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐s ❣✐✈❡♥✳

❚❤❡ r❡s✉❧ts ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ❢♦✉rt❤ ❝❤❛♣t❡r✳ ❋✐rst✱ t❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ✐s ♣r❡s❡♥t❡❞✳ ❚❤❡♥ t❤❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❞r♦♣❧❡t ✢♦✇s ✐♥s✐❞❡ t❤✐s ✇✐♥❞t✉♥♥❡❧ ❛r❡ ❝❛❧❝✉❧❛t❡❞ t♦ ❛❝❤✐❡✈❡ ✐♥s✐❣❤t ✐♥t♦ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥✳ ❆♥♦✈❡r✈✐❡✇ ♦❢ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞ t❤❡ ♣r♦❞✉❝❡❞ ❤❡❛t ✐s ❣✐✈❡♥✱ ❞✐✈✐❞❡❞ ✐♥t♦ t❤❡ s✐♥❣❧❡t❡r♠s t❤❛t ❛r❡ r❡❧❡✈❛♥t✳ ❋✐♥❛❧❧②✱ t❤❡ r❡s✉❧ts ♦❢ ❛ ❈❋❉ s✐♠✉❧❛t✐♦♥ ❛r❡ ❣✐✈❡♥ t❤❛t ✇❛s ❞♦♥❡t♦ ❜❡ ❛❜❧❡ t♦ ❝❤❡❝❦ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ❞❡s✐❣♥ ✇✐t❤ ❛ ♠♦r❡ ♣♦✇❡r❢✉❧ t♦♦❧✳

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

■

❈♦♥t❡♥ts

▲✐st ♦❢ ❋✐❣✉r❡s ■❱

▲✐st ♦❢ ❚❛❜❧❡s ❱■

▲✐st ♦❢ ❙②♠❜♦❧s ❱■■

✶ ■♥tr♦❞✉❝t✐♦♥ ✶

✶✳✶ ❇❛❝❦❣r♦✉♥❞ ✫ ♠♦t✐✈❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✳✷ ❚❤❡ s❝♦♣❡ ♦❢ t❤❡ t❤❡s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✳✸ ❚❤❡ ♦✉t❧✐♥❡ ♦❢ t❤❡ t❤❡s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✷ ❇❛❝❦❣r♦✉♥❞ ✸

✷✳✶ ❆t♠♦s♣❤❡r✐❝ ✐❝✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷✳✶✳✶ ❇❛s✐❝s ♦❢ ❛t♠♦s♣❤❡r✐❝ ✐❝✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷✳✶✳✷ ❚②♣✐❝❛❧ ✐❝❡ s❤❛♣❡s ♦♥ ❛✐r❢♦✐❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷✳✶✳✸ ■❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷✳✷ ❇❛s✐❝s ❛❜♦✉t ✢♦✇ ❞②♥❛♠✐❝s ❛♥❞ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷✳✶ ❋❧♦✇ ❞②♥❛♠✐❝s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷✳✷ ❉r♦♣❧❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷✳✸ ❯♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✸✳✶ ❯❆❱ ❞❛t❛❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✸✳✷ ❉❡s✐❣♥ ❛♥❞ ♠✐ss✐♦♥s ♦❢ ❯❆❱s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✸✳✸ ❉✐✛❡r❡♥❝❡s t♦ ♥♦r♠❛❧ ❛✐r❝r❛❢t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷✳✹ ❲✐♥❞ t✉♥♥❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷✳✹✳✶ ❇❛s✐❝s ♦❢ ✇✐♥❞ t✉♥♥❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✹✳✷ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷✳✹✳✸ ❙❝❛❧✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✸ ▼❡t❤♦❞s ✶✼

✸✳✶ ❇❛s✐❝ ❞❡❝✐s✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸✳✷ ❈♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✸✳✷✳✶ ❚❡st s❡❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸✳✷✳✷ ◆♦③③❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✸✳✷✳✸ ❙❡tt❧✐♥❣ ❛r❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸✳✷✳✹ ❲✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸✳✷✳✺ ❋❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸✳✷✳✻ ❉✐✛✉s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸✳✸ ❉r♦♣❧❡ts ✐♥s✐❞❡ t❤❡ t✉♥♥❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✸✳✸✳✶ ❉r♦♣❧❡t ✈❡❧♦❝✐t② ❛♥❞ tr❛❥❡❝t♦r✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

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❈♦♥t❡♥ts

✸✳✸✳✷ ❉r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺✸✳✹ Pr❡ss✉r❡ ❧♦ss❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼✸✳✺ ❈♦♦❧✐♥❣ ♣♦✇❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵✸✳✻ ❈❧❡❛r❛♥❝❡ r❡q✉✐r❡♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶✸✳✼ ❈❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r t❤✐❝❦♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✹ ❘❡s✉❧ts ✸✸

✹✳✶ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸✹✳✷ ❚❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻✹✳✸ ❋✐♥❛❧ ❞❡s✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✹✳✸✳✶ ❚❡st s❡❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼✹✳✸✳✷ ◆♦③③❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽✹✳✸✳✸ ❙❡tt❧✐♥❣ ❛r❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✹✳✸✳✸✳✶ ❙♣r❛② ❙②st❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹✹✳✸✳✸✳✷ ❚✉r❜✉❧❡♥❝❡ ❙❝r❡❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺✹✳✸✳✸✳✸ ❍♦♥❡②❝♦♠❜s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺✹✳✸✳✸✳✹ ❆ss❡♠❜❧② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✸✳✹ ❲✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻✹✳✸✳✺ ❋❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼✹✳✸✳✻ ❉✐✛✉s❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽✹✳✸✳✼ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✹✳✹ ❉r♦♣❧❡t ❜❡❤❛✈✐♦r ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾✹✳✺ Pr❡ss✉r❡ ❧♦ss❡s ❛♥❞ ❢❛♥ s❡❧❡❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷✹✳✻ ❈♦♦❧✐♥❣ ❝❤❛♠❜❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✻✳✶ ❈♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹✹✳✻✳✷ ❙♣❛❝❡ r❡q✉✐r❡♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✼ ❈♦sts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺✹✳✽ ❍❡❛t ♠❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻✹✳✾ ❈❋❉ s✐♠✉❧❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼✹✳✶✵ ❙♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✺ ❉✐s❝✉ss✐♦♥ ✻✸

✺✳✶ ❈♦♥❝❧✉s✐♦♥ ❛♥❞ ❞✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸✺✳✷ ❋✉rt❤❡r ✇♦r❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

❇✐❜❧✐♦❣r❛♣❤② ✻✺

❆ ❆♣♣❡♥❞✐① ✼✵

❆✳✶ ❯❆❱ ❉❛t❛❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵❆✳✷ ❆❞❞✐t✐♦♥❛❧ ❋✐❣✉r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵❆✳✸ ❚❤❡ ❘●✶✺ ❛✐r❢♦✐❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷❆✳✹ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✉s✐♥❣ t❤❡ ▼❡♥t❡r k − ω ❙❙❚ ♠♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸❆✳✺ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s♣❡❝✐✜❝❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

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▲✐st ♦❢ ❋✐❣✉r❡s

✷✳✶ ❚r❛❥❡❝t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ❛r♦✉♥❞ ❛ ❧❡❛❞✐♥❣ ❡❞❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷✳✷ ❊①❛♠♣❧❡s ❢♦r ❞✐✛❡r❡♥t ✐❝❡ ❝❛s❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷✳✸ ■❝✐♥❣ ❝♦♥❞✐t✐♦♥s st❛t❡❞ ✐♥ t❤❡ ❝❡rt✐✜❝❛t✐♦♥ ❣✉✐❞❡❧✐♥❡s ❢♦r ❛✐r❝r❛❢t ❢♦r t✇♦

❞✐✛❡r❡♥t t②♣❡s ♦❢ ❝❧♦✉❞s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷✳✹ ❚②♣✐❝❛❧ ✐❝❡ s❤❛♣❡s ♦♥ ❛♥ ❛✐r❢♦✐❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷✳✺ ❊①❛♠♣❧❡s ❢♦r t❤❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ ❯❆❱s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷✳✻ ❊①❛♠♣❧❡s ❢♦r t❤❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ ✇✐♥❞ t✉♥♥❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✼ ❚❤❡ t②♣✐❝❛❧ ✢♦✇ ❝♦♥❞✐t✐♦♥❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✸✳✶ ❖r❞❡r ♦❢ ❝♦♠♣♦♥❡♥ts ✐♥ t❤❡ r❡s✉❧t✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸✳✷ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs ❢♦r ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ ✾✳ ✳ ✳ ✷✵

✹✳✶ ❉✐✈✐s✐♦♥ ♦❢ ❯❆❱s ❛❝❝♦r❞✐♥❣ t♦ t❤❡✐r ✢✐❣❤t s♣❡❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸✹✳✷ ❈❤♦r❞ ❧❡♥❣t❤s ❛♥❞ ❝r✉✐s❡ s♣❡❡❞s ♦❢ ❞✐✛❡r❡♥t ❯❆❱s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹✹✳✸ ❚❤❡ ❧✐❢t ❝♦❡✣❝✐❡♥t ♦❢ t❤❡ ❘● ✶✺ ♣❧♦tt❡❞ ♦✈❡r t❤❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ❢♦r

❞✐✛❡r❡♥t ❘❡②♥♦❧❞s ♥✉♠❜❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺✹✳✹ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽✹✳✺ ❚r❛❥❡t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ❞✐❛♠❡t❡r ✐♥ ❛ ♥♦③③❧❡ ✇✐t❤ ❛ t❤✐r❞ ♦r❞❡r

♣♦❧②♥♦♠✐❛❧ ❝♦♥t♦✉r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵✹✳✻ ❚r❛❥❡t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ❞✐❛♠❡t❡r ✐♥ ❛ ♥♦③③❧❡ ✇✐t❤ ❛♥ ❆❱❆

❝♦♥t♦✉r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵✹✳✼ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞r♦♣❧❡t ❛♥❞ t❤❡ ❛✐r ✈❡❧♦❝✐t② ✐♥s✐❞❡ t❤❡ ❆❱❆ ♥♦③③❧❡✳ ✹✶✹✳✽ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❢♦r ❞✐✛❡r❡♥t ♥♦③③❧❡

❝♦♥t♦✉rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶✹✳✾ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ❢♦r ❞✐✛❡r❡♥t

♥♦③③❧❡ ❝♦♥t♦✉rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷✹✳✶✵ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ♥♦③③❧❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸✹✳✶✶ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻✹✳✶✷ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼✹✳✶✸ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ❞✐✛✉s❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽✹✳✶✹ ❚❤❡ ✜♥❛❧ ✇✐♥❞ t✉♥♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾✹✳✶✺ ❱❡❧♦❝✐t② ❞❡✈✐❛t✐♦♥ ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t ❞✐❛♠❡t❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵✹✳✶✻ ❚❡♠♣❡r❛t✉r❡ ❞❡✈✐❛t✐♦♥ ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t ❞✐❛♠❡t❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✹✳✶✼ ◆❡❝❡ss❛r② ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡ t♦ ❢✉❧✜❧❧ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r ❞✐✛❡r❡♥t

❞r♦♣❧❡t ❞✐❛♠❡t❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✹✳✶✽ ❘❡q✉✐r❡❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t ▲❲❈s ❛♥❞

❛♥ ❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −10 ➦C✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺✹✳✶✾ ◆❡❝❡ss❛r② ❝❧❡❛r❛♥❝❡ t♦ t❤❡ ❡♥tr② ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t

❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡rs ♦❢ t❤❡ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

■❱

▲✐st ♦❢ ❋✐❣✉r❡s

✹✳✷✵ P❧♦t ♦❢ t❤❡ ✈❡❧♦❝✐t② ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼✹✳✷✶ P❧♦t ♦❢ t❤❡ s❡♣❛r❛t✐♦♥ ③♦♥❡s ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽✹✳✷✷ ❚❤❡ ✜♥❛❧ ❞❡✈✐❛t✐♦♥s ✐♥ ✈❡❧♦❝✐t② ❛♥❞ t❡♠♣❡r❛t✉r❡ ❢♦r ❞r♦♣❧❡ts ✇✐t❤ ❞✐✛❡r❡♥t

❞✐❛♠❡t❡rs ❛♥❞ ❢♦r ❞✐✛❡r❡♥t ✇❛t❡r ♣r❡ss✉r❡s ✐♥s✐❞❡ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✹✳✷✸ ❘❡q✉✐r❡❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ❢♦r t❤❡ s♠❛❧❧ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t ▲❲❈s ❛t❛♥ ❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −10 ➦C✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

❆✳✶ ❉❡s✐❣♥ r✉❧❡s ❢♦r t❤❡ ❧❡♥❣t❤ ♦❢ ♥♦③③❧❡s ❢♦r ❞✐✛❡r❡♥t r❛t✐♦s ♦❢ ✐♥❧❡t t♦ ♦✉t❧❡t❞✐❛♠❡t❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

❆✳✷ ◆❡❝❡ss❛r② ♥✉♠❜❡r ♦❢ s❝r❡❡♥s ✐♥ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❢♦r ❝❡rt❛✐♥ ♦♣❡♥✐♥❣❛♥❣❧❡s ❛♥❞ ❛r❡❛ r❛t✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶

❆✳✸ ❚❤❡ ❘●✶✺ ❛✐r❢♦✐❧ ✇✐t❤ ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 0◦✳ ❆①❡s ❛r❡ ♥♦r♠❛❧✐③❡❞ ✇✐t❤t❤❡ ❝❤♦r❞ ❧❡♥❣t❤✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

❆✳✹ ❱❡❧♦❝✐t② ♣❧♦t ♦❢ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✇✐t❤ ❛ s❡❝♦♥❞ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧✳ ✽✸❆✳✺ P❧♦t ♦❢ t❤❡ s❡♣❛r❛t✐♦♥ ③♦♥❡s ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✇✐t❤ ❛ s❡❝♦♥❞ t✉r❜✉✲

❧❡♥❝❡ ♠♦❞❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸

❱

▲✐st ♦❢ ❚❛❜❧❡s

✸✳✶ ❉r♦♣❧❡t s✐③❡ ❞✐str✐❜✉t✐♦♥ ✇✐t❤ t❤❡ ▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✹✳✶ ▲✐st ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺✹✳✷ ❚❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ❛✐r ❛♥❞ ✇❛t❡r ❢♦r t❤❡ r❡❢❡r❡♥❝❡ t❡♠♣❡r❛t✉r❡

T ✳ ❉✐✛❡r❡♥t ✇♦rst✲❝❛s❡s ♠✐❣❤t ❡①✐st ❢♦r t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ❛♥❞ t❤❡♣r❡ss✉r❡ ❧♦ss✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✹✳✸ ❉✐♠❡♥s✐♦♥s ♦❢ t❤❡ ✜♥❛❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts✳ ❚✇♦ ✈❛❧✉❡s ❛r❡❣✐✈❡♥ ✐♥ t❤❡ ❞✐♠❡♥s✐♦♥s ❝♦❧✉♠♥ ✐❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ♦♥❡ ✈❛❧✉❡✐❢ t❤❡ s❡❝t✐♦♥ ✐s r♦✉♥❞✳ ■❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ❛❧s♦ t❤❡ ❤②❞r❛✉❧✐❝❞✐❛♠❡t❡r ✐s ❣✐✈❡♥ ✐♥ ❜r❛❝❦❡ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✹✳✹ ❱❡❧♦❝✐t✐❡s ❛t t❤❡ ✐♥❧❡t ❛♥❞ ♦✉t❧❡t ♦❢ ❡✈❡r② ❝♦♠♣♦♥❡♥t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷✹✳✺ ❖✈❡r✈✐❡✇ ♦✈❡r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ ❡✈❡r② ❝♦♠♣♦♥❡♥t ❛♥❞ ✐♥ t♦t❛❧✳ ✳ ✳ ✺✹✹✳✻ ■♠♣❛❝t ♦❢ t❤❡ ✐♥❝r❡❛s❡ ♦❢ ❞✐✛❡r❡♥t ♣❛r❛♠❡t❡rs ♦♥ t❤❡ s✐③❡✱ t❤❡ t♦t❛❧ ♣r❡s✲

s✉r❡ ❧♦ss❡s ❛♥❞ t❤❡ ♥❡❝❡ss❛r② ❢❛♥ ❛♥❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧✱ ❛s ✇❡❧❧ ❛s ♦♥ t❤❡ ✜♥❛❧ ❞r♦♣❧❡t ❞❡✈✐❛t✐♦♥s ✐♥ t❡♠♣❡r❛t✉r❡ ❛♥❞ ✈❡✲❧♦❝✐t②✳ Tdrop,0 ✐s ✉s❡❞ ❢♦r t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡✳ ●r❡❡♥ ❝♦❧♦r✐♥❞✐❝❛t❡ ♣♦s✐t✐✈❡ ❝❤❛♥❣❡s✱ r❡❞ ♥❡❣❛t✐✈❡ ❝❤❛♥❣❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✹✳✼ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❛♥❞t❤❡ ✈❛❧✉❡s ❝❛❧❝✉❧❛t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✺✳ ❆❧❧ ✈❛❧✉❡s ✐♥ Pa✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✹✳✽ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ✭♦❧❞✮ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ❜✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞t❤❡ ✭♥❡✇✮ s✐♠♣❧✐✜❡❞ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ✳ ✳ ✺✾

✹✳✾ ❈♦♠♣❛r✐s♦♥ ♦❢ ❞✐✛❡r❡♥t ♦♣t✐♦♥s ❢♦r ❛ s❤♦rt❡r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✭■❲❚✮✳ ✺✾✹✳✶✵ ❉✐♠❡♥s✐♦♥s ♦❢ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts✳ ❚✇♦ ✈❛❧✉❡s ❛r❡

❣✐✈❡♥ ✐♥ t❤❡ ❞✐♠❡♥s✐♦♥s ❝♦❧✉♠♥ ✐❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ♦♥❡ ✈❛❧✉❡✐❢ t❤❡ s❡❝t✐♦♥ ✐s r♦✉♥❞✳ ■❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ❛❧s♦ t❤❡ ❤②❞r❛✉❧✐❝❞✐❛♠❡t❡r ✐s ❣✐✈❡♥ ✐♥ ❜r❛❝❦❡ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✹✳✶✶ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❝❤❛♥❣❡❞ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ s❤♦rt❡r ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ♦♥ t❤❡ ♦✈❡r❛❧❧ ❧❡♥❣t❤ ❛♥❞ t❤❡ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss❡s✳ ✳ ✳ ✳ ✳ ✻✵

✹✳✶✷ ❖✈❡r✈✐❡✇ ♦✈❡r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ ❡✈❡r② ❝♦♠♣♦♥❡♥t ❛♥❞ ✐♥ t♦t❛❧ ❢♦r t❤❡s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

❆✳✶ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ s♣❡❝✐✜❝❛t✐♦♥s ♦❢ t❤❡ ❜✐❣ ❛♥❞ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥✲♥❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

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▲✐st ♦❢ ❙②♠❜♦❧s

▲❛t✐♥ ❙②♠❜♦❧s

a ms−2 ❛❝❝❡❧❡r❛t✐♦♥A m2 ❛r❡❛AR ❛r❡❛ r❛t✐♦blockage ❜❧♦❝❦❛❣❡ ✈❛❧✉❡cD ❞r❛❣ ❝♦❡✣❝✐❡♥tclatent J kg−1 s♣❡❝✐✜❝ ❧❛t❡♥t ❤❡❛t ♦❢ ❢✉s✐♦♥cp J kg−1 K−1 s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② ❛t ❝♦♥st❛♥t ♣r❡ss✉r❡cv J kg−1 K−1 s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② ❛t ❝♦♥st❛♥t ✈♦❧✉♠❡d m ❞✐❛♠❡t❡rd ❞✐✛❡r❡♥t✐❛❧dh m ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡rD m2 s−1 ❞✐✛✉s✐✈✐t②E W r❛t❡ ♦❢ ❝❤❛♥❣❡ ♦❢ ✐♥t❡r♥❛❧ ❡♥❡r❣②f ❢✉♥❝t✐♦♥F N ❢♦r❝❡~g ms−2 ✈❡❝t♦r ♦❢ ❣r❛✈✐t②H m ❤❡✐❣❤tk Wm−1 K−1 ❤❡❛t ❝♦♥❞✉❝t✐✈✐t②K ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥tKEXP ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t ❢♦r ❡①♣❛♥s✐♦♥sKMESH ♠❡s❤ ❝♦♥st❛♥t ❢♦r ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥tKRe ❘❡②♥♦❧❞s ♥✉♠❜❡r ❞❡♣❡♥❞❡♥❝❡ ♦❢ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥tL m ❧❡♥❣t❤LV J kg−1 ❧❛t❡♥t ❤❡❛t ♦❢ ✈❛♣♦r✐③❛t✐♦♥m kg ♠❛ssM ▼❛❝❤ ♥✉♠❜❡rm kg s−1 ♠❛ss ✢♦✇ r❛t❡Nu ◆✉ss❡❧t ♥✉♠❜❡rp Pa st❛t✐❝ ♣r❡ss✉r❡P m ♣❡r✐♠❡t❡rPr Pr❛♥❞t❧ ♥✉♠❜❡rpT Pa t♦t❛❧ ♣r❡ss✉r❡q Pa ❞②♥❛♠✐❝ ♣r❡ss✉r❡Q W ❤❡❛t ✢✉①r m r❛❞✐✉s

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▲✐st ♦❢ ❚❛❜❧❡s

R m2 s−2 K ❣❛s ❝♦♥st❛♥tRe ❘❡②♥♦❧❞s ♥✉♠❜❡rS ❞r❛❣ ❛r❡❛Sc ❙❝❤♠✐❞t ♥✉♠❜❡rSh ❙❤❡r✇♦♦❞ ♥✉♠❜❡rt s t✐♠❡T K t❡♠♣❡r❛t✉r❡~u ms−1 s♣❡❡❞ ✈❡❝t♦r ♦❢ t❤❡ ❞r♦♣❧❡tsv ms−1 ❛✐r s♣❡❡❞~v ms−1 s♣❡❡❞ ✈❡❝t♦r ♦❢ t❤❡ ❛✐rvS ms−1 s♣❡❡❞ ♦❢ s♦✉♥❞V m3 s−1 ✈♦❧✉♠❡ ✢✉①W m ✇✐❞t❤x m ❝♦♦r❞✐♥❛t❡ ✐♥ str❡❛♠✇✐s❡ ❞✐r❡❝t✐♦♥z m ❝♦♦r❞✐♥❛t❡ ♣❡r♣❡♥❞✐❝✉❧❛r t♦ str❡❛♠ ❞✐r❡❝t✐♦♥

●r❡❡❦ ❙②♠❜♦❧s

γ ❤❡❛t ❝❛♣❛❝✐t② r❛t✐♦δ m ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t∆ m s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜ ❝❡❧❧s∆ ❞✐✛❡r❡♥❝❡ǫ ❡♠✐ss✐✈✐t②ǫ ❞♦✇♥str❡❛♠ ✐♥✢✉❡♥❝❡ ♦❢ ✢♦✇ ♦❜str✉❝t✐♦♥θ ◦ ❛♥❣❧❡λ ❢r✐❝t✐♦♥ ❝♦❡✣❝✐❡♥tµ kg s−1 m−1 ❞②♥❛♠✐❝ ✈✐s❝♦s✐t②ν m2 s−1 ❦✐♥❡♠❛t✐❝ ✈✐s❝♦s✐t②ρ kgm−3 ❞❡♥s✐t②σ Wm−2 K−4 ❙t❡❢❛♥✲❇♦❧t③♠❛♥♥ ❝♦♥st❛♥t

■♥❞✐③❡s

1 ❞✐✛✉s❡r ✐♥❧❡t ♣❧❛♥❡2 ❞✐✛✉s❡r ❡①✐t ♣❧❛♥❡a ❛♠❜✐❡♥tair ✈❛❧✉❡ ❢♦r ❛✐rC ❝♦♥✈❡❝t✐♦♥circular ❝✐r❝✉❧❛r ❞✐✛✉s❡r s❤❛♣❡d ❞r♦♣❧❡te ❡q✉✐✈❛❧❡♥t ✈❛❧✉❡E ❡✈❛♣♦r❛t✐♦♥FLOW ✢♦✇ ✈❛❧✉❡Inlet ✈❛❧✉❡ ❛t t❤❡ ✐♥❧❡t ♦❢ t❤❡ s♣r❛② ♥♦③③❧❡latent ❧❛t❡♥t ❤❡❛t

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▲✐st ♦❢ ❚❛❜❧❡s

m ♠❛t❝❤✐♥❣ ♣♦✐♥tprojected ♣r♦❥❡❝t❡❞ ❞✐♠❡♥s✐♦♥R r❛❞✐❛t✐♦♥sensible s❡♥s✐❜❧❡ ❤❡❛tsquare sq✉❛r❡ ❞✐✛✉s❡r s❤❛♣❡TS t❡st s❡❝t✐♦♥Water ✈❛❧✉❡ ♦❢ ✇❛t❡rwire ✈❛❧✉❡ ❢♦r t❤❡ s❝r❡❡♥ ✇✐r❡

❆❜❜r❡✈✐❛t✐♦♥s

❈❋❉ ❝♦♠♣✉t❛t✐♦♥❛❧ ✢✉✐❞ ❞②♥❛♠✐❝s❊❆❙❆ ❊✉r♦♣❡❛♥ ❯♥✐♦♥ ❆✈✐❛t✐♦♥ ❙❛❢❡t② ❆❣❡♥❝②▲❲❈ kgm−3 ❧✐q✉✐❞ ✇❛t❡r ❝♦♥t❡♥t▼❱❉ ♠❡❞✐❛♥ ✈♦❧✉♠❡ ❞✐❛♠❡t❡rP❱❈ ♣♦❧②✈✐♥②❧ ❝❤❧♦r✐❞❡❯❆❱ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡■❲❚ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧

■❳

✶ ■♥tr♦❞✉❝t✐♦♥

✶✳✶ ❇❛❝❦❣r♦✉♥❞ ✫ ♠♦t✐✈❛t✐♦♥

❊✈❡♥ ❜❡②♦♥❞ ❝❧❛ss✐❝ ♣❛ss❡♥❣❡r ❛♥❞ ❢r❡✐❣❤t tr❛♥s♣♦rt✱ ❛✐r❝r❛❢t ♦✛❡r ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ♣♦s✲s✐❜❧❡ ✉s❡s✳ ❋r♦♠ t❤❡ ❛✐r✱ r❡❝♦♥♥❛✐ss❛♥❝❡✱ s✉r✈❡✐❧❧❛♥❝❡✱ ❛♥❞ s❡❛r❝❤ ❛♥❞ r❡s❝✉❡ ♠✐ss✐♦♥s✱❡s♣❡❝✐❛❧❧② ♦❢ ❧❛r❣❡ ❛r❡❛s✱ ❛r❡ ♦❢t❡♥ ♠✉❝❤ ❡❛s✐❡r t❤❛♥ ❢r♦♠ t❤❡ ❣r♦✉♥❞✳ ◆❡✈❡rt❤❡❧❡ss✱♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛r❡ ♥♦t ❛❧✇❛②s t❤❡ ❜❡st ❝❤♦✐❝❡ ❢♦r t❤❡s❡ ❛♣♣❧✐❝❛t✐♦♥s✳ ❙♦♠❡t✐♠❡s ✉♥✲♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ✭❯❆❱s✮ ♠❛② ❜❡ ❛❜❧❡ t♦ ❢✉❧✜❧❧ t❤❡ t❛s❦ ✐♥ ❝♦♠♣❛r❛❜❧❡ q✉❛❧✐t②❜✉t ❝❤❡❛♣❡r ❛♥❞ s❛❢❡r✳ ❋♦r s♦♠❡ ♠✐ss✐♦♥s ❯❆❱s ❡✈❡♥ ❤❛✈❡ ❤✉❣❡ ❛❞✈❛♥t❛❣❡s ❝♦♠♣❛r❡❞t♦ ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ✇❡✐❣❤t ♦❢ ❛ ♣✐❧♦t ❝❛♥ ❜❡ s❛✈❡❞ ❛♥❞ t❤❡ ❞❡s✐❣♥❞♦❡s ♥♦t ♥❡❡❞ t♦ t❛❦❡ ❛ ♣✐❧♦t ✐♥t♦ ❛❝❝♦✉♥t✳ ❍❡♥❝❡✱ ❯❆❱s ❝❛♥ ❜❡ ❜✉✐❧t ♠✉❝❤ s♠❛❧❧❡rt❤❛♥ ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❇❡❝❛✉s❡ ♦❢ ❛❧❧ t❤❡s❡ r❡❛s♦♥s✱ ❯❆❱s ❛r❡ ❡①♣❡r✐❡♥❝✐♥❣ ✐♥❝r❡❛s❡❞♣♦♣✉❧❛r✐t②✳❚❤❡ ✉s❡ ♦❢ ❯❆❱s ✐♥ ❝♦❧❞❡r r❡❣✐♦♥s ✐s ❤♦✇❡✈❡r ❞✐✣❝✉❧t✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❛✐r❝r❛❢t

♠✐❣❤t ❡①♣❡r✐❡♥❝❡ ✐❝✐♥❣✳ ■❝✐♥❣ ♦❝❝✉rs ✐♥ ❝❧♦✉❞s ✇✐t❤ s✉♣❡r❝♦♦❧❡❞ ❧✐q✉✐❞ ❞r♦♣❧❡ts✳ ❚❤❡r❡✲❢♦r❡ ❛♥ ❛✐r❝r❛❢t ❝❛♥ ❡①♣❡r✐❡♥❝❡ ❧❛r❣❡ ❛❝❝r❡t✐♦♥s ♦❢ ✐❝❡ ♦♥ t❤❡ ✇❤♦❧❡ ✈❡❤✐❝❧❡ ✐❢ ✐t ✢✐❡st❤r♦✉❣❤ ❝❧♦✉❞s ✉♥❞❡r ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ✇✐t❤♦✉t ❛♥② ♣r♦t❡❝t✐♦♥ s②st❡♠✳ ❚❤❡s❡ ✐❝❡ ❛❝❝r❡✲t✐♦♥s ❝❛♥ ❧❡❛❞ t♦ s❡✈❡r❡ ♣r♦❜❧❡♠s✱ ❢♦r ❡①❛♠♣❧❡ s✐❣♥✐✜❝❛♥t ❧♦ss❡s ✐♥ ❛❡r♦❞②♥❛♠✐❝ ♣❡r❢♦r✲♠❛♥❝❡ ✐❢ t❤❡ ✐❝❡ ❛❝❝✉♠✉❧❛t❡s ♦♥ t❤❡ ❛✐r❢♦✐❧ ❛s ♣r❡s❡♥t❡❞ ❜② ❇r❛❣❣ ❡t ❛❧✳ ❬✶❪✳ ❆❧❧ ✐♠♣❛❝ts♦❢ ✐❝❡ ❛❝❝r❡t✐♦♥s r❡❞✉❝❡ t❤❡ ❝❛♣❛❜✐❧✐t② ♦❢ t❤❡ ❯❆❱ ♦r ❝❛♥ ❡✈❡♥ ❝❛✉s❡ t❤❡ ❛✐r❝r❛❢t t♦ ❝r❛s❤✳❚❤❡r❡❢♦r❡✱ t❤❡ r✐s❦ ♦❢ ✐❝✐♥❣ ❧❡❛❞s t♦ ❛ ❧✐♠✐t❛t✐♦♥ ✐♥ t❤❡ ✉s❡ ♦❢ ❯❆❱s✳ ❊✈❡♥ ✇✐t❤ ❛♥ ✐❝❡♣r♦t❡❝t✐♦♥ s②st❡♠✱ t❤❡ ❞❡♣❧♦②♠❡♥t ♦r ✢✐❣❤t ✐♥ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ✐s ♦❢t❡♥ ❛ss♦❝✐❛t❡❞ ✇✐t❤❤✐❣❤ r✐s❦s✳■❝✐♥❣ ✐s ♥♦t ❧✐♠✐t❡❞ t♦ ❯❆❱ ♦♣❡r❛t✐♦♥s ❜✉t ❛❧s♦ ✐♥✢✉❡♥❝❡s ♠❛♥♥❡❞ ❛✐r❝r❛❢t✱ s❡❡ ❑✐♥❞

❡t ❛❧✳ ❬✷❪ ♦r P❡❝❦ ❡t ❛❧✳ ❬✸❪✳ ❍♦✇❡✈❡r✱ ♠❛♥♥❡❞ ❛♥❞ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛r❡ ❞✐✛❡r❡♥t ✐♥ s❡✈✲❡r❛❧ ❝❤❛r❛❝t❡r✐st✐❝s✳ ❋♦r ❡①❛♠♣❧❡✱ ❯❆❱s ❛r❡ ♥♦r♠❛❧❧② s♠❛❧❧❡r ❛♥❞ ✢② s❧♦✇❡r t❤❛♥ ♠❛♥♥❡❞❛✐r❝r❛❢t✳ ❚❤❡r❡❢♦r❡✱ ♠❛♥♥❡❞ ❛♥❞ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t ♦♣❡r❛t❡ ✐♥ ❞✐✛❡r❡♥t ❘❡②♥♦❧❞s ♥✉♠✲❜❡r r❡❣✐♠❡s✳ ❚❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ ❘❡②♥♦❧❞s ♥✉♠❜❡r ❛✛❡❝ts t❤❡ ❛❝❝r❡t✐♦♥ ♣r♦❝❡ss ❛♥❞ t❤❡❝♦♥s❡q✉❡♥t ♣❡r❢♦r♠❛♥❝❡ ♣❡♥❛❧t✐❡s✱ s❡❡ ❙③✐❧❞❡r ❛♥❞ ▼❝■❧✇❛✐♥ ❬✹❪ ❛♥❞ ❍❛♥♥ ❬✺❪✳ ❚❤❡r❡✲❢♦r❡✱ ❛ ❞✐r❡❝t tr❛♥s❢❡r ♦❢ ✐❝✐♥❣ ♦♥ ♠❛♥♥❡❞ ❛✐r❝r❛❢t t♦ ✐❝✐♥❣ ♦♥ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t ✐s ♥♦t♣♦ss✐❜❧❡✳ ❚❤✐s ✐s ❛❧s♦ ✇❤② ❛♥ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ t❤❡ ❡①✐st✐♥❣ ✐❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ❢♦r♠❛♥♥❡❞ ❛✐r❝r❛❢t ✐♥t♦ ❯❆❱s ✐s ♥♦t ♣♦ss✐❜❧❡ ✇✐t❤♦✉t ❛♥ ✐♥✲❞❡♣t❤ ❛♥❛❧②s✐s✱ s❡❡ ❍❛♥♥ ❛♥❞❏♦❤❛♥s❡♥ ❬✻❪✳ ❚❤❡ ✐❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠ ♠✉st ✜rst ❜❡ ❛❞❛♣t❡❞ t♦ ❞✐✛❡r❡♥t ❝❤❛r❛❝t❡r✐st✐❝s♦❢ t❤❡ ❯❆❱✱ ❡✳❣✳ t❤❡ t②♣✐❝❛❧❧② s♠❛❧❧❡r s✐③❡ t❤❛♥ ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳

✶

✶ ■♥tr♦❞✉❝t✐♦♥

✶✳✷ ❚❤❡ s❝♦♣❡ ♦❢ t❤❡ t❤❡s✐s

■♥✲✢✐❣❤t t❡sts ✐♥ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❝❛♥ ❜❡ ❞❛♥❣❡r♦✉s ❛♥❞ ✐t ❝❛♥ ❜❡ ❞✐✣❝✉❧t t♦ ✜♥❞ ✐❝✐♥❣❝♦♥❞✐t✐♦♥s ✐♥ ♥❛t✉r❡✳ ❚❤✐s ❛♥❞ t❤❡ ✇✐s❤ ❢♦r ❛ ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ ✐❝❡ ❛❝❝r❡t✐♦♥ ♣r♦✲❝❡ss❡s ♦♥ ❯❆❱s ❧❡❛❞ t♦ t❤❡ ❞❡s✐r❡ ♦❢ ❤❛✈✐♥❣ s✉✐t❛❜❧❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤❡s❡ ✇✐♥❞t✉♥♥❡❧s s❤❛❧❧ ❜❡ ❝❛♣❛❜❧❡ ♦❢ ♣r♦✈✐❞✐♥❣ r❡❛❧✐st✐❝ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❛♥❞ t❤❡ ♥❡❝❡ss❛r② ❞✐♠❡♥✲s✐♦♥s t♦ t❡st ❢✉❧❧✲s✐③❡❞ ♣❛rts ♦❢ ❛ ❯❆❱✳ ❲❤✐❧❡ s♦♠❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❡①✐st t♦❞❛②✱ ♠♦st♦❢ t❤❡♠ ❛r❡ ❞❡s✐❣♥❡❞ ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❯❆❱s ❛r❡ t②♣✐❝❛❧❧② s♠❛❧❧❡r ❛♥❞ ♦♣❡r❛t❡ ❛t❧♦✇❡r s♣❡❡❞s✳ ❚❤❡r❡❢♦r❡✱ ✐t ✐s ♦❢t❡♥ ♥♦t ♣♦ss✐❜❧❡ t♦ t❡st ✐❝✐♥❣ ♦♥ ❯❆❱s ✉♥❞❡r r❡❛❧✐st✐❝❝♦♥❞✐t✐♦♥s ✐♥ t❤❡ ❡①✐st✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤✐s t❤❡s✐s s❤❛❧❧ ❡①♣❧♦r❡ t❤❡ ❞❡s✐❣♥ ❝♦♥✲s✐❞❡r❛t✐♦♥s ❢♦r ❛ ❧♦✇✲s♣❡❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ t❤❛t ✐s ❝❛♣❛❜❧❡ t♦ ✜t ❛ r❡❛❧ ❯❆❱ ❛✐r❢♦✐❧ ❛♥❞♣r♦❞✉❝❡ ❝♦♥❞✐t✐♦♥s t②♣✐❝❛❧ ❢♦r ❯❆❱s ❛♥❞ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✳

✶✳✸ ❚❤❡ ♦✉t❧✐♥❡ ♦❢ t❤❡ t❤❡s✐s

❚❤❡ ❜❛s✐❝s t♦ ✉♥❞❡rst❛♥❞ ✐❝✐♥❣ ❛♥❞ t❤❡ s♣❡❝✐❛❧ ✐ss✉❡s ♦❢ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s ❛r❡❣✐✈❡♥ ✐♥ ❈❤❛♣t❡r ✷✳ ❚❤✐s ❝❤❛♣t❡r ❛❧s♦ ❝♦♥t❛✐♥s ❛♥ ✐♥tr♦❞✉❝t✐♦♥ ✐♥t♦ ✇✐♥❞ t✉♥♥❡❧s ❛♥❞✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤❡ ♠❡t❤♦❞s ✉s❡❞ t♦ ❞❡✈❡❧♦♣ t❤❡ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛r❡✐♥tr♦❞✉❝❡❞ ✐♥ t❤❡ t❤✐r❞ ❝❤❛♣t❡r✳ ❈❤❛♣t❡r ✸ ❛❧s♦ ❝♦♥t❛✐♥s t❤❡ ♥❡❝❡ss❛r② st❡♣s t♦ ❝❛❧❝✉❧❛t❡t❤❡ ❜❡❤❛✈✐♦r ♦❢ ✇❛t❡r ❞r♦♣❧❡ts ✐♥s✐❞❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧❛♥❞ ✐ts ❡♥✈✐r♦♥♠❡♥t ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❈❤❛♣t❡r ✹✳ ❆❧s♦ t❤❡ r❡s✉❧ts ♦❢ ❞r♦♣❧❡t ❝❛❧❝✉❧❛t✐♦♥s❛r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤❛t ❝❤❛♣t❡r✳ ❆ ❞✐s❝✉ss✐♦♥ ❛❜♦✉t t❤❡ r❡s✉❧ts ❛♥❞ ❛ r❡❝♦♠♠❡♥❞❛t✐♦♥ ♦♥❢✉rt❤❡r ✇♦r❦ ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❈❤❛♣t❡r ✺✳

✷

✷ ❇❛❝❦❣r♦✉♥❞

■♥ t❤✐s ❝❤❛♣t❡r✱ t❤❡ ♥❡❝❡ss❛r② ❜❛s✐❝s ❢♦r t❤❡ t❤❡s✐s ❛r❡ ♣r❡s❡♥t❡❞✳ ❋✐rst✱ t❤❡ t♦♣✐❝ ♦❢❛t♠♦s♣❤❡r✐❝ ✐❝✐♥❣ ✐s ✐♥tr♦❞✉❝❡❞✳ ❆❢t❡r✇❛r❞s✱ t❤❡ ♥❡❝❡ss❛r② ❦♥♦✇❧❡❞❣❡ ♦❢ ✢♦✇ ❞②♥❛♠✐❝s❛s ✇❡❧❧ ❛s ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ✐s ♣r❡s❡♥t❡❞✳ ❆❢t❡r t❤✐s✱ t❤❡r❡ ✐s ❛ ❞❡✜♥✐t✐♦♥ ❢♦r t❤❡ t❡r♠❯❆❱ ❛♥❞ ❛ s❤♦rt ♦✈❡r✈✐❡✇ ♦❢ ❞✐✛❡r❡♥t ❞❡s✐❣♥s ❛♥❞ ♣♦ss✐❜❧❡ ❛r❡❛s ♦❢ ♦♣❡r❛t✐♦♥✳ ❆ s♣❡✲❝✐❛❧ ❝♦♥❝❡r♥ ❛r❡ t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ♠❛♥♥❡❞ ❛♥❞ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛♥❞ ❤♦✇ t❤❡s❡❞✐✛❡r❡♥❝❡s ✐♥✢✉❡♥❝❡ ✐❝✐♥❣✳ ❚❤✐s ✐s ❢♦❧❧♦✇❡❞ ❜② ❛ s❤♦rt ❡①♣❧❛♥❛t✐♦♥ ♦♥ ✇✐♥❞ t✉♥♥❡❧s ❛♥❞❞✐✛❡r❡♥t ❞❡s✐❣♥ ♦♣t✐♦♥s ✐♥ ❣❡♥❡r❛❧✱ ❛♥❞ ❛ s♣❡❝✐❛❧ ❧♦♦❦ ♦♥ ❝❤❛♥❣❡s t❤❛t ♥❡❡❞ t♦ ❜❡ ♠❛❞❡t♦ tr❛♥s❢♦r♠ ❛ ❝♦♥✈❡♥t✐♦♥❛❧ ✇✐♥❞ t✉♥♥❡❧ ✐♥t♦ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

✷✳✶ ❆t♠♦s♣❤❡r✐❝ ✐❝✐♥❣

❆♥ ♦❜❥❡❝t✐✈❡ ❢♦r ❡✈❡r② ❛✐r❝r❛❢t✱ ♥♦ ♠❛tt❡r ✐❢ ♠❛♥♥❡❞ ♦r ✉♥♠❛♥♥❡❞ ✐s t♦ ❜❡ ❛❜❧❡ t♦ ♦♣❡r❛t❡❛❧s♦ ✉♥❞❡r ❜❛❞ ✇❡❛t❤❡r ❝♦♥❞✐t✐♦♥s✳ ❖♥❡ ♣♦t❡♥t✐❛❧❧② ❤❛③❛r❞♦✉s ✇❡❛t❤❡r ❝♦♥❞✐t✐♦♥ ❢♦r❛✐r❝r❛❢t ✐s ✐❝✐♥❣✳ ❆ ♣❤②s✐❝❛❧ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ✐❝✐♥❣ ♣r♦❝❡ss ✇❛s ❣✐✈❡♥ ❜② ❑✐♥❞ ❡t ❛❧✳ ❬✷❪✳❚❤❡✐r ❞❡s❝r✐♣t✐♦♥ s❤❛❧❧ ❜❡ s✉♠♠❛r✐③❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣❛r❛❣r❛♣❤s✳

✷✳✶✳✶ ❇❛s✐❝s ♦❢ ❛t♠♦s♣❤❡r✐❝ ✐❝✐♥❣

■♥✲❝❧♦✉❞ ✐❝✐♥❣ ♦r ❥✉st ❝❛❧❧❡❞ ✐❝✐♥❣ ♠✐❣❤t ♦❝❝✉r ♦♥❝❡ ❛♥ ❛✐r❝r❛❢t ✢✐❡s t❤r♦✉❣❤ ❛ ❝❧♦✉❞ ✇✐t❤s✉♣❡r❝♦♦❧❡❞ ❧✐q✉✐❞ ✇❛t❡r ❞r♦♣❧❡ts✳ ❋♦r t❤❡ ♣r❡s❡♥❝❡ ♦❢ s✉♣❡r❝♦♦❧❡❞ ❞r♦♣❧❡ts✱ t❤❡ ❛♠❜✐❡♥tt❡♠♣❡r❛t✉r❡ ♥❡❡❞s t♦ ❜❡ ❜❡❧♦✇ t❤❡ ❢r❡❡③✐♥❣ t❡♠♣❡r❛t✉r❡ t❤❛t ✐s 0 ➦C ❢♦r ✇❛t❡r✳ ■❢ t❤❡s❡s✉♣❡r❝♦♦❧❡❞ ❞r♦♣❧❡ts ❛r❡ t♦♦ ❜✐❣ t♦ ❢♦❧❧♦✇ t❤❡ str❡❛♠❧✐♥❡s ❛r♦✉♥❞ t❤❡ ❜♦❞②✱ t❤❡② ✇✐❧❧❤✐t t❤❡ s✉r❢❛❝❡s t❤❛t ❛r❡ ❢❛❝✐♥❣ ✉♣str❡❛♠ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✶✳ ❚❤✐s ❝❛♥ ❤❛✈❡

❋✐❣✉r❡ ✷✳✶✿ ❚r❛❥❡❝t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ❛r♦✉♥❞ ❛ ❧❡❛❞✐♥❣ ❡❞❣❡✳ ❆❞❛♣t❡❞ ❢r♦♠ ❍❛♥♥ ❛♥❞❏♦❤❛♥s❡♥ ❬✻❪✳

✸

✷ ❇❛❝❦❣r♦✉♥❞

❡✛❡❝ts ❛t s❡✈❡r❛❧ ♣❛rts ♦❢ t❤❡ ❛✐r♣❧❛♥❡✱ ❡✳❣✳ t❤❡ ♣r♦♣❡❧❧❡rs✱ t❤❡ ✇✐♥❣s✱ t❤❡ ♣✐t♦t t✉❜❡s✱ ♦rs❡♥s♦rs✳ ❍♦✇❡✈❡r✱ t❤✐s t❤❡s✐s ✇✐❧❧ s♦❧❡❧② ❢♦❝✉s ♦♥ ✐❝✐♥❣ ♦♥ t❤❡ ❛✐r❢♦✐❧s✳❚❤❡ ✐♠♣❛❝t✐♥❣ ❞r♦♣❧❡ts ♠❛② ❡✐t❤❡r ❢r❡❡③❡ ❝♦♠♣❧❡t❡❧② ♦r ♣❛rt✐❛❧❧②✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡

❤❡❛t ❜❛❧❛♥❝❡ ✐♥ t❤❡ ✐♠♣❛❝t r❡❣✐♦♥✳ ❚❤✐s ❤❡❛t ❜❛❧❛♥❝❡ ✐s ❢♦r♠❡❞ ❜② ♠✉❧t✐♣❧❡ t❡r♠s✱ ❜✉tt✇♦ ❤❛✈❡ ❛ ♠❛❥♦r ✐♥✢✉❡♥❝❡✳ ❲❤❡♥ ❞r♦♣❧❡ts ❢r❡❡③❡✱ t❤❡ ❡♥t❤❛❧♣② ♦❢ ❢✉s✐♦♥ ❣❡ts s❡t ❢r❡❡ ❛♥❞t❡♥❞s t♦ ✇❛r♠ t❤❡ s✉rr♦✉♥❞✐♥❣✳ ❖♥ t❤❡ ♦t❤❡r s✐❞❡✱ ❞✉❡ t♦ ❝♦♥✈❡❝t✐♦♥✱ ❤❡❛t ✐s tr❛♥s❢❡rr❡❞❢r♦♠ t❤❡ s✉r❢❛❝❡ t♦✇❛r❞s t❤❡ ❝♦❧❞❡r s✉rr♦✉♥❞✐♥❣ ❛✐r✳ ❚❤r❡❡ ❝❧♦✉❞ ♣❛r❛♠❡t❡rs ♣❧❛② ❛♥✐♠♣♦rt❛♥t r♦❧❡ ✐♥ t❤❡ q✉❡st✐♦♥ ✇❤✐❝❤ t❡r♠ ✐s ❜✐❣❣❡r✿ ❚❤❡ ❛♠❜✐❡♥t t❡♠♣❡r❛t✉r❡✱ t❤❡ ❧✐q✉✐❞✇❛t❡r ❝♦♥t❡♥t ✭▲❲❈✮✱ ❛♥❞ t❤❡ ♠❡❞✐❛♥ ✈♦❧✉♠❡ ❞✐❛♠❡t❡r ✭▼❱❉✮✳ ❚❤❡ ▲❲❈ ✐s ❛ ♠❡❛s✉r❡♦❢ t❤❡ ❛♠♦✉♥t ♦❢ ✇❛t❡r ✐♥ t❤❡ ❝❧♦✉❞✳ ■t ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s ❛ ❦✐♥❞ ♦❢ ❞❡♥s✐t② ❛♥❞ ✐s♥♦t❡❞ ✐♥ ♠❛ss ♣❡r ✈♦❧✉♠❡✳ ❚❤❡ ▼❱❉ ✐s t❤❡ ❞✐❛♠❡t❡r ✇❤❡r❡ 50% ♦❢ t❤❡ ✇❤♦❧❡ ✈♦❧✉♠❡♦❢ ❛❧❧ t❤❡ ❞r♦♣❧❡ts ✐s ♠❛❞❡ ✉♣ ♦❢ ❜✐❣❣❡r ❞r♦♣❧❡ts ❛♥❞ 50% ♦❢ s♠❛❧❧❡r ❞r♦♣❧❡ts✳ ❚❤❡r❡❢♦r❡t❤❡ ▼❱❉ ✐s ❛ ❞✐❛♠❡t❡r r❡♣r❡s❡♥t❛t✐✈❡ ❢♦r t❤❡ ❞✐✛❡r❡♥t ❞r♦♣❧❡t s✐③❡s ✐♥ t❤❡ ❞r♦♣❧❡t ❝❧♦✉❞✳❋♦r ♣r♦❜❧❡♠s ✇✐t❤ ❧♦✇ ▲❲❈ ❛♥❞✴♦r t❡♠♣❡r❛t✉r❡s ✇❡❧❧ ❜❡❧♦✇ 0 ➦C✱ t❤❡ ❝♦♥✈❡❝t✐✈❡ ❤❡❛t

tr❛♥s❢❡r ✐s ❤✐❣❤ ❡♥♦✉❣❤ t♦ tr❛♥s♣♦rt ❛✇❛② t❤❡ ❤❡❛t t❤❛t ✐s r❡❧❡❛s❡❞ ✇❤❡♥ t❤❡ ❞r♦♣❧❡ts❢r❡❡③❡✳ ❚❤❡r❡❢♦r❡ t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ s✉r❢❛❝❡ ❛♥❞ t❤❡ ❛❝❝✉♠✉❧❛t❡❞ ✐❝❡ st❛②s ❜❡❧♦✇0 ➦C ❛♥❞ t❤❡ ❞r♦♣❧❡ts ❢r❡❡③❡ ❡♥t✐r❡❧② ✇❤❡♥ t❤❡② ❤✐t t❤❡ s✉r❢❛❝❡✳ ❚❤✐s ❝❛s❡ ✐s ❦♥♦✇♥ ❛sr✐♠❡ ✐❝❡✳ ❚❤❡ s❤❛♣❡ ♦❢ r✐♠❡ ✐❝❡ ✐s r❛t❤❡r s✐♠♣❧❡ ❛s t❤❡ ❞r♦♣❧❡ts ❥✉st ❢r❡❡③❡ ✇❤❡r❡ t❤❡✐rtr❛❥❡❝t♦r② ❤✐ts t❤❡ s✉r❢❛❝❡✳ ❆ ❝❤❛r❛❝t❡r✐st✐❝ ♦❢ r✐♠❡ ✐❝❡ ✐s ✐ts r❛t❤❡r ♠✐❧❦② ❧♦♦❦ t❤❛t❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✷✭❛✮✳ ❚❤✐s ♠✐❧❦② ❧♦♦❦ ❛r✐s❡s ❜❡❝❛✉s❡ ❛✐r ✐s tr❛♣♣❡❞ ❜❡t✇❡❡♥ t❤❡❢r❡❡③✐♥❣ ❞r♦♣❧❡ts ❛♥❞ t❤❡ s✉r❢❛❝❡✳

✭❛✮ ❚②♣✐❝❛❧ ❧♦♦❦ ♦❢ ❛ r✐♠❡ ✐❝❡ ❝❛s❡✳ ❆❞❛♣t❡❞❢r♦♠ ❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥ ❬✻❪✳

✭❜✮ ❚②♣✐❝❛❧ ❧♦♦❦ ♦❢ ❛ ❣❧❛③❡ ✐❝❡ ❝❛s❡✳ ❆❞❛♣t❡❞❢r♦♠ ❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥ ❬✻❪✳

❋✐❣✉r❡ ✷✳✷✿ ❊①❛♠♣❧❡s ❢♦r ❞✐✛❡r❡♥t ✐❝❡ ❝❛s❡s✳

■♥ ❝❛s❡s ♦❢ t❡♠♣❡r❛t✉r❡s ❥✉st s❧✐❣❤t❧② ❜❡❧♦✇ t❤❡ ❢r❡❡③✐♥❣ t❡♠♣❡r❛t✉r❡ ❛♥❞✴♦r ❤✐❣❤▲❲❈✱ t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ✐❝❡ ✐s ❛r♦✉♥❞ 0 ➦C ❛♥❞ ❥✉st ❛ ♣❛rt ♦❢ t❤❡ ❞r♦♣❧❡t ❢r❡❡③❡s✇❤❡♥ ❤✐tt✐♥❣ t❤❡ s✉r❢❛❝❡✳ ❚❤❡ ♦t❤❡r✱ st✐❧❧ ❧✐q✉✐❞✱ ♣❛rt r✉♥s ❜❛❝❦ ♦♥ t❤❡ ❛✐r❢♦✐❧ ❛♥❞ ♠❛②❡✈❡♥t✉❛❧❧② ❢r❡❡③❡ ❞♦✇♥str❡❛♠✳ ❚❤✐s ❜❡❤❛✈✐♦r ✐s ❡✈❡♥ ♠♦r❡ ♣r♦❜❛❜❧❡ ❢♦r ❤✐❣❤ ▼❱❉s✳❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡♥ t❤❡ ❞r♦♣❧❡ts ❤❛✈❡ ❛ ❤✐❣❤❡r ♠❛ss ❛♥❞ t❤❡ ❡♥t❤❛❧♣② ♦❢ ❢✉s✐♦♥ ✐s ♠✉❝❤❧❛r❣❡r✳ ❚❤✐s ❝❛s❡ ✐s ❝❛❧❧❡❞ ❣❧❛③❡ ✐❝❡✳ ❇❡❝❛✉s❡ ♦❢ t❤❡ r✉♥❜❛❝❦ ✇❛t❡r✱ ✐t ❤❛s ❛ ♠✉❝❤ ♠♦r❡❝♦♠♣❧❡① s❤❛♣❡ ❛♥❞ ✐t ❧♦♦❦s ❝❧❡❛r ❛s ❥✉st ❢❡✇ ❛✐r ✐s tr❛♣♣❡❞ ✐♥s✐❞❡ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡

✹

✷ ❇❛❝❦❣r♦✉♥❞

✷✳✷✭❜✮✳ ❖❢t❡♥ ✐♥ r❡❛❧ ✢✐❣❤ts✱ t❤❡ ❛✐r❝r❛❢t ✇✐❧❧ ❡①♣❡r✐❡♥❝❡ ❛ ❝❛s❡ ❜❡t✇❡❡♥ ❣❧❛③❡ ❛♥❞ r✐♠❡✐❝❡✳ ❚❤✐s ❝❛s❡ ✐s ❝❛❧❧❡❞ ♠✐①❡❞ ✐❝❡✳❚❤❡ ❊✉r♦♣❡❛♥ ❆✈✐❛t✐♦♥ ❙❛❢❡t② ❆❣❡♥❝② ❬✼❪ ✭❊❆❙❆✮ ❤❛s ❝❡rt✐✜❝❛t✐♦♥ ❣✉✐❞❡❧✐♥❡s ❢♦r ❛✐r✲

❝r❛❢t✳ ■❢ ❛ ❝♦♠♣❛♥② ✇❛♥ts ❛♥ ❛✐r❝r❛❢t t♦ ❜❡ ❝❡rt✐✜❡❞ ❛♥❞ ❜❡ ❛❧❧♦✇❡❞ t♦ ❛❧s♦ st❛rt ❛♥❞ ✢②❞✉r✐♥❣ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✱ t❤❡ ❛✐r❝r❛❢t ♥❡❡❞s t♦ ❜❡ ❛❜❧❡ t♦ ❞❡❛❧ ✇✐t❤ s♣❡❝✐✜❡❞ ✐❝✐♥❣ ❝♦♥❞✐✲t✐♦♥s✳ ❚❤❡ ❊❆❙❆ ✇♦r❦s ❝❧♦s❡❧② ✇✐t❤ t❤❡ ❋❡❞❡r❛❧ ❆✈✐❛t✐♦♥ ❆❞♠✐♥✐str❛t✐♦♥ ♦♥ t❤❡ t♦♣✐❝♦❢ ✐❝✐♥❣ ❛♥❞ ❜♦t❤ ❛❣❡♥❝✐❡s ❤❛✈❡ t❤❡ s❛♠❡ r✉❧❡s ❢♦r ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✳ ❆s ♥♦ ❝❡rt✐✜❝❛t✐♦♥❣✉✐❞❡❧✐♥❡ ✐s ❛✈❛✐❧❛❜❧❡ ❢♦r ❯❆❱s✱ t②♣✐❝❛❧❧② t❤❡ ❣✉✐❞❡❧✐♥❡s ❢♦r ❧❛r❣❡ ♣❛ss❡♥❣❡r tr❛♥s♣♦rt❛✐r❝r❛❢t ❛r❡ ✉s❡❞✳ ❚❤❡ ❝❡rt✐✜❝❛t✐♦♥ ❣✉✐❞❡❧✐♥❡s ♦❢ t❤❡ ❊❆❙❆ ❝♦♥s✐st ♦❢ ❛ ❝♦♥t✐♥✉♦✉s ❛♥❞❛♥ ✐♥t❡r♠✐tt❡♥t ♠❛①✐♠✉♠ t❤❡ ❛✐r❝r❛❢t ♠✐❣❤t ❡①♣❡r✐❡♥❝❡✳ ❚♦ ❞❡s❝r✐❜❡ t❤❡ ✐❝✐♥❣ s✉rr♦✉♥❞✲✐♥❣✱ t❤❡ ❊❆❙❆ ✉s❡s t❤r❡❡ ❞✐✛❡r❡♥t ♣❛r❛♠❡t❡rs✳ ❚❤❡s❡ ♣❛r❛♠❡t❡rs ❛r❡ t❤❡ ❛❧r❡❛❞② st❛t❡❞❛♠❜✐❡♥t t❡♠♣❡r❛t✉r❡✱ t❤❡ ▲❲❈✱ ❛♥❞ t❤❡ ▼❱❉✳ ❚❤❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ♠❛①✐♠✉♠ ✐❝✐♥❣❝♦♥❞✐t✐♦♥s ❛♥ ❛✐r❝r❛❢t ♠✐❣❤t ❡①♣❡r✐❡♥❝❡ ❛r❡ ✈✐s✉❛❧✐③❡❞ ✐♥ ❋✐❣✉r❡ ✷✳✸✭❛✮ ❢♦r t❤❡ ❝♦♥t✐♥✉♦✉s❝❛s❡ ❛♥❞ ✐♥ ❋✐❣✉r❡ ✷✳✸✭❜✮ ❢♦r t❤❡ ✐♥t❡r♠✐tt❡♥t ❝❛s❡✳ ❲❤✐❧❡ t❤❡ ✈❛❧✉❡s ❛r❡ ❤✐❣❤❡r ❢♦r t❤❡✐♥t❡r♠✐tt❡♥t ❝❛s❡✱ ❝❧♦✉❞s ✇✐t❤ t❤❡s❡ ♠♦r❡ s❡✈❡r❡ ❝♦♥❞✐t✐♦♥s ❛r❡ t②♣✐❝❛❧❧② s♠❛❧❧❡r✳ ◆❡✈✲❡rt❤❡❧❡ss✱ t♦ ♦❜t❛✐♥ ❛ ❝♦♠♣❧❡t❡ ❝♦✈❡r❛❣❡ ♦❢ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✱ t❤❡s❡ ♣❛r❛♠❡t❡rs ❤❛✈❡ t♦❜❡ ❢✉❧✜❧❧❡❞✳ ❚❤❡ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❝♦♥t❛✐♥ ▼❱❉s ❜❡t✇❡❡♥ 15µm ❛♥❞ 50µm ❛♥❞ ▲❲❈s✉♣ t♦ ❛❧♠♦st 3 gm−3✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ✜❣✉r❡s s❤♦✇ t❤❛t t❤❡ ▲❲❈ t❤❡ ❛✐r❝r❛❢t ♠✐❣❤t❡①♣❡r✐❡♥❝❡ ✐s ♠✉❝❤ ❤✐❣❤❡r ❢♦r t❡♠♣❡r❛t✉r❡s ❛r♦✉♥❞ 0 ➦C t❤❛♥ ❢♦r ❧♦✇❡r t❡♠♣❡r❛t✉r❡s✳

✭❛✮ ▼❛①✐♠✉♠ ♣❛r❛♠❡t❡rs ♦❢ ❝♦♥t✐♥✉♦✉s ♠❛①✲✐♠✉♠ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✳ ❆❞❛♣t❡❞ ❢r♦♠ ❊✉r♦✲♣❡❛♥ ❆✈✐❛t✐♦♥ ❙❛❢❡t② ❆❣❡♥❝② ❬✼❪✳

✭❜✮ ▼❛①✐♠✉♠ ♣❛r❛♠❡t❡rs ♦❢ ✐♥t❡r♠✐tt❡♥t ♠❛①✐♠✉♠✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✳ ❆❞❛♣t❡❞ ❢r♦♠ ❊✉r♦♣❡❛♥ ❆✈✐❛t✐♦♥❙❛❢❡t② ❆❣❡♥❝② ❬✼❪✳

❋✐❣✉r❡ ✷✳✸✿ ■❝✐♥❣ ❝♦♥❞✐t✐♦♥s st❛t❡❞ ✐♥ t❤❡ ❝❡rt✐✜❝❛t✐♦♥ ❣✉✐❞❡❧✐♥❡s ❢♦r ❛✐r❝r❛❢t ❢♦r t✇♦ ❞✐❢✲❢❡r❡♥t t②♣❡s ♦❢ ❝❧♦✉❞s✳

✺

✷ ❇❛❝❦❣r♦✉♥❞

✷✳✶✳✷ ❚②♣✐❝❛❧ ✐❝❡ s❤❛♣❡s ♦♥ ❛✐r❢♦✐❧s

❚♦ ✉♥❞❡rst❛♥❞ ✇❤② ✐❝❡ ❛❝❝r❡t✐♦♥s ❝❛♥ ❧❡❛❞ t♦ ❜✐❣ ❛❡r♦❞②♥❛♠✐❝ ♣❡r❢♦r♠❛♥❝❡ ❧♦ss❡s ❛♥❞t❤❡r❡❢♦r❡ ✐♥✢✉❡♥❝❡ t❤❡ ❛❜✐❧✐t✐❡s ♦❢ t❤❡ ❛✐r❝r❛❢t✱ t❤❡ ♥❡①t ♣❛ss❛❣❡s s❤❛❧❧ s❤♦✇ t❤❡ ❢♦✉r♠♦st t②♣✐❝❛❧ ✐❝❡ s❤❛♣❡s ❛♥❞ ❤♦✇ t❤❡② ❝❤❛♥❣❡ t❤❡ ❛❡r♦❞②♥❛♠✐❝s ♦❢ t❤❡ ❛✐r❢♦✐❧✳ ❍♦✇❡✈❡r✱❛s t❤❡ ♠❛❥♦r t♦♣✐❝ ♦❢ t❤✐s ✇♦r❦ ✐s t❤❡ ❞❡s✐❣♥ ♦❢ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ ♦✈❡r✈✐❡✇ ✇✐❧❧♥♦t ❣♦ t♦♦ ♠✉❝❤ ✐♥t♦ ❞❡t❛✐❧✳ ❋♦r ❢✉rt❤❡r ✐♥❢♦r♠❛t✐♦♥ s❡❡ ❇r❛❣❣ ❡t ❛❧✳ ❬✶❪✱ ❛s t❤✐s ✇❛s ❛❧s♦✉s❡❞ ❛s t❤❡ ♠❛✐♥ s♦✉r❝❡ ❢♦r t❤❡ ♥❡①t ♣❛ss❛❣❡s✳❆t t❤❡ ❜❡❣✐♥♥✐♥❣ ♦❢ t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥✱ ♥♦ ♠❛tt❡r ✇❤❡t❤❡r ✐t ✐s ❣❧❛③❡ ♦r r✐♠❡ ✐❝❡✱ t❤❡

♦❝❝✉rr✐♥❣ ♣❤❡♥♦♠❡♥♦♥ ✐s ❝❛❧❧❡❞ ✐❝❡ r♦✉❣❤♥❡ss✳ ❚❤❡ ✐❝❡ ✇✐❧❧ ❛❧✇❛②s ❜❡ r♦✉❣❤ t♦ ❛ ❝❡rt❛✐♥❞❡❣r❡❡✳ ■♥ t❤✐s ✜rst ♣❤❛s❡✱ ❤♦✇❡✈❡r✱ t❤❡ s✉r❢❛❝❡ ✐s ♥♦t ②❡t ❝♦✈❡r❡❞ ✐♥ ❛ ✇❛② t❤❛t t❤❡s❤❛♣❡ ♦❢ t❤❡ ❛✐r❢♦✐❧ ✐s s✐❣♥✐✜❝❛♥t❧② ❝❤❛♥❣❡❞✳ ❚❤❡r❡❢♦r❡ ❛❧s♦ t❤❡ ✢♦✇✜❡❧❞ ❛r♦✉♥❞ t❤❡ ❛✐r❢♦✐❧✐s ❛❧♠♦st ✉♥❝❤❛♥❣❡❞ ❝♦♠♣❛r❡❞ t♦ ❛♥ ✐❝❡✲❢r❡❡ s✐t✉❛t✐♦♥✳ ❚❤❡ r❡s✉❧t✐♥❣ r♦✉❣❤ ③♦♥❡s ❛r❡t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ❛♥❞ ❤❛✈❡ ❛ ❤❡✐❣❤t t②♣✐❝❛❧❧② ❧❛r❣❡r t❤❛♥ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❚❤❡r❡❢♦r❡✐❝❡ r♦✉❣❤♥❡ss ❝❛♥ ❜❡ t❤♦✉❣❤t ♦❢ ❧✐❦❡ ♥♦r♠❛❧ s✉r❢❛❝❡ r♦✉❣❤♥❡ss✳ ■❢ t❤❡ r♦✉❣❤♥❡ss ✐s ❤✐❣❤❡♥♦✉❣❤✱ ✐t ♠❛② ❝❛✉s❡ tr❛♥s✐t✐♦♥ ♦❢ t❤❡ ✢♦✇ ♦r ❡✈❡♥ s❡♣❛r❛t✐♦♥✳ ❚❤✐s ❧❡❛❞s t♦ ❧❡ss ❧✐❢t ❛♥❞❤✐❣❤❡r ❞r❛❣✳❆ t②♣✐❝❛❧ s❤❛♣❡ ❢♦r ❣❧❛③❡ ✐❝❡ ❝♦♥❞✐t✐♦♥s ✐s ❛ ❤♦r♥ ❛t t❤❡ s✉r❢❛❝❡✳ ❆ ❤♦r♥ ✐❝❡ s❤❛♣❡ ❝❛♥

❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✹✳ ❆t t❤❡ ❤♦r♥✬s t♦♣✱ t❤❡ ✢♦✇ ✇✐❧❧ s❡♣❛r❛t❡ ✐❢ t❤❡ ❤♦r♥ ✐s t♦♦ ❤✐❣❤ ❛♥❞✐❢ t❤❡ ♣r❡ss✉r❡ ❣r❛❞✐❡♥t ✐s ♥♦t ❢❛✈♦r❛❜❧❡✳ ❚❤❡ s✐③❡ ♦❢ t❤❡ s❡♣❛r❛t✐♦♥ ③♦♥❡ ❜❡❤✐♥❞ t❤❡ ❤♦r♥❛♥❞ ❛❝❝♦r❞✐♥❣❧② ❤♦✇ ❤✉❣❡ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ❧♦ss❡s ❛r❡✱ ❞❡♣❡♥❞s ♦♥ s❡✈❡r❛❧ ❛ttr✐❜✉t❡s✱❢♦r ❡①❛♠♣❧❡ t❤❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦✱ t❤❡ ❤❡✐❣❤t ♦❢ t❤❡ ❤♦r♥✱ ❛♥❞ ✐ts ❧♦❝❛t✐♦♥ ♦♥ t❤❡ s✉r❢❛❝❡✳❍♦r♥s ♦♥ t❤❡ ❧♦✇❡r s✉r❢❛❝❡ ❥✉st ❤❛✈❡ ❛♥ ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ ❧✐❢t ❝♦❡✣❝✐❡♥t ♦❢ ❧♦✇ ❛♥❣❧❡s ♦❢❛tt❛❝❦✱ ❜✉t t❤❡② ❛❞❞ ✉♣ t♦ t❤❡ ❞r❛❣ ✐♥ ❛ s✐❣♥✐✜❝❛♥t ♠❛♥♥❡r ❛♥❞ t❤❡r❡❢♦r❡ ❝❛♥ ♥♦t ❜❡♥❡❣❧❡❝t❡❞✳ ❆♥ ♦t❤❡r ♣r♦❜❧❡♠ ❛r✐s✐♥❣ ✇✐t❤ ✐❝❡ ❤♦r♥s ✐s t❤❛t t❤❡ ✐♥❞✉❝❡❞ s❡♣❛r❛t✐♦♥ ③♦♥❡s♠❛② ✢✉❝t✉❛t❡✳ ❱♦rt✐❝❡s ❞❡✈❡❧♦♣ ❜❡❤✐♥❞ t❤❡ ❤♦r♥s ❛♥❞ t❤❡ s❡♣❛r❛t✐♦♥ ❜✉❜❜❧❡ ♠♦✈❡s ✇✐t❤t❤❡ r❡❛tt❛❝❤♠❡♥t ♣♦✐♥t ✈❛r②✐♥❣ ♦✈❡r t✐♠❡✳

❋✐❣✉r❡ ✷✳✹✿ ❚②♣✐❝❛❧ ✐❝❡ s❤❛♣❡s ♦♥ ❛♥ ❛✐r❢♦✐❧✳ ❆❞❛♣t❡❞ ❢r♦♠ ❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥ ❬✻❪✳

❲❤✐❧❡ ❤♦r♥ s❤❛♣❡s ❛r❡ t②♣✐❝❛❧ ❢♦r ❣❧❛③❡ ✐❝❡ ❝♦♥❞✐t✐♦♥s✱ s♦✲❝❛❧❧❡❞ str❡❛♠✇✐s❡ ✐❝❡ ✐st②♣✐❝❛❧ ❢♦r r✐♠❡ ✐❝❡ ❝♦♥❞✐t✐♦♥s✳ ❚❤❡ ❞r♦♣❧❡ts ❥✉st ❢r❡❡③❡ ✇❤❡r❡ t❤❡② ❤✐t t❤❡ s✉r❢❛❝❡❛♥❞ t❤❡r❡❢♦r❡ ❢♦r♠ ❛♥ ✐❝❡ s❤❛♣❡ t❤❛t ❞♦❡s ♥♦t r❡❛❧❧② ❝❤❛♥❣❡ t❤❡ s❤❛♣❡ ♦❢ t❤❡ ❛✐r❢♦✐❧✉♥❧❡ss t❤❡ ❛❝❝r❡t✐♦♥ t✐♠❡ ✐s ❧♦♥❣✳ ❚❤✐s s❤❛♣❡ ❝❛♥ ❛❧s♦ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✹✳ ❇❡❝❛✉s❡♦❢ t❤❡ ❧✐tt❧❡ ❝❤❛♥❣❡ ♦❢ s❤❛♣❡✱ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ❡✛❡❝ts ❛r❡ ♠✐♥♦r ❝♦♠♣❛r❡❞ t♦ t❤❡ ❤♦r♥s❤❛♣❡s✳ ❆♥②✇❛②✱ ❛s t❤❡r❡ ✐s ❛ ♣❛ss❛❣❡ ❢r♦♠ t❤❡ ✐❝❡ t♦ t❤❡ ❝❧❡❛♥ s✉r❢❛❝❡✱ ❛♥ ❛❞✈❡rs❡

✻

✷ ❇❛❝❦❣r♦✉♥❞

♣r❡ss✉r❡ ❣r❛❞✐❡♥t ♠❛② ♦❝❝✉r ❛♥❞ ❧❡❛❞ t♦ ✢♦✇ s❡♣❛r❛t✐♦♥s✳ ❚❤❡ ❛❡r♦❞②♥❛♠✐❝ ✐♠♣❛❝t ♦❢str❡❛♠✇✐s❡ ✐❝❡ ✐s ❤♦✇❡✈❡r st✐❧❧ ♠✉❝❤ s♠❛❧❧❡r t❤❛♥ ✐♥ t❤❡ ❤♦r♥ ❝❛s❡✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❛s❡♣❛r❛t✐♦♥ ❞♦❡s ♥♦t ♦❝❝✉r ♦♥ t❤❡ ❧❡❛❞✐♥❣ ❡❞❣❡ ❜✉t ❢✉rt❤❡r ❞♦✇♥str❡❛♠✳❚❤❡ ✐❝❡ s❤❛♣❡s ♣r❡s❡♥t❡❞ s♦ ❢❛r ✇❡r❡ ❛❧❧ ❛ r❡s✉❧t ♦❢ t❤❡ ✐❝✐♥❣ ❝❧♦✉❞ ✐ts❡❧❢✳ ❚❤❡ ❢♦✉rt❤

s❤❛♣❡ ✐s ❛ r❡s✉❧t ♦❢ t❤❡ ✉s❡ ♦❢ ❛♥ ✐❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠✳ ■❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ❛r❡♥♦r♠❛❧❧② ❥✉st ✐♥ t❤❡ r❡❣✐♦♥ ♦❢ t❤❡ ❧❡❛❞✐♥❣ ❡❞❣❡ ❛♥❞ t❤❡r❡❢♦r❡ ❛ ❤✉❣❡ ♣❛rt ♦❢ t❤❡ ❛✐r❢♦✐❧ ✐s♥♦t ❤❡❛t❡❞ ♦r ♣r♦t❡❝t❡❞ s✐♠✐❧❛r❧②✳ ❖♥❝❡ s✉❝❤ ❛ s②st❡♠ ✐s ✉s❡❞ ❜✉t ❞♦❡s ♥♦t r❡♠♦✈❡ ❡✈❡r②♣❛rt ♦❢ t❤❡ ✐♥❝♦♠✐♥❣ ✇❛t❡r✱ t❤❡ r❡♠❛✐♥✐♥❣ ✇❛t❡r ✇✐❧❧ r✉♥ ❜❛❝❦ ❛♥❞ ♠❛② ❡✈❡♥t✉❛❧❧② ❢r❡❡③❡❞♦✇♥str❡❛♠ ❛t ❛ ♣❛rt ♦❢ t❤❡ s✉r❢❛❝❡ t❤❛t ✐s ♥♦t ❤❡❛t❡❞✳ ❆♥ ❡①❡♠♣❧❛r② ♣❧♦t ♦❢ ❤♦✇ t❤❡✐❝❡ s❤❛♣❡s ♠❛② t❤❡♥ ❧♦♦❦ ❧✐❦❡ ✐s ❣✐✈❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✹✳ ❇❡❝❛✉s❡ ♦❢ t❤❡ s❤❛♣❡s ✐t ♣r♦❞✉❝❡s✱♠♦st ♦❢ t❤❡ t✐♠❡ ✐t ✐s ❝❛❧❧❡❞ s♣❛♥✇✐s❡✲r✐❞❣❡ ✐❝❡✳ ❋♦r t❤❡ ❡❛r❧✐❡r ♠❡♥t✐♦♥❡❞ ❤♦r♥ s❤❛♣❡s✱t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ✐s ♥♦t ❞❡✈❡❧♦♣❡❞ ②❡t ❛♥❞ t❤❡ st❛❣♥❛t✐♦♥ ♣♦✐♥t ♦❢ t❤❡ ✢♦✇ ♠✐❣❤t ❡✈❡♥❜❡ ❛t t❤❡ ❤♦r♥✳ ❍♦✇❡✈❡r✱ t❤❡ s♣❛♥✇✐s❡ r✐❞❣❡s ❛r❡ ❧♦❝❛t❡❞ ♠✉❝❤ ❢❛rt❤❡r ❞♦✇♥str❡❛♠ ❛♥❞t❤❡r❡❢♦r❡ s❡❡ ❛ ❜♦✉♥❞❛r② ❧❛②❡r t❤❛t ♠✐❣❤t ❛❧r❡❛❞② ❤❛✈❡ tr❛♥s✐t✐♦♥❡❞ ❞✉❡ t♦ r♦✉❣❤♥❡ss ♦♥t❤❡ s✉r❢❛❝❡✳ ❚❤❡ ✐❝❡ ❛❝ts ♦♥ t❤❡ ✢♦✇ ✐♥ ❛ s✐♠✐❧❛r ✇❛② ❛♥ ♦❜st❛❝❧❡ ✇♦✉❧❞ ❞♦ ❛♥❞ ❝❛✉s❡ss❡♣❛r❛t✐♦♥ ♦❢ t❤❡ ✢♦✇ ✇✐t❤ ✈♦rt✐❝❡s ✐♥s✐❞❡ t❤❡ s❡♣❛r❛t✐♦♥ ❛♥❞ r❡❛tt❛❝❤♠❡♥t r❡❣✐♦♥✳ ❆s✐♥ t❤❡ ♣r❡✈✐♦✉s❧② ♠❡♥t✐♦♥❡❞ ❝❛s❡s✱ t❤✐s r❡❞✉❝❡s t❤❡ ♠❛①✐♠✉♠ ❧✐❢t ❛♥❞ t❤❡ st❛❧❧ ❛♥❣❧❡✱✇❤✐❧❡ ✐♥❝r❡❛s✐♥❣ t❤❡ ❞r❛❣ ❛t t❤❡ s❛♠❡ t✐♠❡✳❉❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❛♠❜✐❡♥t s✐t✉❛t✐♦♥✱ ❛♥ ❛✐r❝r❛❢t ♠✐❣❤t ❛❝❝r❡t❡ ♦♥❡ ♦r ♠♦r❡ ♦❢ t❤❡

♠❡♥t✐♦♥❡❞ ✐❝❡ s❤❛♣❡s ❞✉r✐♥❣ t❤❡ ✢✐❣❤t t❤r♦✉❣❤ ❛ ❝❧♦✉❞✳ ❲❤✐❧❡ t❤❡ ❞✐✛❡r❡♥t s❤❛♣❡s ❢♦r♠❢♦r ❞✐✛❡r❡♥t r❡❛s♦♥s✱ ❛❧❧ ♦❢ t❤❡♠ r❡❞✉❝❡ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❛✐r❝r❛❢t✳◆✉♠❡r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❜② ❋❛❥t ❡t ❛❧✳ ❬✽❪ s❤♦✇❡❞ t❤❛t ❛ ❞❡❝r❡❛s❡ ♦❢ ✸✺✪ ✐♥ ❧✐❢t ❝♦❡✣❝✐❡♥t❛♥❞ ✸✸✪ ✐♥ ❝♦rr❡s♣♦♥❞✐♥❣ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ❛s ✇❡❧❧ ❛s ❛♥ ✐♥❝r❡❛s❡ ♦❢ ❞r❛❣ ❜② ✶✻✵✪ ♠✐❣❤t♦❝❝✉r ✐♥ t❤❡ ✇♦rst✲❝❛s❡ ❝♦♥❞✐t✐♦♥s ❢♦r ❛ ❝♦♥t✐♥✉♦✉s ❝❛s❡✳ ❊①♣❡r✐♠❡♥ts ❜② ❍❛♥♥ ❡t ❛❧✳❬✾❪ ❛❧s♦ s❤♦✇❡❞ s❡✈❡r❡ ❧♦ss❡s ✐♥ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛♥ ✐❝❡❞ ❛✐r❢♦✐❧✳ ❚❤❡s❡♣❡r❢♦r♠❛♥❝❡ ❧♦ss❡s ❛♥❞ t❤❡ r✐s❦s ♦❢ ❧♦s✐♥❣ ❛♥ ❛✐r❝r❛❢t ❛r❡ s♦ ❤✐❣❤ t❤❛t ♦❢t❡♥ ❯❆❱s st❛②❣r♦✉♥❞❡❞ ♦♥❝❡ t❤❡② ♠❛② ❡①♣❡r✐❡♥❝❡ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❛s r❡♣♦rt❡❞ ❜② P❡❝❦ ❡t ❛❧✳ ❬✸❪✳

✷✳✶✳✸ ■❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s

■t ✐s t❤❡ ❣♦❛❧ t♦ ✉s❡ ❛✐r❝r❛❢t ❛❧s♦ ❞✉r✐♥❣ ✇❡❛t❤❡r ❝♦♥❞✐t✐♦♥s t❤❛t ❛r❡ ♥♦t ♣❡r❢❡❝t✳ ❚❤❡r❡✲❢♦r❡ ✐❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ♥❡❡❞ t♦ ❜❡ ✐♥tr♦❞✉❝❡❞ t❤❛t ❛❧❧♦✇ ✢✐❣❤t ✉♥❞❡r ♣♦t❡♥t✐❛❧❧②❞❛♥❣❡r♦✉s ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❛t ❧❡❛st ❢♦r ❛ s❤♦rt t✐♠❡✳■❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ❝❛♥ t②♣✐❝❛❧❧② ❜❡ ❞✐✈✐❞❡❞ ✐♥t♦ t✇♦ ❝❛t❡❣♦r✐❡s✿ ❞❡✲✐❝✐♥❣ ❛♥❞ ❛♥t✐✲

✐❝✐♥❣ s②st❡♠s✳ ❆s ❞❡s❝r✐❜❡❞ ❜② ▲❛✇s♦♥ ❬✶✵❪ ❞❡✲✐❝✐♥❣ ❝♦♥❝❡♣ts s❤❡❞ t❤❡ ✐❝❡ ♦♥❝❡ t❤❡r❡ ✐s♠♦r❡ ✐❝❡ ❛❝❝r❡t✐♦♥ t❤❛♥ ❛ s♣❡❝✐✜❡❞ t❤r❡s❤♦❧❞✳ ❆♥t✐✲✐❝✐♥❣ ❞❡✈✐❝❡s ❛r❡ ❛❝t✐✈❡ ❝♦♥t✐♥✉♦✉s❧②❛♥❞ ♣r❡✈❡♥t t❤❡ ❛❝❝r❡t✐♦♥ ♦❢ ✐❝❡✳ ❚❤❡r❡ ❛r❡ ❛ ❧♦t ♦❢ ❞✐✛❡r❡♥t ♣♦ss✐❜✐❧✐t✐❡s ❛♥❞ t❤✐s t♦♣✐❝✐s ♥♦t ♦❢ ♠✉❝❤ ✐♠♣♦rt❛♥❝❡ ❢♦r t❤✐s ✇♦r❦✳ ❚❤❡r❡❢♦r❡✱ t❤❡ ✇♦r❦s ♦❢ ▲❛✇s♦♥ ❬✶✵❪✱ ❍❛♥♥❛♥❞ ❏♦❤❛♥s❡♥ ❬✻❪ ❛♥❞ ❍❛♥♥ ❡t ❛❧✳ ❬✶✶❪ ❛r❡ r❡❝♦♠♠❡♥❞❡❞ t♦ ❣❡t ❢✉rt❤❡r ✐♥s✐❣❤t ✐♥t♦ ✐❝❡♣r♦t❡❝t✐♦♥ s②st❡♠s✳ ❚❤❡s❡ ❧✐t❡r❛t✉r❡ ❝♦♥t❛✐♥ ❛ ❢✉rt❤❡r ♦✈❡r✈✐❡✇ ♦❢ t❤❡ t❡❝❤♥✐q✉❡s ✉s❡❞❛♥❞ ❤♦✇ t❤❡ ♥❡❝❡ss❛r② ❡♥❡r❣② ✐s ♣r♦✈✐❞❡❞✳

✼

✷ ❇❛❝❦❣r♦✉♥❞

✷✳✷ ❇❛s✐❝s ❛❜♦✉t ✢♦✇ ❞②♥❛♠✐❝s ❛♥❞ ❞r♦♣❧❡t

❜❡❤❛✈✐♦r

❙♦♠❡ ❦♥♦✇❧❡❞❣❡ ✐s ✐♠♣♦rt❛♥t ❢♦r t❤❡ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ t♦♣✐❝ ♦❢ ✐❝✐♥❣ ♦♥ ❯❆❱s✳

✷✳✷✳✶ ❋❧♦✇ ❞②♥❛♠✐❝s

❊✈❡r② t✐♠❡ ❛✐r ♠♦✈❡s r❡❧❛t✐✈❡❧② t♦ ❛ ❜♦❞②✱ ❝❡rt❛✐♥ ✢♦✇ ♣❤❡♥♦♠❡♥❛ ♦❝❝✉r✳ ❚❤❡ r❡❣✐♦♥❝❧♦s❡ t♦ t❤❡ s✉r❢❛❝❡ ✐s ♦❢ s♣❡❝✐❛❧ ✐♥t❡r❡st✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❞✐r❡❝t❧② ❛t t❤❡ s✉r❢❛❝❡✱ t❤❡✈❡❧♦❝✐t② ✐s ③❡r♦✳ ❉✉❡ t♦ ❢r✐❝t✐♦♥✱ t❤❡ s✉rr♦✉♥❞✐♥❣ ✢♦✇ ✐s ❛❧s♦ s❧♦✇❡❞ ❞♦✇♥✳ ❚❤❡r❡❢♦r❡❛ r❡❣✐♦♥ ❞❡✈❡❧♦♣s ✇❤❡r❡ t❤❡ ✈❡❧♦❝✐t② ✐s s♠❛❧❧❡r t❤❛♥ ✐♥ t❤❡ ❢r❡❡ str❡❛♠✳ ❚❤✐s r❡❣✐♦♥ ✐s❝❛❧❧❡❞ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳❆♥ ✐♠♣♦rt❛♥t ♣❛r❛♠❡t❡r t♦ ❝❤❛r❛❝t❡r✐③❡ t❤❡ ✢♦✇ ❜❡❤❛✈✐♦r ✐s t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r

Re =vL

ν✭✷✳✶✮

✇✐t❤ ❛ t②♣✐❝❛❧ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❛✐r v✱ ❛ ❝❤❛r❛❝t❡r✐st✐❝ ❧❡♥❣t❤ L ♦❢ t❤❡ ❜♦❞②✱ ❛♥❞ t❤❡ ❦✐♥❡✲♠❛t✐❝ ✈✐s❝♦s✐t② ν✳ ❚❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ❛♥ ✐♥❞✐❝❛t♦r ♦❢ ✇❤❡t❤❡r ❛ ✢♦✇ ✐s ❧❛♠✐♥❛r ♦rt✉r❜✉❧❡♥t✳ ▲❛♠✐♥❛r ✢♦✇s ❛r❡ ✇❡❧❧ str✉❝t✉r❡❞ ❛♥❞ r❡❣✉❧❛r✳ ❚✉r❜✉❧❡♥t ✢♦✇s ❛r❡ ❝❤❛♦t✐❝✱✉♥st❡❛❞② ❛♥❞ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧✳ ❋♦r ❧♦✇ ❘❡②♥♦❧❞s ♥✉♠❜❡rs✱ t❤❡ ❧❛♠✐♥❛r ✢♦✇ ❡✛❡❝ts❞♦♠✐♥❛t❡✳ ■❢ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ✐♥❝r❡❛s❡❞✱ t❤❡ ✢♦✇ ✇✐❧❧ ❜❡ tr❛♥s✐t✐♦♥❛❧ ❛♥❞ ✜♥❛❧❧②t❤❡ t✉r❜✉❧❡♥t ✢♦✇ ❡✛❡❝ts ✇✐❧❧ ❞♦♠✐♥❛t❡✳ ▲❛♠✐♥❛r ✢♦✇s ♥♦r♠❛❧❧② ❤❛✈❡ ❛ t❤✐♥♥❡r ❜♦✉♥❞✲❛r② ❧❛②❡r t❤❛♥ t✉r❜✉❧❡♥t ✢♦✇s✳ ❍♦✇❡✈❡r✱ t❤❡ ✈❡❧♦❝✐t② ♣r♦✜❧❡ ♦❢ t✉r❜✉❧❡♥t ✢♦✇s ✐s st❡❡♣❡r❛t t❤❡ s✉r❢❛❝❡ t❤❛♥ t❤❡ ✈❡❧♦❝✐t② ♣r♦✜❧❡ ♦❢ ❛ ❧❛♠✐♥❛r ✢♦✇✳ ❆s t❤❡ ✢♦✇ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢❧❛♠✐♥❛r ❛♥❞ t✉r❜✉❧❡♥t ✢♦✇s ❞✐✛❡r str♦♥❣❧②✱ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ♣❧❛②s ❛♥ ✐♠♣♦rt❛♥tr♦❧❡ ✐♥ ✢♦✇ ❡①♣❡r✐♠❡♥ts ❛♥❞ ❝❛❧❝✉❧❛t✐♦♥s✳❆♥♦t❤❡r ❞✐♠❡♥s✐♦♥❧❡ss ❣r♦✉♣ t❤❛t ✐s ♦❢t❡♥ ✉s❡❞ t♦ ❞❡s❝r✐❜❡ ❛ ✢♦✇ ✐s t❤❡ ▼❛❝❤ ♥✉♠❜❡r

M =v

vS=

v√γRT

✭✷✳✷✮

t❤❛t ❞❡s❝r✐❜❡s t❤❡ r❛t✐♦ ♦❢ t❤❡ ❧♦❝❛❧ ❛✐r s♣❡❡❞ v t♦ t❤❡ ❧♦❝❛❧ s♣❡❡❞ ♦❢ s♦✉♥❞ vS✳ ❚❤❡ s♣❡❡❞♦❢ s♦✉♥❞ ✐s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❤❡❛t ❝❛♣❛❝✐t② r❛t✐♦ γ✱ t❤❡ s♣❡❝✐✜❝ ❣❛s ❝♦♥st❛♥t R✱ ❛♥❞t❤❡ ❧♦❝❛❧ t❡♠♣❡r❛t✉r❡ T ✳ ❋♦r M < 0.3✱ ❛ ✢♦✇ ❝❛♥ ❜❡ ❝♦♥s✐❞❡r❡❞ t♦ ❜❡ ✐♥❝♦♠♣r❡ss✐❜❧❡❛s st❛t❡❞ ❜② ❆♥❞❡rs♦♥ ❬✶✷❪✳ ■❢ ❛ ✢♦✇ ✐s ✐♥❝♦♠♣r❡ss✐❜❧❡✱ t❤❡ s✉❜st❛♥t✐❛❧ ❝❤❛♥❣❡ ♦❢ t❤❡❞❡♥s✐t② ✭Dρ/Dt✮ ✐s ③❡r♦✳■❢ ❛ ✢♦✇ ❛r♦✉♥❞ ❛ ❜♦❞② ✐s ♥♦ ❧♦♥❣❡r ❛❜❧❡ t♦ ❢♦❧❧♦✇ t❤❡ ❝♦♥t♦✉r✱ t❤❡ ♣❤❡♥♦♠❡♥♦♥ ✐s

❝❛❧❧❡❞ s❡♣❛r❛t✐♦♥✳ ❙❡♣❛r❛t✐♦♥ ❝❛♥ ❤❛♣♣❡♥ ♦♥❝❡ t❤❡ ♣r❡ss✉r❡ ❞♦✇♥str❡❛♠ ✐s ❤✐❣❤❡r t❤❛♥✉♣str❡❛♠ ❛s ❡①♣❧❛✐♥❡❞ ❜② ❆♥❞❡rs♦♥ ❬✶✷❪✳ ❚❤❡ ✢♦✇ t❤❡♥ ❤❛s t♦ ✜❣❤t ❛❣❛✐♥st t❤✐s s♦✲❝❛❧❧❡❞❛❞✈❡rs❡ ♣r❡ss✉r❡ ❣r❛❞✐❡♥t✳ ❚❤❡ ❛✐r ❝❧♦s❡ t♦ t❤❡ ✇❛❧❧ ❤❛s ❛❧r❡❛❞② ❛ ❧♦✇❡r ✈❡❧♦❝✐t② t❤❛♥ t❤❡❛✐r ♦✉ts✐❞❡ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❆t ❛ ❝❡rt❛✐♥ ♣♦✐♥t✱ t❤❡ ✢♦✇ ♠✐❣❤t st♦♣ ❛♥❞ ❝❤❛♥❣❡ ✐ts❞✐r❡❝t✐♦♥ ❞✉❡ t♦ t❤❡ ❛❞✈❡rs❡ ♣r❡ss✉r❡ ❣r❛❞✐❡♥t✳ ❚❤✐s ✐s ❝❛❧❧❡❞ s❡♣❛r❛t✐♦♥✳ ❆s t❤❡ ✈❡❧♦❝✐t②❝❧♦s❡ t♦ t❤❡ ✇❛❧❧ ✐s ❤✐❣❤❡r ✐♥ t✉r❜✉❧❡♥t ❜♦✉♥❞❛r② ❧❛②❡rs t❤❛♥ ✐♥ ❧❛♠✐♥❛r ♦♥❡s✱ t✉r❜✉❧❡♥t✢♦✇s ❤❛✈❡ ❛ ❤✐❣❤❡r ♠❛r❣✐♥ ❜❡❢♦r❡ t❤❡② s❡♣❛r❛t❡✳ ❙❡♣❛r❛t✐♦♥ ✐♥❝r❡❛s❡s t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s❞r❛st✐❝❛❧❧② ❛♥❞ ✐s t❤❡r❡❢♦r❡ ♥♦r♠❛❧❧② ♥♦t ✇❛♥t❡❞✳ ❚❤❡ ♣♦✐♥t ♦❢ s❡♣❛r❛t✐♦♥ ✐s ❞❡✜♥❡❞ ❛st❤❡ ♣♦s✐t✐♦♥ ✇❤❡r❡ t❤❡ ✇❛❧❧✲♥♦r♠❛❧ ❣r❛❞✐❡♥t ♦❢ t❤❡ ✈❡❧♦❝✐t② ✐s ③❡r♦✳

✽

✷ ❇❛❝❦❣r♦✉♥❞

■❢ ❛✐r ✢♦✇s t❤r♦✉❣❤ ❛ ❞✉❝t✱ t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥

ρvA = const. ✭✷✳✸✮

❞❡s❝r✐❜❡s t❤❡ ❛✈❡r❛❣❡❞ ❛✐r ✈❡❧♦❝✐t② v ❛t ❡✈❡r② ♣♦s✐t✐♦♥ ✐♥ ❞❡♣❡♥❞❡♥❝② ♦❢ t❤❡ ❛✐r ❞❡♥s✐t② ρ❛♥❞ t❤❡ ❛r❡❛ A ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥✳ ❊ss❡♥t✐❛❧❧② t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥ s❛②s t❤❛t ❛❧❧ t❤❡❛✐r t❤❛t ❡♥t❡rs ❛ ❝r♦ss✲s❡❝t✐♦♥ ❛❧s♦ ❤❛s t♦ ❧❡❛✈❡ ✐t✳ ■❢ ❛ ✢♦✇ ✐s ✐♥❝♦♠♣r❡ss✐❜❧❡✱ t❤❡ ❞❡♥s✐t②♠✐❣❤t ❜❡ ❝♦♥s✐❞❡r❡❞ t♦ ❜❡ ❝♦♥st❛♥t ✐♥ t❤❡ ✇❤♦❧❡ ✢♦✇ ❛♥❞ ❝❛♥ t❤❡r❡❢♦r❡ ❜❡ ❡❧✐♠✐♥❛t❡❞❢r♦♠ t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥✳❊q✉❛t✐♦♥s ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ✢♦✇ ♣r♦♣❡rt✐❡s ❢♦r ✢♦✇s t❤r♦✉❣❤ ❞✉❝ts ♦❢t❡♥ r❡q✉✐r❡

t❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ ❞✉❝t✳ ❋♦r ❞✉❝ts ✇✐t❤ ❛ ❝r♦ss✲s❡❝t✐♦♥ t❤❛t ✐s ♥♦t ❝✐r❝✉❧❛r✱ t❤❡ ❤②❞r❛✉❧✐❝❞✐❛♠❡t❡r

dh =4A

P✭✷✳✹✮

❝❛♥ ❜❡ ✉s❡❞ ✐♥st❡❛❞✳ ❚❤❡ ❛r❡❛ A ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ❛♥❞ t❤❡ ❧❡♥❣t❤ P ♦❢ t❤❡ ♣❡r✐♠❡t❡r♦❢ t❤❡ ❞✉❝t ❛r❡ ♥❡❡❞❡❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r✳❚♦ ❤❛✈❡ ❛♥ ✐❞❡❛ ❛❜♦✉t t❤❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❝❡rt❛✐♥ ✢♦✇ s✐t✉❛t✐♦♥s✱ ❡✐t❤❡r ❡①♣❡r✐♠❡♥ts

❝❛♥ ❜❡ ❞♦♥❡ ♦r t❤❡ ❣♦✈❡r♥✐♥❣ ❡q✉❛t✐♦♥s ❝❛♥ ❜❡ s♦❧✈❡❞✳ ❙♦❧✈✐♥❣ t❤❡ ❣♦✈❡r♥✐♥❣ ❡q✉❛t✐♦♥s❛♥❛❧②t✐❝❛❧❧② ✐s ♣♦ss✐❜❧❡ ❢♦r ❢❡✇✱ ♠♦st❧② r❛t❤❡r ❜❛s✐❝ ❝❛s❡s✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❣♦✈❡r♥✲✐♥❣ ❡q✉❛t✐♦♥s ❛r❡ ♥♦♥❧✐♥❡❛r ♣❛rt✐❛❧ ❞✐✛❡r❡♥t✐❛❧ ❡q✉❛t✐♦♥s✳ ❲✐t❤ t❤❡ ✐♠♣r♦✈❡♠❡♥ts ✐♥❝♦♠♣✉t❡r ♣❡r❢♦r♠❛♥❝❡ ♦✈❡r t❤❡ ❧❛st ❞❡❝❛❞❡s✱ ❛ ♥❡✇ ♣♦ss✐❜✐❧✐t② ❛rr✐✈❡❞✱ t❤❡ ✉s❡ ♦❢ ❈♦♠✲♣✉t❛t✐♦♥❛❧ ❋❧✉✐❞ ❉②♥❛♠✐❝s ✭❈❋❉✮✳ ❆s ❈❋❉ ❥✉st ♣❧❛②❡❞ ❛ ♠✐♥♦r r♦❧❡ ✐♥ t❤✐s t❤❡s✐s✱ ❥✉stt❤❡ ❜❛s✐❝s ♦❢ ❈❋❉ s✐♠✉❧❛t✐♦♥s ✇✐❧❧ ❜❡ ❡①♣❧❛✐♥❡❞✳ ❋♦r ❛ ♠♦r❡ t❤♦r♦✉❣❤ ✐♥tr♦❞✉❝t✐♦♥ ✐♥t♦t❤❡ t♦♣✐❝✱ ❱❡rst❡❡❣ ❛♥❞ ▼❛❧❛❧❛s❡❦❡r❛ ❬✶✸❪ ❝❛♥ ❜❡ ❝❤❡❝❦❡❞✳❚❤❡ ✜rst st❡♣ ♦❢ ❛ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✐s t♦ ❞✐✈✐❞❡ t❤❡ ❣❡♦♠❡tr② ♦❢ ✐♥t❡r❡st ✐♥t♦ ♠❛♥②

s♠❛❧❧❡r ❣❡♦♠❡tr✐❡s✳ ❚❤❡ ♣♦✇❡r ♦❢ ❛ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✐s t♦ tr❛♥s❢♦r♠ t❤❡ ❝♦♥s❡r✈❛t✐♦♥❡q✉❛t✐♦♥s ✐♥t♦ ❛❧❣❡❜r❛✐❝ ❡q✉❛t✐♦♥s ❛♥❞ s♦❧✈❡ t❤❡♠ ✇✐t❤ ❛♥ ✐t❡r❛t✐✈❡ ♠❡t❤♦❞ ❢♦r ❡❛❝❤♦❢ t❤❡ s♠❛❧❧ ❣❡♦♠❡tr✐❡s ❛♥❞ ❝♦♠❜✐♥❡ t❤❡ r❡s✉❧ts✳ ▼❛♥② ❞✐✛❡r❡♥t ✐t❡r❛t✐✈❡ s♦❧✈❡rs ❛♥❞♠♦❞❡❧s t♦ ❞❡❝r❡❛s❡ t❤❡ ❝♦♠♣❧❡①✐t② ♦❢ t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ❝❛♥ ❜❡ ✉s❡❞✳ ❆s t❤❡ ❝♦♠♣✉t❛t✐♦♥❛❧❣r✐❞ ♥❡❡❞s t♦ ❜❡ ✈❡r② ✜♥❡ t♦ ❝❛❧❝✉❧❛t❡ t✉r❜✉❧❡♥❝❡ ✇✐t❤♦✉t ❛ ♠♦❞❡❧✱ t❤❡ s✐♠✉❧❛t✐♦♥s ✇♦✉❧❞♥❡❡❞ ♠✉❝❤ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣♦✇❡r ❛♥❞ t✐♠❡✳ ❚❤❡r❡❢♦r❡ t✉r❜✉❧❡♥❝❡ ✐s ♥♦r♠❛❧❧② ♠♦❞❡❧❡❞✳❚♦ ♠♦❞❡❧ t✉r❜✉❧❡♥❝❡✱ ♠❛♥② ❞✐✛❡r❡♥t ♠❡t❤♦❞s ❛r❡ ❦♥♦✇♥✱ s❡❡ ❱❡rst❡❡❣ ❛♥❞ ▼❛❧❛❧❛s❡❦❡r❛❬✶✸❪✳

✷✳✷✳✷ ❉r♦♣❧❡ts

■❢ ❛ ✢♦✇ ❝♦♥t❛✐♥s ❞r♦♣❧❡ts✱ ❜♦t❤ t❤❡ ✢♦✇ ❛♥❞ t❤❡ ❞r♦♣❧❡ts ✇✐❧❧ ✐♥✢✉❡♥❝❡ ❡❛❝❤ ♦t❤❡r✳ ❚❤❡✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ✢♦✇ ♦♥ t❤❡ ❞r♦♣❧❡ts✬ ♣❛t❤ ❝❛♥ ❜❡ ❢♦r♠✉❧❛t❡❞ ✇✐t❤ ◆❡✇t♦♥✬s s❡❝♦♥❞ ❧❛✇

F = ma ✭✷✳✺✮

t❤❛t ❡①♣❧❛✐♥s t❤❛t t❤❡ ❛❝❝❡❧❡r❛t✐♦♥ a ♦❢ ❛ ❜♦❞② ❞❡♣❡♥❞s ♦♥ t❤❡ ❞r✐✈✐♥❣ ❢♦r❝❡ F ❛♥❞ t❤❡♠❛ss m ♦❢ t❤❡ ❜♦❞②✳❚❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❞r♦♣❧❡ts ✐s ✐♥✢✉❡♥❝❡❞ ❜② t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❛✐r ✢♦✇✳ ❚♦

❝❛❧❝✉❧❛t❡ t❤❡ ❝❤❛♥❣❡ ♦❢ t❡♠♣❡r❛t✉r❡ ♦❢ ❛ ❞r♦♣❧❡t ❞✉❡ t♦ t❤❡ ❛✐r✱ ❛ ❤❡❛t ❜❛❧❛♥❝❡ ❝❛♥ ❜❡❞♦♥❡ ❛s ❡①♣❧❛✐♥❡❞ ❜② ●❛t❡s ❡t ❛❧✳ ❬✶✹❪✳ ❍♦✇❡✈❡r✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❝❛s❡✱ ❞✐✛❡r❡♥t ❤❡❛tt❡r♠s ❛r❡ r❡❧❡✈❛♥t✳ ❚❤❡ r❡❧❡✈❛♥t ❤❡❛t t❡r♠s ✇✐❧❧ ❜❡ ❞✐s❝✉ss❡❞ ✐♥ s❡❝t✐♦♥ ✸✳✸✳✷✳

✾

✷ ❇❛❝❦❣r♦✉♥❞

✷✳✸ ❯♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s

❙✉♠♠❛r✐③❡❞ ✉♥❞❡r t❤❡ t❡r♠ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡ ✭❯❆❱✮ ❛r❡ ❛❧❧ ❦✐♥❞s ♦❢ ❛✐r❝r❛❢t t❤❛t❛r❡ ❛❜❧❡ t♦ ✢② ✇✐t❤♦✉t ❛ ♣✐❧♦t ♦♥ ❜♦❛r❞✳ ❚❤❡ ✈❡❤✐❝❧❡ ♠✐❣❤t ❜❡ ♣✐❧♦t❡❞ ❢r♦♠ ❛ ❣r♦✉♥❞st❛t✐♦♥✱ ♥❛✈✐❣❛t❡ ❛❝❝♦r❞✐♥❣ t♦ ❛ ♣r♦❣r❛♠♠❡❞ r♦✉t❡ ♦r ❜❡ ❛❜❧❡ t♦ ❛✉t♦♥♦♠♦✉s❧② ❛❞❛♣t✐ts ❝♦✉rs❡✳

✷✳✸✳✶ ❯❆❱ ❞❛t❛❜❛s❡

❚❤❡r❡ ✐s ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ❞✐✛❡r❡♥t s✐③❡s ❛♥❞ t②♣❡s ♦❢ ❯❆❱s✳ ❚♦ ❣❡t ❛ ✜rst ✐♠♣r❡ss✐♦♥❛❜♦✉t t❤❡ ✇✐❞❡ ✈❛r✐❡t② ♦❢ ❯❆❱s✱ ❛ ❞❛t❛❜❛s❡ ✇❛s ❝r❡❛t❡❞✳ ❚♦ ❞♦ s♦✱ ✐♥❢♦r♠❛t✐♦♥ ❢♦r ✾✸❞✐✛❡r❡♥t ❯❆❱s t❤❛t ❛r❡ ✉s❡❞ t♦❞❛②✱ ✇❡r❡ ✉s❡❞ ❞✉r✐♥❣ t❤❡ ❧❛st ❞❡❝❛❞❡s✱ ♦r ❛r❡ ✐♥ t❤❡✜♥❛❧ st❛❣❡ ♦❢ ♣r♦❞✉❝t✐♦♥ ✇❛s ❝♦❧❧❡❝t❡❞✳ ❚❤❡ ✐♥❢♦r♠❛t✐♦♥ ✇❛s ❢♦✉♥❞ ♦♥ t❤❡ ❤♦♠❡♣❛❣❡s ♦❢t❤❡ ♠❛♥✉❢❛❝t✉r❡rs ♦r t❤❡ ❯❙ ♠✐❧✐t❛r②✱ ❜✉t ❛❧s♦ ✐♥ s❝✐❡♥t✐✜❝ ♣❛♣❡rs✱ ♥❡✇s♣❛♣❡r ❛rt✐❝❧❡s✱❛♥❞ ♦♥❧✐♥❡ ❛rt✐❝❧❡s✳ ❚❤❡ ❞❛t❛❜❛s❡ ❝♦♥t❛✐♥s ♠❛✐♥ ✐♥❢♦r♠❛t✐♦♥ ❧✐❦❡ t❤❡ ✇✐♥❣s♣❛♥✱ t❤❡♠❛①✐♠✉♠ t❛❦❡✲♦✛✲✇❡✐❣❤t ♦r t❤❡ ❝r✉✐s❡ s♣❡❡❞ ♦❢ ❯❆❱s✱ ❜✉t ❛❧s♦ ❝❤♦r❞ ❧❡♥❣t❤s ❛♥❞ t❤❡❛✐r❢♦✐❧ ♣r♦✜❧❡ ✇❤❡r❡ ❛✈❛✐❧❛❜❧❡✳ ❚❤❡ ❞❛t❛❜❛s❡ ✐s ♣r✐♥t❡❞ ✐♥ ❆♣♣❡♥❞✐① ❆✳✶ ✐♥ ❛ s❤♦rt ❢♦r♠✇✐t❤ ❥✉st t❤❡ ♠♦st ✐♠♣♦rt❛♥t ♣❛r❛♠❡t❡rs✳ ❚❤❡ ❝♦♠♣❧❡t❡ ❢♦r♠ ♦❢ t❤❡ ❞❛t❛❜❛s❡ ✇✐t❤ ❛❧❧♣❛r❛♠❡t❡rs ❝❛♥ ❜❡ ❢♦✉♥❞ ♦♥ t❤❡ ❡♥❝❧♦s❡❞ ❈❉✳

✷✳✸✳✷ ❉❡s✐❣♥ ❛♥❞ ♠✐ss✐♦♥s ♦❢ ❯❆❱s

❲❤✐❧❡ t❤❡ s♠❛❧❧❡st ❯❆❱s ❤❛✈❡ ❞✐♠❡♥s✐♦♥s ♦❢ ❥✉st ❛ ❢❡✇ ❝❡♥t✐♠❡t❡rs ❛♥❞ ✇❡✐❣❤ ♠✉❝❤❧❡ss t❤❛♥ ❛ ❦✐❧♦❣r❛♠✱ ❧❛r❣❡ ❯❆❱s ❤❛✈❡ ♣r♦♣♦rt✐♦♥s ❝♦♠♣❛r❛❜❧❡ t♦ ❛ s♠❛❧❧ ❛✐r❧✐♥❡r ❧✐❦❡t❤❡ ❆✐r❜✉s ❆✸✷✵ ♦r t❤❡ ❇♦❡✐♥❣ ✼✸✼✳ ❚❤❡ t②♣❡ ♦❢ t❤❡ ❛✐r❝r❛❢t ❞❡♣❡♥❞s ♦♥ t❤❡ s✐③❡ ❛♥❞❡s♣❡❝✐❛❧❧② t❤❡ ♠✐ss✐♦♥✳ ❚✇♦ ❞✐✛❡r❡♥t t❡❝❤♥✐q✉❡s ❛r❡ r❡❣✉❧❛r❧② ✉s❡❞ t♦ ❣❡♥❡r❛t❡ ❧✐❢t✳ ❚❤❡✜rst ♦♥❡ ✐s ❛ ✜①❡❞✲✇✐♥❣ ❝♦♥✜❣✉r❛t✐♦♥✳ ❆s ✐t ✐s t❤❡ ❝❛s❡ ❢♦r ♥♦r♠❛❧ ❛✐r❧✐♥❡rs✱ t❤❡ ✇✐♥❣✐s ✜①❡❞ ❛♥❞ r✐❣✐❞ ❛♥❞ t❤❡ ❛✐r❝r❛❢t ♥❡❡❞s t♦ ❤❛✈❡ ❛♥ ❛❞❞✐t✐♦♥❛❧ s♦✉r❝❡ ♦❢ t❤r✉st✳ ❆♥❡①❛♠♣❧❡ ❢♦r ❛ ✜①❡❞✲✇✐♥❣ ❯❆❱ ✐s t❤❡ P❳✲✸✶ ❜② ▼❛r✐t✐♠❡ ❘♦❜♦t✐❝s t❤❛t ✐s s❤♦✇♥ ✐♥❋✐❣✉r❡ ✷✳✺✭❛✮✳ ❚❤❡ ❣♦❛❧ ❢♦r ♠❛♥② ❯❆❱ ♠✐ss✐♦♥s ✐s t♦ st❛② ✐♥ t❤❡ ❛✐r ❢♦r ♠❛♥② ❤♦✉rs✳●♦♦❞ ❛❡r♦❞②♥❛♠✐❝s ✐s ✐♠♣♦rt❛♥t t♦ ❢✉❧✜❧❧ t❤✐s r❡q✉✐r❡♠❡♥t✳ ❚❤❡r❡❢♦r❡ t❤❡ ✇✐♥❣ ❞❡s✐❣♥✐s ✈❡r② ✐♠♣♦rt❛♥t✳ ❚❤❡ ♣❛r❛♠❡t❡rs t❤❛t t②♣✐❝❛❧❧② ❞❡♥♦t❡ ❛ ✇✐♥❣ ❛r❡ t❤❡ ✇✐♥❣s♣❛♥✱ t❤❡❝❤♦r❞ ❧❡♥❣t❤✱ ❛♥❞ t❤❡ ❛s♣❡❝t r❛t✐♦✳ ❚❤❡ ❛s♣❡❝t r❛t✐♦ ✐s t❤❡ r❛t✐♦ ♦❢ t❤❡ ✇✐♥❣s♣❛♥ t♦ t❤❡♠❡❛♥ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ t❤❡ ✇✐♥❣✳❆s ❛♥ ❛❧t❡r♥❛t✐✈❡ t♦ ✜①❡❞ ✇✐♥❣s✱ r♦t❛r② ✇✐♥❣s ❝❛♥ ❜❡ ✐♥st❛❧❧❡❞✱ ❛s ✉s❡❞ ❢♦r ♠❛♥♥❡❞

❤❡❧✐❝♦♣t❡rs ❢♦r ❡①❛♠♣❧❡✳ ❲❤✐❧❡ ❛ ❤❡❧✐❝♦♣t❡r ✉s✉❛❧❧② ❥✉st ❤❛s ♦♥❡ r♦t♦r✱ ❯❆❱s ♠✐❣❤t ❤❛✈❡♠✉❧t✐♣❧❡ r♦t♦rs✳ ❯❆❱s ✇✐t❤ ♠✉❧t✐♣❧❡ r♦t♦rs ❛r❡ ♦❢t❡♥ ❛❧s♦ ❝❛❧❧❡❞ ♠✉❧t✐❝♦♣t❡rs✳ ❚❤❡ ❆❣r❛s❚✶✻ ❜② ❉❏■ ✐s ❛♥ ❡①❛♠♣❧❡ ♦❢ r♦t❛r② ✇✐♥❣ ❯❆❱s ❛♥❞ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✷✳✺✭❜✮✳❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞✱ t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ❯❆❱ ❞❡♣❡♥❞s t♦ ❛ ❤✐❣❤ ❞❡❣r❡❡ ♦♥ t❤❡ ♠✐ss✐♦♥s

✐t s❤❛❧❧ ❜❡ ❛❜❧❡ t♦ ❡①❡❝✉t❡✳ ❱❡r② s♠❛❧❧ ❯❆❱s ❛r❡ ✉s✉❛❧❧② ♦❢ t❤❡ r♦t❛r②✲✇✐♥❣ t②♣❡ ❛s ❛✜①❡❞ ✇✐♥❣ ✇♦✉❧❞ ❜❡ ♠✉❝❤ ✇✐❞❡r t♦ ♣r♦❞✉❝❡ t❤❡ s❛♠❡ ❧✐❢t ❛s t❤❡ r♦t♦rs✳ ❋♦r ❧❛r❣❡r❯❆❱s ❤♦✇❡✈❡r✱ t❤❡ ✜①❡❞✲✇✐♥❣ t②♣❡ ✐s ♠✉❝❤ ♠♦r❡ ❝♦♠♠♦♥✳ ■♥ ❤✐st♦r②✱ ♠♦st ♦❢ t❤❡♠✐ss✐♦♥s ❤❛✈❡ ❜❡❡♥ ♠✐❧✐t❛r②✱ ❢♦r ❡①❛♠♣❧❡ t♦ tr❛♥s♣♦rt ❛♥❞ s❤♦♦t ♠✐ss✐❧❡s ♦r ❢♦r t❤❡♣✉r♣♦s❡ ♦❢ s✉r✈❡✐❧❧❛♥❝❡✳ ❇✉t ✇✐t❤ ❜❡tt❡r ❦♥♦✇❧❡❞❣❡ ♦❢ ❯❆❱s ❛♥❞ t❤❡r❡❢♦r❡ ❝❤❡❛♣❡rs♦❧✉t✐♦♥s✱ ❛❧s♦ ❣♦✈❡r♥♠❡♥ts✱ ❝✐✈✐❧ ❛♥❞ ❝✉st♦♠❡r ❛♣♣❧✐❝❛t✐♦♥s ♣❧❛② ❛♥ ✐♥❝r❡❛s✐♥❣ r♦❧❡✳

✶✵

✷ ❇❛❝❦❣r♦✉♥❞

✭❛✮ ❚❤❡ P❳✲✸✶ ❜② ▼❛r✐t✐♠❡ ❘♦❜♦t✐❝s ✐s ❛♥❡①❛♠♣❧❡ ♦❢ ❛ ✜①❡❞✲✇✐♥❣ ❯❆❱✳ ❆❞❛♣t❡❞ ❢r♦♠▼❛r✐t✐♠❡ ❘♦❜♦t✐❝s ❬✶✺❪✳

✭❜✮ ❚❤❡ ❆❣r❛s ❚✶✻ ✐s ❛♥ ❡①❛♠♣❧❡ ♦❢ ❛ r♦t❛r②✲✇✐♥❣ ❯❆❱✳ ❆❞❛♣t❡❞ ❢r♦♠ ❉❏■ ❬✶✻❪✳

❋✐❣✉r❡ ✷✳✺✿ ❊①❛♠♣❧❡s ❢♦r t❤❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ ❯❆❱s

P♦ss✐❜❧❡ ❛r❡❛s ♦❢ ✉s❛❣❡ ❛r❡ s✉r✈❡✐❧❧❛♥❝❡✱ s❡❛r❝❤ ❛♥❞ r❡s❝✉❡✱ ❛t♠♦s♣❤❡r✐❝ ♠♦♥✐t♦r✐♥❣✱❝❛r❣♦✱ ♦r ❛s ❝♦♠♠✉♥✐❝❛t✐♦♥s r❡❧❛② ❛s s✉♠♠❛r✐③❡❞ ❜② ❉❡●❛r♠♦ ❬✶✼❪✳ ❚❤❡s❡ ♠✐ss✐♦♥s❧❡❛❞ t♦ ❛ ✇✐❞❡r r❛♥❣❡ ♦❢ ❯❆❱ ❞❡s✐❣♥s ❛♥❞ ❛r❡❛s ♦❢ ✉s❡✳ ❍♦✇❡✈❡r✱ t❤❡ ♠♦st ♠✐ss✐♦♥s ❛r❡st✐❧❧ ❡♥❞✉r❛♥❝❡✲❞r✐✈❡♥✳ ❚❤✐s ♠❡❛♥s t❤❛t t❤❡ ♣✉r♣♦s❡ ♦❢ t❤❡ ❯❆❱ ✐s t♦ st❛② ✐♥ t❤❡ ❛✐r ❢♦r❛ ✈❡r② ❧♦♥❣ t✐♠❡✳ ❋✉rt❤❡r ❛♣♣❧✐❝❛t✐♦♥s ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❉❡●❛r♠♦ ❬✶✼❪✳ ❲❤✐❧❡ ✐♥ t❤❡ ♣❛st✱❯❆❱s ✇❡r❡ ✉s❡❞ ♠♦st ♦❢ t❤❡ t✐♠❡ ✐♥ r❛t❤❡r ✇❛r♠ ❛r❡❛s✱ ❛ ❧♦t ♦❢ t❤❡ st❛t❡❞ ❛♣♣❧✐❝❛t✐♦♥s❤❛✈❡ ❣r❡❛t ✈❛❧✉❡ ❛❧❧ ♦✈❡r t❤❡ ✇♦r❧❞✳

✷✳✸✳✸ ❉✐✛❡r❡♥❝❡s t♦ ♥♦r♠❛❧ ❛✐r❝r❛❢t

❆❧t❤♦✉❣❤ ❯❆❱s ❡①✐st ✐♥ ❛ ❤✉❣❡ r❛♥❣❡ ♦❢ s✐③❡s✱ ♠♦st ❯❆❱s ❛r❡ ♠✉❝❤ s♠❛❧❧❡r t❤❛♥ t②♣✐❝❛❧♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❇✉t ♥♦t ❥✉st t❤❡ s✐③❡ ✐s ❞✐✛❡r❡♥t ❢♦r ♠❛♥♥❡❞ ❛♥❞ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t✳❇❡❝❛✉s❡ ♦❢ t❤❡✐r s✐③❡✱ t❤❡✐r ❞✐✛❡r❡♥t ♠✐ss✐♦♥ ♣r♦✜❧❡s ❛♥❞ t❤❡ ❧❛❝❦ ♦❢ ❛ ♣✐❧♦t ♦♥✲❜♦❛r❞✱❯❆❱s ❤❛✈❡ ❛ ❧♦t ♦❢ ❞✐✛❡r❡♥t ♣❛r❛♠❡t❡rs ❝♦♠♣❛r❡❞ t♦ ♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛s ♣r❡s❡♥t❡❞ ❜②❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥ ❬✻❪✳ ■♥ t❤✐s s✉❜s❡❝t✐♦♥✱ t②♣✐❝❛❧ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❯❆❱s ✇✐t❤ ❛✇✐♥❣s♣❛♥ ♦❢ ❛ ❢❡✇ ♠❡t❡rs ❛♥❞ t②♣✐❝❛❧ ♠❛♥♥❡❞ ❛✐r❝r❛❢t ✇✐❧❧ ❜❡ ✇♦r❦❡❞ ♦✉t✳ ❚❤✐s ✐s✐♠♣♦rt❛♥t ❜❡❝❛✉s❡ ♦❢ t✇♦ r❡❛s♦♥s✳ ❋✐rst✱ t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❯❆❱s ❛♥❞ ♠❛♥♥❡❞❛✐r❝r❛❢t ❧❡❛❞ t♦ ❞✐✛❡r❡♥❝❡s ✐♥ t❤❡ ✇❛② t❤❡ ✐❝❡ ❛❝❝✉♠✉❧❛t❡s ♦♥ ❡❛❝❤ ❛✐r❝r❛❢t✳ ❙❡❝♦♥❞✱ t❤❡❡✛❡❝ts t❤❛t t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥ ❤❛s ♦♥ t❤❡ ❛✐r❝r❛❢t ❛r❡ ❞✐✛❡r❡♥t ❢♦r ♠❛♥♥❡❞ ❛♥❞ ✉♥♠❛♥♥❡❞❛✐r❝r❛❢t ❜❡❝❛✉s❡ ♦❢ t❤❡✐r ❞✐✛❡r❡♥t ❝❤❛r❛❝t❡r✐st✐❝s ❛s ✇❛s ❡①♣❧❛✐♥❡❞ ❜② ❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥❬✻❪✳●❡♥t ❡t ❛❧✳ ❬✶✽❪ s❤♦✇❡❞ t❤❛t s♠❛❧❧❡r ❛✐r❝r❛❢t ♥♦r♠❛❧❧② ❡①♣❡r✐❡♥❝❡ ❤✐❣❤❡r ❞r♦♣❧❡t ✐♠✲

♣✐♥❣❡♠❡♥t r❛t❡s✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❞r♦♣❧❡t tr❛❥❡❝t♦r② ✐s ❝❤❛♥❣❡❞ str♦♥❣❡r ❜② ❧❛r❣❡♦❜❥❡❝ts✳ ❆s ❯❆❱s ♥♦r♠❛❧❧② ❤❛✈❡ s♠❛❧❧❡r ❧❡❛❞✐♥❣ ❡❞❣❡ ❞✐❛♠❡t❡rs t❤❛♥ ♠❛♥♥❡❞ ❛✐r❝r❛❢t✱t❤❡ ❞r♦♣❧❡t tr❛❥❡❝t♦r✐❡s ❛r❡ ❝❤❛♥❣❡❞ ❧❡ss ❢♦r ❯❆❱s t❤❛♥ ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❚❤❡r❡❢♦r❡♠♦r❡ ❞r♦♣❧❡ts ❤✐t ❛ ❯❆❱ t❤❛♥ ❛ ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ t②♣✐❝❛❧❧② s♠❛❧❧❡r❝❤♦r❞ ❧❡♥❣t❤s ♦❢ ❯❆❱s ❧❡❛❞ t♦ t❤❡ ♣❤❡♥♦♠❡♥♦♥ t❤❛t t❤❡ ✐❝❡ ❛❝❝r❡t❡s ♦✈❡r ❛ ❧❛r❣❡r ♣❛rt♦❢ t❤❡ ❛✐r❢♦✐❧ t❤❛♥ ✐t ✐s t❤❡ ❝❛s❡ ❢♦r ❧❛r❣❡r ❛✐r❝r❛❢t✳ ❇❡❝❛✉s❡ ❛ ❧❛r❣❡r ♣❛rt ♦❢ t❤❡ ❛✐r❝r❛❢t✐s ❝♦✈❡r❡❞ ✇✐t❤ ✐❝❡ ❢♦r s♠❛❧❧❡r ❛✐r❝r❛❢t t❤❛♥ ❢♦r ❜✐❣❣❡r ♦♥❡s✱ ❛❧s♦ t❤❡ ✇❡✐❣❤t ♦❢ t❤❡ ✐❝❡

✶✶

✷ ❇❛❝❦❣r♦✉♥❞

❛❝❝r❡t✐♦♥ ❝♦♠♣❛r❡❞ t♦ t❤❡ ✇❡✐❣❤t ♦❢ t❤❡ ❛✐r❝r❛❢t ✐s ♦❢t❡♥ ❤✐❣❤❡r ❢♦r s♠❛❧❧❡r ❛✐r❝r❛❢t✳▼❛♥♥❡❞ ❛✐r❝r❛❢t t②♣✐❝❛❧❧② tr❛✈❡❧ ❛t ♠✉❝❤ ❤✐❣❤❡r ✈❡❧♦❝✐t✐❡s t❤❛♥ ✉♥♠❛♥♥❡❞ ❛✐r❝r❛❢t✳

❚❤✐s ✐s ❜❡❝❛✉s❡ ♠❛♥② ❯❆❱ ♠✐ss✐♦♥s ❛r❡ ❡♥❞✉r❛♥❝❡ ❞r✐✈❡♥ ❛♥❞ t❤❡ ❡♥❞✉r❛♥❝❡ ✐♥❝r❡❛s❡s✇✐t❤ ❧♦✇❡r s♣❡❡❞s✳ ❚❤✐s ❤❛s ♠✉❧t✐♣❧❡ ❡✛❡❝ts✳ ❋✐rst✱ ❤✐❣❤❡r s♣❡❡❞s ❧❡❛❞ t♦ ❤✐❣❤❡r ❛❡r♦❞②✲♥❛♠✐❝ ❤❡❛t✐♥❣✳ ❆❡r♦❞②♥❛♠✐❝ ❤❡❛t✐♥❣ ✐s t❤❡ ❡✛❡❝t ♦❢ t❤❡ ❤❡❛t✐♥❣ ♦❢ ❛ s✉r❢❛❝❡ ❞✉❡ t♦ ❛ ✢♦✇❜❡✐♥❣ ❞❡❝❡❧❡r❛t❡❞ ❝❧♦s❡ t♦ ✐t✳ ❆❝❝♦r❞✐♥❣ t♦ ❆♥❞❡rs♦♥ ❬✶✷❪✱ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ❤❡❛t✐♥❣ r❛t❡✈❛r✐❡s ✇✐t❤ t❤❡ ❝✉❜❡ ♦❢ t❤❡ ✈❡❧♦❝✐t②✳ ❚❤❡ ✈❡❧♦❝✐t② ♦❢ ♠❛♥♥❡❞ ❛✐r❝r❛❢t ✐s t❤❡r❡❢♦r❡ ♦❢t❡♥❤✐❣❤ ❡♥♦✉❣❤ t♦ ♣r❡✈❡♥t ✐❝✐♥❣ ✐❢ t❤❡ ❛✐r t❡♠♣❡r❛t✉r❡ ✐s ♥♦t t♦♦ ❧♦✇✳ ❉✉❡ t♦ t❤❡ ❧♦✇❡r s♣❡❡❞♦❢ ♠♦st ❯❆❱s✱ ❛❡r♦❞②♥❛♠✐❝ ❤❡❛t✐♥❣ ❤♦✇❡✈❡r ✐s t②♣✐❝❛❧❧② ♥❡❣❧✐❣✐❜❧❡ ❢♦r ❯❆❱s✳ ❆ s❡❝♦♥❞❡✛❡❝t ♦❢ ❧♦✇❡r s♣❡❡❞s ✐s t❤❛t t❤❡ ❛✐r❝r❛❢t ✢✐❡s t❤r♦✉❣❤ ❛ s♠❛❧❧❡r ❛♠♦✉♥t ♦❢ ❛✐r ❛t t❤❡ s❛♠❡t✐♠❡ s♣❛♥ ❛♥❞ t❤❡r❡❢♦r❡ t②♣✐❝❛❧❧② ❛❝❝✉♠✉❧❛t❡s ❛ s♠❛❧❧❡r ❛♠♦✉♥t ♦❢ ✇❛t❡r ❛t t❤❡ s❛♠❡t✐♠❡✳ ❍♦✇❡✈❡r✱ ❜❡❝❛✉s❡ ♦❢ t❤❡ ❧♦✇❡r ✈❡❧♦❝✐t✐❡s ❛❧s♦ t❤❡ t✐♠❡ ❛♥ ❛✐r❝r❛❢t s♣❡♥❞s ✐♥s✐❞❡✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ♥♦r♠❛❧❧② ✐♥❝r❡❛s❡s ❛♥❞ t❤❡r❡❢♦r❡ ❝♦✉♥t❡r❜❛❧❛♥❝❡s t❤✐s s❡❝♦♥❞ ❡✛❡❝t✳❆s ❜♦t❤ t❤❡ s✐③❡ ❛♥❞ t❤❡ s♣❡❡❞ ♦❢ ❯❆❱s ✐s t②♣✐❝❛❧❧② ❧♦✇❡r t❤❛♥ t❤❡ ✈❛❧✉❡s ♦❢ ♠❛♥♥❡❞

❛✐r❝r❛❢t✱ ❛❧s♦ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ❧♦✇❡r ❢♦r t❤❡ ✢✐❣❤ts ♦❢ ❯❆❱s✳ ❙✐♠✉❧❛t✐♦♥s ❜② ❙③✐❧❞❡r❛♥❞ ▼❝■❧✇❛✐♥ ❬✹❪ s❤♦✇❡❞ t❤❛t ❞❡❝r❡❛s✐♥❣ ❘❡②♥♦❧❞s ♥✉♠❜❡rs ❧❡❛❞ t♦ ❛ s♠❛❧❧❡r ♠❛ss ♦❢ ✐❝❡t❤❛t ❛❝❝r❡t❡s ♦♥ ❛ ❜♦❞②✳ ❍♦✇❡✈❡r✱ t❤❡ s✐③❡ ♦❢ t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥s ❝♦♠♣❛r❡❞ t♦ t❤❡ s✐③❡ ♦❢ t❤❡❛✐r❝r❛❢t ✐s ❜✐❣❣❡r ❢♦r ❧♦✇❡r ❘❡②♥♦❧❞s ♥✉♠❜❡r✳ ❚❤❡r❡❢♦r❡ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ♣❡r❢♦r♠❛♥❝❡s✉✛❡rs ♠♦r❡ ❢♦r ❛✐r❝r❛❢t ✇✐t❤ ❧♦✇❡r ❘❡②♥♦❧❞s ♥✉♠❜❡rs✳ ❚❤✐s ✇❛s ❛❧s♦ r❡s❡❛r❝❤❡❞ ❜②❍❛♥♥ ❬✺❪ ❛♥❞ ❍❛♥♥ ❛♥❞ ❏♦❤❛♥s❡♥ ❬✶✾❪✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❧♦✇❡r ❘❡②♥♦❧❞s ♥✉♠❜❡rs ❧❡❛❞t♦ ❧♦♥❣❡r ❧❛♠✐♥❛r ♣❛rts ♦❢ t❤❡ ✢♦✇ ♦✈❡r t❤❡ ❛✐r❢♦✐❧✳ ❆s ❡①♣❧❛✐♥❡❞✱ ❧❛♠✐♥❛r ✢♦✇s ❛r❡♠♦r❡ ♣r♦♥❡ t♦ s❡♣❛r❛t❡✳ ❆s ♦♥❡ ♦❢ t❤❡ ❡✛❡❝ts ♦❢ t❤❡ ✐❝❡ s❤❛♣❡s ♥♦r♠❛❧❧② ✐s t♦ ❡♥❝♦✉r❛❣❡s❡♣❛r❛t✐♦♥✱ ❧❛♠✐♥❛r ✢♦✇s ❛r❡ ❡✈❡♥ ✇♦rs❡ ❢♦r t❤❡s❡ ✐❝❡ s❤❛♣❡s✳❚❤❡ ❛❧t✐t✉❞❡ ♦❢ ❯❆❱s ❝❛♥ ✈❛r② ❛ ❧♦t✳ ❲❤✐❧❡ s♦♠❡ ❯❆❱s ♦♣❡r❛t❡ ❥✉st ❛ ❢❡✇ ♠❡t❡rs ❛❜♦✈❡

t❤❡ ❣r♦✉♥❞✱ ♦t❤❡rs ✢② ♠✉❝❤ ❤✐❣❤❡r t❤❛♥ t②♣✐❝❛❧ ❛✐r❧✐♥❡rs✳ ❚❤❡r❡❢♦r❡✱ ✜♥❞✐♥❣ ❛ t②♣✐❝❛❧❛❧t✐t✉❞❡ ✐s ❛❧♠♦st ✐♠♣♦ss✐❜❧❡✳ ❍♦✇❡✈❡r✱ ●❡♥t ❡t ❛❧✳ ❬✶✽❪ st❛t❡ t❤❛t ❛ ❤❡✐❣❤t ♦❢ ❛❜♦✉t3000 ft t♦ 5000 ft ✭900m t♦ 1500m✮ ✐s t❤❡ ♠♦st ❞❛♥❣❡r♦✉s ❝♦♥❝❡r♥✐♥❣ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s✳❚❤❡ t②♣✐❝❛❧ ❝r✉✐s❡ ❛❧t✐t✉❞❡ ♦❢ ❛✐r❧✐♥❡rs ♦❢ ❛❜♦✉t 30,000 ft t♦ 40,000 ft ✭9000m t♦ 12,000m✮✐s ❧❡ss s❡✈❡r❡ ❢♦r ✐❝✐♥❣✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ t❡♠♣❡r❛t✉r❡s ✐♥ t❤❡s❡ ❤❡✐❣❤ts ❛r❡ ♠✉❝❤ ❧♦✇❡r✳❚❤❡r❡❢♦r❡✱ ❢❡✇❡r s✉♣❡r❝♦♦❧❡❞ ❞r♦♣❧❡ts ❛r❡ ✐♥ t❤❡ ❛✐r✱ ❜✉t ♠♦r❡ ✐❝❡ ❝r②st❛❧s✳ ❚❤❡s❡ ✐❝❡❝r②st❛❧s ❧❡❛❞ t♦ ♦t❤❡r ♣r♦❜❧❡♠s ❢♦r ❛✐r❝r❛❢t ❜✉t ❛r❡ ♥♦t r❡✈✐❡✇❡❞ ✐♥ t❤✐s ✇♦r❦✳ ❍❡♥❝❡✱❛✐r❝r❛❢t ❛t ❧♦✇❡r ❛❧t✐t✉❞❡s ❛r❡ ♠♦r❡ ♣r♦♥❡ t♦ s❡❡ ♣r♦❜❧❡♠s ✇✐t❤ ✐❝✐♥❣✳❆♥♦t❤❡r ♣♦✐♥t t❤❛t ❛rr✐✈❡s ✇✐t❤ t❤❡ ✢✐❣❤t ✇✐t❤♦✉t ❛ ♣✐❧♦t ♦♥ ❜♦❛r❞ ✐s t❤❛t t❤❡ ✐❝✐♥❣

s✐t✉❛t✐♦♥ ♠✉st ❜❡ r❡❝♦❣♥✐③❡❞ ❜② s❡♥s♦rs✳ ❊s♣❡❝✐❛❧❧② ✐❢ t❤❡ ❯❆❱ ✐s ✢②✐♥❣ ❝♦♠♣❧❡t❡❧②❛✉t♦♠❛t✐❝❛❧❧②✱ t❤❡ ❛✐r❝r❛❢t ♠✉st ❜❡ ❛❜❧❡ t♦ r❡❝♦❣♥✐③❡ ❛✉t♦♥♦♠♦✉s❧② t❤❡ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s❛♥❞ ✜♥❞ t❤❡ ❝♦rr❡❝t s♦❧✉t✐♦♥ ♦♥ ✐ts ♦✇♥✳ ❆s ✐❝❡ ❝❛♥ ❛❧s♦ ❛❝❝r❡t❡ ♦♥ s❡♥s♦rs ❛♥❞ ♠❛❦❡t❤❡♠ ✇♦rt❤❧❡ss✱ ❯❆❱s ❛r❡ ♠✉❝❤ ♠♦r❡ ♣r♦♥❡ t♦ ❝r❛s❤ t❤❛♥ ♠❛♥♥❡❞ ❛✐r❝r❛❢t ✇❤❡r❡ ❛ ♣✐❧♦t❝❛♥ ♠❛②❜❡ r❡❝♦❣♥✐③❡ ♣r♦❜❧❡♠s ✇✐t❤ s❡♥s♦rs ✐♥ t✐♠❡ ❛♥❞ ♠❛② ❜❡ ❛❜❧❡ t♦ ❛❝t ✐♥ t✐♠❡ t♦s❡❝✉r❡ t❤❡ ❛✐r❝r❛❢t✳

✷✳✹ ❲✐♥❞ t✉♥♥❡❧s

❲❤✐❧❡ ♠♦r❡ ❞❡t❛✐❧❡❞ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❛r❡ ♣♦ss✐❜❧❡ ♥♦✇❛❞❛②s ❞✉❡ t♦ ✐♥❝r❡❛s✐♥❣ ❝♦♠♣✉✲t❛t✐♦♥❛❧ ♣♦✇❡r✱ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ st✐❧❧ ♥❡❡❞❡❞ t♦ t❡st ❛♥❞ ✈❛❧✐❞❛t❡ ❝♦♠♣♦♥❡♥ts ♦r ❡✈❡♥

✶✷

✷ ❇❛❝❦❣r♦✉♥❞

❝♦♠♣❧❡t❡ ❛✐r❝r❛❢t✳ ❚❤❡② ♦✛❡r t❤❡ ♣♦ss✐❜✐❧✐t② t♦ ❞♦ ♠❡❛s✉r❡♠❡♥ts ❛t t❤❡ ♣❛rts ♦❢ ❛♥ ❛✐r✲❝r❛❢t ✐♥ ❛ ❝♦♥tr♦❧❧❡❞ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤✐s ❝♦♥tr♦❧❧❡❞ ❡♥✈✐r♦♥♠❡♥t ❧❡❛❞s t♦ ❛ ❜✐❣ ❛❞✈❛♥t❛❣❡♦❢ ✐❝✐♥❣ t❡sts ✐♥ ✇✐♥❞ t✉♥♥❡❧s ❝♦♠♣❛r❡❞ t♦ ✐❝✐♥❣ t❡sts ✐♥ ♥❛t✉r❡✳ ❲❤✐❧❡ ✐♥ ♥❛t✉r❡ t❤❡t❡sts ❝❛♥ ❜❡ ❞♦♥❡ ♦♥❧② ✇❤❡♥ ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❡①✐st✱ t❤❡ ❝♦♥❞✐t✐♦♥s ❝❛♥ ❡❛s✐❧② ❜❡ s❡t ✐♥ ❛✇✐♥❞ t✉♥♥❡❧✳

✷✳✹✳✶ ❇❛s✐❝s ♦❢ ✇✐♥❞ t✉♥♥❡❧s

✭❛✮ ❙❝❤❡♠❛t✐❝ ❧♦♦❦ ♦❢ ❛♥ ♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥✲♥❡❧✳ ❆❞❛♣t❡❞ ❢r♦♠ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✳

✭❜✮ ❙❝❤❡♠❛t✐❝ ❧♦♦❦ ♦❢ ❛ ❝❧♦s❡❞✲r❡t✉r♥ ✇✐♥❞t✉♥♥❡❧✳ ❆❞❛♣t❡❞ ❢r♦♠ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✳

❋✐❣✉r❡ ✷✳✻✿ ❊①❛♠♣❧❡s ❢♦r t❤❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ ✇✐♥❞ t✉♥♥❡❧s

❲✐♥❞ t✉♥♥❡❧s ❛r❡ ❞❡✈✐❝❡s t❤❛t ❝❛✉s❡ ❛✐r t♦ ✢♦✇ ♣❛st ❛ t❡st ♦❜❥❡❝t✳ ❋♦r ♠♦st ❝❛s❡s✱t❤✐s ❧❡❛❞s t♦ s✐♠✐❧❛r ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ ✢♦✇ ✜❡❧❞ ❛s ✐❢ t❤❡ ♦❜❥❡❝t ✇❛s ♠♦✈✐♥❣ t❤r♦✉❣❤❛✐r✳ ❚❤❡r❡❢♦r❡ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ❛ ❣r❡❛t ♣♦ss✐❜✐❧✐t② t♦ ♣❡r❢♦r♠ ♠❡❛s✉r❡♠❡♥ts ♦♥ ♦❜❥❡❝ts♠♦✈✐♥❣ t❤r♦✉❣❤ ❛✐r ❧✐❦❡ ❝❛rs✱ tr❛✐♥s✱ ♦r ❛✐r❝r❛❢t✳ ◆♦r♠❛❧❧② ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ❝❤❛r❛❝t❡r✐③❡❞❜② t✇♦ ❞✐✛❡r❡♥t ❝❧❛ss❡s✳ ❆♥ ♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧ s✉❝❦s ❛✐r ❢r♦♠ t❤❡ s✉rr♦✉♥❞✐♥❣✳❚❤✐s ❛✐r ✢♦✇s t❤r♦✉❣❤ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ ✐s t❤❡♥ ❜❧♦✇♥ ✐♥t♦ t❤❡ s✉rr♦✉♥❞✐♥❣ ❛❣❛✐♥ ❛s❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✻✭❛✮✳ ❚❤❡ ♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧ ❝❛♥ ❜❡ ❡✐t❤❡r ♣❧❛❝❡❞ ♦✉ts✐❞❡✇❤❡r❡ ✐t ❤❛s t♦ ❞❡❛❧ ✇✐t❤ ✇✐♥❞ ✐♥✢✉❡♥❝❡s ♦r ✐♥s✐❞❡ ❛ r♦♦♠ ✇❤❡r❡ s✉✣❝✐❡♥t ❝❧❡❛r❛♥❝❡❢r♦♠ t❤❡ ✇❛❧❧s ♠✉st ❜❡ ❡♥s✉r❡❞✳ ❚❤❡ ♦t❤❡r ♦♣t✐♦♥ ✐s t♦ ❤❛✈❡ ❛ ✇✐♥❞ t✉♥♥❡❧ ♦❢ t❤❡❝❧♦s❡❞✲r❡t✉r♥ t②♣❡✳ ❈❧♦s❡❞✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧s ❤❛✈❡ ❛ r❡t✉r♥ s❡❝t✐♦♥ t❤r♦✉❣❤ ✇❤✐❝❤ t❤❡❛✐r ❝✐r❝✉❧❛t❡s ❝♦♥t✐♥✉♦✉s❧② ✇❤✐❧❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐s ✇♦r❦✐♥❣ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡✷✳✻✭❜✮✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ ❧✐st s♦♠❡ ❛❞✈❛♥t❛❣❡s ❢♦r ❡❛❝❤ ♦❢ t❤❡ t✇♦ t②♣❡s✳ ❆♥ ♦♣❡♥✲r❡t✉r♥ t✉♥♥❡❧ ✐s t②♣✐❝❛❧❧② s♠❛❧❧❡r ✐♥ s♣❛❝❡✳ ❚❤✐s ❛❧s♦ ❧❡❛❞s t♦ ❧❡ss ✐♥✐t✐❛❧ ❝♦sts ❢♦r ❛♥♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧ ❛s ✐t ❝♦♥s✐sts ♦❢ ❧❡ss str✉❝t✉r❡✳ ❋✉rt❤❡r♠♦r❡✱ ✐t ✐s ❛❧s♦ ❜❡tt❡r ❢♦r✈✐s✉❛❧✐③❛t✐♦♥ ❡①♣❡r✐♠❡♥ts ❛s ✐t s✉❝❦s ❢r❡s❤ ❛✐r ❛♥❞ ❞♦❡s ♥♦t ❥✉st r❡❝✐r❝✉❧❛t❡ t❤❡ ❛✐r ✐♥s✐❞❡t❤❡ t✉♥♥❡❧✳ ❍♦✇❡✈❡r✱ ❞✉❡ t♦ t❤❡ r❡t✉r♥ s❡❝t✐♦♥✱ ✇✐t❤ ❛ ❝❧♦s❡❞✲r❡t✉r♥ t✉♥♥❡❧✱ t❤❡ ✢♦✇q✉❛❧✐t② ❝❛♥ ❜❡ ❝♦♥tr♦❧❧❡❞ ❜❡tt❡r ❛♥❞ ❧❡ss ❝♦♥❞✐t✐♦♥✐♥❣ ✐s ♥❡❡❞❡❞✳ ❆❞❞✐t✐♦♥❛❧ ❛❞✈❛♥t❛❣❡s♦❢ ❛ ❝❧♦s❡❞✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ t❤❛t t❤❡② ♥❡❡❞ ❧❡ss ♣♦✇❡r ❛♥❞ t❤❛t t❤❡② ❛r❡ t②♣✐❝❛❧❧②❧❡ss ♥♦✐s②✳❚❤❡ s❡❝♦♥❞ ❞✐st✐♥❣✉✐s❤✐♥❣ ❝r✐t❡r✐♦♥ ♦❢ ❛ ✇✐♥❞ t✉♥♥❡❧ ✐s t❤❡ s❡❝t✐♦♥ t❤❛t ❝♦♥t❛✐♥s t❤❡

t❡st ♦❜❥❡❝t✳ ❲❤✐❧❡ ✐t ✇❛s ❡✐t❤❡r ❛ ❝❧♦s❡❞ ♦r ♦♣❡♥ ❞✉❝t ✐♥ t❤❡ ♣❛st✱ ♦✈❡r t❤❡ ❧❛st ②❡❛rss❧♦tt❡❞ ✇❛❧❧s ❤❛✈❡ s❡❡♥ ✐♥❝r❡❛s❡❞ ✉s❡✳ ❖♣❡♥ t❡st s❡❝t✐♦♥s ❛❧❧♦✇ ❡❛s✐❡r ❛❝❝❡ss t♦ t❤❡ ♠♦❞❡❧❛♥❞ ♦✛❡r s♦♠❡ ❛❞✈❛♥t❛❣❡s ✐♥ ❜❧✉✛ ❜♦❞② ❛❡r♦❞②♥❛♠✐❝s✳ ❋♦r ❛❡r♦♥❛✉t✐❝❛❧ ❡①♣❡r✐♠❡♥ts✱❛ ❝❧♦s❡❞ t❡st s❡❝t✐♦♥ ✐s ♦❢t❡♥ ♠♦r❡ r❡❛s♦♥❛❜❧❡✳ ❇❡❝❛✉s❡ ♦♣❡♥ t❡st s❡❝t✐♦♥s s✉❝❦ ❛✐r ❢r♦♠

✶✸

✷ ❇❛❝❦❣r♦✉♥❞

t❤❡ s✉rr♦✉♥❞✐♥❣ t❤❛t ✇❛s ♥♦t ❛❝❝❡❧❡r❛t❡❞ ❜❡❢♦r❡✱ t❤❡ ♣♦✇❡r ♥❡❡❞ ✐s ❤✐❣❤❡r ❢♦r ♦♣❡♥ t❤❛♥❢♦r ❝❧♦s❡❞ t❡st s❡❝t✐♦♥s✳■♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣❛r❛❣r❛♣❤s✱ t❤❡ ♠♦st t②♣✐❝❛❧ ♣❛rts ♦❢ ❛ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡✐r t❛s❦s

s❤❛❧❧ ❜❡ ♣r❡s❡♥t❡❞✳ ❚❤✐s ♣❛ss❛❣❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✇♦r❦ ♦❢ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✳ ❚❤✐s ❜♦♦❦❝❛♥ ❛❧s♦ ❜❡ r❡❝♦♠♠❡♥❞❡❞ ❢♦r ❢✉rt❤❡r ❛♥❞ ♠♦r❡ ❞❡t❛✐❧❡❞ r❡s❡❛r❝❤ ♦♥ t❤❡ t♦♣✐❝ ♦❢ ✇✐♥❞t✉♥♥❡❧s✳❚❤❡ ♠♦st ✐♠♣♦rt❛♥t ♣❛rt ♦❢ ❛ ✇✐♥❞ t✉♥♥❡❧ ✐s ✐ts t❡st s❡❝t✐♦♥✳ ❚❤❡ t❡st ♦❜❥❡❝t ❛♥❞

❛❧❧ t❤❡ ♠❡❛s✉r✐♥❣ ❡q✉✐♣♠❡♥t ✐s ♠♦✉♥t❡❞ ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡ ❣♦❛❧ ✐s t♦ ❜❡❛❜❧❡ t♦ ✉s❡ t❤❡ ❧❛r❣❡st ♣♦ss✐❜❧❡ ♣❛rt ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❢♦r t❤❡ ❡①♣❡r✐♠❡♥t✳ ❖t❤❡r✇✐s❡✱t❤❡ ❝♦♥str✉❝t✐♦♥ ❛♥❞ ❡♥❡r❣② ❝♦sts ✇♦✉❧❞ ❜❡ ❤✐❣❤❡r ✇✐t❤♦✉t ❛♥② ♥❡❡❞✳ ❚❤❡r❡❢♦r❡ t❤❡❝♦♥❞✐t✐♦♥s ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥ ❤❛✈❡ t♦ ❜❡ ❝♦♥st❛♥t ♦✈❡r ❛ ❧❛r❣❡ ♣❛rt ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥ t♦ ❤❛✈❡ ❝♦♠♣❛r❛❜❧❡ ❝♦♥❞✐t✐♦♥s ♦✈❡r t❤❡ ✇❤♦❧❡ ❛r❡❛ ✐♥ ✇❤✐❝❤ t❤❡ ♠❡❛s✉r❡♠❡♥tst❛❦❡ ♣❧❛❝❡✳ ◆♦t ♦♥❧② s♣❛t✐❛❧ ✉♥✐❢♦r♠✐t② ♦❢ t❤❡ ❝♦♥❞✐t✐♦♥s ✐s ✐♠♣♦rt❛♥t✱ ❜✉t ❛❧s♦ t❡♠♣♦r❛❧✉♥✐❢♦r♠✐t②✳ ❚♦ ❡♥s✉r❡ t❤✐s✱ t❤❡r❡ s❤♦✉❧❞ ♥♦t ❜❡ ❛♥② s❡♣❛r❛t✐♦♥ ✐♥s✐❞❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♣♦✇❡r ✉♥✐t ❛♥❞ t❤❡ ❝♦♦❧✐♥❣ ✉♥✐t ❤❛✈❡ t♦ ❜❡ str♦♥❣ ❡♥♦✉❣❤ t♦ ❦❡❡♣ t❤❡✈♦❧✉♠❡ ✢♦✇ ❛♥❞ t❤❡ t❡♠♣❡r❛t✉r❡s ❝♦♥st❛♥t✳ ❆s t✉r❜✉❧❡♥❝❡ ❝❛♥ ❤❛✈❡ ❛ str♦♥❣ ✐♥✢✉❡♥❝❡♦♥ t❤❡ r❡s✉❧ts ♦❢ ❡①♣❡r✐♠❡♥ts✱ ♥♦r♠❛❧❧② t❤❡ ❛✐♠ ✐s ❡✐t❤❡r ❛ ❞❡s✐❣♥ ✇✐t❤ ❛s ❧❡ss t✉r❜✉❧❡♥❝❡❛s ♣♦ss✐❜❧❡ ♦r ❛ ❞❡s✐❣♥ ✇✐t❤ ❛ s♣❡❝✐✜❡❞ t✉r❜✉❧❡♥❝❡ ❧❡✈❡❧✳ ❚❤❡ t❡st s❡❝t✐♦♥ ✐s ✉s✉❛❧❧② ♦❢t❤❡ ❝❧♦s❡❞ t②♣❡✳ ■❢ t❤❡ t❡st s❡❝t✐♦♥ ✐s ❝❧♦s❡❞✱ ♠♦st ♦❢ t❤❡ t✐♠❡ ✐ts ❝r♦ss✲s❡❝t✐♦♥❛❧ s❤❛♣❡✐s ❡✐t❤❡r r❡❝t❛♥❣✉❧❛r ♦r ❝✐r❝✉❧❛r✳❆ ❝♦♥tr❛❝t✐♦♥ ✐s ♣❧❛❝❡❞ ✉♣str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❉✉❡ t♦ ❛❝❝❡❧❡r❛t✐♦♥ t❤r♦✉❣❤

t❤✐s ♥♦③③❧❡✱ ✈❛r✐❛t✐♦♥s ✐♥ ✈❡❧♦❝✐t② ❞❡❝r❡❛s❡✳ ❚❤✐s ✐s ❤♦✇❡✈❡r ♥♦t t❤❡ ♠❛✐♥ r❡❛s♦♥ ❢♦r♣❧❛❝✐♥❣ ❛ ❝♦♥tr❛❝t✐♦♥ ✉♣str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❯♣str❡❛♠ ♦❢ t❤❡ ♥♦③③❧❡ ❛r❡ ✢♦✇❝♦♥❞✐t✐♦♥❡rs✳ ❚♦ r❡❞✉❝❡ t❤❡✐r ♣r❡ss✉r❡ ❧♦ss❡s✱ t❤❡ ✈❡❧♦❝✐t② s❤♦✉❧❞ ❜❡ ❧♦✇✳ ❚❤❡r❡❢♦r❡ ❛♥❛❝❝❡❧❡r❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ✢♦✇ ❝♦♥❞✐t✐♦♥❡rs ❛♥❞ t❤❡ t❡st s❡❝t✐♦♥ ✐s ♥❡❡❞❡❞ t❤❛t ✐s ♣r♦✈✐❞❡❞❜② t❤❡ ♥♦③③❧❡✳ ❲❤✐❧❡ ❛ ✶❉✲❛♥❛❧②s✐s ✐♥❞✐❝❛t❡s ❢❛❧❧✐♥❣ ♣r❡ss✉r❡ ❛♥❞ t❤❡r❡❢♦r❡ ♥♦ r✐s❦ ♦❢s❡♣❛r❛t✐♦♥✱ ✐t ✐s ❞✐✛❡r❡♥t ✐♥ r❡❛❧✐t②✳ ❘❡❣✐♦♥s ✇✐t❤ ✐♥❝r❡❛s✐♥❣ ♣r❡ss✉r❡ ✇✐❧❧ ♦❝❝✉r ♥❡❛r t❤❡✇❛❧❧ ✐♥ t❤❡ ❛r❡❛ ♦❢ t❤❡ ❜❡❣✐♥♥✐♥❣ ❛♥❞ t❤❡ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡✳ ❚❤✐s ❧❡❛❞s t♦ t❤❡ ♥❡❡❞ ❢♦r ❛❣♦♦❞ ❞❡s✐❣♥ ♦❢ t❤❡ ♥♦③③❧❡ ❜❡❝❛✉s❡ s❡♣❛r❛t✐♦♥ r❡❞✉❝❡s t❤❡ ✢♦✇ q✉❛❧✐t②✳❚❤❡ ♠❡♥t✐♦♥❡❞ ✢♦✇ ❝♦♥❞✐t✐♦♥❡rs ❝❛♥ ❜❡ ❞✐✈✐❞❡❞ ✐♥t♦ ❤♦♥❡②❝♦♠❜s ❛♥❞ s❝r❡❡♥s✳ ❇♦t❤

❛r❡ ♣❧❛❝❡❞ ✐♥s✐❞❡ ❛ ♣❛rt ✇✐t❤ ❝♦♥st❛♥t ❝r♦ss✲s❡❝t✐♦♥ t❤❛t ✐s ❝❛❧❧❡❞ s❡tt❧✐♥❣ ❛r❡❛ ❜❡❝❛✉s❡♦❢ t❤❡ ❧♦✇ s♣❡❡❞ ✐♥s✐❞❡✳ ❍♦♥❡②❝♦♠❜s ❛r❡ s♠❛❧❧ ♣✐♣❡s ✐♥s✐❞❡ t❤✐s s❡❝t✐♦♥✳ ❆s t❤❡ ✢♦✇ ❤❛st♦ ❣♦ t❤r♦✉❣❤ t❤♦s❡ ♥❛rr♦✇ ♣✐♣❡s✱ t❤❡ ✈❡❧♦❝✐t② ❝♦♠♣♦♥❡♥t ♥♦r♠❛❧ t♦ t❤❡ ♣✐♣❡ ✐s r❡❞✉❝❡❞❛♥❞ t❤❡ ✢♦✇ ✐s str❛✐❣❤t❡♥❡❞ ✐♥t♦ t❤❡ ❞✐r❡❝t✐♦♥ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❆❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇❡t ❛❧✳ ❬✷✵❪✱ t❤❡ ♠♦st ❝♦♠♠♦♥ ❤♦♥❡②❝♦♠❜s ❛r❡ ❡✐t❤❡r r♦✉♥❞✱ sq✉❛r❡✱ ♦r ❤❡①❛❣♦♥❛❧✳ ❚❤♦s❡s❤❛♣❡s ❝❛♥ ❛❧s♦ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✼✭❛✮✳ ❙❝r❡❡♥s ♦♥ t❤❡ ♦t❤❡r s✐❞❡ ❛r❡ ❣r✐❞s ❝♦♥s✐st✐♥❣ ♦❢r❡❣✉❧❛r❧② ❛rr❛♥❣❡❞ t❤✐♥ ✇✐r❡s ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳✼✭❜✮✳ ❚❤❡ ♥♦♥✲✉♥✐❢♦r♠✐t② ♦❢ t❤❡✢♦✇ ✐s r❡❞✉❝❡❞ ♦✈❡r ❛ s❝r❡❡♥ ❜❡❝❛✉s❡ t❤❡ ✢♦✇ r❡s✐st❛♥❝❡ ✐s ❤✐❣❤❡r ❢♦r ❤✐❣❤❡r ✈❡❧♦❝✐t✐❡st❤❛♥ ❢♦r ❧♦✇ ✈❡❧♦❝✐t✐❡s✳ ❆ ❞♦✇♥s✐❞❡ ♦❢ s❝r❡❡♥s ✐s t❤❛t t❤❡② ❛r❡ r❡s♣♦♥s✐❜❧❡ ❢♦r r❛t❤❡r ❤✐❣❤♣r❡ss✉r❡ ❧♦ss❡s✳❉♦✇♥str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ✐s t❤❡ ❞✐✛✉s❡r ✇❤✐❝❤ ✐s ♦❢ ❞✐✈❡r❣✐♥❣ ❝r♦ss✲s❡❝t✐♦♥✳

❚❤❡ ❞✐✈❡r❣❡♥❝❡ ✐s ♣❧❛❝❡❞ ❛t t❤✐s ♣♦s✐t✐♦♥ t♦ ❤❛✈❡ ❛ ❣♦♦❞ ♣r❡ss✉r❡ r❡❝♦✈❡r② ❛♥❞ t❤❡r❡❢♦r❡❢❡✇❡r ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ■❢ t❤❡ ✐♥❝r❡❛s❡ ✐♥ ❝r♦ss✲s❡❝t✐♦♥ ✐s t♦♦ ❜✐❣ ♦✈❡r ❛s❤♦rt ❧❡♥❣t❤✱ t❤❡ ❞✐✛✉s❡r ♠✐❣❤t ❡①♣❡r✐❡♥❝❡ s❡♣❛r❛t✐♦♥✳ ❚❤✐s ✇✐❧❧ r❡❞✉❝❡ t❤❡ ✢♦✇ q✉❛❧✐t②✐♥ t❤❡ t❡st s❡❝t✐♦♥ ❛♥❞ ♠✐❣❤t ❧❡❛❞ t♦ ✉♥st❡❛❞✐♥❡ss✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ ❤♦✇❡✈❡r st❛t❡

✶✹

✷ ❇❛❝❦❣r♦✉♥❞

✭❛✮ ❉✐✛❡r❡♥t ♦♣t✐♦♥s ❢♦r ❤♦♥❡②❝♦♠❜s✳❆❞❛♣t❡❞ ❢r♦♠ ❑✉❧❦❛r♥✐ ❡t ❛❧✳ ❬✷✶❪✳

✭❜✮ ❙❝❤❡♠❛t✐❝ ♦❢ ❛ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥✳ ❆❞❛♣t❡❞❢r♦♠ ❆r✐❢✉③③❛♠❛♥ ❛♥❞ ▼❛s❤✉❞ ❬✷✷❪✳

❋✐❣✉r❡ ✷✳✼✿ ❚❤❡ t②♣✐❝❛❧ ✢♦✇ ❝♦♥❞✐t✐♦♥❡rs✳

t❤❛t s❡♣❛r❛t✐♦♥ ❝❛♥ ❜❡ ❛❝❝❡♣t❡❞ t♦ ❛ s♠❛❧❧ ❞❡❣r❡❡ ❛s t❤❡ ✉♣str❡❛♠ ✐♠♣❛❝t ✐s ✉s✉❛❧❧②♥❡❣❧✐❣✐❜❧❡✳❆s ♣r❡ss✉r❡ ❧♦ss❡s t❛❦❡ ♣❧❛❝❡ ❛❧❧ ♦✈❡r t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✱ ❛ ♣♦✇❡r ✉♥✐t

✐s ♥❡❡❞❡❞✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤✐s ❢❛♥ ✐s r❡q✉✐r❡❞ t♦ ❢♦r❝❡ t❤❡ ❛✐r t❤r♦✉❣❤ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳■♥ ♦♣❡♥✲r❡t✉r♥ t✉♥♥❡❧s✱ t❤✐s ♣♦✇❡r ✉♥✐t ✐s ❡✐t❤❡r ♣❧❛❝❡❞ ❞♦✇♥str❡❛♠ ♦❢ t❤❡ ❞✐✛✉s❡r ♦r✉♣str❡❛♠ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❚❤❡ ✐♥st❛❧❧❡❞ ❢❛♥ s❤❛❧❧ ❜❛❧❛♥❝❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞♣r♦✈✐❞❡ ❛ st❡❛❞② ❛✐r ✢♦✇ t❤r♦✉❣❤ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳■♥ ❛ ❝❧♦s❡❞✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ r❡t✉r♥ ❞✉❝t ✇✐❧❧ ❢♦❧❧♦✇ ❛❢t❡r t❤❡ ❞✐✛✉s❡r✳ ❚❤❡

r❡t✉r♥ ❞✉❝t ❝♦♥s✐sts ♦❢ ❝♦r♥❡rs ❛♥❞ ❞✉❝ts t♦ ❝♦♥♥❡❝t t❤❡ ❡♥❞ ♦❢ t❤❡ ❞✐✛✉s❡r ❛♥❞ t❤❡❜❡❣✐♥♥✐♥❣ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❆❧s♦✱ t❤❡ ♣♦✇❡r ✉♥✐t ✐s ♣❧❛❝❡❞ s♦♠❡✇❤❡r❡ ✐♥s✐❞❡ t❤❡r❡t✉r♥ ❞✉❝t✱ ♦❢t❡♥ ❛❢t❡r t❤❡ s❡❝♦♥❞ ♦❢ ❢♦✉r ❝♦r♥❡rs✳

✷✳✹✳✷ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s

■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❝♦♥t❛✐♥ t✇♦ ♥❡✇ ❝♦♠♣♦♥❡♥ts ❝♦♠♣❛r❡❞ t♦ ❝♦♠♠♦♥ ✇✐♥❞ t✉♥♥❡❧s ❛s❡①♣❧❛✐♥❡❞ ❜② ■❊❆ ❲✐♥❞ ❚❛s❦ ✶✾ ❬✷✸❪✳ ❆ s♣r❛② s②st❡♠ ♥❡❡❞s t♦ ❜❡ ✐♥❝❧✉❞❡❞ t♦ ✐♥❥❡❝t✇❛t❡r ❞r♦♣❧❡ts ✐♥t♦ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❋✉rt❤❡r♠♦r❡✱ ❡①tr❛ ❝♦♦❧✐♥❣ ✐s r❡q✉✐r❡❞ t♦ ❝♦♦❧t❤❡ t✉♥♥❡❧ t♦ s✉❜③❡r♦ t❡♠♣❡r❛t✉r❡s✳ ❈❧♦s❡❞✲r❡t✉r♥ t✉♥♥❡❧s ♦❢t❡♥ ❤❛✈❡ ❤❡❛t ❡①❝❤❛♥❣❡rs✐♥❝❧✉❞❡❞ ✐♥ t❤❡✐r ❝❤❛♥♥❡❧ t♦ ❝♦♦❧ t❤❡ ✢✉✐❞ ❝♦♥st❛♥t❧②✳ ❖♣❡♥✲r❡t✉r♥ t✉♥♥❡❧s ♥❡❡❞ t♦ ❤❛✈❡❡①t❡r♥❛❧ ❝♦♦❧✐♥❣ ❛♥❞ ❛r❡ t❤❡r❡❢♦r❡ ♦❢t❡♥ ♣❧❛❝❡❞ ✐♥s✐❞❡ ❛ ❝❧✐♠❛t❡ ❝❤❛♠❜❡r t❤❛t ♣r♦✈✐❞❡st❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r✳❚♦❞❛② ❛❧r❡❛❞② s❡✈❡r❛❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❡①✐st✳ ❆ ❧✐st ✇✐t❤ ❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s

✇❛s ❝♦♠♣✐❧❡❞ ❜② ■❊❆ ❲✐♥❞ ❚❛s❦ ✶✾ ❬✷✸❪✳ ❍♦✇❡✈❡r✱ ♠♦st ♦❢ t❤♦s❡ ✇✐♥❞ t✉♥♥❡❧s ❛r❡❞❡s✐❣♥❡❞ ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t✳ ▼❛♥♥❡❞ ❛✐r❝r❛❢t t②♣✐❝❛❧❧② ❛r❡ ❧❛r❣❡r ❛♥❞ ❢❛st❡r t❤❛♥ ❯❆❱s❛♥❞ t❤❡r❡❢♦r❡ ❛❧s♦ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛r❡ ❜✐❣❣❡r ❛♥❞ ❞❡s✐❣♥❡❞❢♦r ❤✐❣❤❡r ❛✐r s♣❡❡❞s✳ ❚❤✐s ✐s ✇❤② ♠♦st ♦❢ t❤❡ ❡①✐st✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ♦♣❡r❛t❡ ❛t✈❡❧♦❝✐t✐❡s ♦❢ 75m s−1 ♦r ❤✐❣❤❡r✱ ❢♦r ❡①❛♠♣❧❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛t ❈■❘❆ ❬✷✹❪ ♦r t❤❡■❝✐♥❣ ❘❡s❡❛r❝❤ ❚✉♥♥❡❧ ❛t ◆❆❙❆ ●❧❡♥♥ ❘❡s❡❛r❝❤ ❈❡♥t❡r ❬✷✺❪ ❛♥❞ t❤❡r❡❢♦r❡ ✇❛② ❢❛st❡rt❤❛♥ t❤❡ ❛✐r s♣❡❡❞ ♦❢ ♠♦st ❯❆❱s✳ ❆❧s♦✱ s♦♠❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ✇✐t❤ ✉♣ t♦ 20m s−1 ♦r

✶✺

✷ ❇❛❝❦❣r♦✉♥❞

25m s−1 ❛r❡ ❛✈❛✐❧❛❜❧❡✳ ❲❤✐❧❡ t❤✐s ✐s ❢❛st ❡♥♦✉❣❤ t♦ t❡st s♦♠❡ ❯❆❱s✱ ✐t ✐s t♦♦ s❧♦✇ ❢♦r♠♦st ♦❢ t❤❡♠✳ ❍❡♥❝❡✱ ✈❡r② ❢❡✇ ♦❢ t❤❡ ❡①✐st✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ❯❆❱❡①♣❡r✐♠❡♥ts✳ ❚✇♦ ❡①❛♠♣❧❡s ❢♦r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s t❤❛t ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts♦♥ ❯❆❱s ❛r❡ t❤❡ ❱❚❚ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✭s❡❡ ❚✐✐❤♦♥❡♥ ❡t ❛❧✳ ❬✷✻❪✮ ❛♥❞ t❤❡ ✐❝✐♥❣ t✉♥♥❡❧❛t ❈r❛♥✜❡❧❞ ❯♥✐✈❡rs✐t② ❬✷✼❪✳ ❚❤❡r❡ ✐s ❤♦✇❡✈❡r ❛ ♥❡❡❞ ❢♦r ♠♦r❡ t❡st ❝❛♣❛❜✐❧✐t✐❡s✳ ❚❤✐s ✐s✇❤② ♥❡✇ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ♥❡❝❡ss❛r② t❤❛t ❛r❡ s♣❡❝✐❛❧❧② ❞❡s✐❣♥❡❞ ❢♦r ❯❆❱ t❡sts✳❚❤❡ ❜❛s✐❝ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥ ♣r❡s❡♥t❡❞ t❤✐s ❢❛r ✐s ♣❡r❢❡❝t❧② s✉✐t❡❞ ❢♦r ❡①♣❡r✐♠❡♥ts ✇✐t❤

❛✐r❢♦✐❧s✳ ❚❤❡ s✐t✉❛t✐♦♥ ✐s ♠♦r❡ ❝♦♠♣❧❡① ✇❤❡♥ r♦t❛r②✲✇✐♥❣ ❯❆❱s ♦r ♠❛♥♥❡❞ ❤❡❧✐❝♦♣t❡rs❛r❡ t❤❡ ♦❜❥❡❝ts ♦❢ ✐♥t❡r❡st✳ ❋❧❡♠♠✐♥❣ ❡t ❛❧✳ ❬✷✽❪ ♠♦✉♥t❡❞ t❤❡ ♠❛✐♥ r♦t♦r ♦❢ ❛ ❤❡❧✐❝♦♣t❡r✐♥s✐❞❡ ❛ ❝♦♥✈❡♥t✐♦♥❛❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡✐r r❡s✉❧ts ✜t ✇❡❧❧ t♦ t❤❡♦r❡t✐❝❛❧ ♣r❡❞✐❝t✐♦♥s✳❲✐t❤ ❝♦♠♠♦♥ ✇✐♥❞ t✉♥♥❡❧s✱ ✐t ✐s ❤♦✇❡✈❡r ♥♦t ♣♦ss✐❜❧❡ t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ ❝❡♥tr✐❢✉❣❛❧❢♦r❝❡s t❤❛t ❛r❡ ✐♠♣♦rt❛♥t ❢♦r ❤❡❧✐❝♦♣t❡r ✐❝✐♥❣ ❛s ❡①♣❧❛✐♥❡❞ ❜② ❇r♦✉✇❡rs ❡t ❛❧✳ ❬✷✾❪✳ ❚❤❡s❡❛✉t❤♦rs t❤❡r❡❢♦r❡ ✉s❡❞ ❛ t❡st ❢❛❝✐❧✐t② t❤❛t ❤❛s t❤❡ s♣r❛② ♥♦③③❧❡s ♠♦✉♥t❡❞ t♦ t❤❡ ❝❡✐❧✐♥❣✳❚❤❡ ❝♦♠♣❧❡① ✜❡❧❞ ♦❢ ❞♦✐♥❣ ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ♦♥ r♦t❛r②✲✇✐♥❣ ❛✐r❝r❛❢t ❛❧s♦ ❧❡❛❞ t♦ ❞✐✛❡r❡♥t♠❡t❤♦❞s ♦❢ s✐♠✉❧❛t✐♥❣ ✐❝✐♥❣ ❞✉r✐♥❣ t❤❡ ✢✐❣❤t✳ ❚♦ ❞♦ s♦✱ t❤❡ r♦t♦r❝r❛❢t ✐s ✢②✐♥❣ ✐♥s✐❞❡ ❛❞r♦♣❧❡t ❝❧♦✉❞ ♣r♦❞✉❝❡❞ ❜② ❛♥ ❛✐r❝r❛❢t ✢②✐♥❣ ✐♥ ❢r♦♥t ♦r ❜② ❛ st❛t✐♦♥❛r② ❢❛❝✐❧✐t② ❛s ❝❛♥ ❜❡s❡❡♥ ✐♥ ❈❛♦ ❛♥❞ ❈❤❡♥ ❬✸✵❪✳ ❍♦✇❡✈❡r✱ ❛❧❧ ♦❢ t❤♦s❡ s②st❡♠s ❤❛✈❡ s❤♦rt❝♦♠✐♥❣s✳ ❚❤❡r❡❢♦r❡r❡s❡❛r❝❤ ♦♥ t❡st ❢❛❝✐❧✐t✐❡s ❢♦r r♦t♦r❝r❛❢t ✐❝✐♥❣ ✐s st✐❧❧ ♥❡❝❡ss❛r②✳

✷✳✹✳✸ ❙❝❛❧✐♥❣

❉✉r✐♥❣ t❤❡ ♣❧❛♥✐♥❣ ♦❢ ❡①♣❡r✐♠❡♥ts✱ ♦❢t❡♥ t❤❡ q✉❡st✐♦♥ ❛r✐s❡s ✇❤❡t❤❡r ✐t ✐s ♣♦ss✐❜❧❡ t♦s❝❛❧❡ t❤❡ ❡①♣❡r✐♠❡♥t✳ ❙❝❛❧✐♥❣ ✐s ❡s♣❡❝✐❛❧❧② ❞❡s✐r❡❞ ✐❢ t❤❡ t❡sts ✇♦✉❧❞ ♦t❤❡r✇✐s❡ ❜❡ ✈❡r②❡①♣❡♥s✐✈❡ ♦r t❤❡ ♥✉♠❜❡r ♦❢ s✉✐t❛❜❧❡ t❡st ❢❛❝✐❧✐t✐❡s ✐s ✈❡r② s♠❛❧❧✳ ❖❢t❡♥ t❤❡ ❛✈❛✐❧❛❜❧❡ s♣❛❝❡✐s ❛ ♣r♦❜❧❡♠ ❛♥❞ t❤❡r❡❢♦r❡ s♠❛❧❧❡r ♠♦❞❡❧s ♦❢ t❤❡ r❡❛❧ ♣❛rts ❛r❡ ✉s❡❞✳ ❚❤❡ ❞✐♠❡♥s✐♦♥❧❡ssq✉❛♥t✐t✐❡s ✇❤✐❝❤ ❛r❡ t❤❡ ♠♦st ✐♠♣♦rt❛♥t ❢♦r ❞❡s❝r✐❜✐♥❣ t❤❡ ✢♦✇ s❤♦✉❧❞ ❜❡ t❤❡ s❛♠❡ ❢♦rt❤❡ ❡①♣❡r✐♠❡♥t ❛♥❞ t❤❡ r❡❛❧✲❧✐❢❡ s✐t✉❛t✐♦♥✳ ■❢ t❤✐s ✐s ♣♦ss✐❜❧❡✱ ❛ tr❛♥s❢❡r ♦❢ t❤❡ r❡s✉❧ts ♦❢t❤❡ ❡①♣❡r✐♠❡♥t t♦ r❡❛❧ ❧✐❢❡ s✐t✉❛t✐♦♥s ✐s r❛t❤❡r ❡❛s②✳❙❝❛❧✐♥❣ t❤❡ ♠♦❞❡❧s ❢♦r ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ✐s ❤♦✇❡✈❡r ✈❡r② ❞✐✣❝✉❧t✳ ❚❤✐s ✐s ❜❡❝❛✉s❡

18 ❞✐♠❡♥s✐♦♥❧❡ss q✉❛♥t✐t✐❡s ❤❛✈❡ t♦ ❜❡ ♠❛t❝❤❡❞ ❢♦r ❝♦♠♣❧❡t❡ ❡q✉❛❧✐t② ❛❝❝♦r❞✐♥❣ t♦ ❑✐♥❞❡t ❛❧✳ ❬✷❪✳ ❚❤❡ ❧❛r❣❡ ♥✉♠❜❡r ❝❛♥ ❜❡ ❡①♣❧❛✐♥❡❞ ✇✐t❤ t❤❡ ♥❡❡❞ ♦❢ ♠❛t❝❤✐♥❣ t❤❡ ❞✐♠❡♥s✐♦♥❧❡ss♣❛r❛♠❡t❡rs ❢♦r t❤r❡❡ ❞✐✛❡r❡♥t ✜❡❧❞s✿ t❤❡ ❛✐r ✢♦✇✱ t❤❡ tr❛❥❡❝t♦r✐❡s ♦❢ t❤❡ ❞r♦♣❧❡ts ❛♥❞ t❤❡✐♠♣✐♥❣❡♠❡♥t ❛♥❞ ❢r❡❡③✐♥❣ ♦❢ t❤❡ ❞r♦♣❧❡ts✳ ❋♦r ❝♦♥✈❡♥t✐♦♥❛❧ ✇✐♥❞ t✉♥♥❡❧ t❡sts ♠♦st ♦❢t❡♥❥✉st t❤❡ ❛✐r ✢♦✇ ✐s ♦❢ ✐♥t❡r❡st✳ ❚❤❡♥ ♥♦r♠❛❧❧② ❛ ♠❛t❝❤✐♥❣ ♦❢ ❘❡②♥♦❧❞s ❛♥❞ ▼❛❝❤ ♥✉♠❜❡r❜❡t✇❡❡♥ t❡st ❛♥❞ r❡❛❧✐t② ✐s ♥❡❝❡ss❛r②✳ ▼❛t❝❤✐♥❣ s♦♠❡ ♦❢ t❤❡ ❞✐♠❡♥s✐♦♥❧❡ss q✉❛♥t✐t✐❡s ❢♦r✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❡①♣❡r✐♠❡♥ts ✐s r❛t❤❡r ❡❛s②✱ ❢♦r ❡①❛♠♣❧❡ ❜② ✉s✐♥❣ ❛✐r ❛♥❞ ✇❛t❡r ❛s ✐♥ t❤❡r❡❛❧ ❧✐❢❡ s✐t✉❛t✐♦♥✳ ❊s♣❡❝✐❛❧❧② ♠❛t❝❤✐♥❣ t❤❡ q✉❛♥t✐t✐❡s ❢♦r t❤❡ ✐♠♣✐♥❣❡♠❡♥t ❛♥❞ ❢r❡❡③✐♥❣✐s ❤♦✇❡✈❡r ♠✉❝❤ ♠♦r❡ ❞✐✣❝✉❧t✳ ❚❤❡r❡❢♦r❡✱ ✉♥t✐❧ t♦❞❛②✱ s❝❛❧✐♥❣ ♦❢ t❤❡ r❡s✉❧ts ♦❢ ✐❝✐♥❣❡①♣❡r✐♠❡♥ts ❝❛♥ ♥♦t ❜❡ ❞♦♥❡ ✇✐t❤ ❣♦♦❞ ❛❝❝✉r❛❝②✳ ❍❡♥❝❡✱ ❡①♣❡r✐♠❡♥ts ❤❛✈❡ t♦ ❜❡ ❞♦♥❡✇✐t❤ ❢✉❧❧✲s❝❛❧❡ ♠♦❞❡❧s t♦ ❤❛✈❡ ♠❡❛♥✐♥❣❢✉❧ r❡s✉❧ts✳ ❚❤✐s ✐s ❤♦✇❡✈❡r ❛ ❜✐❣❣❡r ♣r♦❜❧❡♠ ❢♦r♠❛♥♥❡❞ ❛✐r❝r❛❢t t❤❛♥ ❢♦r ❯❆❱s✳ ❆s ♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛r❡ t②♣✐❝❛❧❧② ❧❛r❣❡r ❛♥❞ ♦♣❡r❛t❡ ❛t❤✐❣❤❡r s♣❡❡❞s t❤❛♥ ❯❆❱s✱ t❤❡② ♥❡❡❞ ❜✐❣❣❡r t❡st ❢❛❝✐❧✐t✐❡s ❛♥❞ t❤❡ t❡sts ❝♦st ♠✉❝❤ ♠♦r❡✳❚❤❡r❡❢♦r❡✱ s❝❛❧✐♥❣ ✇♦✉❧❞ ❜❡ ♠♦r❡ ❜❡♥❡✜❝✐❛❧ ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t t❤❛♥ ❢♦r ✉♥♠❛♥♥❡❞✳

✶✻

✸ ▼❡t❤♦❞s

❚❤✐s ❝❤❛♣t❡r ✐s ❛❜♦✉t t❤❡ st❡♣s ✐t t♦♦❦ t♦ ❞❡s✐❣♥ t❤❡ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧✳ ❉❡❝✐s✐♦♥s ♠❛❞❡ ❞✉r✐♥❣ t❤✐s ❞❡s✐❣♥ ❛r❡ ❡①♣❧❛✐♥❡❞✳ ❙❡✈❡r❛❧ r✉❧❡s ❛♥❞ ❡q✉❛t✐♦♥s✇❡r❡ ✉s❡❞ t♦ ❞❡s✐❣♥ t❤❡ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ■♥ t❤✐s ❝❤❛♣t❡r✱ t❤❡s❡ r✉❧❡s ❛♥❞❡q✉❛t✐♦♥s ❛r❡ ♣r❡s❡♥t❡❞ ❛♥❞ ❡①♣❧❛✐♥❡❞✳ ❚❤❡ ♥❡❝❡ss❛r② ❢♦r♠✉❧❛s t♦ ❛♥❛❧②③❡ t❤❡ ❜❡❤❛✈✐♦r♦❢ t❤❡ ❞r♦♣❧❡ts ❛r❡ ❛❧s♦ s❤♦✇♥ ❛♥❞ ❝♦♠♠❡♥t❡❞ ♦♥✳ ❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r✱ ❝❡rt❛✐♥ ❡q✉❛t✐♦♥s ✇❡r❡ ♥❡❡❞❡❞✳ ❚❤♦s❡ ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s❝❤❛♣t❡r ❛s ✇❡❧❧✳

✸✳✶ ❇❛s✐❝ ❞❡❝✐s✐♦♥s

❙♦♠❡ ❞❡❝✐s✐♦♥s ❤❛✈❡ t♦ ❜❡ ♠❛❞❡ ❜❡❢♦r❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts ❝❛♥ ❜❡ ❞❡s✐❣♥❡❞✳❆♥ ♦♣❡♥✲r❡t✉r♥ ❞❡s✐❣♥ ✇❛s ❝❤♦s❡♥ t♦ ❞❡❝r❡❛s❡ t❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧❛♥❞ t❤❡ ❝♦sts✳ ❆ ❝❧♦s❡❞ t❡st s❡❝t✐♦♥ ✇❛s ❝❤♦s❡♥ ❛s ♦t❤❡r✇✐s❡ ❞r♦♣❧❡ts ❝♦✉❧❞ ❧❡❛✈❡ t❤❡✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ ❝❤❛♥❣❡ t❤❡ ▲❲❈ ❛♥❞ t❤❡ ▼❱❉✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ❝❧♦s❡❞ t❡st s❡❝t✐♦♥sr❡❞✉❝❡ t❤❡ ♣♦✇❡r r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❢❛♥✳ ■t ❤❛s t♦ ❜❡ ❝♦♥s✐❞❡r❡❞ t❤❛t ♥♦t❛❧❧ ❞r♦♣❧❡ts ✇✐❧❧ ❤✐t t❤❡ ❛✐r❢♦✐❧✳ ❚❤❡ ♦♥❡s t❤❛t ❞♦ ♥♦t✱ ✇✐❧❧ tr❛✈❡❧ ❢✉rt❤❡r ✐♥ t❤❡ t✉♥♥❡❧✳ ■❢t❤❡ ❢❛♥ ✇❛s ♣❧❛❝❡❞ ❛❢t❡r t❤❡ ❞✐✛✉s❡r✱ ❞r♦♣❧❡ts ✇♦✉❧❞ ❤✐t t❤❡ ❢❛♥✳ ❚❤♦s❡ ❞r♦♣❧❡ts ✇♦✉❧❞❛❝❝r❡t❡ t❤❡r❡ ❛♥❞ ✐♥✢✉❡♥❝❡ t❤❡ ❢❛♥✬s ♣❡r❢♦r♠❛♥❝❡✳ ❚❤❡r❡❢♦r❡ t❤❡ ❢❛♥ ✇✐❧❧ ❜❡ ♣❧❛❝❡❞ ❛tt❤❡ ✐♥❧❡t ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ r❡s✉❧t✐♥❣ ♦r❞❡r ♦❢ ❝♦♠♣♦♥❡♥ts ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✸✳✶ ❛♥❞ ✐s ❢❛♥✭❆✮✱ ✇✐❞❡✲❛♥❣❧❡✲❞✐✛✉s❡r✭❇✮✱ s❡tt❧✐♥❣ ❛r❡❛✭❈✮✱♥♦③③❧❡✭❉✮✱ t❡st s❡❝t✐♦♥✭❊✮✱ ❞✐✛✉s❡r✭❋✮✳

A B C D E F

❋✐❣✉r❡ ✸✳✶✿ ❖r❞❡r ♦❢ ❝♦♠♣♦♥❡♥ts ✐♥ t❤❡ r❡s✉❧t✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

✸✳✷ ❈♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧

✸✳✷✳✶ ❚❡st s❡❝t✐♦♥

❚❤❡ ✜rst q✉❡st✐♦♥ ✇❤❡♥ ❞❡s✐❣♥✐♥❣ ❛ ✇✐♥❞ t✉♥♥❡❧ ✐s t❤❡ ♥❡❝❡ss❛r② s✐③❡ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❚❤❡ t❡st s❡❝t✐♦♥ ❝♦♥t❛✐♥s t❤❡ t❡st ♦❜❥❡❝t ❛♥❞ t❤❡r❡❢♦r❡ ✐s t❤❡ ❛r❡❛ ♦❢ t❤❡ ♠♦st ✐♥t❡r❡st✳

✶✼

✸ ▼❡t❤♦❞s

❚❤❡ s✐③❡ ♦❢ t❤❡ t❡st ♦❜❥❡❝t ♠✉st ♥♦t ❜❡ t♦♦ ❜✐❣ ❝♦♠♣❛r❡❞ t♦ t❤❡ s✐③❡ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❚❤❡ ♠❛✐♥ ❞❡s✐❣♥ ♣❛r❛♠❡t❡r ✐s t❤❡ ❜❧♦❝❦❛❣❡✳ ❚❤❡ ❜❧♦❝❦❛❣❡ ✐s ❝❛❧❝✉❧❛t❡❞ ❛s t❤❡ ❢r❛❝t✐♦♥ ♦❢t❤❡ ♣r♦❥❡❝t❡❞ ❛r❡❛ ♦❢ t❤❡ t❡st ♦❜❥❡❝t t♦ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡♣r♦❥❡❝t❡❞ ❛r❡❛ ♦❢ t❤❡ t❡st ♦❜❥❡❝t ✐s t❤❡ ❛r❡❛ t❤❡ s❤❛❞♦✇ ♦❢ t❤❡ t❡st ♦❜❥❡❝t ✇♦✉❧❞ ❤❛✈❡♦♥ ❛ ♣❧❛♥❡ ♥♦r♠❛❧ t♦ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❞✐r❡❝t✐♦♥✳ ❇❡❝❛✉s❡ ♦❢ t❤❡ ❜❧♦❝❦❛❣❡✱ t❤❡ ❡✛❡❝t✐✈❡✢♦✇ ❛r❡❛ ❞❡❝r❡❛s❡s✳ ❚❤❡r❡❢♦r❡ t❤❡ ✢♦✇ ✈❡❧♦❝✐t② ✐♥❝r❡❛s❡s ❛s ✇❡❧❧ ❛s t❤❡ s✉r❢❛❝❡ str❡ss❡s✳❚❤✐s ❧❡❛❞s t♦ r❡s✉❧ts t❤❛t ❛r❡ ❞✐✛❡r❡♥t ❢r♦♠ r❡s✉❧ts ✐♥ ❢r❡❡ ❛✐r ✇❤❡r❡ ♥♦ ❜❧♦❝❦❛❣❡ ♦❝❝✉rs✳❚♦ ❦❡❡♣ t❤❡ ❞✐✛❡r❡♥❝❡s s♠❛❧❧✱ t❤❡ ❜❧♦❝❦❛❣❡ s❤♦✉❧❞ ❜❡ ❛t ♠♦st 10% ❛❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇❡t ❛❧✳ ❬✷✵❪✳◆♦t ♦♥❧② t❤❡ t❡st ♦❜❥❡❝t ❤❛s ❛♥ ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ ✢♦✇ ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥ ❜✉t ❛❧s♦

t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❚❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ✐s ❛❝t✐✈❡ ✉♥t✐❧ ❛ ❞✐st❛♥❝❡ ♦❢ t❤❡✇❛❧❧ ♦❢ 10% ♦❢ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ t✇♦ ✇❛❧❧s ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ♦❢ ❇❛♥s♠❡r❡t ❛❧✳ ❬✸✶❪ ❛♥❞ 12% ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧ ♦❢ ❆r✐❢✉③③❛♠❛♥ ❛♥❞ ▼❛s❤✉❞ ❬✷✷❪✳ ❆s t❤✐s ✐s t❤❡❝❛s❡ ♦♥ ❜♦t❤ s✐❞❡s ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ✇✐❧❧ ✐♥✢✉❡♥❝❡ ❛❜♦✉t 20% ♦❢ t❤❡✇✐❞t❤ ❛♥❞ ❤❡✐❣❤t✳ ❍♦✇❡✈❡r✱ t❤✐s ✐s ❥✉st ❛ r✉❧❡ ♦❢ t❤✉♠❜✳ ❍❡♥❝❡✱ ✐t s❤♦✉❧❞ ♦♥❧② ❜❡ ✉s❡❞❛s ❛ ✜rst ❤✐♥t ❢♦r t❤❡ t❡st s❡❝t✐♦♥ ❞✐♠❡♥s✐♦♥s✳ ❋♦r t❤❡ ✜♥❛❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥✱ ❛❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r t❤✐❝❦♥❡ss s❤♦✉❧❞ ❜❡ ❞♦♥❡✳ ❚❤❡ st❡♣s t♦ ❝❛❧❝✉❧❛t❡ t❤❡❜♦✉♥❞❛r② ❧❛②❡r t❤✐❝❦♥❡ss ❡①❛❝t❧② ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ s❡❝t✐♦♥ ✸✳✼✳❚❤❡ ✢♦✇ ❛t t❤❡ tr❛♥s✐t✐♦♥ ❢r♦♠ t❤❡ ♥♦③③❧❡ t♦ t❤❡ t❡st s❡❝t✐♦♥ ✐s ✉♥s❡tt❧❡❞ ❛♥❞ ❝♦♥t❛✐♥s

❞✐st✉r❜❛♥❝❡s✳ ❚❤❡r❡❢♦r❡ ❛ s❤♦rt ❧❡♥❣t❤ ✇✐t❤ ❛ ❝♦♥st❛♥t ❝r♦ss✲s❡❝t✐♦♥ ✐s r❡❝♦♠♠❡♥❞❡❞❜❡❢♦r❡ t❤❡ t❡st ♦❜❥❡❝t✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞ t♦ ❛❧❧♦✇ t❤❡ ✢♦✇ ❛ s❡tt❧✐♥❣ ❧❡♥❣t❤♦❢ ❛❜♦✉t ✵✳✺ t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❢♦r t❤✐s ♣✉r♣♦s❡✳ ❚❤✐ss❡tt❧✐♥❣ ❧❡♥❣t❤ ✇✐❧❧ ❜❡ ✐♥❝❧✉❞❡❞ ❞✐r❡❝t❧② ✐♥t♦ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡ t❤❡ t❡st s❡❝t✐♦♥s❤♦✉❧❞ ♥♦t ❜❡ t♦♦ s❤♦rt ✐♥ ♦r❞❡r t♦ ❤❛✈❡ ❣♦♦❞ ✢♦✇ ❝♦♥❞✐t✐♦♥s✳ ■❢ t❤❡ t❡st s❡❝t✐♦♥ ✐s t♦♦❧♦♥❣ ❤♦✇❡✈❡r✱ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ✇✐❧❧ ❜❡ r❛t❤❡r t❤✐❝❦ ❛♥❞ ✇✐❧❧ ❞❡❝r❡❛s❡ t❤❡ ❡✛❡❝t✐✈❡ ✢♦✇❛r❡❛ ♠❛ss✐✈❡❧②✳ ■❢ ❛ ❧♦♥❣❡r t❡st s❡❝t✐♦♥ ✐s ♥❡❡❞❡❞ ♦r ✐❢ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✐s ❛❧r❡❛❞② t♦♦ ❜✐❣✱ t❤❡ t❡st s❡❝t✐♦♥ ❝❛♥ ❜❡ ❞❡s✐❣♥❡❞ ✇✐t❤ ❛ ✈❡r② s♠❛❧❧ ♦♣❡♥✐♥❣ ❛♥❣❧❡✳❚❤❡♥ t❤❡ ❡✛❡❝ts ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❣r♦✇t❤ ❛♥❞ t❤❡ ✐♥❝r❡❛s✐♥❣ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛❜❛❧❛♥❝❡ ❡❛❝❤ ♦t❤❡r✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞ ❛♥ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ 0.5◦ ✐♥ t❤✐s ❝❛s❡✳

✸✳✷✳✷ ◆♦③③❧❡

❲❤✐❧❡ t❤❡ t❡st s❡❝t✐♦♥ ❤❛s ❛ ❝♦♥st❛♥t ❝r♦ss✲s❡❝t✐♦♥❛❧ s❤❛♣❡✱ t❤❡ ♥♦③③❧❡ ❝♦♥tr❛❝ts t♦✇❛r❞st❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡ t❤❡ ✜rst ❞❡❝✐s✐♦♥ ❢♦r t❤❡ ❞❡s✐❣♥ ♦❢ ❛ ♥♦③③❧❡ ✐s ✐ts ❝♦♥tr❛❝t✐♦♥r❛t✐♦✱ ❛❧s♦ ❝❛❧❧❡❞ ❛r❡❛ r❛t✐♦✳ ❆❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✱ ♥♦③③❧❡s ♥♦r♠❛❧❧② ❤❛✈❡ ❛❝♦♥tr❛❝t✐♦♥ r❛t✐♦ ❜❡t✇❡❡♥ 6 ❛♥❞ 12 ❜✉t ❛❧s♦ s♠❛❧❧❡r ❛♥❞ ❧❛r❣❡r ✈❛❧✉❡s ❛r❡ ✉s❡❞✳ ❍✐❣❤❝♦♥tr❛❝t✐♦♥ r❛t✐♦s ❧❡❛❞ t♦ ❜❡tt❡r ✢♦✇ q✉❛❧✐t② ❛♥❞ r❡❞✉❝❡❞ s♣❡❡❞ ❛t t❤❡ ✉♣str❡❛♠ ❡♥❞✳ ❆tt❤❡ s❛♠❡ t✐♠❡✱ ❤✐❣❤ ❝♦♥tr❛❝t✐♦♥ r❛t✐♦s ❧❡❛❞ t♦ ❜✐❣❣❡r ❛♥❞ ❧♦♥❣❡r ❝♦♠♣♦♥❡♥ts ✉♣str❡❛♠♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❖♥❝❡ t❤❡ ❛r❡❛ r❛t✐♦ ✐s ❦♥♦✇♥✱ t❤❡ ❧❡♥❣t❤ ✐s t❤❡ ♥❡①t t♦♣✐❝ t♦ t❤✐♥❦ ❛❜♦✉t✳ ❚❤✐s ✐s

❜❡❝❛✉s❡ s❤♦rt ♥♦③③❧❡s ❤❛✈❡ ❛ ❤✐❣❤❡r ❝❤❛♥❝❡ ♦❢ s❡♣❛r❛t✐♦♥✱ ✇❤✐❧❡ ❧♦♥❣ ♥♦③③❧❡s ✐♥❝r❡❛s❡ t❤❡✇✐♥❞ t✉♥♥❡❧ ❧❡♥❣t❤✳ ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪ ❝♦❧❧❡❝t❡❞ ❞❛t❛ ❢r♦♠ ❡①✐st✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❲✐t❤t❤♦s❡ r❡s✉❧ts✱ t❤❡② ❡st✐♠❛t❡❞ ❤♦✇ ❧♦♥❣ ❛ ♥♦③③❧❡ s❤♦✉❧❞ ❜❡ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ r❛t✐♦ ♦❢ ✐♥❧❡t❛♥❞ ♦✉t❧❡t ❞✐❛♠❡t❡r✳ ❚❤❡ ❞❛t❛ ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ❆✳✶✳ ❲❤✐❧❡ ❛ ❢❡✇ ✇✐♥❞ t✉♥♥❡❧s ❤❛✈❡s❤♦rt❡r ♥♦③③❧❡s✱ t❤❡② ❞♦ r❡❝♦♠♠❡♥❞ t♦ ♥♦t ❣♦ ❜❡❧♦✇ t❤❡ s❤♦✇♥ ♠✐♥✐♠✉♠ ✈❛❧✉❡✳

✶✽

✸ ▼❡t❤♦❞s

❋✐♥❛❧❧②✱ t❤❡ ♥♦③③❧❡ ❝♦♥t♦✉r ✐s ✐♠♣♦rt❛♥t ❛s ✇❡❧❧ ❢♦r t❤❡ s❡♣❛r❛t✐♦♥ ❛♥❞ ❛❧s♦ ❢♦r t❤❡❞r♦♣❧❡t ❜❡❤❛✈✐♦r✳ ❆❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✱ t❤❡ ✇❛❧❧ r❛❞✐✉s ♦❢ t❤❡ ❝✉r✈❛t✉r❡ ❛t t❤❡✇✐❞❡r ❡♥❞ s❤♦✉❧❞ ❜❡ ❤✐❣❤❡r t❤❛♥ ❛t t❤❡ s♠❛❧❧❡r ❡♥❞✳ ❚❤✐s ✐s ❞♦♥❡ t♦ r❡❞✉❝❡ t❤❡ ❝❤❛♥❝❡♦❢ s❡♣❛r❛t✐♦♥ ✐♥s✐❞❡ t❤❡ ♥♦③③❧❡✳❉✐✛❡r❡♥t ♥♦③③❧❡ ❞❡s✐❣♥s ✇❡r❡ ❝♦♠♣❛r❡❞ ❢♦r t❤✐s t❛s❦✳ ❋♦r t❤❡ ❡❛s❡ ♦❢ ❝♦♠♣❛r✐s♦♥✱ t❤❡②

❛r❡ ✇r✐tt❡♥ ❛❧❧ ✐♥ t❤❡ s❛♠❡ ❢♦r♠✿ z st❛♥❞s ❢♦r ❤❛❧❢ t❤❡ ✇✐❞t❤ ♦r ❤❡✐❣❤t ♦❢ t❤❡ ♥♦③③❧❡❛♥❞ t❤❡ s✉❜s❝r✐♣t TS ❞❡s❝r✐❜❡s t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡ ✐s L✱ x ✐s t❤❡❝♦♦r❞✐♥❛t❡ ✐♥ ✢♦✇ ❞✐r❡❝t✐♦♥✳ ❚❤❡ ✈❛❧✉❡ AR ❞❡♥♦t❡s t❤❡ ❝♦♥tr❛❝t✐♦♥ r❛t✐♦ ♦❢ t❤❡ ♥♦③③❧❡✳❚❤❡ ✜rst ♥♦③③❧❡ ❞❡s✐❣♥ ✐s t❤❡ ❆❱❆ ♥♦③③❧❡ ✇❤✐❝❤ ❝♦♥t♦✉r ✐s

z (x)

zTS

=(√

AR− 1)(

1− x

L

)3[

2−(

1− x

L

)3]

+ 1 ✭✸✳✶✮

❛❝❝♦r❞✐♥❣ t♦ ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✳❚❤❡ s❡❝♦♥❞ ♥♦③③❧❡ ❞❡s✐❣♥ ✐s t❤❡ ❲✐t♦s③②♥s❦✐ ♥♦③③❧❡ ✇❤♦s❡ ❝♦♥t♦✉r

z (x)

zTS

=1

√

1 +(

1AR

− 1)

[

1−( xL)

2]2

[

1+ 1

3( xL)

2]3

✭✸✳✷✮

✐s ❛❧s♦ ❣✐✈❡♥ ❜② ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✳❇❡❧❧ ❛♥❞ ▼❡❤t❛ ❬✸✸❪ ❝♦♠♣❛r❡❞ ❞✐✛❡r❡♥t ❝♦♥tr❛❝t✐♦♥ ❞❡s✐❣♥s✳ ❖♥❡ ✇❛s ❛ t❤✐r❞ ♦r❞❡r

♣♦❧②♥♦♠✐❛❧ ✇✐t❤ t❤❡ ❝♦♥t♦✉r

z (x)

zTS

=√AR−

(√AR− 1

)

[

−2(x

L

)3

+ 3(x

L

)2]

. ✭✸✳✸✮

❚❤❡ s❛♠❡ ❛✉t❤♦rs ❛❧s♦ r❡❝♦♠♠❡♥❞❡❞ ❛ ✜❢t❤ ♦r❞❡r ♣♦❧②♥♦♠✐❛❧ ✇✐t❤ t❤❡ ❝♦♥t♦✉r

z (x)

zTS

=√AR−

(√AR− 1

)

[

6(x

L

)5

− 15(x

L

)4

+ 10(x

L

)3]

. ✭✸✳✹✮

❇r❛ss❛r❞ ❛♥❞ ❋❡r❝❤✐❝❤✐ ❬✸✹❪ ♣r♦♣♦s❡❞ ❛♥ ✐♠♣r♦✈❡♠❡♥t t♦ t❤❡ ✜❢t❤ ♦r❞❡r ♣♦❧②♥♦✲

♠✐❛❧✳ ❚♦ ❞♦ t❤✐s✱ t❤❡② ✐♥tr♦❞✉❝❡❞ ❛ tr❛♥s❢♦r♠❛t✐♦♥ ❢✉♥❝t✐♦♥ f(

xL

)

✳ ❚❤✐s ❢✉♥❝t✐♦♥ ❤❛st♦ ❜❡ ❞❡✜♥❡❞ ❢♦r 0 ≤ x

L≤ 1 ✇✐t❤ ❛ ✈❛❧✉❡ 0 < f

(

xL

)

< 1✳ ❚❤❡♥ t❤❡ ❡q✉❛t✐♦♥ ❝❤❛♥❣❡s t♦

z (x)

zTS

=

[

−(

6(x

L

)5

− 15(x

L

)4

+ 10(x

L

)3)

[

1−√

1

AR

1/f(x/L)]

+ 1

]f(x)

. ✭✸✳✺✮

❆s ✇✐❧❧ ❜❡ ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♥❡①t ❝❤❛♣t❡r✱ ✐t ✐s ❜❡♥❡✜❝✐❛❧ ❢♦r t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ✐❢ t❤❡♣♦✐♥t ♦❢ st❡❡♣ ❝♦♥tr❛❝t✐♦♥ ✐s ❢✉rt❤❡r ✉♣str❡❛♠✳ ❆s t❤❡ ♣❛♣❡r ❜② ❇r❛ss❛r❞ ❛♥❞ ❋❡r❝❤✐❝❤✐❬✸✹❪ ✐♥❞✐❝❛t❡s✱ ✈❛❧✉❡s ♦❢ f

(

xL

)

❝❧♦s❡ t♦ 1 ❧❡❛❞ t♦ t❤❡ ❝♦♥t♦✉r ❜❡✐♥❣ st❡❡♣ ✐♥ ❛ ♠♦r❡✉♣str❡❛♠ ♣♦s✐t✐♦♥✳ ❚❤❡r❡❢♦r❡ f

(

xL

)

= 0.7 ✇❛s ❝❤♦s❡♥ ❢♦r t❤✐s t❤❡s✐s✳❚❤❡ ❧❛st ❝♦♥t♦✉r ❝❤❡❝❦❡❞ ✐♥ t❤✐s ✇♦r❦ ✐s ♠❛❞❡ ✉♣ ♦❢ t✇♦ ♠❛t❝❤❡❞ ❝✉❜✐❝s ❛s r❡❝♦♠✲

♠❡♥❞❡❞ ❜② ▼♦r❡❧ ❬✸✺❪✳ ❚❤❡ ❡①❛❝t ❡q✉❛t✐♦♥s ❛r❡ ❝♦♣✐❡❞ ❢r♦♠ ▼❛rt✐♥ ❬✸✻❪✳ ❚❤❡ ❡q✉❛t✐♦♥❢♦r t❤❡ ✜rst ❝✉❜✐❝ ✐s

z (x)

zTS

=(√

AR− 1)

[

1− 1(

xm

L

)2

(x

L

)3]

+ 1 ✭✸✳✻✮

✶✾

✸ ▼❡t❤♦❞s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tunnel axis normalized by nozzle length

-1

-0.5

0

0.5

1norm

aliz

ed a

xis

perp

endic

ula

r

to the tunnel axis

AVA

Witoszynski

fifth-order

transformed fifth-order

third-order

matched cubics

❋✐❣✉r❡ ✸✳✷✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs ❢♦r ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ ✾✳

❛♥❞ t❤❡ ❡q✉❛t✐♦♥ ❢♦r t❤❡ s❡❝♦♥❞ ❝✉❜✐❝ ✐s

z (x)

zTS

=

√AR− 1

(

1− xm

L

)2

(

1− x

L

)3

+ 1. ✭✸✳✼✮

❚❤❡ ❝♦♦r❞✐♥❛t❡ xm ✐s t❤❡ ❝♦♦r❞✐♥❛t❡ ✐♥ ①✲❞✐r❡❝t✐♦♥ ✇❤❡r❡ t❤❡ t✇♦ ❝✉❜✐❝s ♠❡❡t✳ ❚♦ ❤❛✈❡ ❛st❡❡♣ ❝♦♥tr❛❝t✐♦♥ ❢✉rt❤❡r ✉♣str❡❛♠✱ ❛ ❧♦✇ ✈❛❧✉❡ ♦❢ xm ✐s ❜❡♥❡✜❝✐❛❧✳ ❚❤✐s ✐s ✇❤② xm = 0.2✇❛s ❝❤♦s❡♥✳❆❧❧ ♥♦③③❧❡ ❝♦♥t♦✉rs ❛r❡ ❝♦♠♣❛r❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✷✳ ■t ❝❛♥ ❜❡ s❡❡♥ t❤❛t t❤❡ ❆❱❆ ❝♦♥t♦✉r✱

t❤❡ ❲✐t♦s③②♥s❦✐ ❝♦♥t♦✉r✱ ❛♥❞ t❤❡ ❝♦♥t♦✉r ✇✐t❤ t❤❡ ♠❛t❝❤❡❞ ❝✉❜✐❝s ❤❛✈❡ ❛ ❧❛r❣❡r s❧♦♣❡♦♥ ❛♥ ✉♣str❡❛♠ ♣♦s✐t✐♦♥ t❤❛♥ t❤❡ ♦t❤❡r ♥♦③③❧❡ ❝♦♥t♦✉rs✳ ❚❤✐s ✇✐❧❧ ❜❡ ✐♠♣♦rt❛♥t ✐♥ t❤❡❢♦❧❧♦✇✐♥❣ ❝❤❛♣t❡r✳❆♥♦t❤❡r ♣❛r❛♠❡t❡r t❤❛t ❝❛♥ ❜❡ ❝❤♦s❡♥ ✐s t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ s❤❛♣❡ ♦❢ t❤❡ ♥♦③③❧❡✳ ▼♦st

♦❢ t❤❡ ♥♦③③❧❡s ❛r❡ ❞❡s✐❣♥❡❞ ❝✐r❝✉❧❛r✳ ❙♦♠❡ s♦✉r❝❡s r❡♣♦rt ❛ ❤✐❣❤❡r ❝❤❛♥❝❡ ♦❢ s❡♣❛r❛t✐♦♥❢♦r r❡❝t❛♥❣✉❧❛r s❤❛♣❡❞ ♥♦③③❧❡s✳ ❚❤✐s ✐s ❞✉❡ t♦ t❤❡ s❡❝♦♥❞❛r② ✢♦✇ ❜❡t✇❡❡♥ t❤❡ ❝♦r♥❡rs❛♥❞ t❤❡ ❝❡♥t❡r❧✐♥❡✳ ▼❡❤t❛ ❬✸✼❪ ❤♦✇❡✈❡r st❛t❡s t❤❛t t❤❡ ❝♦r♥❡r ✢♦✇ st❛②s ❧♦❝❛❧✐③❡❞ ✐♥ t❤❡❛❜s❡♥❝❡ ♦❢ s❡♣❛r❛t✐♦♥✳ ❚❤❡r❡❢♦r❡ ❛ r❡❝t❛♥❣✉❧❛r ♥♦③③❧❡ ❝r♦ss✲s❡❝t✐♦♥ ✐s ❛❧s♦ ♣♦ss✐❜❧❡✳ ■❢s❡♣❛r❛t✐♦♥ ♦❝❝✉rs ✐♥s✐❞❡ r❡❝t❛♥❣✉❧❛r ♥♦③③❧❡s ♥❡✈❡rt❤❡❧❡ss✱ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞✉s✐♥❣ ❝♦r♥❡r ✜❧❧❡ts t♦ ❣✐✈❡ t❤❡ ♥♦③③❧❡ ❛♥ ♦❝t❛❣♦♥❛❧ s❤❛♣❡✳ ❚❤❡s❡ ✜❧❧❡ts s❤♦✉❧❞ ❤♦✇❡✈❡r❜❡ ❝♦♥t✐♥✉❡❞ t❤r♦✉❣❤ t❤❡ t❡st s❡❝t✐♦♥ ❛s ✇❡❧❧✳ ❉♦✇♥✐❡ ❡t ❛❧✳ ❬✸✽❪ ❞✐❞ ❝❛❧❝✉❧❛t✐♦♥s ♦❢r❡❝t❛♥❣✉❧❛r s❤❛♣❡❞ ❝♦♥tr❛❝t✐♦♥s ✇✐t❤ ❝❤❛♥❣✐♥❣ ❛s♣❡❝t r❛t✐♦s✳ ❚❤❡✐r ❝❛❧❝✉❧❛t✐♦♥s s❤♦✇❡❞t❤❛t ❞❡s✐❣♥s ✇✐t❤ ❝❤❛♥❣✐♥❣ ❛s♣❡❝t r❛t✐♦s ❛r❡ ♣♦ss✐❜❧❡✳ ❍♦✇❡✈❡r✱ t❤❡② ❛❧s♦ st❛t❡❞ t❤❛tt❤❡ ♣♦✐♥t ♦❢ ♠❛①✐♠✉♠ s❧♦♣❡ s❤♦✉❧❞ ❜❡ ❛t t❤❡ s❛♠❡ ♣♦s✐t✐♦♥ ❢♦r ❜♦t❤ t❤❡ ✈❡rt✐❝❛❧ ❛♥❞t❤❡ ❤♦r✐③♦♥t❛❧ ✇❛❧❧s✳

✷✵

✸ ▼❡t❤♦❞s

✸✳✷✳✸ ❙❡tt❧✐♥❣ ❛r❡❛

❚❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❝♦♥t❛✐♥s t❤❡ ❤♦♥❡②❝♦♠❜s ❛♥❞ t❤❡ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥✳ ■♥ t❤❡ ❝❛s❡ ♦❢ ❛♥✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ ❛❧s♦ t❤❡ s♣r❛② s②st❡♠ ✐s ❧♦❝❛t❡❞ ✐♥ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳❚❤❡ ❤♦♥❡②❝♦♠❜s ❛r❡ t②♣✐❝❛❧❧② ♣❧❛❝❡❞ ❢✉rt❤❡st ✉♣str❡❛♠✳ ❋♦r t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ❤♦♥❡②✲

❝♦♠❜s✱ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞ ❛ ❧❡♥❣t❤✲t♦✲❞✐❛♠❡t❡r r❛t✐♦ ❜❡t✇❡❡♥ ✻ ❛♥❞ ✽✳ ❚❤❡s❛♠❡ ❛✉t❤♦rs ❛❧s♦ st❛t❡ t❤❛t ❛r♦✉♥❞ ✶✺✵ ❤♦♥❡②❝♦♠❜s ♣❡r s❡tt❧✐♥❣ ❝❤❛♠❜❡r ❞✐❛♠❡t❡rs❤♦✉❧❞ ❜❡ ✉s❡❞✳ ❚❤✐s ✇♦✉❧❞ r❡s✉❧t ✐♥ ❛ t♦t❛❧ ♦❢ ✷✺✵✵✵ ❤♦♥❡②❝♦♠❜s✳❚❤❡ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥s ❞❛♠♣ t❤❡ ✢♦✇ ♥♦♥✲✉♥✐❢♦r♠✐t②✳ ❚♦ ❞♦ s♦ ❛ ❤✐❣❤ ❜❧♦❝❦❛❣❡ ♦❢

t❤❡ ❛✐r ✢♦✇ ✐s ♥❡❝❡ss❛r②✳ ❚❤❡ ❜❧♦❝❦❛❣❡ ✐s ❞❡s❝r✐❜❡❞ ❜② t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ♣♦r♦s✐t②✳ ❚❤❡♣♦r♦s✐t② ✐s t❤❡ r❛t✐♦ ♦❢ t❤❡ ❛r❡❛ t❤❡ ✢♦✇ ❝❛♥ ♣❛ss t❤r♦✉❣❤ t♦ t❤❡ t♦t❛❧ ❝r♦ss✲s❡❝t✐♦♥❛❧❛r❡❛ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ▲♦✇❡r ✈❛❧✉❡s ♦❢ ♣♦r♦s✐t② t❤❡r❡❢♦r❡ ✐♥❝r❡❛s❡ t❤❡ ❞❛♠♣✐♥❣ ♦❢t❤❡ ♥♦♥✲✉♥✐❢♦r♠✐t✐❡s✳ ❍♦✇❡✈❡r✱ ❛❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ t❤❡ s❝r❡❡♥s ♠✉st ❤❛✈❡ ❛♣♦r♦s✐t② ❣r❡❛t❡r t❤❛♥ 0.57✳ ❖t❤❡r✇✐s❡ t❤❡ ✢♦✇ ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥ ✇♦✉❧❞ ❜❡ ✉♥st❛❜❧❡✳❚❤❡ ♠❛①✐♠✉♠ ✈❛❧✉❡ ♦❢ ❛ ✉s❡❢✉❧ ♣♦r♦s✐t② ✐s ✵✳✽ ❛❝❝♦r❞✐♥❣ t♦ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✳▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇ ❬✸✾❪ r❡❝♦♠♠❡♥❞ t♦ ❦❡❡♣ ❛ ❞✐st❛♥❝❡ ♦❢ 0.2 t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝

❞✐❛♠❡t❡r ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❜❡t✇❡❡♥ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥s✳ ❚❤❡② ❛❧s♦ st❛t❡❞ t❤❛t t❤❡❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❧❛st s❝r❡❡♥ ❛♥❞ t❤❡ ♥♦③③❧❡ ❡♥tr② s❤♦✉❧❞ ❜❡ ❛❜♦✉t 0.2 s❡tt❧✐♥❣ ❛r❡❛❞✐❛♠❡t❡rs✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞ ✉s✐♥❣ ❛ t♦t❛❧ ❧❡♥❣t❤ ♦❢ 0.5 t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐✲❛♠❡t❡r ❢♦r s❡tt❧✐♥❣ ❛r❡❛s t❤❛t ❝♦♥t❛✐♥ ♦♥❡ ❤♦♥❡②❝♦♠❜ s❡❝t✐♦♥ ❛♥❞ ♦♥❡ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥✳

✸✳✷✳✹ ❲✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r

❇❡❝❛✉s❡ t❤❡ ❢❛♥ ✐s ❝❤♦s❡♥ t♦ ❜❡ ♦♥ t❤❡ ✉♣str❡❛♠ ❡♥❞ ❛♥❞ ♥♦t ♦♥ t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞✱t❤❡ ❢❛♥ ✐s ✉♣str❡❛♠ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❆s t❤❡ ❢❛♥ ✐s ♥♦r♠❛❧❧② s♠❛❧❧❡r ✐♥ s✐③❡ t❤❛♥ t❤❡s❡tt❧✐♥❣ ❛r❡❛✱ ❛ ❞✐✛✉s❡r ✐s ♥❡❡❞❡❞ t♦ ❝♦♥♥❡❝t t❤❡ ❢❛♥ ✇✐t❤ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❚♦ ❦❡❡♣ t❤❡❧❡♥❣t❤ ♦❢ t❤❡ ❞✐✛✉s❡r s❤♦rt✱ t②♣✐❝❛❧❧② ✈❡r② ❤✐❣❤ ♦♣❡♥✐♥❣ ❛♥❣❧❡s ❛r❡ ❝❤♦s❡♥✳ ❚❤❡r❡❢♦r❡s❡♣❛r❛t✐♦♥ ✇♦✉❧❞ ♦❝❝✉r ✐❢ ♥♦ ❛❝t✐♦♥ ✇❛s t❛❦❡♥✳ ❚♦ ♣r❡✈❡♥t s❡♣❛r❛t✐♦♥✱ ❞✐✛❡r❡♥t ♠❡t❤♦❞s❝❛♥ ❜❡ ✉s❡❞✳ ▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇ ❬✸✾❪ r❡♣♦rt t❤❛t t❤❡ ♠♦st ❝♦♠♠♦♥ ♠❡t❤♦❞ ✐s t♦✐♥❝❧✉❞❡ s❝r❡❡♥s ✐♥ t❤❡ ❞✐✛✉s❡r✳ ❆ ❞❡s✐❣♥ r✉❧❡ ✇❛s ❢♦r♠✉❧❛t❡❞ ❜② t❤❡ s❛♠❡ ❛✉t❤♦rs ❢♦rt❤❡ ✉s❛❣❡ ♦❢ s❝r❡❡♥s✳ ❋✐❣✉r❡ ❆✳✷ s❤♦✇s t❤❡ ♣♦ss✐❜❧❡ t♦t❛❧ ♦♣❡♥✐♥❣ ❛♥❣❧❡s ♦❢ ❛ ✇✐❞❡✲❛♥❣❧❡❞✐✛✉s❡r ❢♦r ❞✐✛❡r❡♥t ❛r❡❛ r❛t✐♦s ❛♥❞ ❞✐✛❡r❡♥t ♥✉♠❜❡rs ♦❢ s❝r❡❡♥s✳ ❚❤❡ s❝r❡❡♥s s❤♦✉❧❞ ❜❡s♣❛❝❡❞ ❡q✉❛❧❧② ✐♥s✐❞❡ t❤❡ ❞✐✛✉s❡r ❛❝❝♦r❞✐♥❣ t♦ ▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇ ❬✸✾❪ ✐❢ ♥♦ ♣♦s✐t✐♦♥ ♦❢t❤❡ ❞✐✛✉s❡r ✐s ♠♦r❡ ♣r♦♥❡ t♦ s❡♣❛r❛t❡ t❤❛♥ t❤❡ ♦t❤❡rs✳ ❚❤❡ ✜rst s❝r❡❡♥ s❤♦✉❧❞ ♥♦r♠❛❧❧②❜❡ ♣❧❛❝❡❞ ✈❡r② ❝❧♦s❡ t♦ t❤❡ ❡♥tr❛♥❝❡ ♦❢ t❤❡ ❞✐✛✉s❡r✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ r❛♣✐❞ ♦♣❡♥✐♥❣ ❛tt❤❡ ❡♥tr❛♥❝❡ ♦❢t❡♥ ❧❡❛❞s t♦ s❡♣❛r❛t✐♦♥ ❛❧r❡❛❞②✳ ❖t❤❡r ♣❛ss✐✈❡ ♦♣t✐♦♥s ❛r❡ t♦ ✉s❡ s♣❧✐tt❡rs♦r ✈❛♥❡s t♦ r❡❞✉❝❡ t❤❡ ❡✛❡❝t✐✈❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ t❤❡ ❞✐✛✉s❡r✳ ❆❧s♦ ✈♦rt❡① ❣❡♥❡r❛t♦rs♦r s✉❝t✐♦♥ ❝❛♥ ❜❡ ✉s❡❞ t♦ ♣r❡✈❡♥t s❡♣❛r❛t✐♦♥✳ ❚❤♦s❡ ♠❡t❤♦❞s ❤♦✇❡✈❡r ❛r❡ ♠✉❝❤ ♠♦r❡❝♦♠♣❧✐❝❛t❡❞✱ ❛❧s♦ ❜❡❝❛✉s❡ t❤❡② ❛r❡ ❛❝t✐✈❡ s②st❡♠s✳

✸✳✷✳✺ ❋❛♥

❚❤❡ ❡q✉❛t✐♦♥s t♦ ❝❛❧❝✉❧❛t❡ t❤❡ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss❡s ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ ❡①♣❧❛✐♥❡❞ ✐♥❙❡❝t✐♦♥ ✸✳✹✳ ❆❞❞✐t✐♦♥❛❧❧② t♦ ❝♦♠♣❡♥s❛t✐♥❣ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s✱ t❤❡ ❢❛♥ ♠✉st ❛❧s♦ ❜❡ ❛❜❧❡

✷✶

✸ ▼❡t❤♦❞s

t♦ ❞❡❧✐✈❡r t❤❡ ♥❡❝❡ss❛r② ✈♦❧✉♠❡ ✢♦✇

V = uA ✭✸✳✽✮

t❤r♦✉❣❤ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❋♦r ρ = const.✱ t❤❡ ✈♦❧✉♠❡ ✢♦✇ ✐s t❤❡ s❛♠❡ ✐♥ t❤❡ ✇❤♦❧❡✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡r❡❢♦r❡ ✐t ✐s ❡❛s✐❡st t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♠❛①✐♠✉♠ ✈♦❧✉♠❡ ✢♦✇ ✇✐t❤ t❤❡❝♦♥❞✐t✐♦♥s ❛t t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ♠❛①✐♠✉♠ s♣❡❡❞ ❛t t❤❡ t❡st s❡❝t✐♦♥ ✐s❛ r❡q✉✐r❡♠❡♥t ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ♥❡❡❞st♦ ❜❡ ❦♥♦✇♥ ❜❡❢♦r❡ ❜❡✐♥❣ ❛❜❧❡ t♦ ❞❡s✐❣♥ t❤❡ ♦t❤❡r ❝♦♠♣♦♥❡♥ts✳❉✐✛❡r❡♥t ❢❛♥ ♦♣t✐♦♥s ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣❡♥s❛t❡ ❢♦r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞ ❞❡❧✐✈❡r t❤❡

♥❡❝❡ss❛r② ✈♦❧✉♠❡ ✢♦✇✳ ❋♦r t❤✐s t❤❡s✐s✱ t❤r❡❡ ♣♦ss✐❜❧❡ ❢❛♥ s❡❝t✐♦♥ ❞❡s✐❣♥s ❛r❡ ❞❡s❝r✐❜❡❞✳❚❤❡ ✜rst ♦♥❡ ✐s t❤❡ ✉s❡ ♦❢ ❛ ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡r✳ ▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇ ❬✸✾❪ ❞❡s❝r✐❜❡

t❤❡ ❛❞✈❛♥t❛❣❡ ♦❢ ❝❡♥tr✐❢✉❣❛❧ ❢❛♥s t♦ ❜❡ t❤❛t t❤❡✐r ♣❡r❢♦r♠❛♥❝❡ ✐s t②♣✐❝❛❧❧② ♠♦r❡ st❛❜❧❡♦✈❡r ❛ ✇✐❞❡r r❛♥❣❡ ♦❢ ❧♦❛❞s✳ ❆♥♦t❤❡r ❛r❣✉♠❡♥t ❢♦r ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡rs ✐s t❤❛t t❤❡ s❤❛♣❡♦❢ t❤❡ ❡①✐t ❝❛♥ ✈❛r② ❛♥❞ ❜❡ ❡✐t❤❡r r❡❝t❛♥❣✉❧❛r ♦r sq✉❛r❡✳ ❚❤✐s ✐s ❛♥ ❛❞✈❛♥t❛❣❡ ❛s ❛❝❤❛♥❣❡ ♦❢ s❤❛♣❡ ♥❡❡❞s t♦ t❛❦❡ ♣❧❛❝❡ ✐❢ t❤❡ ❢❛♥ ❛♥❞ t❤❡ t❡st s❡❝t✐♦♥ ❤❛✈❡ ❞✐✛❡r❡♥t s❤❛♣❡s✳❙✉❝❤ ❛ ❝❤❛♥❣❡ ♦❢ s❤❛♣❡ ❝❛♥ ✐♥tr♦❞✉❝❡ ♣r♦❜❧❡♠s ✇✐t❤ t❤❡ ✢♦✇ q✉❛❧✐t② ❛♥❞ ❡✈❡♥ ❧❡❛❞ t♦s❡♣❛r❛t✐♦♥✳ ❚❤❡ ❜✐❣❣❡st ❛r❣✉♠❡♥t ❛❣❛✐♥st t❤❡ ✉s❡ ♦❢ ❛ ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡r ✐s t❤❛t t❤❡②♥❡❡❞ ❛ ❧♦t ♦❢ s♣❛❝❡✳ ❖❢t❡♥ t❤❡ ❧❡♥❣t❤ ♦❢ ❛ ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡r ✐s ❛❜♦✉t t✇♦ t✐♠❡s t❤❡❧❡♥❣t❤ ♦❢ ❛♥ ❛①✐❛❧ ❢❛♥ ✇✐t❤ ❝♦♠♣❛r❛❜❧❡ ♣♦✇❡r✳❚❤❡ s❡❝♦♥❞ ♦♣t✐♦♥ ✐s t❤❡ ✉s❡ ♦❢ ♦♥❡ ❛①✐❛❧ ❢❛♥✳ ❆❝❝♦r❞✐♥❣ t♦ ❙❛✈✐♦ ❙r❧ ❬✹✵❪✱ ❛①✐❛❧ ❢❛♥s

❛r❡ t②♣✐❝❛❧❧② s♠❛❧❧❡r✱ ❧✐❣❤t❡r✱ ❛♥❞ ❧❡ss ❡①♣❡♥s✐✈❡ t❤❛♥ ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡rs✳ ❆❞❞✐t✐♦♥❛❧❧②✱❛❝❝♦r❞✐♥❣ t♦ t❤✐s s♦✉r❝❡✱ ♥♦ ❞✐r❡❝t ✐♠♣❛❝t ♦❢ t❤❡ ❝❤♦✐❝❡ ♦❢ t❤❡ ❢❛♥ ♦♥ t❤❡ ✢♦✇ q✉❛❧✐t② ❝❛♥❜❡ s❡❡♥✳ ❆s ❛①✐❛❧ ❢❛♥s ❛r❡ ❛❧✇❛②s ❝✐r❝✉❧❛r✱ t❤❡② ✜t ❣♦♦❞ ❢♦r ❝✐r❝✉❧❛r ✇✐♥❞ t✉♥♥❡❧s ❛♥❞❝❛♥ ❛❧s♦ ❜❡ ✐♥tr♦❞✉❝❡❞ ✐♥t♦ sq✉❛r❡ ♦♥❡s ✇✐t❤♦✉t ♠❛♥② ♣r♦❜❧❡♠s✳ ■❢ ❛①✐❛❧ ❢❛♥s s❤❛❧❧ ❜❡✐♥❝❧✉❞❡❞ ✐♥ ✇✐♥❞ t✉♥♥❡❧s ✇✐t❤ r❡❝t❛♥❣✉❧❛r ❝r♦ss✲s❡❝t✐♦♥s✱ ✐t r❡q✉✐r❡s ♠♦r❡ ❡✛♦rt ❤♦✇❡✈❡r✱❛s ❛ ❝❤❛♥❣❡ ♦❢ s❤❛♣❡ ♥❡❡❞s t♦ t❛❦❡ ♣❧❛❝❡ ❜❡t✇❡❡♥ t❤❡ t❡st s❡❝t✐♦♥ ❛♥❞ t❤❡ ❢❛♥✳❚❤❡ t❤✐r❞ ♣♦ss✐❜✐❧✐t② ✐s t❤❡ ✉s❡ ♦❢ ♠✉❧t✐♣❧❡ ❛①✐❛❧ ❢❛♥s ❛s ♣r♦♣♦s❡❞ ❜② ❍❡r♥á♥❞❡③

❡t ❛❧✳ ❬✹✶❪✳ ❖♥❡ ♦❢ t❤❡ ❛❞✈❛♥t❛❣❡s ♦❢ t❤✐s ♦♣t✐♦♥ ✐s t❤❛t s♠❛❧❧❡r ❢❛♥s ❝❛♥ ❜❡ ❝❤♦s❡♥✳❚❤✐s ❞❡❝r❡❛s❡s t❤❡ ❝♦sts ❢♦r t❤❡ ❢❛♥s✳ ❆❞❞✐t✐♦♥❛❧❧② s♠❛❧❧❡r ❢❛♥s ✐♥ ❞✐❛♠❡t❡r ❛r❡ ♥♦r♠❛❧❧②❛❧s♦ s❤♦rt❡r ✐♥ ❧❡♥❣t❤✳ ❚❤❡r❡❢♦r❡ ♣r♦❜❛❜❧② ❧❡ss s♣❛❝❡ ✇♦✉❧❞ ❜❡ ♥❡❡❞❡❞ ❝♦♠♣❛r❡❞ t♦ t❤❡♦t❤❡r ♦♣t✐♦♥s✳ ❆♥♦t❤❡r ❛❞✈❛♥t❛❣❡ ✐s t❤❛t ❞❡s✐❣♥s ✇✐t❤ ❞✐✛❡r❡♥t ❛♠♦✉♥ts ♦❢ ❢❛♥s ✐♥ ❡❛❝❤❞✐r❡❝t✐♦♥ ❛r❡ ♣♦ss✐❜❧❡✳ ❍❡♥❝❡✱ ❛❧s♦ ❛ r❡❝t❛♥❣✉❧❛r ❢❛♥ s❡❝t✐♦♥ s❤❛♣❡ ❝❛♥ ❜❡ ❛❝❤✐❡✈❡❞✳❍♦✇❡✈❡r✱ t❤❡r❡ ✐s ♦♥❡ ❜✐❣ ❞✐s❛❞✈❛♥t❛❣❡✳ ❲✐t❤ t❤❡ ✉s❡ ♦❢ ♠✉❧t✐♣❧❡ ❢❛♥s✱ t❤❡ ✉♥✐❢♦r♠✐t② ♦❢t❤❡ ✢♦✇ ♠✐❣❤t ❜❡ ❛✛❡❝t❡❞ ♥❡❣❛t✐✈❡❧②✳ ▼♦st ♦❢ t❤❡ t✐♠❡ ✇❤❡♥ ♠✉❧t✐♣❧❡ ❢❛♥s ❛r❡ ✉s❡❞✱ t❤❡②❛r❡ ♣❧❛❝❡❞ ❞♦✇♥str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤✐s ♥♦r♠❛❧❧② ❤❛s ❧♦✇❡r ✐♥✢✉❡♥❝❡s ♦♥ t❤❡ ✢♦✇q✉❛❧✐t② ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥✳ ■♥ ♦✉r ❝❛s❡✱ t❤❡ ❢❛♥ ✐s ♣❧❛❝❡❞ ✉♣str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❚❤❡r❡❢♦r❡ s❤♦rt❝♦♠✐♥❣s ✐♥ ✢♦✇ q✉❛❧✐t② ♦r ✢♦✇ ✉♥✐❢♦r♠✐t② ♠❛② ❤❛✈❡ ❛ ❤✉❣❡ ❞♦✇♥str❡❛♠✐♥✢✉❡♥❝❡ ❛♥❞ ❞❡❝r❡❛s❡ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ♠❡❛s✉r❡♠❡♥ts ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥ str♦♥❣❧②✳

✸✳✷✳✻ ❉✐✛✉s❡r

❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞ t❤❡ t❛s❦ ♦❢ t❤❡ ❡①✐t ❞✐✛✉s❡r ✐s t♦ ❡♥s✉r❡ ❛ ❣♦♦❞ ♣r❡ss✉r❡ r❡❝♦✈❡r②✳❋❧♦✇ s❡♣❛r❛t✐♦♥ ❝❛♥ ♠❛②❜❡ ❜❡ ❛❝❝❡♣t❡❞ ✉♥t✐❧ ❛ ❝❡rt❛✐♥ ❞❡❣r❡❡✳ ❚❤✐s ✐s ✇❤② ❇❛r❧♦✇ ❡t ❛❧✳

✷✷

✸ ▼❡t❤♦❞s

❬✷✵❪ r❡❝♦♠♠❡♥❞ ❛♥ ❡q✉✐✈❛❧❡♥t ❝♦♥✐❝❛❧ ❛♥❣❧❡

θe = arctan

(

r2 − r1L

)

= arctan

(

1

2

√AR− 1

L/d1

)

✭✸✳✾✮

❜❡t✇❡❡♥ 2◦ ❛♥❞ 3.5◦✳ ❚❤❡ ❤②❞r❛✉❧✐❝ r❛❞✐✐ ri ❛♥❞ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡rs di ❛r❡ ♠❡❛s✉r❡❞ ❛tt❤❡ ❡♥tr❛♥❝❡ ♣♦s✐t✐♦♥ 1 ❛♥❞ t❤❡ ❡①✐t ♣♦s✐t✐♦♥ 2 ♦❢ t❤❡ ❞✐✛✉s❡r✳ ❚❤❡ r❡❝♦♠♠❡♥❞❡❞ ❛r❡❛r❛t✐♦ ♦❢ t❤❡ ❞✐✛✉s❡r ✐s ❜❡t✇❡❡♥ ✷ ❛♥❞ ✸✳ ❚❤❡ r❡s✉❧t✐♥❣ ❞✐✛✉s❡r ❧❡♥❣t❤ s❤♦✉❧❞ ❜❡ ❛❜♦✉t ✸♦r ✹ t✐♠❡s t❤❡ t❡st s❡❝t✐♦♥ ❧❡♥❣t❤✳ ❲❤✐❧❡ t❤♦s❡ r❡❝♦♠♠❡♥❞❛t✐♦♥s ❛♥❞ r✉❧❡s ❛r❡ ❞❡✈❡❧♦♣❡❞❢♦r ❝❧♦s❡❞✲r❡t✉r♥ t✉♥♥❡❧s✱ ✇✐t❤ ❛ s♠❛❧❧ s❛❢❡t② ♠❛r❣✐♥ t❤❡② ❝❛♥ ❛❧s♦ ❜❡ ❛♣♣❧✐❡❞ ❢♦r ♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ s❤❛♣❡ ♦❢ t❤❡ ❞✐✛✉s❡r ✐s ♥♦t t♦♦ ✐♠♣♦rt❛♥t✱❛❧t❤♦✉❣❤ ❛ ❝r♦ss✲s❡❝t✐♦♥ ✇✐t❤ ❝♦r♥❡rs ♠✐❣❤t ✐♥❝r❡❛s❡ t❤❡ r✐s❦ ♦❢ s❡♣❛r❛t✐♦♥ ❛ ❧✐tt❧❡ ❜✐t✳

✸✳✸ ❉r♦♣❧❡ts ✐♥s✐❞❡ t❤❡ t✉♥♥❡❧

❆s ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ ❞r♦♣❧❡t ❝❧♦✉❞s ♥♦r♠❛❧❧② ❝♦♥t❛✐♥ ❛ r❛♥❣❡ ♦❢ ❞✐✛❡r❡♥t❞r♦♣❧❡t s✐③❡s✳ ❚❤❡ ❞✐str✐❜✉t✐♦♥ ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥ t♦ ❞♦ ❝❛❧❝✉❧❛t✐♦♥s ❢♦r ❝❡rt❛✐♥ ▼❱❉s✳❖t❤❡r✇✐s❡✱ t❤❡ ❞✐✛❡r❡♥t ❜❡❤❛✈✐♦r ♦❢ ❞r♦♣❧❡ts ✇✐t❤ ❛ s♠❛❧❧❡r ♦r ❜✐❣❣❡r ❞✐❛♠❡t❡r t❤❛♥ t❤❡▼❱❉ ✇✐❧❧ ♥♦t ❜❡ ❝♦♥s✐❞❡r❡❞✳ ❚❤✐s ✇♦✉❧❞ ❧❡❛❞ t♦ ❡rr♦rs ✐❢ t❤❡ r❡s✉❧ts ❛r❡ ❝♦♠♣❛r❡❞ t♦ r❡❛❧✲❧✐❢❡ ❡①♣❡r✐♠❡♥ts✳ ❆❝❝♦r❞✐♥❣ t♦ ●❡♥t ❡t ❛❧✳ ❬✶✽❪✱ t❤❡ ♠♦st ❝♦♠♠♦♥ ❛♣♣r♦❛❝❤ t♦ r❡❜✉✐❧❞✐♥❣t❤❡ ❞✐str✐❜✉t✐♦♥ t❤❛t ♦❝❝✉rs ✐♥ ♥❛t✉r❡ ✐s t❤❡ ▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥✳ ❚❤❡s❡ ❛✉t❤♦rs❛❧s♦ st❛t❡ t❤❛t t❤✐s ❞✐str✐❜✉t✐♦♥ ✐s ✇❡❧❧ s✉✐t❡❞ t♦ ❝♦✈❡r t❤❡ t②♣✐❝❛❧ ❞r♦♣❧❡t ❞✐str✐❜✉t✐♦♥♦❢ ❛ s♣r❛② s②st❡♠ ♦❢ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞r♦♣❧❡t s✐③❡s ❛❝❝♦r❞✐♥❣t♦ ▲❛♥❣♠✉✐r ❉ ✐s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✸✳✶✳ ❍❡♥❝❡✱ t❤❡ ❜✐❣❣❡st ❞r♦♣❧❡ts ✇✐❧❧ ❜❡ ❛❜♦✉t 2.22t✐♠❡s ❜✐❣❣❡r t❤❛♥ t❤❡ ▼❱❉✳ ❚❤✐s ✐s ✇❤② s✐♠✉❧❛t✐♦♥s ❛r❡ ❞♦♥❡ ✇✐t❤ ✇❛② ❜✐❣❣❡r ❞r♦♣❧❡t❞✐❛♠❡t❡rs t❤❛♥ t❤❡ ▼❱❉s t❤❛t ❛r❡ ♥❡❝❡ss❛r② ❢♦r ♦❜t❛✐♥✐♥❣ ✢✐❣❤t ❛❧❧♦✇❛♥❝❡ ❜② t❤❡ ❊❆❙❆✳❚❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ ❞r♦♣❧❡ts ✇❤❡♥ t❤❡② ❛r❡ ✐♥❥❡❝t❡❞ ✐♥t♦ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡

❞✐✛❡r❡♥t ❢r♦♠ t❤❡ t❡♠♣❡r❛t✉r❡ t❤❡ ❞r♦♣❧❡ts s❤❛❧❧ ❤❛✈❡ ✇❤❡♥ r❡❛❝❤✐♥❣ t❤❡ t❡st ♦❜❥❡❝t✳❚❤❡ s❛♠❡ ✇✐❧❧ ✉s✉❛❧❧② ❜❡ tr✉❡ ❢♦r t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❞r♦♣❧❡ts✳ ❚❤❡r❡❢♦r❡ ❝❛❧❝✉❧❛t✐♦♥s ♦♥t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛♥❞ t❡♠♣❡r❛t✉r❡ ♥❡❡❞ t♦ ❜❡ ❞♦♥❡✳

❞✐❛♠❡t❡r✴▼❱❉ ❢r❛❝t✐♦♥ ♦❢ ▲❲❈ ❬%❪

0.31 50.52 100.71 201.00 301.37 201.74 102.22 5

❚❛❜❧❡ ✸✳✶✿ ❉r♦♣❧❡t s✐③❡ ❞✐str✐❜✉t✐♦♥ ✇✐t❤ t❤❡ ▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥ ❛❝❝♦r❞✐♥❣ t♦ ▲❛♥❣✲♠✉✐r ❛♥❞ ❇❧♦❞❣❡tt ❬✹✷❪✳

✷✸

✸ ▼❡t❤♦❞s

✸✳✸✳✶ ❉r♦♣❧❡t ✈❡❧♦❝✐t② ❛♥❞ tr❛❥❡❝t♦r✐❡s

❚❤❡ ✈❡❧♦❝✐t② ♦❢ ❛ ❞r♦♣❧❡t ✐♥s✐❞❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❡q✉❛t✐♦♥s ♦❢♠♦t✐♦♥s✳ ❋♦r ❛ s✐♥❣❧❡ ❞r♦♣❧❡t✱ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥ ❜❡❝♦♠❡s

mdd~u

dt= −md~g +

1

2ρairAdcD |~u− ~v| (~v − ~u) ✭✸✳✶✵✮

❛❝❝♦r❞✐♥❣ t♦ ●❛t❡s ❡t ❛❧✳ ❬✶✹❪✳ ❚❤❡ s❛♠❡ ❛✉t❤♦rs ❛❧s♦ st❛t❡ t❤❛t t❤❡ ❞r♦♣❧❡ts ❝❛♥ ❜❡❛ss✉♠❡❞ t♦ ❜❡ r✐❣✐❞ s♣❤❡r❡s✳ ❚❤❡r❡❢♦r❡ t❤❡✐r ♠❛ss ✐s

md = 4/3πr3dρd. ✭✸✳✶✶✮

❚❤❡ s❡❝♦♥❞ t❡r♠ ♦♥ t❤❡ ❧❡❢t s✐❞❡ ✐s t❤❡ t✐♠❡ ❞❡r✐✈❛t✐✈❡ ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ~u✳ ❚❤❡ ✜rstt❡r♠ ♦♥ t❤❡ r✐❣❤t s✐❞❡ ❞❡♥♦t❡s t❤❡ ❣r❛✈✐t❛t✐♦♥❛❧ ❢♦r❝❡s✳ ●r❛✈✐t❛t✐♦♥ ✐s ❥✉st r❡❧❡✈❛♥t ❢♦rt❤❡ ❞✐r❡❝t✐♦♥ ♣♦✐♥t✐♥❣ t♦✇❛r❞s ❡❛rt❤✳ ❚❤❡♥ t❤❡ ❣r❛✈✐t❛t✐♦♥ g = 9.81m s−2 ✐s ❛❝t✐✈❡✳ ❚❤❡s❡❝♦♥❞ t❡r♠ ♦♥ t❤❡ r✐❣❤t s✐❞❡ ❞❡s❝r✐❜❡s t❤❡ ❞r❛❣ ❢♦r❝❡s✳ ❚❤❡ ❞r❛❣ ❢♦r❝❡ ❞❡♣❡♥❞s ♦♥ t❤❡❞✐✛❡r❡♥❝❡ ♦❢ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❞r♦♣❧❡ts ~u ❛♥❞ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❛✐r ~v✳ ❚❤❡ ♣r♦❥❡❝t❡❞❛r❡❛ ♦❢ t❤❡ ❞r♦♣❧❡t

Ad = πr2 = 0.25πd2 ✭✸✳✶✷✮

✐s t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t ❛s ✇❡❧❧ ❛s t❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t cD✳ ❆s ✇❛t❡r ❞r♦♣❧❡ts ✐♥ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧s ❝❛♥ ✉s✉❛❧❧② ❜❡ ❛ss✉♠❡❞ t♦ ❜❡ r✐❣✐❞ s♣❤❡r❡s✱ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ▼♦rr✐s♦♥ ❬✹✸❪ ❢♦r t❤❡❞r❛❣ ❝♦❡✣❝✐❡♥t

cD =24

Re+

2.6(

Re5.0

)

1 +(

Re5.0

)1.52 +0.411

(

Re2.63·105

)

−7.94

1 +(

Re2.63·105

)

−8.00 +0.25

(

Re106

)

1 +(

Re106

) ✭✸✳✶✸✮

❝❛♥ ❜❡ ✉s❡❞ ✐♥ t❤✐s ❝❛s❡✳ ❚❤❡ ✈❡❧♦❝✐t② ✐♥ t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s t❤❡✈❡❧♦❝✐t② ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛✐r ❛♥❞ ❞r♦♣❧❡t✳ ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪ ❛❧s♦ ❝❛❧❝✉❧❛t❡❞ t❤❡ s♣❡❡❞♦❢ ❞r♦♣❧❡ts ❞✉r✐♥❣ t❤❡✐r ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥✳ ❍♦✇❡✈❡r✱ t❤❡② ✉s❡❞ ❛ ❞✐✛❡r❡♥t ❡q✉❛t✐♦♥ t♦❝❛❧❝✉❧❛t❡ t❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t✳ ❆ ❝♦♠♠❡♥t ❛❜♦✉t t❤❡✐r ❝❤♦✐❝❡ ❛♥❞ t❤❡ ✐♥✢✉❡♥❝❡ ❝❛♥ ❜❡❢♦✉♥❞ ♦♥ t❤❡ ❈❉✳❚♦ s♦❧✈❡ ❡q✉❛t✐♦♥ ✸✳✶✵✱ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❛✐r ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥✳ ■❢ t❤❡ ❝♦♥t♦✉r ♦❢

t❤❡ ♥♦③③❧❡ ✐s ❦♥♦✇♥✱ ❛❧s♦ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ♦❢ t❤❡ ♥♦③③❧❡ ✐s ❦♥♦✇♥ ❛t ❡❛❝❤ ♣♦s✐t✐♦♥✳❲✐t❤ t❤✐s ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥✱ t❤❡ ✈❡❧♦❝✐t② ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞✳ ❆st❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ♦♣❡r❛t❡ ❛t ❧♦✇ ▼❛❝❤ ♥✉♠❜❡rs✱ t❤❡ ❞❡♥s✐t② ❝❛♥ ❜❡ ❛ss✉♠❡❞ t♦ ❜❡❝♦♥st❛♥t✳ ❚❤❡r❡❢♦r❡ t❤❡ ❡q✉❛t✐♦♥ ❝❛♥ ❜❡ s✐♠♣❧✐✜❡❞ ❛♥❞ ❥✉st t❤❡ ✈❡❧♦❝✐t② ❛t ♦♥❡ s♣♦t♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥✳ ❚❤❡ ❛✐r s♣❡❡❞ ❛t t❤❡ t❡st s❡❝t✐♦♥ ✐s ✉s✉❛❧❧② t❤❡ t❛r❣❡t ✈❡❧♦❝✐t② ♦❢ t❤❡❞r♦♣❧❡ts✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❞r♦♣❧❡ts ❛❞❥✉st ❛s②♠♣t♦t✐❝❛❧❧② t♦ t❤❡ ❛✐r s♣❡❡❞✳ ❆s t❤❡✈❡❧♦❝✐t② ♦❢ t❤❡ ❛✐r ❛t t❤❡ ❡①✐t ♦❢ t❤❡ ♥♦③③❧❡ ✐s t❤❡ s❛♠❡ ❛s ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥✱ t❤❡ ❛✐rs♣❡❡❞ ❛t ❡❛❝❤ ♣♦s✐t✐♦♥ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤

v (x) =vTSATS

A (x). ✭✸✳✶✹✮

❚❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥ ✐s ❛ ❞✐✛❡r❡♥t✐❛❧ ❡q✉❛t✐♦♥✳ ❇♦t❤ t❤❡ ❞❡r✐✈❛t✐✈❡ ♦❢ t❤❡ ❞r♦♣❧❡t✈❡❧♦❝✐t② ❛♥❞ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛r❡ ✐♥❝❧✉❞❡❞ ❛s ✇❡❧❧ ❛s t❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t t❤❛t ❛❧s♦

✷✹

✸ ▼❡t❤♦❞s

❞❡♣❡♥❞s ♦♥ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t②✳ ❚❤❡r❡❢♦r❡ ❛♥ ❡❛s② ❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥ ✐s ♥♦t ♣♦ss✐✲❜❧❡✳ ❍♦✇❡✈❡r✱ t❤❡ ❞❡r✐✈❛t✐✈❡s ❝❛♥ ❜❡ ❛ss✉♠❡❞ t♦ ❜❡ ❞✐✛❡r❡♥❝❡s✳ ❲✐t❤ t❤✐s st❡♣ ❛♥❞ ❛r❡❛rr❛♥❣❡♠❡♥t ♦❢ t❤❡ ❞✐✛❡r❡♥t t❡r♠s✱ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥s ❝❛♥ ❜❡ ❢♦r♠✉❧❛t❡❞ ❛s✿

∆u =1

2ρair

Ad

md

cD |~u− ~v| (~v − ~u)∆t. ✭✸✳✶✺✮

◆♦✇ ❛ t✐♠❡✲st❡♣ ♣r♦❝❡❞✉r❡ ❝❛♥ ❜❡ ✉s❡❞✳ ❊q✉❛t✐♦♥ ✸✳✶✺ ✐s s♦❧✈❡❞ ❢♦r ❡✈❡r② t✐♠❡ st❡♣ ❛♥❞t❤❡ ♥❡✇ ✈❡❧♦❝✐t② ✐s s✉♠♠❡❞ ✉♣ ❜② t❤❡ ♦❧❞ ✈❡❧♦❝✐t② ❛♥❞ t❤❡ ♥❡✇ ❝❛❧❝✉❧❛t❡❞ ∆u✳ ❚❤❡r❡q✉✐r❡❞ ✈❛❧✉❡s ❢♦r t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ♦♥ t❤❡ r✐❣❤t s✐❞❡ ♦❢ t❤❡ ❡q✉❛t✐♦♥ ❝❛♥ ❥✉st ❜❡t❛❦❡♥ ❢r♦♠ t❤❡ ❧❛st t✐♠❡ st❡♣✳ ❚❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛t t❤❡ ✜rst t✐♠❡ st❡♣ ✐s t❤❡ ✈❡❧♦❝✐t②t❤❛t t❤❡ ❞r♦♣❧❡ts ❤❛✈❡ ✇❤❡♥ t❤❡② ❧❡❛✈❡ t❤❡ s♣r❛② ♥♦③③❧❡✳ ❚❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛t t❤❡s♣r❛② ♥♦③③❧❡ ❡①✐t ❝❛♥ r♦✉❣❤❧② ❜❡ ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ t❤❡ ❇❡r♥♦✉❧❧✐ ❧❛✇ ❛❝❝♦r❞✐♥❣ t♦ t❤❡♠❛♥✉❢❛❝t✉r❡r ♦❢ s♣r❛② ♥♦③③❧❡s P◆❘ ❬✹✹❪✳ ■t ❢♦❧❧♦✇s t❤❛t t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t ✈❡❧♦❝✐t②

u =

√

2

ρpInlet ✭✸✳✶✻✮

❥✉st ❞❡♣❡♥❞s ♦♥ t❤❡ ❞❡♥s✐t② ρ ❛♥❞ t❤❡ ♣r❡ss✉r❡ pInlet ❛t t❤❡ ✐♥❧❡t t♦ t❤❡ s♣r❛② ♥♦③③❧❡✳❋♦r s♣r❛② ♥♦③③❧❡s t❤❛t ✉s❡ ❛✐r ❛♥❞ ✇❛t❡r✱ ρ ✐s t❤❡ ❞❡♥s✐t② ♦❢ t❤❡ ♠✐①t✉r❡✳❚❤❡r❡❢♦r❡ ❡✈❡r② ✐♥❢♦r♠❛t✐♦♥ ✐s ❣✐✈❡♥ t❤❛t ✐s ♥❡❝❡ss❛r② t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡

❞r♦♣❧❡t✳ ❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❝♦♠♣❧❡t❡ tr❛❥❡❝t♦r✐❡s✱ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥ ✸✳✶✺ ✐s s♦❧✈❡❞❛❣❛✐♥✱ ❜✉t t❤✐s t✐♠❡ ✐♥ ②✲ ❛♥❞ ③✲❞✐r❡❝t✐♦♥✳ ❚❤✐s ✐s ❞♦♥❡ t♦ ❝❤❡❝❦ ✐❢ ❞r♦♣❧❡ts ✇♦✉❧❞ ❤✐tt❤❡ ✇❛❧❧ ❜❡❢♦r❡ r❡❛❝❤✐♥❣ t❤❡ t❡st s❡❝t✐♦♥ ❛♥❞ ❤♦✇ t❤❡② ❞✐str✐❜✉t❡ ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥✳

✸✳✸✳✷ ❉r♦♣❧❡t t❡♠♣❡r❛t✉r❡

❚❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❞r♦♣❧❡ts ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ❢r♦♠ t❤❡ ✜rst ❧❛✇ ♦❢ t❤❡r♠♦❞②♥❛♠✐❝s✳❚❤✐s r❡s✉❧ts ❢♦r t❤❡ ♣r❡s❡♥t ❝❛s❡ ✐♥ t❤❡ ❡q✉❛t✐♦♥

E = QC + QR + QE ✭✸✳✶✼✮

✇❤✐❝❤ ❝♦♥t❛✐♥s ❢♦✉r t❡r♠s✳ ❚❤❡ t❡r♠ ♦♥ t❤❡ ❧❡❢t ✐s t❤❡ ❝❤❛♥❣❡ ♦❢ t❤❡ ❞r♦♣❧❡t✬s ✐♥t❡r♥❛❧❡♥❡r❣② ♦✈❡r t✐♠❡

E =4

3πr3dρdcv

dTd

dt✭✸✳✶✽✮

✇✐t❤ t❤❡ s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② ❛t ❝♦♥st❛♥t ✈♦❧✉♠❡ cv ❛♥❞ t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ Td✳❚❤❡ ✜rst t❡r♠ ♦♥ t❤❡ r✐❣❤t ❤❛♥❞ s✐❞❡ ✐s t❤❡ r❛t❡ ♦❢ ❤❡❛t tr❛♥s❢❡r ❞✉❡ t♦ ❝♦♥✈❡❝t✐♦♥

QC = 4πrdk (Ta − Td)Nu

2✭✸✳✶✾✮

✇✐t❤ t❤❡ t❤❡r♠❛❧ ❝♦♥❞✉❝t✐✈✐t② ♦❢ ❛✐r k✱ t❤❡ ❛♠❜✐❡♥t t❡♠♣❡r❛t✉r❡ Ta✱ ❛♥❞ t❤❡ ◆✉ss❡❧t♥✉♠❜❡r Nu✳ ❚❤❡ ◆✉ss❡❧t ♥✉♠❜❡r ✐s ❛ ❞✐♠❡♥s✐♦♥❧❡ss q✉❛♥t✐t② t❤❛t ❞❡s❝r✐❜❡s t❤❡ ❤❡❛ttr❛♥s❢❡r ❜❡t✇❡❡♥ ❛ ❜♦❞② ❛♥❞ t❤❡ s✉rr♦✉♥❞✐♥❣ ❛✐r✳ ❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞✱ t❤❡ ❞r♦♣❧❡ts

✷✺

✸ ▼❡t❤♦❞s

❝❛♥ ❜❡ tr❡❛t❡❞ ❛s s♣❤❡r❡s✳ ❚❤❡r❡❢♦r❡ t❤❡ ❝♦rr❡❧❛t✐♦♥ ❢♦r t❤❡ ◆✉ss❡❧t ♥✉♠❜❡r ♦❢ s♣❤❡r❡s❜② ❑♥✉❞s❡♥ ❛♥❞ ❑❛t③ ❬✹✺❪

Nu = 2 + 0.6Pr1/3Re1/2 ✭✸✳✷✵✮

❝❛♥ ❜❡ ✉s❡❞✳ ❚❤❡ t❡r♠ Pr ✐s t❤❡ Pr❛♥❞t❧ ♥✉♠❜❡r ♦❢ ❛✐r✳❚❤❡ s❡❝♦♥❞ t❡r♠ ♦♥ t❤❡ r✐❣❤t ❤❛♥❞ s✐❞❡ ✐s t❤❡ ❤❡❛t ✢✉① ❞✉❡ t♦ r❛❞✐❛t✐♦♥

QR = 4πr2dσǫd(

T 4a − T 4

d

)

✭✸✳✷✶✮

✇✐t❤ t❤❡ ❙t❡❢❛♥✲❇♦❧t③♠❛♥♥ ❝♦♥st❛♥t σ = 5.67 · 10−8 kg s−3 K−4 ❛♥❞ t❤❡ ❡♠✐ss✐✈✐t② ǫd ♦❢t❤❡ ❞r♦♣❧❡t✳ ❆s r❡❝♦♠♠❡♥❞❡❞ ❜② ●❛t❡s ❡t ❛❧✳ ❬✶✹❪✱ t❤❡ ❡♠✐ss✐✈✐t② ✇✐❧❧ ❜❡ t❛❦❡♥ t♦ ❜❡ 1✳❚❤❡ ❧❛st t❡r♠ ♦♥ t❤❡ r✐❣❤t ❤❛♥❞ s✐❞❡ ✐s t❤❡ ❤❡❛t ✢✉① ❞✉❡ t♦ ❡✈❛♣♦r❛t✐♦♥

Qe = 4πrdLvD

[

paTa

− pdTd

]

Sh

2R. ✭✸✳✷✷✮

❚❤❡ ❡q✉❛t✐♦♥ ❝♦♥t❛✐♥s t❤❡ ❧❛t❡♥t ❤❡❛t ♦❢ ✈❛♣♦r✐③❛t✐♦♥ ♦❢ ✇❛t❡r Lv✱ t❤❡ ❞✐✛✉s✐✈✐t② ♦❢ ✇❛t❡r✈❛♣♦r ✐♥ ❛✐r D✱ ❛♥❞ t❤❡ ❙❤❡r✇♦♦❞ ♥✉♠❜❡r Sh✳ ❚❤❡ ❙❤❡r✇♦♦❞ ♥✉♠❜❡r ✐s ❛ ❞✐♠❡♥s✐♦♥❧❡ssq✉❛♥t✐t② t❤❛t ❞❡s❝r✐❜❡s t❤❡ ♠❛ss tr❛♥s❢❡r ♦❢ ❛ ❞r♦♣❧❡t t♦ t❤❡ s✉rr♦✉♥❞✐♥❣ ❛✐r ❛♥❞ ❝❛♥ ❜❡❝❛❧❝✉❧❛t❡❞ ✇✐t❤

Sh = 2 + 0.6Sc1/3Re1/2 ✭✸✳✷✸✮

❛❝❝♦r❞✐♥❣ t♦ ❑♥✉❞s❡♥ ❛♥❞ ❑❛t③ ❬✹✺❪✳ ❚❤❡ t❡r♠ Sc ❞❡♥♦t❡s t❤❡ ❙❝❤♠✐❞t ♥✉♠❜❡r ♦❢ ❛✐r✳❚❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❡✈❛♣♦r❛t✐♦♥ ❤♦✇❡✈❡r ✐s ✉♥❞❡r ❞✐s❝✉ss✐♦♥✳ ❋♦r ❡①❛♠♣❧❡✱ ❇❛♥s♠❡r

❡t ❛❧✳ ❬✸✶❪ ♥❡❣❧❡❝t❡❞ t❤✐s t❡r♠ ❢♦r t❤❡✐r ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r✳ ❆❞❞✐t✐♦♥❛❧❧②✱●❛t❡s ❡t ❛❧✳ ❬✶✹❪ ❛❧s♦ st❛t❡ t❤❡♠s❡❧✈❡s t❤❛t t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❡✈❛♣♦r❛t✐♦♥ ✐s ♠✐♥♦r✳ ■♥ t❤❡❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ t❤❡ r❡❧❛t✐✈❡ ❤✉♠✐❞✐t② ♦❢ t❤❡ ❛✐r ✇✐❧❧ ❜❡ ❛r♦✉♥❞ ♦♥❡✳ ❚❤✐s✈❛❧✉❡ ✐♥❞✐❝❛t❡s t❤❛t t❤❡ ❛✐r ✐s s❛t✉r❛t❡❞✳ ❚❤❡r❡❢♦r❡✱ t❤❡r❡ ✇✐❧❧ ❜❡ ♥♦ ❞r♦♣❧❡t ❡✈❛♣♦r❛t✐♦♥✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡ ❡✈❛♣♦r❛t✐✈❡ t❡r♠ ✇✐❧❧ ❜❡ ♥❡❣❧❡❝t❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣✳❇② r❡❛rr❛♥❣✐♥❣ t❤❡ t❡r♠s ✐♥ ❡q✉❛t✐♦♥ ✸✳✶✼✱ t❤❡ ❢♦❧❧♦✇✐♥❣ ❡q✉❛t✐♦♥ ❝❛♥ ❜❡ ❣❛✐♥❡❞✿

dTd

dt=

3(

QC + QR

)

4πr3dρdcv✭✸✳✷✹✮

❆s ✇❛s ❞♦♥❡ ❢♦r t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥✱ t❤❡ ❞❡r✐✈❛t✐✈❡s ❝❛♥ ❜❡ ❛ss✉♠❡❞ t♦ ❜❡ ❞✐✛❡r❡♥❝❡s✳❚❤✐s ②✐❡❧❞s

∆Td =3(

QC + QR

)

4πr3dρdcv∆t ✭✸✳✷✺✮

❛♥❞ ❛❣❛✐♥ ❛ t✐♠❡✲st❡♣ ♣r♦❝❡❞✉r❡ ❝❛♥ ❜❡ ✉s❡❞✳ ❚❤❡ t❡♠♣❡r❛t✉r❡s ✐♥ ❡q✉❛t✐♦♥s ✸✳✶✾✱ ✸✳✷✶❛♥❞ ✸✳✷✷ ❝❛♥ ❜❡ t❛❦❡♥ ❢r♦♠ t❤❡ ❧❛st t✐♠❡ st❡♣✳❚❤❡ ✇❤♦❧❡ r❡❛s♦♥ ❢♦r ❞❡s✐❣♥✐♥❣ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s t♦ ❤❛✈❡ st❡❛❞② r❡❛❧✲✢✐❣❤t

❝♦♥❞✐t✐♦♥s ❛t t❤❡ t❡st s❡❝t✐♦♥✳ ❚♦ ❡♥s✉r❡ t❤✐s ✐s t❤❡ ❝❛s❡✱ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥s ❛♥❞t❤❡ ❤❡❛t ❜❛❧❛♥❝❡ ❛r❡ ❝❛❧❝✉❧❛t❡❞ ❢♦r ❞✐✛❡r❡♥t ♣❛r❛♠❡t❡rs✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ❛❧❧ ♦❢ t❤❡ ❡q✉❛t✐♦♥s❛❜♦✈❡ ❛r❡ s♦❧✈❡❞ ❢♦r ❞✐✛❡r❡♥t ♥♦③③❧❡s t♦ ❞❡t❡r♠✐♥❡ ✇❤✐❝❤ ♥♦③③❧❡ ✐s t❤❡ ♠♦st s✉✐t❛❜❧❡ ❢♦rt❤❡ ✇✐♥❞ t✉♥♥❡❧✳❚❤❡ ❣✐✈❡♥ ❡q✉❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ s♦❧✈❡❞ ✉s✐♥❣ ▼❆❚▲❆❇✳ ❚❤❡ ✉s❡❞ ▼❆❚▲❆❇ ❝♦❞❡ ❝❛♥

❜❡ ❢♦✉♥❞ ♦♥ t❤❡ ❈❉✳

✷✻

✸ ▼❡t❤♦❞s

✸✳✹ Pr❡ss✉r❡ ❧♦ss❡s

❆❧❧ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❧❡❛❞ t♦ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❚♦ ❝❤♦♦s❡ ❛ s✉✐t❛❜❧❡ ❢❛♥✱t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ♥❡❡❞ t♦ ❜❡ ❦♥♦✇♥✳ ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪ ♣r❡s❡♥t❡❞ r✉❧❡s ❛♥❞ ❡q✉❛t✐♦♥s❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❆❧♠♦st ❛❧❧ ❡q✉❛t✐♦♥s ✐♥ t❤✐s ♣❛r❛❣r❛♣❤ ✇❡r❡ t❛❦❡♥❢r♦♠ t❤❡♠✳ ❚❤❡r❡❢♦r❡ ❥✉st t❤❡ ✐❞❡❛s t❤❛t ✇❡r❡ ♥♦t t❛❦❡♥ ❢r♦♠ t❤❡♠ ✇✐❧❧ ❜❡ ♠❛r❦❡❞ t♦❡♥❤❛♥❝❡ t❤❡ r❡❛❞❛❜✐❧✐t② ♦❢ t❤✐s s❡❝t✐♦♥✳

❚❤❡ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ❜② s✐♠♣❧② ❛❞❞✐♥❣ ✉♣ t❤❡♣r❡ss✉r❡ ❧♦ss❡s ♦❢ ❡❛❝❤ ❝♦♠♣♦♥❡♥t✳ ❚❤❡ ❡q✉❛t✐♦♥s ✉s❡❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s❝❛♥ ♦♥❧② ❜❡ ✉s❡❞ ❢♦r r❡❝t❛♥❣✉❧❛r✱ ❝✐r❝✉❧❛r✱ ♦r ✢❛t✲♦✈❛❧ s❤❛♣❡s✳ ❚❤❡ ❣✐✈❡♥ ❡q✉❛t✐♦♥s❝❛❧❝✉❧❛t❡ ♠♦st ♦❢ t❤❡ t✐♠❡s t❤❡ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t K r❛t❤❡r t❤❛♥ t❤❡ r❡❛❧ ♣r❡ss✉r❡❧♦ss✳ ❚❤✐s ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t

K =∆pTq

✭✸✳✷✻✮

✐s t❤❡ ♥♦♥✲❞✐♠❡♥s✐♦♥❛❧ ♣r❡ss✉r❡ ❧♦ss ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❧♦ss ✐♥ t♦t❛❧ ♣r❡ss✉r❡ ∆pT ❛♥❞t❤❡ ❞②♥❛♠✐❝ ♣r❡ss✉r❡ q✳ ❚❤❡ ❞②♥❛♠✐❝ ♣r❡ss✉r❡ ✉s❡❞ t♦ ♥♦♥✲❞✐♠❡♥s✐♦♥❛❧✐③❡ t❤❡ ❧♦ss ✐♥t♦t❛❧ ♣r❡ss✉r❡ ✐s t❛❦❡♥ ❛t t❤❡ s♠❛❧❧❡st✲❛r❡❛ ❛t t❤❡ ❡♥❞ ♦❢ ❡❛❝❤ s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡

∆pT = Kq = K(

0.5ρv2)

✭✸✳✷✼✮

✐s t❤❡ ❡q✉❛t✐♦♥ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ r❡❛❧ ♣r❡ss✉r❡ ❧♦ss✳Pr❡ss✉r❡ ❧♦ss❡s ✐♥ ❞✉❝ts ✇✐t❤ ❝♦♥st❛♥t ❝r♦ss✲s❡❝t✐♦♥ ❛r❡ ❞✉❡ t♦ ❢r✐❝t✐♦♥✳ ❚❤❡

❝♦rr❡s♣♦♥❞✐♥❣ ❧♦ss ❝♦❡✣❝✐❡♥t ✐s

K =λL

dh. ✭✸✳✷✽✮

❚❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❞❡♣❡♥❞ ♦♥ t❤❡ ❢r✐❝t✐♦♥ ❧♦ss ❝♦❡✣❝✐❡♥t λ✳ ❆❝❝♦r❞✐♥❣ t♦ ❊❝❦❡rt ❡t ❛❧✳❬✸✷❪✱ t❤❡ ❢r✐❝t✐♦♥ ❝♦❡✣❝✐❡♥t ❢♦r s♠♦♦t❤ ✇❛❧❧s ✐s ❞❡s❝r✐❜❡❞ ❜②

1√λ= 2 log10

(

Re√λ)

− 0.8. ✭✸✳✷✾✮

❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❢r✐❝t✐♦♥ ❧♦ss ❝♦❡✣❝✐❡♥t✱ t❤❡ ❡q✉❛t✐♦♥ ❝❛♥ ❜❡ r❡❢♦r♠✉❧❛t❡❞ t♦

λ =[

log10(

λRe2)

− 0.8]

−2. ✭✸✳✸✵✮

◆♦✇✱ t❤✐s ❡q✉❛t✐♦♥ ❝❛♥ ❜❡ s♦❧✈❡❞ ✐t❡r❛t✐✈❡❧② ❜② t❛❦✐♥❣ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❧❛st ✐t❡r❛t✐♦♥ ❢♦rλ ♦♥ t❤❡ r✐❣❤t s✐❞❡ t♦ ❝❛❧❝✉❧❛t❡ ❛ ♥❡✇ ✈❛❧✉❡ ♦❢ λ✳ ❆s st❛rt ✈❛❧✉❡✱ λ ✇✐❧❧ ❜❡ s❡t t♦ 1✳ 5✐t❡r❛t✐♦♥s ♥♦r♠❛❧❧② ❧❡❛❞ t♦ ❛ ✈❛❧✉❡ ✇✐t❤ s✉✣❝✐❡♥t q✉❛❧✐t②✳

❚❤❡ ♣r❡ss✉r❡ ❧♦ss ✐♥ ❝♦♥tr❛❝t✐♦♥s ✐s ❛❧s♦ ♠♦st❧② ❞✉❡ t♦ ❢r✐❝t✐♦♥✳ ❚❤❡ ❧♦ss ❝♦❡✣❝✐❡♥t❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ❛♣♣r♦①✐♠❛t❡❧② ❜②

K = 0.32λL

dh✭✸✳✸✶✮

✷✼

✸ ▼❡t❤♦❞s

✇✐t❤ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ❜❡✐♥❣ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❛❝❝♦r❞✐♥❣ t♦ ❊❝❦❡rt❡t ❛❧✳ ❬✸✷❪✳ ❈♦♥tr❛❝t✐♦♥s ❤❛✈❡ ❞✐✛❡r❡♥t ✐♥❧❡t ❛♥❞ ♦✉t❧❡t ❛r❡❛s ❛♥❞ t❤❡r❡❢♦r❡ ❛ ❝❤❛♥❣✐♥❣✈❡❧♦❝✐t② ♦✈❡r ✐ts ❧❡♥❣t❤✳ ❍❡♥❝❡✱ ❛ ❝❤♦✐❝❡ ❤❛s t♦ ❜❡ ♠❛❞❡ ✇❤✐❝❤ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ❢♦rt❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❢r✐❝t✐♦♥ ❧♦ss ❝♦❡✣❝✐❡♥t✳ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ r❡❝♦♠♠❡♥❞ ✉s✐♥❣ t❤❡❛✈❡r❛❣❡ ♦❢ t❤❡ ❢r✐❝t✐♦♥ ❧♦ss ❝♦❡✣❝✐❡♥t ✈❛❧✉❡s ❛t t❤❡ ✐♥❧❡t ❛♥❞ t❤❡ ♦✉t❧❡t✳❚❤❡ ♣r❡ss✉r❡ ❧♦ss ✐♥ ❛ ❞✐✛✉s❡r ✐s ❜♦t❤ ❞✉❡ t♦ ❢r✐❝t✐♦♥ ❛♥❞ ❡①♣❛♥s✐♦♥✳ ❊❝❦❡rt ❡t ❛❧✳

❬✸✷❪ t❤❡r❡❢♦r❡ ♣✉❜❧✐s❤❡❞ ❛♥ ❡q✉❛t✐♦♥ ❢♦r t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❧♦ss ❝♦❡✣❝✐❡♥t

K =

[

KEXP +

(

λ

8sinθ

AR + 1

AR− 1

)](

AR− 1

AR

)2

✭✸✳✸✷✮

t❤❛t ✐s ♠❛❞❡ ✉♣ ♦❢ ♦♥❡ t❡r♠ ❢♦r t❤❡ ❡①♣❛♥s✐♦♥ ❧♦ss❡s ❛♥❞ ♦♥❡ ❢♦r t❤❡ ❢r✐❝t✐♦♥ ❧♦ss❡s✳ ❚❤❡❢r✐❝t✐♦♥ ❧♦ss ❝♦❡✣❝✐❡♥t ❤❛s t♦ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❡♥tr② ❘❡②♥♦❧❞s ♥✉♠❜❡r ❛❝❝♦r❞✐♥❣t♦ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ ❛♥❞ t❤❡r❡❢♦r❡ ✐s t❤❡ s❛♠❡ ❛s ❢♦r t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡ ✈❛❧✉❡ ♦❢ t❤❡❡①♣❛♥s✐♦♥ ♣❛r❛♠❡t❡r KEXP ❞❡♣❡♥❞s ♦♥ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ s❤❛♣❡ ♦❢ t❤❡ ❞✐✛✉s❡r ❛♥❞ t❤❡s❡♠✐✲♦♣❡♥✐♥❣ ❛♥❣❧❡ θ✿❋♦r ❝✐r❝✉❧❛r ❝r♦ss✲s❡❝t✐♦♥s✿

KEXPCircular= 1.033395 · 10−1 − 1.1465 · 10−2(2θ) ❢♦r 0◦ < θ < 1.5◦ ✭✸✳✸✸✮

KEXPCircular=1.70925 · 10−1 − 5.84932 · 10−2(2θ) + 8.14936 · 10−3(2θ)2 ✭✸✳✸✹✮

+1.34777 · 10−4(2θ)3 − 5.67258 · 10−5(2θ)4 − 4.15879 · 10−6(2θ)5 ✭✸✳✸✺✮

+2.10219 · 10−7(2θ)6 ❢♦r 1.5◦ < θ < 5◦ ✭✸✳✸✻✮

KEXPCircular= −9.66135 · 10−2 + 2.336135 · 10−2(2θ) ❢♦r θ > 5◦ ✭✸✳✸✼✮

❋♦r sq✉❛r❡ ❝r♦ss✲s❡❝t✐♦♥s✿

KEXPSquare= 9.62274 · 10−2 − 2.07582 · 10−3(2θ) ❢♦r 0◦ < θ < 1.5◦ ✭✸✳✸✽✮

KEXPSquare=1.22156 · 10−1 − 2.29480 · 10−2(2θ) + 5.50704 · 10−3(2θ)2 ✭✸✳✸✾✮

−4.08644 · 10−4(2θ)3 − 3.84056 · 10−5(2θ)4 + 8.74969 · 10−6(2θ)5 ✭✸✳✹✵✮

−3.65217 · 10−7(2θ)6 ❢♦r 1.5◦ < θ < 5◦ ✭✸✳✹✶✮

KEXPSquare= −1.1321685 · 10−1 + 2.93315 · 10−2(2θ) ❢♦r θ > 5◦ ✭✸✳✹✷✮

❚❤❡ ✈❛r✐❛❜❧❡ AR ✐♥ t❤❡ t❡r♠ ❢♦r t❤❡ ❢r✐❝t✐♦♥ ❧♦ss❡s ❞❡♥♦t❡s t❤❡ ❛r❡❛ r❛t✐♦ ♦✈❡r t❤❡ ❞✐✛✉s❡r✳❆t t❤❡ ❡①✐t ♦❢ ❛♥ ♦♣❡♥✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ ❦✐♥❡t✐❝ ❡♥❡r❣② ♦❢ t❤❡ ✢♦✇ t❤❛t

❧❡❛✈❡s t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐s ❧♦st✳ ❚❤❡ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss ✐s t❤❡r❡❢♦r❡ ❡q✉❛❧ t♦ t❤❡ ❞②♥❛♠✐❝♣r❡ss✉r❡ ♦❢ t❤❡ ✢♦✇ ❛t t❤❡ ❡①✐t✳ ❯s✐♥❣ ❝♦♠♣r❡ss✐❜✐❧✐t② r❡❧❛t✐♦♥s❤✐♣s✱ t❤❡ ❞②♥❛♠✐❝ ♣r❡ss✉r❡

✷✽

✸ ▼❡t❤♦❞s

♦❢ t❤❡ ✢♦✇ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✉♥❞❡r t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡ st❛t✐❝ ♣r❡ss✉r❡ ♦❢ t❤❡ ✢♦✇✐s ❡q✉❛❧ t♦ t❤❡ ❛t♠♦s♣❤❡r✐❝ ♣r❡ss✉r❡✳ ❚❤✐s r❡s✉❧ts ✐♥ ❛ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t ♦❢

K =2{

[

1 +(

γ−12M2)]

γγ−1 − 1

}

γM2. ✭✸✳✹✸✮

❚❤❡ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t ♦❢ ❤♦♥❡②❝♦♠❜s ✇❛s ❞❡✜♥❡❞ ❜② ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪ t♦ ❜❡

K = λ

(

3 +L

dh

)(

A

AFLOW

)2

+

(

A

AFLOW

− 1

)2

✭✸✳✹✹✮

✇✐t❤ dh ❜❡✐♥❣ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ ❛ ❤♦♥❡②❝♦♠❜ ❝❡❧❧✳ ❚❤❡ ❢r✐❝t✐♦♥ ❝♦❡✣❝✐❡♥t ✐s❝❛❧❝✉❧❛t❡❞ ✇✐t❤

λ = 0.375Re−0.1

(

∆

dh

)0.4

✭✸✳✹✺✮

❢♦r Re ≤ 275 ❛♥❞

λ = 0.214

(

∆

dh

)0.4

✭✸✳✹✻✮

❢♦r Re > 275✳ ■♥ t❤♦s❡ ❡q✉❛t✐♦♥s ∆ ✐s t❤❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜ ❝❡❧❧s✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ❛♥❞ t❤❡ ❛✐r✈❡❧♦❝✐t②✳ ❚❤❡ t❡r♠ AFLOW/A ❞❡s❝r✐❜❡s t❤❡ r❛t✐♦ ♦❢ t❤❡ ❧♦❝❛❧ ✢♦✇ ❛r❡❛ t♦ t❤❡ ❛r❡❛ ♦❢ t❤❡❧♦❝❛❧ ❝r♦ss✲s❡❝t✐♦♥ ❛♥❞ ✐s t❤❡r❡❢♦r❡ ❡q✉❛❧ t♦ t❤❡ ♣♦r♦s✐t②✳❊✈❡r② str✉❝t✉r❡ ✐♥s✐❞❡ t❤❡ t✉♥♥❡❧ ❧❡❛❞s t♦ ❞r❛❣ ❛♥❞ t❤❡r❡❢♦r❡ t♦ ♣r❡ss✉r❡ ❧♦ss❡s ❛s

✇❡❧❧✳ ❚❤❡ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥ts ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤

K = cDS

AFLOW

ǫ. ✭✸✳✹✼✮

❇❡❝❛✉s❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss ❞❡♣❡♥❞s ♦♥ t❤❡ ❞r❛❣ ♦❢ t❤❡ str✉❝t✉r❡✱ t❤❡ ❞r❛❣ ❛r❡❛ S ♦❢ t❤❡❝♦♥s✐❞❡r❡❞ ✐♥t❡r♥❛❧ str✉❝t✉r❡ ♥❡❡❞s t♦ ❜❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ t❡r♠ǫ ≥ 1 ✐s ✐♥❝❧✉❞❡❞ t❤❛t ❞❡s❝r✐❜❡s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❞r❛❣ ♦♥ ❞♦✇♥str❡❛♠ ❝♦♠♣♦♥❡♥ts✳❆ ♣❛rt ♦❢ t❤❡ r❡❛s♦♥ ❜❡❤✐♥❞ t❤❡ ✉s❡ ♦❢ ♠❡s❤ s❝r❡❡♥s ❛r❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❚❤❡

❝♦rr❡s♣♦♥❞✐♥❣ ❧♦ss ❝♦❡✣❝✐❡♥t ✐♥ t❤❡ ❢♦r♠ ♣✉❜❧✐s❤❡❞ ❜② ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪

K = KReKMESH

(

1− AFLOW

A

)

+

(

A

AFLOW

− 1

)2

✭✸✳✹✽✮

❝♦♥t❛✐♥s t✇♦ ♣❛r❛♠❡t❡rs✳ ❚❤❡ ❞❡♣❡♥❞❡♥❝❡ ♦♥ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t✇✐t❤ KRe✳ ❋♦r t❤✐s ✈❛❧✉❡✱ ❜♦t❤ ❛♥ ❡q✉❛t✐♦♥ ❛♥❞ ❛ ❣r❛♣❤ ❛r❡ ❣✐✈❡♥✳ ❍♦✇❡✈❡r✱ t❤❡② ❞♦♥♦t ♠❛t❝❤✳ ❆s ✐♥❞✐❝❛t❡❞ ❜② ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ♣r❡ss✉r❡ ❧♦ss❡s ✐s r❛t❤❡r✐♥❛❝❝✉r❛t❡✳ ❚❤❡r❡❢♦r❡ t❤❡ ✇♦rs❡ ❝❛s❡ ✇✐❧❧ ❜❡ ❝♦♥s✐❞❡r❡❞ ✐♥ t❤❡ ❞❡s✐❣♥ ♦❢ t❤✐s ✇✐♥❞ t✉♥♥❡❧❛♥❞ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐♥✢✉❡♥❝❡ ❢❛❝t♦r ❜❡❝♦♠❡s

KRe = 0.785

(

1− Rewire

354

)

+ 1.01 ✭✸✳✹✾✮

✷✾

✸ ▼❡t❤♦❞s

❢♦r 0 ≤ Rewire < 400 ❛♥❞

KRe = 1.0 ✭✸✳✺✵✮

❢♦r Rewire ≥ 400✳ ❚❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ♦❢ t❤❡ ✇✐r❡ Rewire ✐s ❜✉✐❧t ✇✐t❤ t❤❡ ✈❡❧♦❝✐t②❛t t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❛♥❞ t❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ s❝r❡❡♥ ✇✐r❡✳ ❚❤❡ ♠❡s❤ ❝♦♥st❛♥t KMESH

❞❡♣❡♥❞s ♦♥ t❤❡ ♠❛t❡r✐❛❧ ♦❢ t❤❡ ♠❡s❤✳ ❋♦r ❛✈❡r❛❣❡ ❝✐r❝✉❧❛r ♠❡t❛❧ ✇✐r❡ KMESH ❜❡❝♦♠❡s1.3✱ ❢♦r ♥❡✇ ♠❡t❛❧ ✇✐r❡ 1.0 ❛♥❞ 2.1 ❢♦r s✐❧❦ t❤r❡❛❞✳❚❤❡ ♣r❡ss✉r❡ ❧♦ss ♦✈❡r t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❞❡♣❡♥❞s ♦♥ ✐ts ❛r❡❛ r❛t✐♦✳ ▼❡❤t❛ ❛♥❞

❇r❛❞s❤❛✇ ❬✸✾❪ ♣✉❜❧✐s❤❡❞ t❤❡ ❢♦❧❧♦✇✐♥❣ ❡q✉❛t✐♦♥ ❢♦r t❤❡ ♠✐♥✐♠✉♠ ♣r❡ss✉r❡ ❧♦ss ❝♦❡✣❝✐❡♥t♦❢ ❛ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✇✐t❤ ❛ ❣✐✈❡♥ ❛r❡❛ r❛t✐♦✿

K ≥ AR− 1

1.14. ✭✸✳✺✶✮

✸✳✺ ❈♦♦❧✐♥❣ ♣♦✇❡r

❉✉r✐♥❣ ❛ r✉♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✱ ❤❡❛t ✐s r❡❧❡❛s❡❞ ✐♥ ❞✐✛❡r❡♥t ✇❛②s✳ ■❢ t❤❡r❡ ✇❛s ♥♦❝♦♦❧✐♥❣ ✐♥❝❧✉❞❡❞✱ t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❛✐r ✇♦✉❧❞ r✐s❡ r❛t❤❡r q✉✐❝❦❧② ❛s ❝❛❧❝✉❧❛t✐♦♥s ❜②❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪ s❤♦✇✳ ❆s t❤❡ ❞❡s✐❣♥❡❞ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡ ♣❧❛❝❡❞ ✐♥s✐❞❡ ❛ ❝♦♦❧✐♥❣❝❤❛♠❜❡r✱ t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤✐s ❝❤❛♠❜❡r ♥❡❡❞s t♦ ❜❡ ❝❛❧❝✉❧❛t❡❞✳ ❋✐rst✱t❤❡ ❢❛♥ ♣r♦❞✉❝❡s ❤❡❛t ✇❤✐❧❡ ✐t ✐s r✉♥♥✐♥❣✳ ❆❧❧ ♦❢ t❤❡ ❡♥❡r❣② s✉♣♣❧✐❡❞ t♦ t❤❡ ❢❛♥ ♥❡❡❞st♦ ❜❡ ❜❛❧❛♥❝❡❞ ❜② t❤❡ ❝♦♦❧✐♥❣ s②st❡♠✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❛ ♣❛rt ♦❢ t❤❡ ❡♥❡r❣② ✐s ❞✐r❡❝t❧②tr❛♥s❢❡rr❡❞ ✐♥t♦ ❤❡❛t ❛♥❞ t❤❡ ♦t❤❡r ♣❛rt ✇✐❧❧ ❡✈❡♥t✉❛❧❧② ❜❡❝♦♠❡ ❤❡❛t ❞✉❡ t♦ ❢r✐❝t✐♦♥❛❧❤❡❛t✐♥❣ ♦❢ t❤❡ ❛✐r ✢♦✇ ❛t t❤❡ ✇❛❧❧s ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❙❡❝♦♥❞✱ ❝♦♦❧✐♥❣ ✐s r❡q✉✐r❡❞✱❛s ❤❡❛t ✐s tr❛♥s❢❡rr❡❞ ❢r♦♠ t❤❡ ❞r♦♣❧❡ts t♦ t❤❡ ❛✐r✳ ❚❤✐s ❤❡❛t tr❛♥s❢❡r t❛❦❡s ♣❧❛❝❡ ✐♥t✇♦ ✇❛②s ❛s ❡①♣❧❛✐♥❡❞ ❜② ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✳ ❋✐rst✱ ❝♦♦❧✐♥❣ ✐s r❡q✉✐r❡❞ t♦ ❝♦♦❧ t❤❡❞r♦♣❧❡ts ❞♦✇♥ ❢r♦♠ t❤❡✐r ✐♥✐t✐❛❧ t❡♠♣❡r❛t✉r❡ ✇❤❡♥ t❤❡② ❧❡❛✈❡ t❤❡ s♣r❛② ♥♦③③❧❡ t♦ t❤❡ ❛✐rt❡♠♣❡r❛t✉r❡✳ ❚❤✐s t❡r♠ ✐s ❝❛❧❧❡❞ t❤❡ s❡♥s✐❜❧❡ ❤❡❛t ❛♥❞ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞

Qsensible = mwatercp,water∆T ✭✸✳✺✷✮

✇✐t❤ t❤❡ s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② ❛t ❝♦♥st❛♥t ♣r❡ss✉r❡ cp✳❚❤❡ s❡❝♦♥❞ t❡r♠ ❢♦r ❤❡❛t tr❛♥s❢❡r ❜❡t✇❡❡♥ ❞r♦♣❧❡ts ❛♥❞ ❛✐r ✐s t❤❡ ❧❛t❡♥t ❤❡❛t✳ ❚❤❡

❧❛t❡♥t ❤❡❛t ✐s r❡❧❡❛s❡❞ ✇❤❡♥ ❛ ❞r♦♣❧❡t ❢r❡❡③❡s ♦♥ ❛ s✉r❢❛❝❡✳ ■t ✐s

Qlatent = mwaterclatent,water ✭✸✳✺✸✮

❛♥❞ ❞❡♣❡♥❞s ♦♥ t❤❡ s♣❡❝✐✜❝ ❧❛t❡♥t ❤❡❛t ♦❢ ❢✉s✐♦♥ clatent ♦❢ ✇❛t❡r✳ ❚♦ ❜❡ ❛❜❧❡ t♦ ❝❛❧❝✉❧❛t❡t❤❡ t✇♦ ❤❡❛t tr❛♥s❢❡r t❡r♠s✱ t❤❡ ✢♦✇ r❛t❡ ♦❢ ✇❛t❡r

mwater = VairLWC = (vTSATS)LWC ✭✸✳✺✹✮

♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥ t❤❛t ❞❡♣❡♥❞s ♦♥ t❤❡ ✈♦❧✉♠❡tr✐❝ ✢♦✇ r❛t❡ V ♦❢ ❛✐r✳

✸✵

✸ ▼❡t❤♦❞s

✸✳✻ ❈❧❡❛r❛♥❝❡ r❡q✉✐r❡♠❡♥ts

❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞✱ ♦♣❡♥ r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ♦❢t❡♥ ♣❧❛❝❡❞ ✐♥s✐❞❡ ❛ ❝♦♦❧✐♥❣ ❝❤❛♠✲❜❡r✳ ❚❤❡r❡❢♦r❡ t❤❡ ✇❛❧❧s ♦❢ t❤✐s ❝❤❛♠❜❡r ✇✐❧❧ ❧✐♠✐t t❤❡ s✉rr♦✉♥❞✐♥❣✳ ▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇❬✸✾❪ r❡❝♦♠♠❡♥❞ t♦ ♦❜t❛✐♥ ❡♥♦✉❣❤ s♣❛❝❡ ✐♥ t❤❡ r♦♦♠ ✐♥ ✇❤✐❝❤ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡♣❧❛❝❡❞✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡② ❝♦♠♣❛r❡ t❤❡ ♣❛t❤ t❤❡ ✢♦✇ t❛❦❡s ❜❡t✇❡❡♥ t❤❡ ♦✉t❧❡t ❛♥❞t❤❡ ✐♥❧❡t t♦ ❛ ❜❛❞❧② ❞❡s✐❣♥❡❞ r❡t✉r♥ ❞✉❝t✳●r❡❡♥✇❛② ❛♥❞ ❲♦♦❞ ❬✹✻❪ ❞✐❞ s♦♠❡ ❡①♣❡r✐♠❡♥ts ❜❡❢♦r❡ t❤❡② ♣✉t t❤❡✐r ✇✐♥❞ t✉♥♥❡❧ ✐♥t♦

❛ ❣✐✈❡♥ r♦♦♠✳ ❚❤❡② ❝❤❛♥❣❡❞ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ✇❛❧❧ ❛♥❞ t❤❡ ✐♥❧❡t ❛♥❞ ♠❡❛s✉r❡❞t❤❡ ✢♦✇ q✉❛❧✐t②✳ ❋♦r t❤❡✐r ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ ❛r❡❛ ♦❢ t❤❡ ✐♥❝♦♠✐♥❣ ✢♦✇ ♥❡❡❞❡❞ t♦ ❜❡ ❛t❧❡❛st 1.8 t❤❡ ❛r❡❛ ♦❢ t❤❡ ✐♥❧❡t ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ t♦ ❛❝❤✐❡✈❡ ❛ ❣♦♦❞ ✢♦✇ q✉❛❧✐t②✳ ❲❤✐❧❡t❤✐s ✐s ❥✉st t❤❡ r❡s✉❧t ❢♦r ♦♥❡ ✇✐♥❞ t✉♥♥❡❧✱ ✐t ❝❛♥ st✐❧❧ ❜❡ ✉s❡❞ ❛s ❛ ❝♦❛rs❡ r✉❧❡ ♦❢ t❤✉♠❜❢♦r ♦t❤❡r ❞❡s✐❣♥s✳

✸✳✼ ❈❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r t❤✐❝❦♥❡ss

❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♥❡❝❡ss❛r② ✇✐❞t❤ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✱ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ♥❡❡❞s t♦❜❡ ❦♥♦✇♥✳ ❆s t❤❡ t❤✐❝❦♥❡ss ♦❢ ❜♦✉♥❞❛r② ❧❛②❡rs ✐s ❞✐✛❡r❡♥t ❢♦r t✉r❜✉❧❡♥t ❛♥❞ ❧❛♠✐♥❛r✢♦✇s✱ t❤❡ t②♣❡ ♦❢ t❤❡ ✢♦✇ ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥ ❜❡❢♦r❡ t❤❡ ❝❛❧❝✉❧❛t✐♦♥✳ ❈❤♠✐❡❧❡✇s❦✐❬✹✼❪ ♣r❡s❡♥ts ❜❛s✐❝ r✉❧❡s ♦❢ t❤✉♠❜ t❤❛t ❛r❡ r❡♣r❡s❡♥t❛t✐✈❡ ♦❢ t②♣✐❝❛❧ ❝♦♥❞✐t✐♦♥s ✐♥ ✇✐♥❞t✉♥♥❡❧s✳ ❚❤❡ ❜❡❣✐♥♥✐♥❣ ♦❢ t❤❡ ♥♦③③❧❡ s❤♦✉❧❞ ❜❡ ✉s❡❞ ❛s t❤❡ ❧❡❛❞✐♥❣ ❡❞❣❡ ♦❢ t❤❡ ❜♦✉♥❞❛r②❧❛②❡r✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡② ❛ss✉♠❡ t❤❛t t❤❡ tr❛♥s✐t✐♦♥ ❢r♦♠ ❧❛♠✐♥❛r t♦ t✉r❜✉❧❡♥t ✢♦✇t❛❦❡s ♣❧❛❝❡ ❛t 0.15 t✐♠❡s t❤❡ ✐♥❧❡t r❛❞✐✉s✳ ❍♦✇❡✈❡r✱ ❛ ❞✐✛❡r❡♥t ❛♣♣r♦❛❝❤ ✇❛s ♣r♦♣♦s❡❞❜② ▼♦r❡❧ ❬✸✺❪✳ ❍❡ r❡❝♦♠♠❡♥❞s ✉s✐♥❣ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ❧❛st t✉r❜✉❧❡♥❝❡ s❝r❡❡♥ ❛s t❤❡st❛rt✐♥❣ ♣♦✐♥t ❢♦r t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❚♦ ❞♦ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s ❝♦♥s❡r✈❛t✐✈❡❧②✱ t❤❡ st❛rt✐♥❣♣♦✐♥t ✇✐❧❧ ❜❡ ❝❤♦s❡♥ ❛t t❤❡ ❧❛st t✉r❜✉❧❡♥❝❡ s❝r❡❡♥ ❛s r❡❝♦♠♠❡♥❞❡❞ ❜② ▼♦r❡❧ ❬✸✺❪✳ ❚❤❡♣♦✐♥t ♦❢ tr❛♥s✐t✐♦♥ ❤♦✇❡✈❡r ✐s ❛ss✉♠❡❞ t♦ ❜❡ ❛t 0.15 t✐♠❡s t❤❡ ✐♥❧❡t r❛❞✐✉s ♦❢ t❤❡ ♥♦③③❧❡❛s r❡❝♦♠♠❡♥❞❡❞ ❜② ❈❤♠✐❡❧❡✇s❦✐ ❬✹✼❪✳ ❚❤✐s ✐s ❝❤♦s❡♥ ❛s ♥♦ s✉✐t❛❜❧❡ ♣♦✐♥t ♦❢ tr❛♥s✐t✐♦♥✇❛s ❣✐✈❡♥ ❜② ▼♦r❡❧ ❬✸✺❪✳❚❤❡ ❡q✉❛t✐♦♥s ❢♦r t❤❡ t❤✐❝❦♥❡ss ♦❢ ❜♦✉♥❞❛r② ❧❛②❡rs ❛r❡ ✉s✉❛❧❧② ❥✉st ❣✐✈❡♥ ❢♦r ✢❛t ♣❧❛t❡s✳

❚❤❡ ♥♦③③❧❡ ❤♦✇❡✈❡r ✐s ❝✉r✈❡❞✳ ◆❡✈❡rt❤❡❧❡ss✱ ❙❝❤❧✐❝❤t✐♥❣ ❬✹✽❪ s❤♦✇s t❤❛t ❛s ❧♦♥❣ ❛s t❤❡r❛❞✐✉s ♦❢ t❤❡ ❝✉r✈❛t✉r❡ ✐s ♠✉❝❤ ❧❛r❣❡r t❤❛♥ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t✱ t❤❡ ❡q✉❛t✐♦♥s ❢♦r✢❛t ♣❧❛t❡s ❝❛♥ st✐❧❧ ❜❡ ✉s❡❞✳ ❚♦ ❞♦ s♦✱ ❛ ✈✐rt✉❛❧ ❝♦♦r❞✐♥❛t❡ s②st❡♠ ✐s ❝r❡❛t❡❞ ✇✐t❤ ♦♥❡❛①✐s ❢♦❧❧♦✇✐♥❣ t❤❡ ✇❛❧❧ ❝♦♥t♦✉r ❛♥❞ t❤❡ s❡❝♦♥❞ ❛①✐s ❜❡✐♥❣ ♣❡r♣❡♥❞✐❝✉❧❛r t♦ t❤❡ ✜rst ❛①✐s✳❚❤❡ ❡q✉❛t✐♦♥ ❢♦r t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ♦❢ ❛ ❧❛♠✐♥❛r ✢♦✇

δ (x) = 5

√

νx

v✭✸✳✺✺✮

✐s ❣✐✈❡♥ ❜② ❙❝❤❧✐❝❤t✐♥❣ ❬✹✽❪ ❛s ✇❡❧❧ ❛s t❤❡ ❡q✉❛t✐♦♥ ❢♦r t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ♦❢ ❛t✉r❜✉❧❡♥t ✢♦✇

δ (x) = 0.37x(vx

ν

)

−1/5

. ✭✸✳✺✻✮

❆ ♥❡❝❡ss✐t② ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ✐s t♦ ❦♥♦✇ t❤❡ ✈❡❧♦❝✐t② ♦❢t❤❡ ❛✐r✳ ❍♦✇❡✈❡r✱ t❤❡ ✈❡❧♦❝✐t② ✐s ❞✐✛❡r❡♥t ❛t ❡✈❡r② ♣♦s✐t✐♦♥ ✐♥ t❤❡ ♥♦③③❧❡✳ ❚♦ ❝❛❧❝✉❧❛t❡

✸✶

✸ ▼❡t❤♦❞s

t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ♥❡✈❡rt❤❡❧❡ss✱ t❤❡ ♥♦③③❧❡ ✐s s❡♣❛r❛t❡❞ ✐♥ ❛ ❧♦t ♦❢ s♠❛❧❧ s❡❝t✐♦♥s✳❆t ❡✈❡r② ❧♦❝❛t✐♦♥✱ t❤❡ ✈❡❧♦❝✐t② ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥✳ ❆s t❤❡❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ❞❡✈❡❧♦♣s ♦✈❡r t❤❡ ✇❤♦❧❡ ❧❡♥❣t❤ ❜❡t✇❡❡♥ t❤❡ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥ ❛♥❞t❤❡ t❡st ♦❜❥❡❝t✱ ❛ ♠❡t❤♦❞ ♥❡❡❞❡❞ t♦ ❜❡ ❢♦✉♥❞ t♦ ❝❛♣t✉r❡ t❤✐s ❞❡✈❡❧♦♣♠❡♥t ❛s ✇❡❧❧✳ ❚♦ ❞♦s♦✱ ❛t ❡✈❡r② ♣♦s✐t✐♦♥✱ ❛♥ ❡q✉✐✈❛❧❡♥t ❧❡♥❣t❤ ✇❛s ❝❛❧❝✉❧❛t❡❞✳ ❚❤✐s ✐s t❤❡ ❧❡♥❣t❤ ♦❢ ❛ ♣❧❛t❡✇✐t❤ t❤❡ s❛♠❡ ❜♦✉♥❞❛r② ❧❛②❡r ❛♥❞ ✈❡❧♦❝✐t②✳ ❆❢t❡r✇❛r❞s✱ t❤❡ ♥❡✇ ❜♦✉♥❞❛r② ❧❛②❡r ❝❛♥ ❜❡❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❡q✉✐✈❛❧❡♥t ❧❡♥❣t❤ ❜❡✐♥❣ ✐♥❝r❡❛s❡❞ ❜② t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ s♠❛❧❧ ♣❛rt✳❚❤✐s ❝❛♥ ❜❡ ❞♦♥❡ t❤r♦✉❣❤ ❛❧❧ t❤❡ ❝♦♠♣♦♥❡♥ts st❛rt✐♥❣ ❢r♦♠ t❤❡ ❧❛st t✉r❜✉❧❡♥❝❡ s❝r❡❡♥t♦ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ t❡st ♦❜❥❡❝t✳❚❤✐s ♣r♦❝❡❞✉r❡ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ❛t t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ t❡st ♦❜❥❡❝t

✐s ❛❧s♦ ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ▼❆❚▲❆❇ s❝r✐♣t✳ ■t ❝❛♥ t❤❡r❡❢♦r❡ ❜❡ ❢♦✉♥❞ ♦♥ t❤❡ ❈❉✳

✸✷

✹ ❘❡s✉❧ts

■♥ t❤✐s ❝❤❛♣t❡r✱ ✜rst t❤❡ ❞❡s✐❣♥ r❡q✉✐r❡♠❡♥ts t❤❛t t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❤❛s t♦ ❢✉❧✜❧❧ ❛r❡♣r❡s❡♥t❡❞✳ ❲✐t❤ t❤❡ r❡q✉✐r❡♠❡♥ts ❛♥❞ t❤❡ ❡q✉❛t✐♦♥s ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts ✐s ❡①♣❧❛✐♥❡❞✳ ❚❤❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❞r♦♣❧❡ts✐♥s✐❞❡ t❤❡ t✉♥♥❡❧ ❛r❡ ❛♥❛❧②③❡❞ ❛s ✇❡❧❧ ❛s t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞ t❤❡ ❝♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts✳❆ ♣r❡❧✐♠✐♥❛r② ❈❋❉ s✐♠✉❧❛t✐♦♥ ✐s ❛❧s♦ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ❝❤❛♣t❡r✳ ❋✐♥❛❧❧②✱ ❞❡s✐❣♥ ♦♣t✐♦♥s❢♦r ❛ s♠❛❧❧❡r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ ❣✐✈❡♥✳

✹✳✶ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥

❈❡rt❛✐♥ ❞❡s✐❣♥ s♣❡❝✐✜❝❛t✐♦♥s ♥❡❡❞ t♦ ❜❡ ❞❡✜♥❡❞ t♦ ❜❡ ❛❜❧❡ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ s✐③❡ ❛♥❞ ♣♦✇❡r♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ t❡st ♦❜❥❡❝ts t❤❛t ✇✐❧❧ ❜❡ t❡st❡❞ ✐♥ t❤✐s ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡t②♣✐❝❛❧ ❯❆❱ ❛✐r❢♦✐❧s✳ ❙❝❛❧✐♥❣ ♦❢ t❤❡ r❡s✉❧ts ♦❢ ❡①♣❡r✐♠❡♥ts ✐s ❛❧✇❛②s ♣r♦❜❧❡♠❛t✐❝ ❛♥❞ ❡✈❡♥♠♦r❡ ❢♦r ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ❛s ♣r❡s❡♥t❡❞ ✐♥ s✉❜s❡❝t✐♦♥ ✷✳✹✳✸✳ ❚❤❡r❡❢♦r❡ ❛♥ ♦❜❥❡❝t✐✈❡ ❢♦rt❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s t♦ s✐♠✉❧❛t❡ r❡❛❧✲❧✐❢❡ s✐t✉❛t✐♦♥s ♦❢ ❯❆❱s✳ ❚❤✐s ♠❡❛♥s t❤❛t ❛✐r❢♦✐❧s✇✐t❤ ❧✐❢❡✲s✐③❡❞ ❝❤♦r❞ ❧❡♥❣t❤s ❛r❡ s✉♣♣♦s❡❞ t♦ ❜❡ t❡st❡❞ ❛t t②♣✐❝❛❧ ✢✐❣❤t ✈❡❧♦❝✐t✐❡s✳ ❋✐❣✉r❡✹✳✶ s❤♦✇s ❤♦✇ t❤❡ ❯❆❱s ✐♥ t❤❡ ❝r❡❛t❡❞ ❞❛t❛❜❛s❡ ✐♥ ❆♣♣❡♥❞✐① ❆✳✶ ❝❛♥ ❜❡ ❛rr❛♥❣❡❞ ✐♥t♦❞✐✛❡r❡♥t ❝❛t❡❣♦r✐❡s ❢♦r ✢✐❣❤t s♣❡❡❞s✳ ❋♦r t❤✐s ♣✉r♣♦s❡✱ 5 ❯❆❱s ✇✐t❤ ✢✐❣❤t s♣❡❡❞s ♦✈❡r60m s−1 ✇❡r❡ ❡①❝❧✉❞❡❞✱ ❜❡❝❛✉s❡ ✈❡r② ❧❛r❣❡ ❯❆❱s ❛r❡ ♦✉t ♦❢ s❝♦♣❡ ❢♦r t❤✐s ✇♦r❦✳ ❚❤✐s✇❛s ❛❧s♦ ❞♦♥❡ t♦ ❤❛✈❡ ❛ ❝❧❡❛r❡r ♣✐❝t✉r❡ ♦❢ t❤❡ t②♣✐❝❛❧ ✢✐❣❤t s♣❡❡❞s ♦❢ ❯❆❱s ✇✐t❤♦✉t ❛ t♦♦❧♦♥❣ ❛①✐s✳ ❚❤❡ ♣❧♦t s❤♦✇s t❤❛t ♠♦st ❯❆❱s ❤❛✈❡ t②♣✐❝❛❧ ✢✐❣❤t s♣❡❡❞s ❜❡t✇❡❡♥ 15m s−1

❛♥❞ 35m s−1✳ ❚❤❡ r❡q✉✐r❡♠❡♥t r❡s✉❧t✐♥❣ ❢r♦♠ t❤✐s ❦♥♦✇❧❡❞❣❡ ✐s t♦ ♦❜t❛✐♥ s♣❡❡❞s ✉♣ t♦

024681012

0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60number of UAVs cruise speed [m/s]❋✐❣✉r❡ ✹✳✶✿ ❉✐✈✐s✐♦♥ ♦❢ ❯❆❱s ❛❝❝♦r❞✐♥❣ t♦ t❤❡✐r ✢✐❣❤t s♣❡❡❞✳

✸✸

✹ ❘❡s✉❧ts

35m s−1 ✐♥ t❤❡ t❡st s❡❝t✐♦♥ ♦❢ t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳❚♦ ✜♥❞ t②♣✐❝❛❧ ❝❤♦r❞ ❧❡♥❣t❤s ❢♦r ❯❆❱s ✇✐t❤ s♣❡❡❞s ✉♣ t♦ 35m s−1✱ t❤❡ t❛❜❧❡ ✐♥ ❆♣✲

♣❡♥❞✐① ❆✳✶ ✇❛s ✉s❡❞ ❛❣❛✐♥✳ ❍♦✇❡✈❡r✱ ❞❛t❛ ❢♦r ❝❤♦r❞ ❧❡♥❣t❤s ❝♦✉❧❞ ❥✉st ❜❡ ❢♦✉♥❞ ❢♦r 12❯❆❱s✳ ❆s ❡①♣❧❛✐♥❡❞ ✐♥ ❈❤❛♣t❡r ✷✱ t❤❡ ❝❤♦r❞ ❧❡♥❣t❤ ❛♥❞ t❤❡ ✇✐♥❣s♣❛♥ ♦❢ ❛♥ ❛✐r❝r❛❢t ❛r❡❧✐♥❦❡❞ ✇✐t❤ t❤❡ ❛s♣❡❝t r❛t✐♦✳ ❚❤❡r❡❢♦r❡ t❤❡ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ t❤❡ ❛✐r❢♦✐❧ ❝❛♥ ❛❧s♦ ❜❡ ❝❛❧❝✉✲❧❛t❡❞ ✐❢ t❤❡ ✇✐♥❣s♣❛♥ ❛♥❞ t❤❡ ❛s♣❡❝t r❛t✐♦ ♦❢ t❤❡ ✇✐♥❣ ❛r❡ ❦♥♦✇♥✳ ❲❤✐❧❡ t❤❡ ✇✐♥❣s♣❛♥✐s ❣✐✈❡♥ ❢♦r ♠❛♥② ❯❆❱s✱ t❤❡ ❛s♣❡❝t r❛t✐♦ ✐s ♦❢t❡♥ ♥♦t ❛✈❛✐❧❛❜❧❡✳ ❍♦✇❡✈❡r✱ t❤❡ ❛✈❡r❛❣❡ ♦❢t❤❡ ❦♥♦✇♥ ❛s♣❡❝t r❛t✐♦s ✐♥ t❤❡ ❞❛t❛❜❛s❡ ✐s ❛❜♦✉t 11✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ❛❝❝♦r❞✐♥❣ t♦ ◆❛❣❡❧❛♥❞ ❙❤❡♣s❤❡❧♦✈✐❝❤ ❬✹✾❪✱ t②♣✐❝❛❧ ❛s♣❡❝t r❛t✐♦s ❢♦r ❯❆❱s ❛r❡ ❛❜♦✉t 12✳ ❚❤❡r❡❢♦r❡✱ ❝❤♦r❞❧❡♥❣t❤s ✇❡r❡ ❛❧s♦ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❣✐✈❡♥ ✇✐♥❣s♣❛♥ ❛♥❞ ❛♥ ❡st✐♠❛t❡❞ ❛s♣❡❝t r❛t✐♦ ♦❢12✳ ❲✐t❤ t❤✐s ✐♥❢♦r♠❛t✐♦♥✱ ❋✐❣✉r❡ ✹✳✷ ✇❛s ❝r❡❛t❡❞✳ ■t ❝♦♥t❛✐♥s t❤❡ ❦♥♦✇♥ ❝❤♦r❞ ❧❡♥❣t❤s✱t❤❡ ❝❤♦r❞ ❧❡♥❣t❤s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❦♥♦✇♥ ✇✐♥❣s♣❛♥ ❛♥❞ ❛s♣❡❝t r❛t✐♦✱ ❛♥❞ t❤❡ ❝❤♦r❞❧❡♥❣t❤s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❦♥♦✇♥ ✇✐♥❣s♣❛♥ ❛♥❞ ❛♥ ❡st✐♠❛t❡❞ ❛r❡❛ r❛t✐♦ ♦❢ 12✳ ■♥ t♦t❛❧61 ❞❛t❛ ♣♦✐♥ts ❛r❡ ♣r❡s❡♥t❡❞✳ ❆❝❝♦r❞✐♥❣ t♦ t❤✐s ❋✐❣✉r❡✱ t❤❡ ♠♦st ❯❆❱s ✇✐t❤ s♣❡❡❞s ✐♥t❤❡ r❛♥❣❡ t♦ 35m s−1 ❤❛✈❡ ❝❤♦r❞ ❧❡♥❣t❤s s♠❛❧❧❡r t❤❛♥ 0.4m✳ ❚❤❡r❡❢♦r❡ ❛ ❝❤♦r❞ ❧❡♥❣t❤♦❢ 0.4m ✇❛s ❝❤♦s❡♥ ❛s t❤❡ ♠❛①✐♠✉♠ ❢♦r t❤✐s ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

00.20.40.60.811.21.41.60 10 20 30 40 50 60chord length [m] cruise speed [m/s]

❋✐❣✉r❡ ✹✳✷✿ ❈❤♦r❞ ❧❡♥❣t❤s ❛♥❞ ❝r✉✐s❡ s♣❡❡❞s ♦❢ ❞✐✛❡r❡♥t ❯❆❱s✳

❲❤✐❧❡ t❤❡ ❝❤♦r❞ ❧❡♥❣t❤ ♦❜✈✐♦✉s❧② ❤❛s ❛ ❤✉❣❡ ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✱✐t ✐s ❛❧s♦ r❡❧❡✈❛♥t ❢♦r t❤❡ ❤❡✐❣❤t✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ♦❢ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ s♦❧✐❞ ❜❧♦❝❦❛❣❡❡✛❡❝t t❤❛t ✇❛s ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✳ ❚❤❡ ❜❧♦❝❦❛❣❡ ❞❡♣❡♥❞s ♦♥ t❤❡ t❤✐❝❦♥❡ss♦❢ t❤❡ ❛✐r❢♦✐❧✱ ✐ts ❝❤♦r❞ ❧❡♥❣t❤✱ ❛♥❞ t❤❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦✳ ❚❤✐s ✇✐❧❧ ❜❡ ❢✉rt❤❡r ❡①♣❧❛✐♥❡❞ ✐♥t❤❡ ♥❡①t s✉❜s❡❝t✐♦♥✳ ❋♦r t❤❡ ❞❡s✐❣♥ ♦❢ t❤✐s ✇✐♥❞ t✉♥♥❡❧✱ ❛♥ ❘●✶✺ ❛✐r❢♦✐❧ ✇❛s t❛❦❡♥ ❛s❛♥ ❡①❛♠♣❧❡ ♦❢ t❤❡ ❛✐r❢♦✐❧s t❤❛t ✇✐❧❧ ❜❡ t❡st❡❞✳ ❚❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ❛✐r❢♦✐❧ s✉r❢❛❝❡ ❛r❡❧✐st❡❞ ✐♥ ❆♣♣❡♥❞✐① ❆✳✸ ❛s ✇❡❧❧ ❛s ❛ ♣❧♦t ♦❢ t❤❡ ♣r♦✜❧❡ ✇✐t❤ ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 0◦✳ ■♥s✐❞❡t❤❡ ✇✐♥❞ t✉♥♥❡❧✱ ❥✉st t❤❡ ❧✐♥❡❛r s❡❝t✐♦♥ ♦❢ t❤❡ cL✲α✲❝✉r✈❡ s❤❛❧❧ ❜❡ t❡st❡❞✳ ❚❤✐s ✐s ❜❡❝❛✉s❡t❤❡ ❧✐♥❡❛r ♣❛rt r❡❢❡rs t♦ t❤♦s❡ ❛♥❣❧❡s ♦❢ ❛tt❛❝❦ ✇❤❡r❡ ♥♦ st❛❧❧ ❛♣♣❡❛rs✳ ❋✐❣✉r❡ ✹✳✸ s❤♦✇st❤❡ cL✲α✲❝✉r✈❡ ❢♦r ❞✐✛❡r❡♥t ❘❡②♥♦❧❞s ♥✉♠❜❡rs ✇✐t❤ ✈❛❧✉❡s t❛❦❡♥ ❜② ❆✐r❢♦✐❧ ❚♦♦❧s ❬✺✵❪✳❆s ❤✐❣❤❡r ❛♥❣❧❡s ♦❢ ❛tt❛❝❦s ❧❡❛❞ t♦ ❜✐❣❣❡r ❛♥❞ ❧♦♥❣❡r ✇✐♥❞ t✉♥♥❡❧s✱ ❛ ♠❛①✐♠✉♠ ❛♥❣❧❡♦❢ ❛tt❛❝❦ ♦❢ ❛❜♦✉t 8◦ ✇❛s ❝❤♦s❡♥✳ ■t ❢♦❧❧♦✇s t❤❛t t❤❡ t❡st s❡❝t✐♦♥ ♠✉st ❜❡ ❤✐❣❤ ❡♥♦✉❣❤t♦ ❝♦♥t❛✐♥ t❤❡ ❘●✶✺ ❛✐r❢♦✐❧ ✇✐t❤ ❛ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ 0.4m ✉♥❞❡r ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 8◦

✸✹

✹ ❘❡s✉❧ts

✇✐t❤♦✉t s✐❣♥✐✜❝❛♥t ❜❧♦❝❦❛❣❡ ❡✛❡❝ts✳

❋✐❣✉r❡ ✹✳✸✿ ❚❤❡ ❧✐❢t ❝♦❡✣❝✐❡♥t ♦❢ t❤❡ ❘● ✶✺ ♣❧♦tt❡❞ ♦✈❡r t❤❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ❢♦r ❞✐✛❡r❡♥t❘❡②♥♦❧❞s ♥✉♠❜❡rs✳ ❱❛❧✉❡s t❛❦❡♥ ❢r♦♠ ❆✐r❢♦✐❧ ❚♦♦❧s ❬✺✵❪✳

❆❧t❤♦✉❣❤ ✇✐♥❞ t✉♥♥❡❧s ❛✐♠ t♦ ❤❛✈❡ ✉♥✐❢♦r♠ ❝♦♥❞✐t✐♦♥s ✐♥s✐❞❡ t❤❡ ✇❤♦❧❡ t❡st s❡❝t✐♦♥✱t❤✐s ✐s t②♣✐❝❛❧❧② ♥♦t tr✉❡✳ ■♥st❡❛❞✱ t❤❡ ❝♦♥❞✐t✐♦♥s ✇✐❧❧ ♥♦r♠❛❧❧② ❞❡✈✐❛t❡ ✐♥ s♣❛❝❡ ❛♥❞t✐♠❡✳ ❲✐t❤ ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts✱ ❛♥ ❛❞❞✐t✐♦♥❛❧ ♣r♦❜❧❡♠ ❛rr✐✈❡s✳ ■❝❡ s❤❛♣❡s ❛r❡ ❛❧r❡❛❞②✈❛r②✐♥❣ ✐♥ ♥❛t✉r❡✳ ❚❤❡r❡❢♦r❡✱ ✐❝❡ s❤❛♣❡s ❛r❡ ♥♦r♠❛❧❧② ♠❡❛s✉r❡❞ ♦♥ ♠✉❧t✐♣❧❡ ❧♦❝❛t✐♦♥s❛❧♦♥❣ t❤❡ s♣❛♥ ❛s ✇❛s ❢♦r ❡①❛♠♣❧❡ ❞♦♥❡ ❜② ❍❛♥♥ ❬✺✶❪✳ ❚❤❡ ❞✐✛❡r❡♥t ♠❡❛s✉r❡♠❡♥ts ❝❛♥❜❡ ❝♦♠♣❛r❡❞ t♦ ❤❛✈❡ ❛ ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ q✉❛❧✐t② ❛♥❞ t♦❤❛✈❡ ♠❡❛♥ ✈❛❧✉❡s t❤❛t ❜❛❧❛♥❝❡ ♥♦♥✲✉♥✐❢♦r♠✐t②✳ ❋♦r t❤✐s ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ ✐t s❤❛❧❧ ❜❡♣♦ss✐❜❧❡ t♦ ❞♦ ♠❡❛s✉r❡♠❡♥ts ♦✈❡r ❛ ✇✐❞t❤ ♦❢ 0.3m✳ ❚❤❡r❡❢♦r❡ t❤❡ t❡st s❡❝t✐♦♥ ♠✉st ❜❡✇✐❞❡ ❡♥♦✉❣❤ t♦ ❝♦♥t❛✐♥ ✉♥✐❢♦r♠ ✢♦✇ ❝♦♥❞✐t✐♦♥s ♦✈❡r ❛ ✇✐❞t❤ ♦❢ 0.3m✳❚❤❡ ❊❆❙❆ ❧✐sts ✐❝✐♥❣ ❝♦♥❞✐t✐♦♥s ❢♦r t❡♠♣❡r❛t✉r❡s ❛s ❧♦✇ ❛s −40 ➦C ✐♥ t❤❡✐r r❡q✉✐r❡✲

♠❡♥ts ❢♦r ❛✐r❝r❛❢t ❛❧❧♦✇❛♥❝❡✳ ❍♦✇❡✈❡r✱ t❤❡ ▲❲❈ ✐s ❞❡❝r❡❛s✐♥❣ ✇✐t❤ ❞❡❝r❡❛s✐♥❣ t❡♠♣❡r❛✲t✉r❡s✳ ❚❤❡r❡❢♦r❡✱ t❡♠♣❡r❛t✉r❡s ❝❧♦s❡r t♦ 0 ➦C ❛r❡ ♠♦r❡ s❡✈❡r❡ ❝♦♥❝❡r♥✐♥❣ t❤❡ ❛♠♦✉♥t ♦❢✇❛t❡r ✐♥ t❤❡ ❛✐r✳ ■t ✇❛s ❛❧s♦ s❤♦✇♥ ❜② ❋❛❥t ❡t ❛❧✳ ❬✽❪ t❤❛t ✐❝✐♥❣ ❛t t❡♠♣❡r❛t✉r❡s ♥❡❛r t❤❡❢r❡❡③✐♥❣ ♣♦✐♥t ❧❡❛❞s t♦ ❤✐❣❤❡r ❛❡r♦❞②♥❛♠✐❝ ♣❡♥❛❧t✐❡s t❤❛♥ ✐❝✐♥❣ ❛t ❧♦✇❡r t❡♠♣❡r❛t✉r❡s✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ tr❛♥s✐t✐♦♥ ❜❡t✇❡❡♥ r✐♠❡ ✐❝❡ ❛♥❞ ❣❧❛❝❡ ✐❝❡ t❛❦❡s ♣❧❛❝❡ ✐♥ ❛ t❡♠♣❡r❛t✉r❡r❡❣✐♦♥ ❛r♦✉♥❞ −3 ➦C✳ ❚❤❡r❡❢♦r❡ t❡♠♣❡r❛t✉r❡s ❛r♦✉♥❞ −40 ➦C ❞♦ ♥♦t ♦✛❡r ♠✉❝❤ ✐♠✲♣r♦✈❡♠❡♥t t♦ t❤❡ ✜❡❧❞ t❤❛t ❝❛♥ ❜❡ st✉❞✐❡❞ ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❆❞❞✐t✐♦♥❛❧❧② ❧♦✇❡rt❡♠♣❡r❛t✉r❡s ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❧❡❛❞ t♦ ❤✐❣❤❡r ❝♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts ❛s ♠♦r❡

♣❛r❛♠❡t❡r ✈❛❧✉❡

s♣❡❡❞ ❛t t❡st s❡❝t✐♦♥ 35m s−1

❝❤♦r❞ ❧❡♥❣t❤ 0.4m♠❛①✐♠✉♠ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ 8◦

✇✐❞t❤ ✇✐t❤♦✉t ❜♦✉♥❞❛r② ❧❛②❡r ✐♥t❡r❢❡r❡♥❝❡ 0.3m❛✐r t❡♠♣❡r❛t✉r❡ −15 ➦C

❚❛❜❧❡ ✹✳✶✿ ▲✐st ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

✸✺

✹ ❘❡s✉❧ts

❤❡❛t ❤❛s t♦ ❜❡ r❡♠♦✈❡❞✳ ❚❤❡r❡❢♦r❡✱ ✐t ✇❛s ❞❡❝✐❞❡❞ t❤❛t t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ♥❡❡❞s t♦❣✉❛r❛♥t❡❡ t❡♠♣❡r❛t✉r❡s ♦❢ −15 ➦C ❜✉t ♥♦t ❧♦✇❡r✳❆❧❧ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡ ✹✳✶✳

✹✳✷ ❚❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s

❚❤❡ ❡q✉❛t✐♦♥s ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ❧❛st ❝❤❛♣t❡r ❤❛✈❡ t♦ ❜❡ ✉s❡❞ t♦ r❡❝❡✐✈❡ t❤❡ r❡s✉❧ts t❤❛t ❛r❡♣r❡s❡♥t❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡❝t✐♦♥s✳ ❚❤❡s❡ ❡q✉❛t✐♦♥s ❝♦♥t❛✐♥ t❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s♦❢ ❡✐t❤❡r ❛✐r ♦r ✇❛t❡r✳ ❚❤❡s❡ t❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ❞❡♣❡♥❞ ♦♥ t❡♠♣❡r❛t✉r❡✳ ❆st❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ♦♣❡r❛t❡ ✇✐t❤ ✈❛r✐♦✉s t❡♠♣❡r❛t✉r❡s✱ ❛ ❝❤♦✐❝❡ ❢♦r t❤❡ r❡❢❡r❡♥❝❡t❡♠♣❡r❛t✉r❡ ❤❛s t♦ ❜❡ ♠❛❞❡✳ ❚♦ ❜❡ ❝♦♥s❡r✈❛t✐✈❡ ✇✐t❤ ❡✈❡r② ❝❛❧❝✉❧❛t✐♦♥✱ t❤❡ ✇♦rst ❝❛s❡✇❛s ❝❤♦s❡♥ ❢♦r ❡✈❡r② ♣r♦♣❡rt②✳ ❚♦ ❞♦ s♦✱ t❤❡ ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ ❧✐♠✐t ❢♦r ❜♦t❤t❤❡ ❛✐r ❛♥❞ t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ♥❡❡❞ t♦ ❜❡ ❦♥♦✇♥✳ ❚❤❡ ❛✐r ✇✐❧❧ ❛❧✇❛②s ❜❡ ❜❡❧♦✇t❤❡ ❢r❡❡③✐♥❣ ♣♦✐♥t ❛♥❞ ❛s st❛t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✶ ♥❡✈❡r ❧♦✇❡r t❤❛♥ −15 ➦C✳ ❚❤❡ ❞r♦♣❧❡ts✇✐❧❧ ❧❡❛✈❡ t❤❡ s♣r❛② ♥♦③③❧❡ ✇✐t❤ ❛ t❡♠♣❡r❛t✉r❡ ♦❢ 15 ➦C✳ ❆s t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡✇✐❧❧ ❛❞❥✉st ❛s②♠♣t♦t✐❝❛❧❧② t♦ t❤❡ ❛✐r t❡♠♣❡r❛t✉r❡✱ ❞r♦♣❧❡ts ❝❛♥ ♥❡✈❡r ❣❡t ❝♦❧❞❡r t❤❛♥−15 ➦C✳ ❲✐t❤ t❤❡ ❦♥♦✇♥ ❧✐♠✐ts✱ t❤❡ ✈❛❧✉❡s ♦❢ t❤❡ t❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ❜❡❝♦♠❡t❤❡ ✈❛❧✉❡s s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡ ✹✳✷✳ ❚❤❡ ❞❡♥s✐t② ❛♥❞ t❤❡ ❦✐♥❡♠❛t✐❝ ✈✐s❝♦s✐t② ♦❢ ❛✐r❤❛✈❡ ❞✐✛❡r❡♥t ✇♦rst ❝❛s❡s ❢♦r t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ❛♥❞ t❤❡ ♣r❡ss✉r❡ ❧♦ss ❝❛❧❝✉❧❛t✐♦♥s✳❚❤❡r❡❢♦r❡ ❢♦r ❡❛❝❤ ♦❢ t❤❡ t✇♦ ❝❛s❡s ❛ ❞✐✛❡r❡♥t ✇♦rst ❝❛s❡ ✇❛s s❡❧❡❝t❡❞✳ ❆❧❧ ✈❛❧✉❡s ❢♦r

♣r♦♣❡rt② ✫ s②♠❜♦❧ ✈❛❧✉❡ T [➦C]

t❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ❛✐r

❦✐♥❡♠❛t✐❝ ✈✐s❝♦s✐t② ν ✭❉r♦♣❧❡t ❜❡❤❛✈✐♦r✮ 12.11 · 10−6 m2 s−1 −15❦✐♥❡♠❛t✐❝ ✈✐s❝♦s✐t② ν ✭Pr❡ss✉r❡ ❧♦ss✮ 13.38 · 10−6 m2 s−1 0❞②♥❛♠✐❝ ✈✐s❝♦s✐t② µ 16.55 · 10−6 kg s−1 m−1 −15❤❡❛t ❝❛♣❛❝✐t② r❛t✐♦ γ 1.4 ✲s♣❡❝✐✜❝ ❣❛s ❝♦♥st❛♥t R 287.0m2 s−2 K ✲Pr❛♥❞t❧ ♥✉♠❜❡r Pr 0.7362 0t❤❡r♠❛❧ ❝♦♥❞✉❝t✐✈✐t② k 0.0225Wm−1 K−1 −15❞❡♥s✐t② ρ ✭❉r♦♣❧❡t ❜❡❤❛✈✐♦r✮ 1.292 kgm−3 0❞❡♥s✐t② ρ ✭Pr❡ss✉r❡ ❧♦ss✮ 1.367 kgm−3 −15

t❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ✇❛t❡r

❞❡♥s✐t② ρ 999.9 kgm−3 5s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② cp 4349 J kg−1 K−1 −15s♣❡❝✐✜❝ ❤❡❛t ❝❛♣❛❝✐t② cv 4349 J kg−1 K−1 −15s♣❡❝✐✜❝ ❧❛t❡♥t ❤❡❛t ♦❢ ❢✉s✐♦♥ clatent 334,000 J kg−1 0

❚❛❜❧❡ ✹✳✷✿ ❚❤❡r♠♦♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ❛✐r ❛♥❞ ✇❛t❡r ❢♦r t❤❡ r❡❢❡r❡♥❝❡ t❡♠♣❡r❛t✉r❡ T ✳❉✐✛❡r❡♥t ✇♦rst✲❝❛s❡s ♠✐❣❤t ❡①✐st ❢♦r t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ❛♥❞ t❤❡ ♣r❡ss✉r❡❧♦ss✳

✸✻

✹ ❘❡s✉❧ts

❛✐r ✇❡r❡ t❛❦❡♥ ❜② ➬❡♥❣❡❧ ❛♥❞ ❈✐♠❜❛❧❛ ❬✺✷❪✳ ❍♦✇❡✈❡r✱ t❤❡s❡ ❛✉t❤♦rs ❥✉st ♦✛❡r ✈❛❧✉❡s❢♦r ✇❛t❡r ❢♦r t❡♠♣❡r❛t✉r❡s ❛❜♦✈❡ t❤❡ ❢r❡❡③✐♥❣ ♣♦✐♥t✳ ❚❤❡r❡❢♦r❡ t❤❡✐r ♣r♦♣❡rt✐❡s ♦❢ ✇❛t❡r✇❡r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ ❍❛r❡ ❛♥❞ ❙♦r❡♥s❡♥ ❬✺✸❪✱ ❙t❡♣❛♥♦✈ ❬✺✹❪ ❛♥❞ ❙③❡❞❧❛❦ ❡t ❛❧✳ ❬✺✺❪✳ ■♥❝❛s❡s ✇❤❡r❡ t❤❡ ✈❛❧✉❡ ✇❛s ♥♦t ❣✐✈❡♥ ❢♦r t❤❡ ❡①❛❝t t❡♠♣❡r❛t✉r❡✱ ❛ ❧✐♥❡❛r ✐♥t❡r♣♦❧❛t✐♦♥❜❡t✇❡❡♥ t❤❡ t✇♦ ♥❡①t ❝❧♦s❡st ✈❛❧✉❡s ✇❛s ❞♦♥❡✳

✹✳✸ ❋✐♥❛❧ ❞❡s✐❣♥

■♥ t❤✐s s❡❝t✐♦♥✱ t❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ ❡✈❡r② s✐♥❣❧❡ ❝♦♠♣♦♥❡♥t ✐s ♣r❡s❡♥t❡❞✳ ❉✉r✐♥❣ t❤❡❞❡s✐❣♥✱ t❤❡ q✉❡st✐♦♥ ❛❜♦✉t t❤❡ ♥❡❝❡ss❛r② ♥✉♠❜❡r ♦❢ s✐❣♥✐✜❝❛♥t ❞✐❣✐ts ❝❛♠❡ ✉♣✳ ❚❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❤❛✈❡ ❞✐♠❡♥s✐♦♥s ♦❢ ♠✉❧t✐♣❧❡ ♠❡t❡rs✳ ❚❤❡r❡❢♦r❡✱ ❜❡✐♥❣ ♠♦r❡ ♣r❡❝✐s❡ t❤❛♥r♦✉♥❞✐♥❣ ♦♥ ❝❡♥t✐♠❡t❡rs s❡❡♠s ♥♦t r❡q✉✐r❡❞✳

✹✳✸✳✶ ❚❡st s❡❝t✐♦♥

❆✐r❢♦✐❧s ❛r❡ ❡ss❡♥t✐❛❧❧② t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ♦❜❥❡❝ts ❡①tr❛❝t❡❞ ✐♥ t❤❡ s♣❛♥✇✐s❡ ❞✐r❡❝t✐♦♥✳ ❚♦❤❛✈❡ ❝♦♠♣❛r❛❜❧❡ ❝♦♥❞✐t✐♦♥s ♦✈❡r t❤❡ ✇❤♦❧❡ ✇✐❞t❤ ✐t ✐s t❤❡r❡❢♦r❡ t❤❡ ❡❛s✐❡st t♦ ❤❛✈❡ ❛r❡❝t❛♥❣✉❧❛r s❤❛♣❡❞ t❡st s❡❝t✐♦♥✳ ❲✐t❤ t❤✐s ❞❡❝✐s✐♦♥✱ t❤❡ s♣❛❝❡ ✉♥❞❡r ❛♥❞ ❛❜♦✈❡ t❤❡ ❛✐r❢♦✐❧✐s t❤❡ s❛♠❡ ✐♥s✐❞❡ t❤❡ ✇❤♦❧❡ t❡st s❡❝t✐♦♥✳ ❍❡♥❝❡✱ ❜♦t❤ t❤❡ t❡st s❡❝t✐♦♥ ❛♥❞ t❤❡ ❛✐r❢♦✐❧ ❛r❡❡ss❡♥t✐❛❧❧② t✇♦✲❞✐♠❡♥s✐♦♥❛❧✳ ❆s ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ ❛r❡❛ ♦❢ t❤❡ t❡sts❡❝t✐♦♥ ♠✉st ❜❡ ❝❤♦s❡♥ ✐♥ ❛ ♠❛♥♥❡r t❤❛t t❤❡ ❜❧♦❝❦❛❣❡ st❛②s ❜❡❧♦✇ 10%✳ ■❢ ❛♥ ♦❜s❡r✈❡r❧♦♦❦s ✐♥s✐❞❡ t❤❡ t❡st s❡❝t✐♦♥ ❢r♦♠ ❛♥ ✉♣str❡❛♠ ♣♦s✐t✐♦♥✱ ❤❡ ✇✐❧❧ r❡❝♦❣♥✐③❡ ❜♦t❤ t❤❡ ❛✐r❢♦✐❧❛♥❞ t❤❡ t❡st s❡❝t✐♦♥ ❛s r❡❝t❛♥❣✉❧❛r s❤❛♣❡s ✇✐t❤ t❤❡ s❛♠❡ ✇✐❞t❤✳ ❚❤❡r❡❢♦r❡ t❤❡ ❡q✉❛t✐♦♥❢♦r t❤❡ ❜❧♦❝❦❛❣❡ ❝❛♥ ❜❡ s✐♠♣❧✐✜❡❞ t♦

Aprojected

ATS

=HprojectedWTS

HTSWTS

≈ Hprojected

HTS

. ✭✹✳✶✮

❚❤❡ ❛r❡❛ ✐s ❞❡♥♦t❡❞ ✇✐t❤ A✱ t❤❡ ❤❡✐❣❤t ✇✐t❤ H✱ ❛♥❞ t❤❡ ✇✐❞t❤ ✇✐t❤ W ✳ ❚❤❡ ✐♥❞❡①projected ✐s ✉s❡❞ ❢♦r t❤❡ ♣r♦❥❡❝t❡❞ ✈❛❧✉❡s ♦❢ t❤❡ ❛✐r❢♦✐❧ ❛♥❞ t❤❡ ✐♥❞❡① TS ✐♥❞✐❝❛t❡s t❤❡✈❛❧✉❡s ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❲✐t❤ ❡q✉❛t✐♦♥ ✹✳✶ t❤❡ ❜❧♦❝❦❛❣❡ r❡❞✉❝❡s t♦ t❤❡ ❢r❛❝t✐♦♥ ♦❢ t✇♦❧❡♥❣t❤s✳ ❚❤❡ ♣r♦❥❡❝t❡❞ ❤❡✐❣❤t ✐s t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❤✐❣❤❡st ♣♦✐♥t ♦❢ t❤❡ ❛✐r❢♦✐❧❛♥❞ t❤❡ ❧♦✇❡st ♦♥❡✳ ❚❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ ❛♥ ❛✐r❢♦✐❧ ❞❡♣❡♥❞ ♦♥ ✐ts s❤❛♣❡✱ t❤❡ ❝❤♦r❞ ❧❡♥❣t❤✱❛♥❞ t❤❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦✳ ❚❤❡ ❛✐r❢♦✐❧ ❝♦♦r❞✐♥❛t❡s ♦❢ ❛♥ ❘●✶✺ ❢♦r ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 0◦

❛r❡ ❧✐st❡❞ ✐♥ ❆♣♣❡♥❞✐① ❆✳✸✳ ❚❤❡ ❝♦✉♥t❡r✲❝❧♦❝❦✇✐s❡ r♦t❛t✐♦♥ ♦❢ ❛ ❜♦❞② ❝❛♥ ❜❡ ❢♦r♠✉❧❛t❡❞✇✐t❤

x′ = x cos (θ)− y sin (θ) ✭✹✳✷❛✮

y′ = x sin (θ) + y cos (θ) ✭✹✳✷❜✮

❛❝❝♦r❞✐♥❣ t♦ ❑r❡②s③✐❣ ❡t ❛❧✳ ❬✺✻❪✳ ❚❤❡ ❝♦♦r❞✐♥❛t❡s ✇✐t❤ ❛♥ ❛♣♦str♦♣❤❡ ❞❡♥♦t❡ t❤❡ ❝♦✲♦r❞✐♥❛t❡s ❛❢t❡r r♦t❛t✐♦♥✳ ❲✐t❤ t❤❡ ❡q✉❛t✐♦♥s ✹✳✷❛ ❛♥❞ ✹✳✷❜✱ t❤❡ ♣r♦❥❡❝t❡❞ ❤❡✐❣❤t ♦❢ ❛♥❘●✶✺ ❛✐r❢♦✐❧ ✇✐t❤ ❛ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ 0.4m ✉♥❞❡r ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ✐s 0.068m✳ ❚♦ ❡♥s✉r❡t❤❡ ❜❧♦❝❦❛❣❡ ✐s 10% ❛t ♠♦st✱ t❤❡ ❤❡✐❣❤t ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❤❡♥❝❡ ♥❡❡❞s t♦ ❜❡ 0.68m✳❆s ❡①♣❧❛✐♥❡❞ ✐♥ s❡❝t✐♦♥ ✹✳✶✱ ❛ ✇✐❞t❤ ♦❢ 0.3m ✇✐t❤♦✉t ❛♥② ❜♦✉♥❞❛r② ❧❛②❡r ✐♥t❡r❛❝t✐♦♥

✐s r❡q✉✐r❡❞✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ r✉❧❡ ♦❢ t❤✉♠❜ ❜② ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✱ t❤❛t ✇❛s ♣r❡s❡♥t❡❞

✸✼

✹ ❘❡s✉❧ts

✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r ✇✐❧❧ ✐♥✢✉❡♥❝❡ 20% ♦❢ t❤❡ ✇✐❞t❤ ❛♥❞ ❤❡✐❣❤t✳❚❤❡r❡❢♦r❡ t❤❡ t❡st s❡❝t✐♦♥ ✇✐❞t❤ ✇♦✉❧❞ ❤❛✈❡ t♦ ❜❡ ✐♥❝r❡❛s❡❞ ❜② 25%✳ ❚❤✐s r❡s✉❧ts ✐♥ ❛s❛❢❡t② ♠❛r❣✐♥ ♦❢ ❛❜♦✉t 0.038m ♦♥ ❡❛❝❤ s✐❞❡✳ ▼♦r❡ ❞❡t❛✐❧❡❞ s✐♠✉❧❛t✐♦♥s ✇✐t❤ t❤❡ ♠❡t❤♦❞♣r❡s❡♥t❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r ❤♦✇❡✈❡r ❧❡❛❞ t♦ ❛ ❜♦✉♥❞❛r② ❧❛②❡r ❤❡✐❣❤t ♦❢ 0.043m❛t t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡ ❛t ❧❡❛st 0.086m ❤❛✈❡ t♦ ❜❡ ❛❞❞❡❞ t♦ t❤❡ ❛✐r❢♦✐❧ ✇✐❞t❤ t♦❛✈♦✐❞ ❜♦✉♥❞❛r② ❧❛②❡r ✐♥t❡r❛❝t✐♦♥s✳ ❚♦ ✐♥tr♦❞✉❝❡ ❛ s♠❛❧❧ s❛❢❡t② ♠❛r❣✐♥✱ ❛ t❡st s❡❝t✐♦♥✇✐❞t❤ ♦❢ 0.39m ✇❛s ❝❤♦s❡♥✳❍❡♥❝❡✱ t❤❡ t❡st s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r ✇✐t❤ ❛ ✇✐❞t❤ ♦❢ 0.39m ❛♥❞ ❛ ❤❡✐❣❤t ♦❢ 0.68m✳

❚❤✐s r❡s✉❧ts ✐♥ ❛ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ 0.50m✳❆s ♠❡♥t✐♦♥❡❞✱ t❤❡ ✢♦✇ s❤♦✉❧❞ ❜❡ ❛❧❧♦✇❡❞ ❛ s❡tt❧✐♥❣ ❧❡♥❣t❤ ♦❢ ❤❛❧❢ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠✲

❡t❡r ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ♥♦③③❧❡ ❡①✐t ❛♥❞ t❤❡ t❡st ♦❜❥❡❝t✳ ❚❤❡r❡❢♦r❡✱ ❢♦r t❤❡st❛t❡❞ ❞❡s✐❣♥✱ t❤❡ s❡tt❧✐♥❣ ❧❡♥❣t❤ ✐s 0.25m✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ❢♦r t❤✐s ❞❡s✐❣♥✱ ✐t ✇❛s ❝❤♦s❡♥t♦ ✐♥❝r❡❛s❡ t❤❡ t❡st s❡❝t✐♦♥ ❧❡♥❣t❤ ❜② 0.05m ❜❡❤✐♥❞ t❤❡ t❡st ♦❜❥❡❝t✳ ❚❤✐s r❡❞✉❝❡s t❤❡♣r♦❜❛❜✐❧✐t② ♦❢ s❡♣❛r❛t✐♦♥ ♦♥ t❤❡ tr❛♥s✐t✐♦♥ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ❛♥❞ t❤❡ ❞✐✛✉s❡r ❛♥❞ ❛❧❧♦✇st♦ ✐♥s❡rt ❧♦♥❣❡r ❛✐r❢♦✐❧s ❛s ✇❡❧❧✳ ❍❡♥❝❡✱ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ✐s ❝❛❧❝✉❧❛t❡❞ ❜②❛❞❞✐♥❣ ✉♣ t❤❡ s❡tt❧✐♥❣ ❧❡♥❣t❤✱ t❤❡ ❝♦♥s✐❞❡r❡❞ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ 0.4m✱ ❛♥❞ t❤❡ ❡♥❧❛r❣❡♠❡♥t♦❢ 0.05m✳ ❚❤✐s s✉♠ ✐s ❛❧s♦ ✈✐s✉❛❧✐③❡❞ ✐♥ ❋✐❣✉r❡ ✹✳✹✳ ❚❤❡r❡❢♦r❡ t❤❡ ✜♥❛❧ ❧❡♥❣t❤ ♦❢ t❤❡t❡st s❡❝t✐♦♥ ✐s 0.70m✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✹✳

❋✐❣✉r❡ ✹✳✹✿ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳

✹✳✸✳✷ ◆♦③③❧❡

❚❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡ ❝♦♥♥❡❝ts t♦ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡ t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ♦❢ t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡ ✐s t❤❡ s❛♠❡ ❛s t❤❡ t❡st s❡❝t✐♦♥✬s ❝r♦ss✲s❡❝t✐♦♥✳ ❍❡♥❝❡✱ ❛t t❤✐s ❡♥❞✱ t❤❡ ♥♦③③❧❡ ❤❛s ❛ r❡❝t❛♥❣✉❧❛r s❤❛♣❡ ✇✐t❤ ❛ ✇✐❞t❤ ♦❢ 0.39m❛♥❞ ❛ ❤❡✐❣❤t ♦❢ 0.68m✳

✸✽

✹ ❘❡s✉❧ts

❋♦r t❤✐s ✇♦r❦✱ ❛ ♠❡❞✐✉♠ ❝♦♥tr❛❝t✐♦♥ r❛t✐♦ ♦❢ 9 ✇❛s ❝❤♦s❡♥✳ ❚❤✐s s❤♦✉❧❞ ♦✛❡r ❛ ❜❛❧❛♥❝❡❜❡t✇❡❡♥ ❣♦♦❞ ✢♦✇ q✉❛❧✐t② ❛♥❞ ❢❡✇ ♣r❡ss✉r❡ ❧♦ss❡s ♦♥ ♦♥❡ s✐❞❡ ❛♥❞ ❛ s♠❛❧❧ ✇✐♥❞ t✉♥♥❡❧s✐③❡ ♦♥ t❤❡ ♦t❤❡r s✐❞❡✳ ❲✐t❤ t❤❡ ❝♦♥tr❛❝t✐♦♥ r❛t✐♦ t❤❛t ✐s ❡✛❡❝t✐✈❡❧② t❤❡ ❛r❡❛ r❛t✐♦✱ ❛❧s♦t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ♦❢ t❤❡ ✉♣str❡❛♠ ❡♥❞ ✐s ❣✐✈❡♥✱ ❜✉t t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ❝❛♥ st✐❧❧ ❜❡❞❡t❡r♠✐♥❡❞✳ ❯♣str❡❛♠ ♦❢ t❤❡ ♥♦③③❧❡✱ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✱ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❛♥❞ t❤❡❢❛♥ ✇✐❧❧ ❜❡ ♠♦✉♥t❡❞✳ ❆s ✇✐❧❧ ❜❡ ❡①♣❧❛✐♥❡❞ ✐♥ s✉❜s❡❝t✐♦♥ ✹✳✸✳✺✱ t❤❡ ❢❛♥ ♦❢ t❤✐s ✇✐♥❞ t✉♥♥❡❧✇✐❧❧ ❜❡ ❝✐r❝✉❧❛r✳ ❚❤❡ t❡st s❡❝t✐♦♥ ❤♦✇❡✈❡r ❤❛s ❛ r❡❝t❛♥❣✉❧❛r ❝r♦ss✲s❡❝t✐♦♥ ✇✐t❤ ❛♥ ❛s♣❡❝tr❛t✐♦ ♦❢ ❛❧♠♦st ✷✿✶✳ ❚❤❡r❡❢♦r❡✱ t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ♠✉st ❝❤❛♥❣❡ s♦♠❡✇❤❡r❡ ❢r♦♠ ❝✐r❝✉❧❛rt♦ r❡❝t❛♥❣✉❧❛r ❜❡t✇❡❡♥ t❤❡ ❢❛♥ ❛♥❞ t❤❡ t❡st s❡❝t✐♦♥✳ ❆s ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ❧❛st ❝❤❛♣t❡r✱r❡❝t❛♥❣✉❧❛r ♥♦③③❧❡s ✇✐t❤ ❛ ❝❤❛♥❣✐♥❣ ❛s♣❡❝t r❛t✐♦ ❛r❡ ❛♥ ♦♣t✐♦♥✳ ❆ ❝❤❛♥❣❡ ♦❢ ❝r♦ss✲s❡❝t✐♦♥❢r♦♠ ❝✐r❝✉❧❛r t♦ r❡❝t❛♥❣✉❧❛r ♦r sq✉❛r❡ ✐s ❤♦✇❡✈❡r ✐♥tr♦❞✉❝✐♥❣ ♥❡✇ ♣r♦❜❧❡♠s✳ ❚❤✐s ✐s❜❡❝❛✉s❡ t❤❡ ♥♦③③❧❡ ✐ts❡❧❢ ✐s ❞❡s✐❣♥❡❞ ✇✐t❤ ❛ ♥❛rr♦✇ ♠❛r❣✐♥ t♦ s❡♣❛r❛t✐♦♥ ❛♥❞ ❝❤❛♥❣❡s ♦❢t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ❜❡t✇❡❡♥ ❝✐r❝✉❧❛r ❛♥❞ r❡❝t❛♥❣✉❧❛r ❤❛✈❡ t❤❡ s❛♠❡ ❞♦✇♥s✐❞❡✳❍❛✈✐♥❣ ❛ sq✉❛r❡ ❝r♦ss✲s❡❝t✐♦♥ ❛t t❤❡ ✉♣str❡❛♠ ❡♥❞ ♠❛❦❡s t❤❡ tr❛♥s✐t✐♦♥ t♦ ❛ ❝✐r❝✉❧❛r

s❤❛♣❡ ❢✉rt❤❡r ✉♣str❡❛♠ ❡❛s✐❡r✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♠❛①✐♠✉♠ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ t❤❡ ♥♦③③❧❡✇✐t❤ ❝❤❛♥❣✐♥❣ ❛s♣❡❝t r❛t✐♦ ✐s s♠❛❧❧❡r ❝♦♠♣❛r❡❞ t♦ ❦❡❡♣✐♥❣ t❤❡ ❛s♣❡❝t r❛t✐♦✳ ❆s s❡♣❛r❛t✐♦♥❞❡♣❡♥❞s ♦♥ t❤❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ❛♥❞ t❤❡ ♠❛①✐♠✉♠ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ t❤❡ ♥♦③③❧❡ ✐s r❡❞✉❝❡❞✱t❤❡ s❡♣❛r❛t✐♦♥ r✐s❦ ✐s r❡❞✉❝❡❞✳ ❍❡♥❝❡✱ t❤❡ ✉♣str❡❛♠ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡ ✇❛s ❝❤♦s❡♥ t♦ ❜❡sq✉❛r❡✳ ❆s ❜♦t❤ t❤❡ ❛r❡❛ ❛t t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ❛♥❞ t❤❡ ❛r❡❛ r❛t✐♦ ❛r❡ ❣✐✈❡♥✱ t❤❡ s✐❞❡❧❡♥❣t❤ ♦❢ t❤❡ sq✉❛r❡ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ t♦ 1.54m✳■♥ ❋✐❣✉r❡ ❆✳✶ ✐♥ t❤❡ ❆♣♣❡♥❞✐①✱ t❤❡ ♠✐♥✐♠✉♠ ❧❡♥❣t❤ ♦❢ ♥♦③③❧❡s ✐s ♣❧♦tt❡❞ ♦✈❡r t❤❡

r❛t✐♦ ♦❢ t❤❡ ❡q✉✐✈❛❧❡♥t ❞✐❛♠❡t❡rs ❛t ✐♥❧❡t ❛♥❞ ♦✉t❧❡t✳ ❋♦r ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ 9✱ t❤❡ r❛t✐♦ ♦❢t❤❡ ❡q✉✐✈❛❧❡♥t ❞✐❛♠❡t❡rs ❜❡❝♦♠❡s 3✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ st❛t❡❞ ✜❣✉r❡✱ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡♥♦③③❧❡ s❤♦✉❧❞ ❜❡ ❛t ❧❡❛st 0.9 t✐♠❡s t❤❡ ❡q✉✐✈❛❧❡♥t ❞✐❛♠❡t❡r ❛t t❤❡ ✐♥❧❡t ❢♦r t❤✐s ❝❛s❡✳ ❆ss❤♦rt ♥♦③③❧❡s ❤❛✈❡ ❛ ❤✐❣❤❡r r✐s❦ ♦❢ s❡♣❛r❛t✐♦♥ ❛♥❞ ❧♦♥❣ ♥♦③③❧❡s ✐♥❝r❡❛s❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧❧❡♥❣t❤✱ ❛ ❝♦♠♣r♦♠✐s❡ ♥❡❡❞s t♦ ❜❡ ❢♦✉♥❞✳ ❚❤❡r❡❢♦r❡✱ ❛ ❧❡♥❣t❤ ♦❢ ❡①❛❝t❧② t❤❡ ❡q✉✐✈❛❧❡♥t❞✐❛♠❡t❡r ♦❢ t❤❡ ✉♣str❡❛♠ ❡♥❞ ✇❛s ❝❤♦s❡♥✳ ❚❤❡ ❡q✉✐✈❛❧❡♥t ❞✐❛♠❡t❡r ♦❢ ❛ sq✉❛r❡ ✇✐t❤s✐❞❡s ♦❢ 1.54m ✐s 1.74m✳ ❍❡♥❝❡✱ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡ ✐s 1.74m✳ ❚❤❡ ❞❡s✐❣♥ ♦❢ t❤❡♥♦③③❧❡ ✐s ✈✐s✉❛❧✐③❡❞ ✐♥ ❋✐❣✉r❡ ✹✳✶✵✳❲✐t❤ t❤❡ ✐♥❧❡t ❛♥❞ ♦✉t❧❡t ❣❡♦♠❡tr② ❣✐✈❡♥ ❛s ✇❡❧❧ ❛s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡✱ t❤❡

❧❛st q✉❡st✐♦♥ ✐s t❤❡ s❤❛♣❡ ♦❢ t❤❡ ♥♦③③❧❡ ✇❛❧❧s✳ ❆ ❝❧♦s❡r ❧♦♦❦ ❛t t❤❡ ❝♦♥t♦✉rs ♣r❡s❡♥t❡❞✐♥ s✉❜s❡❝t✐♦♥ ✸✳✷✳✷ s❤♦✇s t❤❛t t❤❡ s❤❛♣❡s ♦❢ t❤❡ t❤✐r❞✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧✱ t❤❡ ✜❢t❤✲♦r❞❡r♣♦❧②♥♦♠✐❛❧✱ ❛♥❞ t❤❡ tr❛♥s❢♦r♠❡❞ ✜❢t❤✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧ ❛r❡ st❡❡♣❡r ♥❡❛r t❤❡ ❡♥tr② ♦❢ t❤❡t❡st s❡❝t✐♦♥ t❤❛♥ t❤❡ ❆❱❆ ♥♦③③❧❡✱ t❤❡ ❲✐t♦s③②♥s❦✐ ♥♦③③❧❡✱ ❛♥❞ t❤❡ ♠❛t❝❤❡❞ ❝✉❜✐❝s ♥♦③③❧❡❝♦♥t♦✉rs✳ ❋✐❣✉r❡ ✹✳✺ s❤♦✇s t❤❡ tr❛❥❡❝t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ❞r♦♣❧❡t ❞✐❛♠❡t❡r ❢♦r❛ ♥♦③③❧❡ s❤❛♣❡ ❜❛s❡❞ ♦♥ ❛ t❤✐r❞✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧✳ ❲❤❡♥ t❤❡ ❞r♦♣❧❡ts r❡❛❝❤ t❤❡ t❡sts❡❝t✐♦♥✱ t❤❡② st✐❧❧ ❤❛✈❡ ❛ s✐❣♥✐✜❝❛♥t ✈❡❧♦❝✐t② ♥♦r♠❛❧ t♦ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❞✐r❡❝t✐♦♥✳ ❚❤✐s✐s ❞✉❡ t♦ t❤❡✐r ❝❤❛r❛❝t❡r t♦ ❢♦❧❧♦✇ t❤❡ ❛✐r str❡❛♠❧✐♥❡s t♦ ❛ ❝❡rt❛✐♥ ❞❡❣r❡❡✳ ❉✉❡ t♦ t❤❡st❡❡♣ ❝♦♥tr❛❝t✐♦♥ ❛t t❤❡ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡✱ ❛❧s♦ t❤❡ str❡❛♠❧✐♥❡s ♦❢ t❤❡ ❛✐r ❤❛✈❡ ❛ st❡❡♣❝♦♥tr❛❝t✐♦♥✳ ❍❡♥❝❡✱ t❤❡ ❞r♦♣❧❡ts r❡❝❡✐✈❡ ❛ ❤✉❣❡ ✈❡❧♦❝✐t② ♥♦r♠❛❧ t♦ t❤❡ ✇✐♥❞ t✉♥♥❡❧❞✐r❡❝t✐♦♥ t♦ ❜❡ ❛❜❧❡ t♦ ❢♦❧❧♦✇ t❤❡ ❛✐r str❡❛♠❧✐♥❡s✳ ❚❤❡ ✈❡❧♦❝✐t② ❝♦♠♣♦♥❡♥t ♥♦r♠❛❧ t♦ t❤❡✇✐♥❞ t✉♥♥❡❧ ❞✐r❡❝t✐♦♥ ❝❤❛♥❣❡s t❤❡ ❡✛❡❝t✐✈❡ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ❢♦r t❤❡ ❛✐r❢♦✐❧ ❛♥❞ t❤❡r❡❢♦r❡❞❡❝r❡❛s❡s t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ♠❡❛s✉r❡♠❡♥ts ❛♥❞ r❡s✉❧ts✳❆s ❛ ❝♦♠♣❛r✐s♦♥✱ t❤❡ tr❛❥❡❝t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ✐♥s✐❞❡ t❤❡ ❆❱❆ ♥♦③③❧❡ ❛r❡

s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✻✳ ❆s t❤❡ ❣r❛❞✐❡♥t ♦❢ t❤❡ ♥♦③③❧❡ ❝♦♥t♦✉r ❝❧♦s❡ t♦ t❤❡ t❡st s❡❝t✐♦♥ ✐s

✸✾

✹ ❘❡s✉❧ts

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

axis in flow direction [m]

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6a

xis

no

rma

l to

flo

w d

ire

ctio

n [

m] Droplet Trajectory

Air streamline

Boundary

❋✐❣✉r❡ ✹✳✺✿ ❚r❛❥❡t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ❞✐❛♠❡t❡r ✐♥ ❛ ♥♦③③❧❡ ✇✐t❤ ❛ t❤✐r❞ ♦r❞❡r♣♦❧②♥♦♠✐❛❧ ❝♦♥t♦✉r✳

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

axis in flow direction [m]

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

axis

no

rma

l to

flo

w d

ire

ctio

n [

m] Droplet Trajectory

Air streamline

Boundary

❋✐❣✉r❡ ✹✳✻✿ ❚r❛❥❡t♦r✐❡s ♦❢ ❞r♦♣❧❡ts ✇✐t❤ 50 ➭m ❞✐❛♠❡t❡r ✐♥ ❛ ♥♦③③❧❡ ✇✐t❤ ❛♥ ❆❱❆ ❝♦♥t♦✉r✳

s♠❛❧❧✱ t❤❡ ❞r♦♣❧❡ts ❤❛✈❡ ❛ ♠✉❝❤ s♠❛❧❧❡r ✈❡❧♦❝✐t② ❝♦♠♣♦♥❡♥t ✐♥ t❤❡ ✉♣✇❛r❞s ❞✐r❡❝t✐♦♥✳❚❤❡r❡❢♦r❡ t❤❡ ♥♦③③❧❡ ❝♦♥t♦✉rs t❤❛t ❛r❡ ❧❡ss st❡❡♣ ✐♥ t❤❡✐r ✜♥❛❧ ♣❛rt ❛r❡ ♣r❡❢❡r❛❜❧❡ ❢♦r t❤❡❝♦♥❝❡r♥ ♦❢ t❤❡ tr❛❥❡❝t♦r✐❡s✳❆ ♣❧♦t ♦❢ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ✈❡❧♦❝✐t✐❡s ♦❢ t❤❡ ❞r♦♣❧❡ts t❤r♦✉❣❤ t❤❡ ♥♦③③❧❡ ❝❛♥ ❜❡

r❛t❤❡r ❞✐✣❝✉❧t t♦ ✉♥❞❡rst❛♥❞✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❞r♦♣❧❡ts ❛❞❥✉sts t♦t❤❡ ❛✐r s♣❡❡❞✳ ❍♦✇❡✈❡r✱ ✐❢ ❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs ❛r❡ ❝♦♠♣❛r❡❞✱ t❤❡ ❛✐r s♣❡❡❞ ♦❢ t❤❡❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs ✐s ❞✐✛❡r❡♥t ❛t ❡✈❡r② ♣♦s✐t✐♦♥✳ ❚❤❡r❡❢♦r❡✱ ❋✐❣✉r❡ ✹✳✼ ❝♦♥t❛✐♥s ❛♥❡①❡♠♣❧❛r② ♣❧♦t ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② t❤r♦✉❣❤ t❤❡ ❆❱❆ ♥♦③③❧❡ ❛s ✇❡❧❧ ❛s t❤❡ ❛✐r s♣❡❡❞❛♥❞ t❤❡ ♥♦③③❧❡ ❝♦♥t♦✉r✳ ■t ❝❛♥ ❜❡ s❡❡♥ t❤❛t t❤❡ ❞r♦♣❧❡ts ❧❡❛✈❡ t❤❡ s♣r❛② ♥♦③③❧❡ ✇✐t❤ ❛✈❡❧♦❝✐t② ❤✐❣❤❡r t❤❛♥ t❤❡ ❛✐r s♣❡❡❞✳ ❚❤❡② ❛r❡ ❤♦✇❡✈❡r ❞❡❝❡❧❡r❛t❡❞ ✐♥ t❤❡ s❡tt❧✐♥❣ ❛r❡❛❛♥❞ ❤❛✈❡ ❛❧♠♦st t❤❡ s❛♠❡ ✈❡❧♦❝✐t② ❛s t❤❡ ❛✐r ❛t t❤❡ ❜❡❣✐♥♥✐♥❣ ♦❢ t❤❡ ♥♦③③❧❡✳ ❉✉❡ t♦ t❤❡❝♦♥tr❛❝t✐♦♥ ♦❢ t❤❡ ♥♦③③❧❡✱ t❤❡ ❛✐r s♣❡❡❞ ✐♥❝r❡❛s❡s ❛♥❞ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛❞❥✉sts s❧♦✇❧②

✹✵

✹ ❘❡s✉❧ts

t♦ t❤✐s ❝❤❛♥❣❡❞ ❛✐r s♣❡❡❞✳ ❚❤❡ ❞r♦♣❧❡ts ❛r❡ ❤♦✇❡✈❡r ♥♦t ❛❜❧❡ t♦ r❡❛❝❤ t❤❡ ❛✐r s♣❡❡❞ ✉♥t✐❧t❤❡② r❡❛❝❤ t❤❡ t❡st ♦❜❥❡❝t✳

0 0.5 1 1.5

axis in flow direction [m]

0

10

20

30

40ve

locity [

m/s

]

0

0.2

0.4

0.6

0.8

1

axis

no

rma

l to

flo

w d

ire

ctio

n [

m]

droplet velocity

air velocity

contour

❋✐❣✉r❡ ✹✳✼✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞r♦♣❧❡t ❛♥❞ t❤❡ ❛✐r ✈❡❧♦❝✐t② ✐♥s✐❞❡ t❤❡ ❆❱❆ ♥♦③③❧❡✳

❋✐❣✉r❡ ✹✳✽ s❤♦✇s t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ♦✈❡r t❤❡ ❧❡♥❣t❤ ❜❡t✇❡❡♥ t❤❡s♣r❛② ♥♦③③❧❡ ❛♥❞ t❤❡ t❡st ♦❜❥❡❝t ❢♦r ❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs✳ ❚❤❡ s✐♠✉❧❛t❡❞ ❞r♦♣❧❡t❞✐❛♠❡t❡r ✇❛s 75 ➭m✳ ❚❤❡ ❧❛r❣❡ ❞r♦♣❧❡t ❞✐❛♠❡t❡r ✇❛s ❝❤♦s❡♥ t♦ ❤✐❣❤❧✐❣❤t t❤❡ ❞✐✛❡r❡♥❝❡s✐♥ t❤❡ ♣❧♦ts✳ ❚❤❡ ❛✐r ✈❡❧♦❝✐t② ❛t t❤❡ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡ ✐s 35m s−1✳ ❋✐❣✉r❡ ✹✳✽ s❤♦✇st❤❛t t❤❡ ❞r♦♣❧❡ts ❝♦♠❡ ❝❧♦s❡r t♦ t❤❡ t❛r❣❡t ✈❡❧♦❝✐t② ✐♥ t❤❡ ♥♦③③❧❡s t❤❛t ❛r❡ st❡❡♣ ✐♥ ❛♠♦r❡ ✉♣str❡❛♠ ♣♦s✐t✐♦♥✳ ❇❡❝❛✉s❡ ♦❢ t❤❡ ❝♦♥tr❛❝t✐♦♥✱ t❤❡ ❛✐r ✈❡❧♦❝✐t② ✐s ✐♥❝r❡❛s❡❞ ❛♥❞ t❤❡✈❡❧♦❝✐t② ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❞r♦♣❧❡t ❛♥❞ ❛✐r ❛s ✇❡❧❧✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥✸✳✶✺✱ t❤❡ ❝❤❛♥❣❡ ✐♥ t❤❡ ❞r♦♣❧❡t✬s ✈❡❧♦❝✐t② ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛✐r✈❡❧♦❝✐t② ❛♥❞ ❞r♦♣❧❡t ✈❡❧♦❝✐t②✳ ❆ ❤✐❣❤❡r ✈❡❧♦❝✐t② ❞✐✛❡r❡♥❝❡ ❢r♦♠ t❤❡ st❛rt ♦❢ t❤❡ ♥♦③③❧❡t❤❡r❡❢♦r❡ ❧❡❛❞s t♦ ❛ str♦♥❣❡r ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ t❤❡ ❞r♦♣❧❡t ❛♥❞ ❤✐❣❤❡r ✜♥❛❧ ✈❡❧♦❝✐t✐❡s✳ ■❢ t❤❡♥♦③③❧❡ ❝♦♥tr❛❝t✐♦♥ ♦❝❝✉rs ❢✉rt❤❡r ❞♦✇♥str❡❛♠✱ t❤❡ ❧❛r❣❡st ✈❡❧♦❝✐t② ❞✐✛❡r❡♥❝❡ ♦❝❝✉rs ❥✉stt❤❡r❡✳ ❚❤❡r❡❢♦r❡✱ t❤❡ t✐♠❡ ❢♦r t❤❡ ❞r♦♣❧❡ts t♦ ❛❞❥✉st t❤❡✐r ✈❡❧♦❝✐t② ✐s ♠✉❝❤ ❧❡ss✳ ❍❡♥❝❡✱

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

axis in flow direction [m]

0

10

20

30

velo

city [m

/s]

AVA

Witoszynski

fifth-order

transformed fifth-order

third-order

matched cubics

target velocity

❋✐❣✉r❡ ✹✳✽✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❢♦r ❞✐✛❡r❡♥t ♥♦③③❧❡❝♦♥t♦✉rs✳

✹✶

✹ ❘❡s✉❧ts

✐t ✐s ♣r❡❢❡r❛❜❧❡ t♦ ❤❛✈❡ ❛ ♥♦③③❧❡ ✇✐t❤ ❛♥ ❡❛r❧✐❡r ♣♦✐♥t ♦❢ str♦♥❣ ❝♦♥tr❛❝t✐♦♥ t♦ ✐♥❝r❡❛s❡t❤❡ ❞r♦♣❧❡t✬s ✈❡❧♦❝✐t②✳❚❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ♦✈❡r t❤❡ ❧❡♥❣t❤ ❜❡t✇❡❡♥ t❤❡ s♣r❛② ♥♦③③❧❡

❛♥❞ t❤❡ t❡st ♦❜❥❡❝t ❢♦r ❞✐✛❡r❡♥t ♥♦③③❧❡s ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✾✭❛✮✳ ❚♦ ❤✐❣❤❧✐❣❤t t❤❡❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t ♥♦③③❧❡ ❝♦♥t♦✉rs✱ ❛ ③♦♦♠ ✇❛s ❝❤♦s❡♥ ❢♦r t❤❡ ✜♥❛❧ ♣❛rt ♦❢t❤❡ ♥♦③③❧❡✳ ❚❤❡ ③♦♦♠ ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✹✳✾✭❜✮✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥❛r❡ t❤❡ s❛♠❡ ❛s ❢♦r ❋✐❣✉r❡ ✹✳✽✳ ❚❤❡ ❞r♦♣❧❡ts st❛rt ✇✐t❤ ❛ t❡♠♣❡r❛t✉r❡ ♦❢ 288.15K❛♥❞ ❛♥ ❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ 270.15K✳ ❚❤❡ t❡♠♣❡r❛t✉r❡ ❞❡✈❡❧♦♣♠❡♥t ✐s ❞✐✛❡r❡♥t ❢r♦♠t❤❡ ✈❡❧♦❝✐t② ❞❡✈❡❧♦♣♠❡♥t✳ ◆♦③③❧❡s ✇✐t❤ ❛ str♦♥❣ ❝♦♥tr❛❝t✐♦♥ ❢✉rt❤❡r ✉♣str❡❛♠ r❡s✉❧t ✐♥❤✐❣❤❡r ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡s ❛t t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ t❡st ♦❜❥❡❝t✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❛ str♦♥❣❝♦♥tr❛❝t✐♦♥ ✉♣str❡❛♠ ❧❡❛❞s t♦ ❤✐❣❤❡r ✈❡❧♦❝✐t✐❡s t❤❡r❡ ❛♥❞ t❤❡ ❞r♦♣❧❡ts t❤❡r❡❢♦r❡ r❡❛❝❤t❤❡ t❡st ♦❜❥❡❝t s♦♦♥❡r✳ ❍❡♥❝❡✱ t❤❡ ❞r♦♣❧❡ts ❤❛✈❡ ❧❡ss t✐♠❡ t♦ ❛❞❥✉st t❤❡✐r t❡♠♣❡r❛t✉r❡✳❚❤❡r❡❢♦r❡ ♥♦③③❧❡s ✇✐t❤ ❛ ❧❛t❡r ♣♦✐♥t ♦❢ str♦♥❣ ❝♦♥tr❛❝t✐♦♥ ❛r❡ ❜❡tt❡r t♦ ❛❝❤✐❡✈❡ s♣❡❝✐✜❡❞t❡♠♣❡r❛t✉r❡s ♦❢ t❤❡ ❞r♦♣❧❡ts✳

0 0.5 1 1.5

axis in flow direction [m]

270

275

280

285

tem

pera

ture

[K

]

✭❛✮ ❉r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ♦✈❡r t❤❡ ❢✉❧❧ ♥♦③✲③❧❡ ❧❡♥❣t❤✳

1 1.2 1.4 1.6 1.8

axis in flow direction [m]

270.5

271

271.5

tem

pera

ture

[K

] AVA

Witoszynski

fifth-order

transformed fifth-order

third-order

matched cubics

air temperature

✭❜✮ ❉r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ♦✈❡r t❤❡ ③♦♦♠❡❞ s❡❝t✐♦♥✳

❋✐❣✉r❡ ✹✳✾✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ❢♦r ❞✐✛❡r❡♥t ♥♦③✲③❧❡ ❝♦♥t♦✉rs✳

❚❤❡ ✜♥❛❧ ❞❡❝✐s✐♦♥ ❢♦r t❤❡ ♥♦③③❧❡ ❞❡s✐❣♥ ✇❛s ❞r✐✈❡♥ ❜② t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❞❡✈❡❧♦♣♠❡♥t✱t❤❡ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ❞❡✈❡❧♦♣♠❡♥t✱ ❛♥❞ t❤❡ ❞r♦♣❧❡t tr❛❥❡❝t♦r✐❡s✳ ❆ ♣❡r❢❡❝t ♥♦③③❧❡ ❝❛♥♥♦t ❜❡ ❢♦✉♥❞✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ♥♦③③❧❡s ✇✐t❤ ❛ str♦♥❣ ❝♦♥tr❛❝t✐♦♥ ❢✉rt❤❡r ✉♣str❡❛♠ ❤❛✈❡❛ s♠❛❧❧❡r ❞❡✈✐❛t✐♦♥ ✐♥ t❤❡ ✜♥❛❧ ✈❡❧♦❝✐t②✱ ❜✉t ❛ ❤✐❣❤❡r ❞❡✈✐❛t✐♦♥ ✐♥ t❤❡ ✜♥❛❧ t❡♠♣❡r❛t✉r❡✳❚❤❡r❡❢♦r❡✱ ❛ ❝♦♠♣r♦♠✐s❡ ❤❛s t♦ ❜❡ ❢♦✉♥❞✳ ◆♦③③❧❡s t❤❛t ❛r❡ st❡❡♣❡r t♦✇❛r❞s t❤❡ ♥♦③③❧❡✬s❡♥❞ ❛❧s♦ ❝❤❛♥❣❡ t❤❡ ❡✛❡❝t✐✈❡ ❛♥❣❧❡ ✉♥❞❡r ✇❤✐❝❤ t❤❡ ❞r♦♣❧❡ts ❤✐t t❤❡ t❡st ♦❜❥❡❝t✳ ❚❤❡r❡❢♦r❡✐t ✇❛s ❞❡❝✐❞❡❞ t❤❛t t❤❡ t❤✐r❞✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧✱ t❤❡ ✜❢t❤✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧✱ ❛♥❞ t❤❡tr❛♥s❢♦r♠❡❞ ✜❢t❤✲♦r❞❡r ♣♦❧②♥♦♠✐❛❧ ❛r❡ ♥♦t t❤❡ ❜❡st ♦♣t✐♦♥s✳ ❚❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡t❤r❡❡ r❡♠❛✐♥✐♥❣ ♥♦③③❧❡s ❛r❡ r❛t❤❡r s♠❛❧❧✳ ❆s t❤❡ t❡♠♣❡r❛t✉r❡ ♣❧❛②s ❛ ♠♦r❡ ✐♠♣♦rt❛♥tr♦❧❡ ❢♦r t❤❡ ✐❝✐♥❣ r❡s✉❧ts t❤❛♥ t❤❡ ✈❡❧♦❝✐t②✱ t❤❡ ❆❱❆ ♥♦③③❧❡ ✇❛s ❝❤♦s❡♥✳ ❚❤✐s ✐s ❜❡❝❛✉s❡♦✉t ♦❢ t❤❡ r❡♠❛✐♥✐♥❣ ♥♦③③❧❡s✱ t❤❡ ❆❱❆ ♥♦③③❧❡ ❧❡❛❞s t♦ t❤❡ ❞r♦♣❧❡ts r❡❛❝❤✐♥❣ t❤❡ t❛r❣❡tt❡♠♣❡r❛t✉r❡ t❤❡ ❝❧♦s❡st✳❊q✉❛t✐♦♥ ✸✳✶ ✇❛s ❝r❡❛t❡❞ ❢♦r ♥♦③③❧❡s ✇✐t❤ ❛ sq✉❛r❡ ♦r r♦✉♥❞ ❝r♦ss✲s❡❝t✐♦♥✳ ❆s t❤❡

♥♦③③❧❡ ✇✐❧❧ ❜❡ r❡❝t❛♥❣✉❧❛r ✐♥ t❤✐s ✇♦r❦✱ ♥♦✇ t✇♦ ❡q✉❛t✐♦♥s ❛r❡ ♥❡❡❞❡❞✿ ♦♥❡ ❢♦r t❤❡ ✉♣♣❡r❛♥❞ ❧♦✇❡r ♣❛rt ❛♥❞ ♦♥❡ ❢♦r t❤❡ s✐❞❡s✳ ❆ ❧♦♦❦ ❛t t❤❡ ❡q✉❛t✐♦♥ s❤♦✇s t❤❛t ❥✉st t❤❡ ❛r❡❛

✹✷

✹ ❘❡s✉❧ts

❋✐❣✉r❡ ✹✳✶✵✿ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ♥♦③③❧❡✳

r❛t✐♦ ❝❛♥ ❜❡ ❝❤❛♥❣❡❞✳ ❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❝♦♥t♦✉rs ❝♦rr❡❝t❧②✱ ❛♥ ❡q✉✐✈❛❧❡♥t ❛r❡❛ r❛t✐♦ ✐s❝❛❧❝✉❧❛t❡❞✳ ❚♦ ❞♦ t❤✐s✱ t❤❡ ❤❡✐❣❤t✴✇✐❞t❤ ❛t t❤❡ t❡st s❡❝t✐♦♥ ✐s ❞✐✈✐❞❡❞ ❜② t❤❡ ✈❛❧✉❡ ❛tt❤❡ ♥♦③③❧❡ ❡♥tr② ❛♥❞ t❤✐s ✈❛❧✉❡ ✐s sq✉❛r❡❞✳❆s ❡①♣❧❛✐♥❡❞ ❡❛r❧✐❡r✱ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ st❡❡♣❡st s❧♦♣❡ s❤♦✉❧❞ ❜❡ t❤❡ s❛♠❡ ❢♦r ❡✈❡r②

s✐❞❡✳ ❚❤❡ ♦♥❧② ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❝♦♥t♦✉r ❡q✉❛t✐♦♥s ✐s t❤❡ ❛r❡❛ r❛t✐♦✳ ❆s t❤❡ ❛r❡❛r❛t✐♦ ✐s ❥✉st ❛ ❝♦♥st❛♥t✱ ✐t ❞♦❡s ♥♦t ❝❤❛♥❣❡ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ st❡❡♣❡st s❧♦♣❡ ❛t ❛❧❧✳❚❤❡r❡❢♦r❡ ♥♦ ❢✉rt❤❡r ❛❝t✐♦♥ ♥❡❡❞s t♦ ❜❡ t❛❦❡♥ t♦ ♠❛t❝❤ t❤❡ ♣♦s✐t✐♦♥s ♦❢ t❤❡ st❡❡♣❡sts❧♦♣❡s✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ♥♦③③❧❡ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✶✵

✹✳✸✳✸ ❙❡tt❧✐♥❣ ❛r❡❛

❚❤❡ s❡tt❧✐♥❣ ❛r❡❛ ✐s ✉♣str❡❛♠ ♦❢ t❤❡ ♥♦③③❧❡ ❛♥❞ ❞♦❡s ♥♦t ❝❤❛♥❣❡ ✐ts s❤❛♣❡ ♦✈❡r ✐ts ❧❡♥❣t❤✳❚❤❡r❡❢♦r❡ ✐t ❤❛s t❤❡ s❛♠❡ s❤❛♣❡ ❛s t❤❡ ✉♣str❡❛♠ ❡♥❞ ♦❢ t❤❡ ♥♦③③❧❡✳ ❍❡♥❝❡✱ t❤❡ s❡tt❧✐♥❣❛r❡❛ ✐s sq✉❛r❡ ✇✐t❤ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ s✐❞❡s ❜❡✐♥❣ 1.54m✳ ❚❤✐s r❡s✉❧ts ✐♥ ❛ ❤②❞r❛✉❧✐❝❞✐❛♠❡t❡r ♦❢ 1.54m ❛s ✇❡❧❧✳❚❤❡ s♣r❛② s②st❡♠ ✐s t❤❡ ❝♦♠♣♦♥❡♥t ♣❧❛❝❡❞ t❤❡ ♠♦st ❞♦✇♥str❡❛♠ ✐♥s✐❞❡ t❤❡ s❡tt❧✐♥❣

❛r❡❛✳ ❖t❤❡r✇✐s❡✱ t❤❡ ❞r♦♣❧❡ts ✇♦✉❧❞ ❤✐t t❤❡ ❤♦♥❡②❝♦♠❜s ❛♥❞ s❝r❡❡♥s✳ ❚❤✐s ✇♦✉❧❞ ❧❡❛❞t♦ ✐❝❡ ❛❝❝r❡t✐♦♥ ♦♥ t❤❡s❡ ❝♦♠♣♦♥❡♥ts✳ ❆s ❛ r❡s✉❧t✱ t❤❡ ✢♦✇ q✉❛❧✐t② ❛♥❞ ✉♥✐❢♦r♠✐t② ✇♦✉❧❞s✉✛❡r s❡✈❡r❡❧②✳ ❍❡♥❝❡✱ t❤❡ ❤♦♥❡②❝♦♠❜s ❛♥❞ s❝r❡❡♥s ❤❛✈❡ t♦ ❜❡ ♣❧❛❝❡❞ ✉♣str❡❛♠ ♦❢ t❤❡s♣r❛② ♥♦③③❧❡s✳

✹✸

✹ ❘❡s✉❧ts

✹✳✸✳✸✳✶ ❙♣r❛② ❙②st❡♠

❚❤❡ s♣r❛② s②st❡♠ ✐s ♦❢ ❤✉❣❡ ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ s②st❡♠ ♠✉st ❜❡ ❛❜❧❡ t♦ ✐♥❥❡❝t ❞r♦♣❧❡ts✇✐t❤ t❤❡ ✇❛♥t❡❞ ▼❱❉s t❤❛t ❛r❡ s♠❛❧❧ ❝♦♠♣❛r❡❞ t♦ ♠❛♥② ♦t❤❡r ❞r♦♣❧❡t ♦♣❡r❛t✐♦♥s✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ▲❲❈♠✉st ❛❧s♦ ♠❛t❝❤ t❤❡ ✈❛❧✉❡s t❤❛t ♥❡❡❞ t♦ ❜❡ t❡st❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡❝❡rt✐✜❝❛t✐♦♥ r❡❣✉❧❛t✐♦♥s✳ ❋✉rt❤❡r♠♦r❡✱ t❤♦s❡ ✈❛❧✉❡s ♥❡❡❞ t♦ ❜❡ ❝♦♥tr♦❧❧❛❜❧❡ ❡①❛❝t❧② t♦ ❞♦❡①♣❡r✐♠❡♥ts ✇✐t❤ ❡①❛❝t❧② ❦♥♦✇♥ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s✳ ❆♥♦t❤❡r ✐♠♣♦rt❛♥t r❡q✉✐r❡♠❡♥t❢♦r t❤❡ s♣r❛② s②st❡♠ ✐s t❤❛t t❤❡ ❞r♦♣❧❡t ❞✐str✐❜✉t✐♦♥ ✐♥ t❤❡ t❡st s❡❝t✐♦♥ ❤❛s t♦ ❜❡ ✈❡r②❝❧♦s❡ t♦ ✉♥✐❢♦r♠✳ ❖t❤❡r✇✐s❡✱ t❤❡ ❧♦❝❛❧ ❝♦♥❞✐t✐♦♥s ✇♦✉❧❞ ❜❡ ❞✐✛❡r❡♥t ✐♥ ▼❱❉ ❛♥❞ ▲❲❈❝♦♠♣❛r❡❞ t♦ t❤❡ ❣❧♦❜❛❧ ✈❛❧✉❡s✳ ❚❤✐s ✇♦✉❧❞ ❧❡❛❞ t♦ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts t❤❛t ❞♦ ♥♦t♠❛t❝❤ t❤❡ r❡❛❧✐t②✳❙❡❧❡❝t✐♥❣ ❛ s✉✐t❛❜❧❡ s♣r❛② s②st❡♠ ✐s ❛ ❞✐✣❝✉❧t t♦♣✐❝✳ ❚❤✐s ✐s ❞✉❡ t♦ t✇♦ r❡❛s♦♥s✳

❋✐rst✱ ♠♦st ♠❛♥✉❢❛❝t✉r❡rs ♦❢ s♣r❛② ♥♦③③❧❡s ❛♥❞ s♣r❛② s②st❡♠s ❞♦ ♥♦t ♦✛❡r ❛❧❧ ♥❡❝❡ss❛r②✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡✐r ♣r♦❞✉❝ts ♦♣❡♥❧②✳ ❊s♣❡❝✐❛❧❧② t❤❡ ❞r♦♣❧❡t ❞✐❛♠❡t❡rs t❤❛t ❝❛♥ ❜❡♦❜t❛✐♥❡❞ ✇✐t❤ ❛ s♣r❛② ♥♦③③❧❡ ❛r❡ t②♣✐❝❛❧❧② ♥♦t ❣✐✈❡♥ ❜✉t ♦❢ s✐❣♥✐✜❝❛♥❝❡ ❢♦r t❤✐s ✇♦r❦✳❆❞❞✐t✐♦♥❛❧❧②✱ t✉r❜✉❧❡♥❝❡ ❡♥❤❛♥❝❡s t❤❡ ♠✐①✐♥❣ ✐♥ ❛♥ ❛✐r ✢♦✇ s✐❣♥✐✜❝❛♥t❧② ❛♥❞ t❤❡r❡❢♦r❡❛❧s♦ t❤❡ s♣r❡❛❞✐♥❣ ♦❢ ❞r♦♣❧❡ts✳ ❲✐t❤ t❤❡ ❜❛s✐❝ ❡q✉❛t✐♦♥ ♦❢ ♠♦t✐♦♥s ✉s❡❞ ✐♥ t❤✐s t❤❡s✐s✱t❤❡ t✉r❜✉❧❡♥❝❡ ❝❛♥ ♥♦t ❜❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t✳ ❚❤❡r❡❢♦r❡✱ ❝❛❧❝✉❧❛t✐♥❣ t❤❡ s♣r❡❛❞✐♥❣ ♦❢t❤❡ ❞r♦♣❧❡ts ✐s ♥♦t ♣♦ss✐❜❧❡ ✐♥ t❤❡ s❝♦♣❡ ♦❢ t❤✐s ✇♦r❦✳ ❍❡♥❝❡✱ t❤❡ s❡❧❡❝t✐♦♥ ♦❢ ❛ s♣r❛②s②st❡♠ ❝❛♥ ♥♦t ❜❡ ❞♦♥❡ ✐♥ t❤✐s t❤❡s✐s ❛♥❞ ✇✐❧❧ ❜❡ ❛ t♦♣✐❝ ❢♦r t❤❡ ❢✉t✉r❡✳◆❡✈❡rt❤❡❧❡ss✱ s♦♠❡ r❡❝♦♠♠❡♥❞❛t✐♦♥s ❢♦r s✉✐t❛❜❧❡ s♣r❛② s②st❡♠s s❤❛❧❧ ❜❡ ♣r❡s❡♥t❡❞✳

❚❤❡ ❞r♦♣❧❡ts ✐♥ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡ s♠❛❧❧❡r t❤❛♥ ❢♦r ♠♦st ♦t❤❡r ❡①♣❡r✐♠❡♥ts✳ ❚♦❛❝❤✐❡✈❡ s♠❛❧❧ ❞r♦♣❧❡t s✐③❡s✱ t②♣✐❝❛❧❧② ❛✐r✲❛ss✐st❡❞ ❛t♦♠✐③❡rs ❛r❡ ✉s❡❞✳ ■♥ t❤❡s❡ s♣r❛②♥♦③③❧❡s✱ t❤❡ ✇❛t❡r ❥❡t ✐s ❜r♦❦❡♥ ✐♥t♦ s♠❛❧❧ ❞r♦♣❧❡ts ❜❡❝❛✉s❡ ♦❢ t❤❡ s❤❡❛r str❡ss❡s ❜❡t✇❡❡♥❛♥ ❛✐r ✢♦✇ ❛♥❞ t❤❡ ✇❛t❡r ❥❡t✳ ❋♦r ❡①❛♠♣❧❡ ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✱ ❚✐✐❤♦♥❡♥ ❡t ❛❧✳ ❬✷✻❪✱ ❛♥❞▲❡♦♥❡ ❡t ❛❧✳ ❬✺✼❪ ✉s❡❞ ❛✐r✲❛ss✐st❡❞ ❛t♦♠✐③❡rs ✐♥ t❤❡✐r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤❡ s❡❝♦♥❞ ♣♦✐♥t✐s t❤❛t t❤❡ ▲❲❈ ✐s ❧♦✇ ❢♦r t❤✐s ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡r❡❢♦r❡✱ s♣r❛② s②st❡♠s✇✐t❤ ❧♦✇ ✇❛t❡r ✢✉① ❛r❡ ♥❡❡❞❡❞✳ ❆ ♣♦ss✐❜✐❧✐t② ✐s t❤❡ ✉s❡ ♦❢ ♣✉❧s❛t✐♥❣ s♣r❛② ♥♦③③❧❡s ❛s❞♦♥❡ ❜② ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✳ ❚❤❡s❡ ♥♦③③❧❡s ❛r❡ ♥♦t ✐♥❥❡❝t✐♥❣ t❤❡ ✇❛t❡r ❝♦♥t✐♥✉♦✉s❧② ❜✉t✐♥t❡r♠✐tt❡♥t❧②✳ ❲✐t❤ t❤✐s t❡❝❤♥✐q✉❡✱ ❧♦✇❡r ✇❛t❡r ✢✉①❡s ❝❛♥ r❡❛❧✐③❡❞✳❚❤❡ q✉❡st✐♦♥ ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ s♣r❛② ♥♦③③❧❡s ♥❡❡❞s t♦ ❜❡ ❝❛❧❝✉❧❛t❡❞ ❝❛r❡❢✉❧❧②✳ ●✐✈✐♥❣

❤✐♥ts ✐s ❤♦✇❡✈❡r ❞✐✣❝✉❧t✱ ❜❡❝❛✉s❡ ❡①✐st✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❞✐✛❡r s✐❣♥✐✜❝❛♥t❧② ✐♥ t❤❡✐r♥✉♠❜❡r ♦❢ s♣r❛② ♥♦③③❧❡s✳ ❚❤❡ ❇r❛✉♥s❝❤✇❡✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞❡s❝r✐❜❡❞ ❜② ❇❛♥s♠❡r❡t ❛❧✳ ❬✸✶❪ ✐s ❝♦♠♣❛r❛❜❧❡ ✐♥ t❡st s❡❝t✐♦♥ s✐③❡ ❛♥❞ ❛✐r s♣❡❡❞ t♦ t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ❛♥❞ ✉s❡s ✷✺ s♣r❛② ♥♦③③❧❡s✳ ❚❤❡ ❱❚❚ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞❡s❝r✐❜❡❞ ❜② ❚✐✐❤♦♥❡♥❡t ❛❧✳ ❬✷✻❪✱ ❤♦✇❡✈❡r✱ ✐s s❧✐❣❤t❧② ❧❛r❣❡r ❛♥❞ ❤❛s ❛ ❝♦♠♣❛r❛❜❧❡ ❛✐r s♣❡❡❞✱ ❜✉t ♦♥❧② ✉s❡s ✾s♣r❛② ♥♦③③❧❡s✳ ❚❤❡r❡❢♦r❡✱ t❤❡s❡ ❝♦♥✜❣✉r❛t✐♦♥s ❝❛♥ ❜❡ ✉s❡❞ ❛s ❛ ✜rst ✐❞❡❛ ❢♦r t❤❡ ✜♥❛❧s♣r❛② s②st❡♠ ❞❡s✐❣♥✱ ❜✉t ❛♥ ❛♥❛❧②s✐s ♥❡❡❞s t♦ ❜❡ ❞♦♥❡ ❜❡❢♦r❡ t❤❡ ✜♥❛❧ s❡❧❡❝t✐♦♥✳❆♥ ✐♥✐t✐❛❧ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r✳ ❙♦♠❡

❡①❛♠♣❧❡s ❢♦r ♣✉❧s❛t✐♥❣ ❛✐r✲❛ss✐st❡❞ ❛t♦♠✐③❡rs ❛r❡ ❣✐✈❡♥ ❜② ❙♣r❛②✐♥❣ ❙②st❡♠s ❈♦✳ ❬✺✽❪✳❚❤❡s❡ ♥♦③③❧❡s ♦♣❡r❛t❡ ✇✐t❤ ♣r❡ss✉r❡s ❜❡t✇❡❡♥ 0.34 bar ❛♥❞ 7 bar✳ ❇❡❝❛✉s❡ ❛ ♣❛rt ♦❢ t❤❡♣r❡ss✉r❡ ❡♥❡r❣② ✐s ❛❧s♦ ♥❡❡❞❡❞ t♦ ❜r❛❦❡ t❤❡ ✇❛t❡r ❥❡t ✐♥t♦ s♠❛❧❧ ❞r♦♣❧❡ts✱ ❛ ♣r❡ss✉r❡ ♦❢3.5 bar ✐s ✉s❡❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t ✈❡❧♦❝✐t②✳ ❆s st❛t❡❞ ❜② ❙♣r❛②✐♥❣ ❙②st❡♠s ❈♦✳❬✺✾❪✱ t❤❡ ♦r✐✜❝❡ ❢♦r ❛✐r ❛♥❞ ❧✐q✉✐❞ ❛r❡ t❤❡ s❛♠❡ ❢♦r t❤❡ s②st❡♠s ♦❢ ✐♥t❡r❡st✳ ❆❞❞✐t✐♦♥❛❧❧②✱t❤❡ ♣r❡ss✉r❡s ❛r❡ ♦❢t❡♥ ❝♦♠♣❛r❛❜❧❡ ❢♦r t❤❡ ❛✐r ❛♥❞ t❤❡ ✇❛t❡r✳ ❚❤❡r❡❢♦r❡✱ ❛♥ ❛ss✉♠♣t✐♦♥

✹✹

✹ ❘❡s✉❧ts

✐s ♠❛❞❡ t❤❛t t❤❡ ✈♦❧✉♠❡tr✐❝ ✢♦✇ ♦❢ ❛✐r ❛♥❞ ✇❛t❡r ✐s t❤❡ s❛♠❡✳ ❍❡♥❝❡✱ t❤❡ ❞❡♥s✐t② ♦❢ t❤❡♠✐①t✉r❡ ✐s t❤❡ ❛✈❡r❛❣❡ ♦❢ t❤❡ ❞❡♥s✐t② ♦❢ ❛✐r ❛♥❞ t❤❡ ❞❡♥s✐t② ♦❢ ✇❛t❡r✳ ❯s✐♥❣ ❡q✉❛t✐♦♥✸✳✶✻✱ t❤✐s r❡s✉❧ts ✐♥ ❛ ✐♥✐t✐❛❧ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ♦❢ ❛❜♦✉t 37.5m s−1✳

✹✳✸✳✸✳✷ ❚✉r❜✉❧❡♥❝❡ ❙❝r❡❡♥s

❯♣str❡❛♠ ♦❢ t❤❡ s♣r❛② ♥♦③③❧❡s✱ ♦♥❡ ♦r ♠♦r❡ t✉r❜✉❧❡♥❝❡ s❝r❡❡♥s ❛r❡ ♣❧❛❝❡❞✳ ▼✉❧t✐♣❧❡s❝r❡❡♥s ✇✐❧❧ ✐♥❝r❡❛s❡ t❤❡ ✢♦✇ q✉❛❧✐t② ❜✉t ❛t t❤❡ ❡①♣❡♥s❡ ♦❢ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞ ❛❧♦♥❣❡r ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡r❡❢♦r❡✱ ❢♦r t❤✐s ❞❡s✐❣♥✱ ♦♥❧② ♦♥❡ s❝r❡❡♥ ✇❛s ❝❤♦s❡♥✳ ❆s st❛t❡❞❜❡❢♦r❡✱ t❤❡ ♣♦r♦s✐t② s❤♦✉❧❞ ❜❡ ❜❡t✇❡❡♥ 0.57 ❛♥❞ 0.8✳ ❍✐❣❤❡r ✈❛❧✉❡s ♦❢ t❤❡ ♣♦r♦s✐t② ❧❡❛❞t♦ ❢❡✇❡r ♣r❡ss✉r❡ ❧♦ss❡s✳ ❆t t❤❡ s❛♠❡ t✐♠❡✱ ❤✐❣❤❡r ♣♦r♦s✐t✐❡s ❛❧s♦ ❧❡❛❞ t♦ ❧❡ss ❜❛❧❛♥❝✐♥❣ ♦❢t❤❡ ♥♦♥✉♥✐❢♦r♠✐t✐❡s ♦❢ t❤❡ ✢♦✇✳ ❚❤❡r❡❢♦r❡ ❛ ❜❛❧❛♥❝❡ ♥❡❡❞s t♦ ❜❡ ❢♦✉♥❞✳ ❆s ✇✐❧❧ ❜❡ s❤♦✇♥✐♥ ✹✳✺✱ t❤❡ ♣r❡ss✉r❡ ❧♦ss ♦❢ t❤❡ s❝r❡❡♥ ❤❛s ❥✉st ❛ ♠✐♥♦r ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ t♦t❛❧ ♣r❡ss✉r❡❧♦ss❡s✳ ❚❤❡r❡❢♦r❡ ❛ ❧♦✇ ✈❛❧✉❡ ♦❢ ♣♦r♦s✐t② ♦❢ 0.6 ✇❛s ❝❤♦s❡♥ t♦ ✐♥❝r❡❛s❡ t❤❡ ✉♥✐❢♦r♠✐t② ♦❢t❤❡ ✢♦✇ ♦♥ t❤❡ ❡①♣❡♥s❡ ♦❢ s❧✐❣❤t❧② ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s✳

✹✳✸✳✸✳✸ ❍♦♥❡②❝♦♠❜s

❚❤❡ ♠♦st ✉♣str❡❛♠ ❝♦♠♣♦♥❡♥ts ✐♥s✐❞❡ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❛r❡ t❤❡ ❤♦♥❡②❝♦♠❜s✳ ❆s st❛t❡❞✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ r❛t✐♦ ♦❢ t❤❡ ❧❡♥❣t❤ t♦ t❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜s s❤♦✉❧❞❜❡ ❜❡t✇❡❡♥ 6 ❛♥❞ 8✳ ▲❛r❣❡r ✈❛❧✉❡s ❧❡❛❞ t♦ ❛ ❤✐❣❤❡r q✉❛❧✐t② ♦❢ t❤❡ ✢♦✇✳ ❚❤❡r❡❢♦r❡ t❤❡❞❡s✐❣♥❡❞ ❤♦♥❡②❝♦♠❜s ❞♦ ❤❛✈❡ ❛ r❛t✐♦ ♦❢ t❤❡ ❧❡♥❣t❤ t♦ t❤❡ ❞✐❛♠❡t❡r ♦❢ 8✳ ❋♦❧❧♦✇✐♥❣t❤❡ r❡❝♦♠♠❡♥❞❛t✐♦♥ ♦❢ ❇❛r❧♦✇ ❡t ❛❧✳ ❬✷✵❪✱ t❤❡r❡ s❤♦✉❧❞ ❜❡ ✶✺✵ ❝❡❧❧s ♣❡r ❞✐❛♠❡t❡r ♦❢t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❆s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ✐s 1.54m✱ t❤❡ ❤②❞r❛✉❧✐❝❞✐❛♠❡t❡r ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜s ✐s 0.01m✳ ❚❤❡r❡❢♦r❡ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜s ✐s 0.08m✳

✹✳✸✳✸✳✹ ❆ss❡♠❜❧②

❆s ♠❡♥t✐♦♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ s❝r❡❡♥s ❛♥❞ ❛❧s♦ ❜❡t✇❡❡♥t❤❡ ❧❛st s❝r❡❡♥ ❛♥❞ t❤❡ ♥♦③③❧❡ ❡①✐t s❤♦✉❧❞ ❜❡ 0.2 t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ t❤❡s❡tt❧✐♥❣ ❛r❡❛✳ ❇② ❞♦✐♥❣ t❤✐s✱ t❤❡ ♥♦♥✲✉♥✐❢♦r♠✐t✐❡s ♦❢ t❤❡ ✢♦✇ ❝❛♥ ❜❡ r❡❞✉❝❡❞✳ ❚❤❡ s♣r❛②s②st❡♠ ✐s ♥♦ s❝r❡❡♥ ❜✉t ✇✐❧❧ ❜❡ ❤❛♥❞❧❡❞ ❧✐❦❡ ❛ s❝r❡❡♥ ❝♦♥❝❡r♥✐♥❣ t❤✐s ♠❛tt❡r✳ ❚❤❡r❡❢♦r❡❜❡t✇❡❡♥ t❤❡ t❤r❡❡ ❝♦♠♣♦♥❡♥ts ✐♥s✐❞❡ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❛♥❞ ❛❢t❡r t❤❡ s♣r❛② s②st❡♠ s❤♦✉❧❞❜❡ ❛ s♣❛❝✐♥❣ ♦❢ 0.2 t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ❡❛❝❤✳ ◆♦ t②♣✐❝❛❧ r✉❧❡ ✐s ❣✐✈❡♥ ❢♦r t❤❡❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ♥♦③③❧❡ ❡♥tr② ❛♥❞ t❤❡ ❤♦♥❡②❝♦♠❜s✳ ❋♦r ♠♦st ❝♦♥✈❡♥t✐♦♥❛❧ ✇✐♥❞t✉♥♥❡❧ ❞❡s✐❣♥s ✇✐t❤ ❥✉st ♦♥❡ ❤♦♥❡②❝♦♠❜ s❡❝t✐♦♥ ❛♥❞ ♦♥❡ s❝r❡❡♥✱ t②♣✐❝❛❧❧② 0.5 t✐♠❡s t❤❡❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ✐s ✉s❡❞ ❛s t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❚❤❡r❡❢♦r❡ t❤❡s❡ ✇✐♥❞t✉♥♥❡❧s ✇♦✉❧❞ ❤❛✈❡ ❛ ❞✐st❛♥❝❡ ♦❢ 0.1 t✐♠❡s t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ❜❡t✇❡❡♥ t❤❡ ❜❡❣✐♥♥✐♥❣♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ❛♥❞ t❤❡ ❤♦♥❡②❝♦♠❜s✳ ❚❤✐s ❞✐st❛♥❝❡ s❤❛❧❧ ❛❧s♦ ❜❡ ✐♥❝❧✉❞❡❞ ✐♥ t❤✐s❞❡s✐❣♥✳ ❚♦ st✐❧❧ ❜❡ ❛❜❧❡ t♦ ✐♥s❡rt t❤❡ s♣r❛② s②st❡♠✱ ❛♥ ❡①tr❛ ❧❡♥❣t❤ ♦❢ ♦♥❡✲t❡♥t❤ ♦❢ t❤❡❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ✐s ✐♥s❡rt❡❞✳ ❍❡♥❝❡✱ t❤❡ ♦✈❡r❛❧❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ✐s 0.8 t✐♠❡st❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ 1.54m✳ ❚❤✐s r❡s✉❧ts ✐♥ ❛ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ♦❢1.23m✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✶✶✳

✹✺

✹ ❘❡s✉❧ts

❋✐❣✉r❡ ✹✳✶✶✿ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳

✹✳✸✳✹ ❲✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r

❚❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✐s t❤❡ ❝♦♥♥❡❝t✐♦♥ ♦❢ t❤❡ ❢❛♥ s❡❝t✐♦♥ ❛♥❞ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❍❡♥❝❡✱t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❤❛s t❤❡ s❛♠❡ s❤❛♣❡ ❛s t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳❚❤❡r❡❢♦r❡ t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ♦❢ t❤❡ ❞✐✛✉s❡r ✐s sq✉❛r❡ ✇✐t❤ ❛ ❧❡♥❣t❤ ♦❢ t❤❡ s✐❞❡s ♦❢1.54m✳ ❚❤❡ s✐③❡ ♦❢ t❤❡ ❢❛♥ s❡❝t✐♦♥ ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥ ❢♦r t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ✉♣str❡❛♠❡♥❞ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ❆t t❤❡ s❛♠❡ t✐♠❡✱ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❝❛♥ ❤❛✈❡ ❛❜✐❣ ♣r❡ss✉r❡ ❧♦ss ❛♥❞ ❤❡♥❝❡ ❝❤❛♥❣❡ t❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ t❤❡ ♥❡❡❞❡❞ ❢❛♥✳ ❚❤❡r❡❢♦r❡ ✐t ✐s ❛♥✐t❡r❛t✐✈❡ ♣r♦❝❡ss t♦ ❞❡s✐❣♥ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❛♥❞ s❡❧❡❝t ❛ ❢❛♥✳❙♠❛❧❧❡r ❛r❡❛ r❛t✐♦s ♦✈❡r t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❧❡❛❞ t♦ ❛ s❤♦rt❡r ❝♦♠♣♦♥❡♥t ❛♥❞ ❢❡✇❡r

♣r❡ss✉r❡ ❧♦ss❡s✳ ❍♦✇❡✈❡r✱ t❤✐s ❧❡❛❞s t♦ ❜✐❣❣❡r ❢❛♥s✳ ❇✐❣❣❡r ❢❛♥s ♥❡❡❞ ♠♦r❡ s♣❛❝❡ ❛♥❞t②♣✐❝❛❧❧② ❝♦st ♠♦r❡✳ ❆s ❛ ❝♦♠♣r♦♠✐s❡✱ ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ ❛❜♦✉t 2.5 ❛♥❞ ❛ ❢❛♥ ❞✐❛♠❡t❡r ♦❢❛❜♦✉t 1.1m ✇❡r❡ ❝❤♦s❡♥✳ ❆s ✇✐❧❧ ❜❡ ♣r❡s❡♥t❡❞ ✐♥ s❡❝t✐♦♥ ✹✳✺✱ ✐♥ t❤❡ ❡♥❞✱ ❛ ❢❛♥ ✇✐t❤ ❛❞✐❛♠❡t❡r ♦❢ 1.09m ✇❛s ❝❤♦s❡♥ ❛s ✇❡❧❧ ❛s ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ 2.55✳❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞✱ t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ❛t t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞ ✐s t❤❡ s❛♠❡ ❛s t❤❡

❝r♦ss✲s❡❝t✐♦♥ ♦❢ t❤❡ s❡tt❧✐♥❣ ❛r❡❛✳ ❚❤❡ ❝r♦ss✲s❡❝t✐♦♥ ❛t t❤❡ ✉♣str❡❛♠ ❡♥❞ ✐s t❤❡ ❝r♦ss✲s❡❝t✐♦♥ ♦❢ t❤❡ ❢❛♥✳ ❚❤❡r❡❢♦r❡ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✐s ❝✐r❝✉❧❛r ❛t t❤❡ ✉♣str❡❛♠ ❡♥❞❛♥❞ sq✉❛r❡ ❛t t❤❡ ❞♦✇♥str❡❛♠ ❡♥❞✳ ❚❤❡ ❝r♦ss✲s❡❝t✐♦♥ ✇✐❧❧ ❝❤❛♥❣❡ ♦✈❡r t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳❚♦ ❦❡❡♣ t❤❡ ❞✐✛✉s❡r ❛s s❤♦rt ❛s ♣♦ss✐❜❧❡✱ ❛♥ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ 60◦ ✇❛s ❝❤♦s❡♥✳ ❚❤❡

❧❡♥❣t❤ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✐s t❤❡♥ 0.56m✳ ❚♦ ❜❡ ❛❜❧❡ t♦ ♣r❡✈❡♥t s❡♣❛r❛t✐♦♥ ❞❡s♣✐t❡t❤✐s ❤✐❣❤ ❛♥❣❧❡✱ ♦♥❡ ♦❢ t❤❡ ♦♣t✐♦♥s ♣r❡s❡♥t❡❞ ✐♥ ❙✉❜s❡❝t✐♦♥ ✸✳✷✳✹ ❤❛s t♦ ❜❡ ❝❤♦s❡♥✳❙❝r❡❡♥s ❛r❡ t❤❡ ❡❛s✐❡st ♦♣t✐♦♥ t♦ ❞❡s✐❣♥ ❛♥❞ ♦♣❡r❛t❡ ❜❡❝❛✉s❡ t❤❡② ❛r❡ ♣❛ss✐✈❡ ❝♦♠♣♦♥❡♥ts✳❚❤❡r❡❢♦r❡ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✇✐❧❧ ❝♦♥t❛✐♥ s❝r❡❡♥s✳ ❋✐❣✉r❡ ❆✳✷ ❧✐sts t❤❡ ♥✉♠❜❡r ♦❢s❝r❡❡♥s ♥❡❝❡ss❛r② ❢♦r ❞✐✛❡r❡♥t ❝♦♥✜❣✉r❛t✐♦♥s ♦❢ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡rs✳ ❋♦r ❛♥ ❛r❡❛ r❛t✐♦♦❢ 2.5 ❛♥❞ ❛♥ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ 60◦✱ t✇♦ s❝r❡❡♥s ❛r❡ ♥❡❝❡ss❛r② t♦ ♣r❡✈❡♥t s❡♣❛r❛t✐♦♥✐♥s✐❞❡ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ❆s ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ ✜rst s❝r❡❡♥s❤♦✉❧❞ ♣r♦❜❛❜❧② ❜❡ ♣❧❛❝❡❞ ♥❡❛r t❤❡ ♥♦③③❧❡ ❡♥tr② ❛♥❞ t❤❡ s❡❝♦♥❞ s❝r❡❡♥ s♦♠❡✇❤❡r❡ ✐♥ t❤❡

✹✻

✹ ❘❡s✉❧ts

❋✐❣✉r❡ ✹✳✶✷✿ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳

♠✐❞❞❧❡ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ✐s s❤♦✇♥ ✐♥❋✐❣✉r❡ ✹✳✶✷✳

✹✳✸✳✺ ❋❛♥

❚❤❡ ❢❛♥ ✐s ♣❧❛❝❡❞ ❛s t❤❡ ♠♦st ✉♣str❡❛♠ ♣❛rt ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❆s ♠❡♥t✐♦♥❡❞✱ t❤❡ ❞❡s✐❣♥✇❛s ❞❡✈❡❧♦♣❡❞ ✐♥ ❛♥ ✐t❡r❛t✐✈❡ ♣r♦❝❡ss t♦❣❡t❤❡r ✇✐t❤ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ❍♦✇❡✈❡r✱❛❧r❡❛❞② ❜❡❢♦r❡ t❤✐s ✐t❡r❛t✐♦♥s✱ ❛ ❞❡❝✐s✐♦♥ ❛❜♦✉t t❤❡ t②♣❡ ♦❢ ❢❛♥ s❡❝t✐♦♥ ❤❛❞ t♦ ❜❡ ♠❛❞❡✳ ❆s❡①♣❧❛✐♥❡❞ ✐♥ s✉❜s❡❝t✐♦♥ ✸✳✷✳✺✱ ❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡rs ♠✐❣❤t ❤❛✈❡ ❛ s♠❛❧❧ ❛❞✈❛♥t❛❣❡ ♦✈❡r ❛①✐❛❧❢❛♥s✱ ❜✉t ✐t ✐s ♥♦t ✉♥❞✐s♣✉t❡❞✳ ❈❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡rs ❞♦ ❤♦✇❡✈❡r ❤❛✈❡ t❤❡ ❞✐s❛❞✈❛♥t❛❣❡♦❢ ♥❡❡❞✐♥❣ ♠✉❝❤ ♠♦r❡ s♣❛❝❡ t❤❛♥ ❛①✐❛❧ ❢❛♥s✳ ❚❤❡r❡❢♦r❡ ❛①✐❛❧ ❢❛♥s ❛r❡ ❢❛✈♦r❡❞ ♦✈❡r❝❡♥tr✐❢✉❣❛❧ ❜❧♦✇❡rs✳ ❲❤✐❧❡ t❤❡ ✉s❡ ♦❢ ♠✉❧t✐♣❧❡ ❢❛♥s ♠✐❣❤t ❤❛✈❡ s♦♠❡ ❛❞✈❛♥t❛❣❡s✱ t❤❡✉♥❝❡rt❛✐♥t② ❛❜♦✉t t❤❡ ✢♦✇ q✉❛❧✐t② ❛♥❞ ✢♦✇ ✉♥✐❢♦r♠✐t② ❧❡❛❞ t♦ t❤❡ ❞❡❝✐s✐♦♥ ❢♦r ❛ s✐♥❣❧❡❛①✐❛❧ ❢❛♥✳ ❚❤❡ ✜♥❛❧ ❡✛❡❝ts ♦❢ t❤❡ ♥❡❝❡ss❛r② ❝❤❛♥❣❡ ♦❢ ❝r♦ss✲s❡❝t✐♦♥ ♦♥ t❤❡ ✢♦✇ ❛r❡ ♥♦t❝❧❡❛r✳ ❍♦✇❡✈❡r✱ t❤❡ ❝❤❛♥❣❡ ♦❢ ❝r♦ss✲s❡❝t✐♦♥ ♠✐❣❤t ❡✈❡♥ r❡❞✉❝❡ t❤❡ s❡♣❛r❛t✐♦♥ r✐s❦ ✐♥s✐❞❡t❤❡ ♥♦③③❧❡ ❛s ❡①♣❧❛✐♥❡❞ ✐♥ ✹✳✸✳✷✳ ❚❤❡r❡❢♦r❡ ❛ s✐♥❣❧❡ ❛①✐❛❧ ❢❛♥ ✇❛s ❝❤♦s❡♥ ❢♦r t❤❡ ❞❡s✐❣♥♦❢ t❤✐s ✇✐♥❞ t✉♥♥❡❧✳❲❤✐❧❡ t❤❡ ❝❤♦✐❝❡ ♦❢ ❛ s♣❡❝✐✜❝ ❢❛♥ ✇✐❧❧ ❜❡ ❡①♣❧❛✐♥❡❞ ✐♥ s❡❝t✐♦♥ ✹✳✺✱ t❤❡ s✐③❡ ♦❢ t❤❡ ❢❛♥

❞✉❝t ✇✐❧❧ ❛❧r❡❛❞② ❜❡ ♥❛♠❡❞ ❤❡r❡✳ ❚❤❡ t❡r♠ ❢❛♥ ❞✉❝t ✐s ✉s❡❞ ❢♦r t❤❡ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ t❤❡❢❛♥ ✐ts❡❧❢ ❛♥❞ ❛ s❤♦rt s❡❝t✐♦♥ ✇✐t❤ t❤❡ s❛♠❡ ❝r♦ss✲s❡❝t✐♦♥ ❜❡❤✐♥❞✳ ❚❤✐s s❤♦rt s❡❝t✐♦♥ ✐s❜❡♥❡✜❝✐❛❧ ❢♦r t❤❡ ✢♦✇ ❝♦♥❞✐t✐♦♥s ❛♥❞ ✇✐❧❧ ❤❛✈❡ ❛ ❧❡♥❣t❤ ♦❢ 0.1m✳ ❚❤❡r❡❢♦r❡ t❤❡ ❢❛♥ ❞✉❝t❤❛s ❛ ❞✐❛♠❡t❡r ♦❢ 1.09m ❛♥❞ ❛ ❧❡♥❣t❤ ♦❢ 1.01m✳

✹✼

✹ ❘❡s✉❧ts

✹✳✸✳✻ ❉✐✛✉s❡r

❚❤❡ ❞✐✛✉s❡r ✐s t❤❡ ❝♦♠♣♦♥❡♥t ❝♦♥♥❡❝t❡❞ ❞♦✇♥str❡❛♠ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳ ❚❤❡r❡❢♦r❡ t❤❡❞✐✛✉s❡r ❤❛s ❛ r❡❝t❛♥❣✉❧❛r ✐♥❧❡t ✇✐t❤ ❛ ✇✐❞t❤ ♦❢ 0.39m ❛♥❞ ❛ ❤❡✐❣❤t ♦❢ 0.68m✳ ❚❤❡ ❞❡s✐❣♥♦❢ t❤❡ ❞✐✛✉s❡r ✐ts❡❧❢ ✐s ❛ ✇❡✐❣❤✐♥❣ ❜❡t✇❡❡♥ ❧❡♥❣t❤ ❛♥❞ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❋♦r t❤✐s t❤❡s✐s✱ ❛❝♦♠♣r♦♠✐s❡ ✇❛s ❝❤♦s❡♥ ✇✐t❤ ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ 2.5✳ ❚♦ ❦❡❡♣ t❤❡ ❧❡♥❣t❤ s❤♦rt ♥❡✈❡rt❤❡❧❡ss✱❛ r❛t❤❡r ❤✐❣❤ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ 3◦ ✇❛s ❝❤♦s❡♥✳ ❆s t❤❡ ❞✐✛✉s❡r ✐♥❧❡t ✐s r❡❝t❛♥❣✉❧❛r✱ t✇♦♣♦ss✐❜❧❡ ❞✐✛✉s❡r ❞❡s✐❣♥s ✇❡r❡ ❝♦♥s✐❞❡r❡❞✳ ❚❤❡ ❞✐✛✉s❡r ❝♦✉❧❞ ❡✐t❤❡r ❦❡❡♣ t❤❡ ❛s♣❡❝t r❛t✐♦♦✈❡r ✐ts ❧❡♥❣t❤ ♦r ❤❛✈❡ t❤❡ s❛♠❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ❛t ❡✈❡r② s✐❞❡✳ ❚❤❡ ❞✐✛✉s❡r ✐s ♣r♦♥❡ t♦ ✢♦✇s❡♣❛r❛t✐♦♥✳ ❆ss✉♠✐♥❣ t❤❛t t❤❡ ♣r♦❜❧❡♠ ♦❢ ✢♦✇ s❡♣❛r❛t✐♦♥ ✐s ❛❜♦✉t t❤❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡✐ts❡❧❢ ❛♥❞ ♥♦t ❛❜♦✉t t❤❡ ❛s♣❡❝t r❛t✐♦✱ ❛❧❧ s✐❞❡s ❛r❡ ❞❡s✐❣♥❡❞ t♦ ❤❛✈❡ t❤❡ s❛♠❡ ♦♣❡♥✐♥❣❛♥❣❧❡✳ ❖t❤❡r✇✐s❡✱ t✇♦ s✐❞❡s ✇♦✉❧❞ ❤❛✈❡ ❛ ❤✐❣❤❡r ♦♣❡♥✐♥❣ ❛♥❣❧❡ t❤❛♥ 3◦ ❛♥❞ t❤❡ ♦t❤❡rt✇♦ ❛ ❧♦✇❡r ♦♥❡✳ ❚❤❡ ❝❤♦s❡♥ ❞❡s✐❣♥ ✇✐t❤ t❤❡ s❛♠❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦♥ ❡✈❡r② s✐❞❡ r❡s✉❧ts✐♥ ❛ ✇✐❞t❤ ♦❢ 0.68m ❛♥❞ ❛ ❤❡✐❣❤t ♦❢ 0.97m ❛t t❤❡ ❡①✐t ♦❢ t❤❡ ❞✐✛✉s❡r✳ ❚❤❡ ❧❡♥❣t❤ ♦❢ t❤❡❞✐✛✉s❡r ✐s 2.79m✳ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✶✸✳

❋✐❣✉r❡ ✹✳✶✸✿ ❋✐♥❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ❞✐✛✉s❡r✳

✹✳✸✳✼ ❚❤❡ ✜♥❛❧ ❞❡s✐❣♥

❲✐t❤ t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ s✐♥❣❧❡ ❝♦♠♣♦♥❡♥ts ♣r❡s❡♥t❡❞ s♦ ❢❛r✱ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇♦✉❧❞❤❛✈❡ ❛♥ ♦✈❡r❛❧❧ ❧❡♥❣t❤ ♦❢ 8.03m✳ ❚❤❡ ♠❛①✐♠✉♠ ✇✐❞t❤ ❛♥❞ ❤❡✐❣❤t ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ✇♦✉❧❞ ❜❡ t❤❡ ✈❛❧✉❡s ♦❢ t❤❡ ✢♦✇ ❝♦♥❞✐t✐♦♥✐♥❣ ❞✉❝t ❛♥❞ t❤❡r❡❢♦r❡ 1.54m✳ ❆❧❧❞✐♠❡♥s✐♦♥s ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡ ✹✳✸✳❚❤❡ ❝♦♠♣❧❡t❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐t❤ ❛❧❧ ❝♦♠♣♦♥❡♥ts ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✶✹✳

✹✽

✹ ❘❡s✉❧ts

❈♦♠♣♦♥❡♥t ▲❡♥❣t❤❬m❪ ❉✐♠❡♥s✐♦♥s❬m❪

■♥❧❡t ❖✉t❧❡t

❢❛♥ ❞✉❝t 1.01 1.09 1.09✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r 0.56 1.09 1.54 ① 1.54 ✭1.54✮

s❡tt❧✐♥❣ ❛r❡❛ 1.23 1.54 ① 1.54 ✭1.54✮ 1.54 ① 1.54 ✭1.54✮♥♦③③❧❡ 1.74 1.54 ① 1.54 ✭1.54✮ 0.39 ① 0.68 ✭0.50✮

t❡st s❡❝t✐♦♥ 0.70 0.39 ① 0.68 ✭0.50✮ 0.39 ① 0.68 ✭0.50✮❞✐✛✉s❡r 2.79 0.39 ① 0.68 ✭0.50✮ 0.68 ① 0.97 ✭0.80✮

✇✐♥❞ t✉♥♥❡❧ 8.03 ♠❛① 1.54 ① 1.54 ✭1.54✮

❚❛❜❧❡ ✹✳✸✿ ❉✐♠❡♥s✐♦♥s ♦❢ t❤❡ ✜♥❛❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts✳ ❚✇♦ ✈❛❧✉❡s ❛r❡ ❣✐✈❡♥✐♥ t❤❡ ❞✐♠❡♥s✐♦♥s ❝♦❧✉♠♥ ✐❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ♦♥❡ ✈❛❧✉❡ ✐❢ t❤❡ s❡❝t✐♦♥✐s r♦✉♥❞✳ ■❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ❛❧s♦ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ✐s ❣✐✈❡♥ ✐♥❜r❛❝❦❡ts✳

❋✐❣✉r❡ ✹✳✶✹✿ ❚❤❡ ✜♥❛❧ ✇✐♥❞ t✉♥♥❡❧✳

✹✳✹ ❉r♦♣❧❡t ❜❡❤❛✈✐♦r ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧

❚❤❡ ❞❡s✐❣♥ t♦ t❤✐s ♣♦✐♥t ✇❛s ♠♦st❧② ❛❜♦✉t ❛❡r♦❞②♥❛♠✐❝ ✐ss✉❡s ❛♥❞ ♥♦t ❛❜♦✉t t❤❡ t❤❡r✲♠♦❞②♥❛♠✐❝s ❛♥❞ t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r✳ ❍♦✇❡✈❡r✱ ❛s t❤❡ ♣✉r♣♦s❡ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✐s t♦ ❞♦ ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts✱ t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ♥❡❡❞s t♦ ❜❡ ❝❤❡❝❦❡❞✳ ❆s ♣r❡s❡♥t❡❞ ✐♥s❡❝t✐♦♥ ✸✳✸✱ ❞r♦♣❧❡ts ✇✐t❤ ❛ ❧❛r❣❡r ❞✐❛♠❡t❡r ❛♥❞ t❤❡r❡❢♦r❡ ❤✐❣❤❡r ♠❛ss ✇✐❧❧ ❛❞❥✉st ♠♦r❡s❧♦✇❧② t❤❛♥ s♠❛❧❧❡r ❞r♦♣❧❡ts✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❞r♦♣❧❡ts ❛❞❥✉st t♦ t❤❡ s♣❡❡❞ ❛♥❞ t❡♠♣❡r✲❛t✉r❡ ♦❢ t❤❡ ❛✐r ❛s②♠♣t♦t✐❝❛❧❧②✳ ❚❤❡r❡❢♦r❡ t❤❡ ❞r♦♣❧❡ts ✇✐❧❧ ♥❡✈❡r r❡❛❝❤ t❤❡ t❡♠♣❡r❛t✉r❡❛♥❞ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❛✐r ❡①❛❝t❧②✳ ❍♦✇❡✈❡r✱ ❛ ❧♦♥❣❡r ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ s♣r❛② s②st❡♠❛♥❞ t❤❡ t❡st ♦❜❥❡❝t r❡❞✉❝❡s t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❞r♦♣❧❡t ❛♥❞ ❛✐r ✈❛❧✉❡s✳ ❆♥ ✐♠♣♦rt❛♥t❝❤❛r❛❝t❡r✐st✐❝ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡ t❤❡ ♠❛①✐♠✉♠ ▼❱❉ t❤❛t ❝❛♥ ❜❡ t❡st❡❞

✹✾

✹ ❘❡s✉❧ts

✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ r❡q✉✐r❡♠❡♥ts✳ ❚❤❡r❡❢♦r❡✱ ❛ ♠❛①✐♠✉♠ ❢♦rt❤❡ ✜♥❛❧ ❞❡✈✐❛t✐♦♥ ❜❡t✇❡❡♥ ❛✐r ❛♥❞ ❞r♦♣❧❡t ✈❛❧✉❡s ❤❛s t♦ ❜❡ ❝❤♦s❡♥✳❆s ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ❤❛s ❛ s✐❣♥✐✜❝❛♥t ✐♥✢✉❡♥❝❡

♦♥ t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥s✳ ❍❡♥❝❡✱ t♦ ❤❛✈❡ ❛ ❣♦♦❞ tr❛♥s❢❡r❛❜✐❧✐t② ♦❢ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ❡①♣❡r✲✐♠❡♥ts✱ t❤❡ ✈❡❧♦❝✐t② ♦❢ t❤❡ ❞r♦♣❧❡ts ♥❡❡❞s t♦ ❜❡ ❝❧♦s❡ t♦ t❤❡ t❛r❣❡t ✈❛❧✉❡✳ ❚❤❡r❡❢♦r❡ ✐t✇❛s ❞❡❝✐❞❡❞ t❤❛t t❤❡ ✜♥❛❧ ❞❡✈✐❛t✐♦♥ ♦❢ t❤❡ ❞r♦♣❧❡t s♣❡❡❞ ❤❛s t♦ ❜❡ ❛t ♠♦st 2m s−1 ✐♥❝❛s❡ ♦❢ t❤❡ ❞❡s✐❣♥ s♣❡❡❞ ♦❢ 35m s−1✳❈❛❧❝✉❧❛t✐♦♥s ✇✐t❤ ❛♥ ❛✐r ✈❡❧♦❝✐t② ♦❢ 35m s−1 ❛t t❤❡ t❡st s❡❝t✐♦♥ ✇❡r❡ ❞♦♥❡✳ ❚❤❡ ✜♥❛❧

✈❡❧♦❝✐t② ❞❡✈✐❛t✐♦♥s ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t s✐③❡s ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✶✺✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡✜❣✉r❡✱ ❞r♦♣❧❡ts ✇✐t❤ ❛ ♠❛①✐♠✉♠ ❞✐❛♠❡t❡r ♦❢ ❛❜♦✉t 95µm ❝❛♥ ❜❡ t❡st❡❞ ✇✐t❤♦✉t ❤❛✈✐♥❣❛ ❤✐❣❤❡r ❞❡✈✐❛t✐♦♥ t❤❛♥ 2m s−1 ❢r♦♠ t❤❡ ❛✐r ✈❡❧♦❝✐t②✳ ❯s✐♥❣ t❤❡ ▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥✱t❤✐s r❡s✉❧ts ✐♥ ❛ ♠❛①✐♠✉♠ ▼❱❉ ♦❢ ❛❜♦✉t 42µm t❤❛t ❝❛♥ ❜❡ t❡st❡❞ ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ❛♥❞ st✐❧❧ ❛❞❥✉st ❢❛st ❡♥♦✉❣❤ t♦ t❤❡ ❛✐r ✈❡❧♦❝✐t②✳

0 20 40 60 80 100 120

droplet diameter [ m]

0

1

2

3

ve

locity d

evia

tio

n [

m/s

]

velocity deviation

maximum allowed deviation

❋✐❣✉r❡ ✹✳✶✺✿ ❱❡❧♦❝✐t② ❞❡✈✐❛t✐♦♥ ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t ❞✐❛♠❡t❡rs✳

❘❡❣❛r❞✐♥❣ t❤❡ t❡♠♣❡r❛t✉r❡✱ t❤❡ r❡❣✐♦♥ ❛r♦✉♥❞ −3 ➦C ❛♥❞ −2 ➦C ✐s t❤❡ ♠♦st ✐♠♣♦rt❛♥tt♦ ❜❡ ❛❝❤✐❡✈❡❞ ❡①❛❝t❧②✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ t②♣❡ ♦❢ ✐❝❡ ❛❝❝r❡t✐♦♥s ❝❤❛♥❣❡s ❢r♦♠ r✐♠❡ t♦❣❧❛③❡ ✐❝❡ ✐♥ t❤✐s t❡♠♣❡r❛t✉r❡ r❡❣✐♦♥✳ ❚♦ ❤❛✈❡ ❣♦♦❞ ❝♦♥tr♦❧ ♦✈❡r t❤❡ t②♣❡ ♦❢ t❤❡ ✐❝❡s❤❛♣❡✱ t❤❡ ❞r♦♣❧❡t✬s t❡♠♣❡r❛t✉r❡ ❛t t❤❡ t❡st ♦❜❥❡❝t s❤❛❧❧ ❞✐✛❡r ❛t ♠♦st 0.5 ➦C ❢r♦♠ ❛♥❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −3 ➦C✳❚♦ ✜♥❞ ♦✉t ✇❤✐❝❤ ▼❱❉s ❝❛♥ ❜❡ t❡st❡❞ ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ ❝❛❧❝✉❧❛t✐♦♥s ✇✐t❤

❞✐✛❡r❡♥t ❞r♦♣❧❡t s✐③❡s ✇❡r❡ ❞♦♥❡✳ ❆s ❤✐❣❤❡r ✈❡❧♦❝✐t✐❡s ❞❡❝r❡❛s❡ t❤❡ t❡♠♣❡r❛t✉r❡ ❝❤❛♥❣❡✱t❤❡ ✇♦rst ❝❛s❡ ✇❛s ❝❤♦s❡♥✳ ❚❤❡r❡❢♦r❡ t❤❡ ❛✐r ✈❡❧♦❝✐t② ❛t t❤❡ t❡st s❡❝t✐♦♥ ✐s 35m s−1 ❢♦rt❤❡ ❝❛❧❝✉❧❛t✐♦♥s✳ ❆s t❤❡ ♥❡❝❡ss❛r② ❛❞❛♣t✐♦♥ q✉❛❧✐t② ✇❛s ❞❡❝✐❞❡❞ ❢♦r ❛♥ ❛✐r t❡♠♣❡r❛t✉r❡♦❢ −3 ➦C✱ t❤❡ ❛✐r t❡♠♣❡r❛t✉r❡ ✇❛s s❡t t♦ −3 ➦C✳ ❚❤❡ ✜♥❛❧ t❡♠♣❡r❛t✉r❡ ❞❡✈✐❛t✐♦♥s ❢♦r❞✐✛❡r❡♥t ❞r♦♣❧❡t s✐③❡s ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❋✐❣✉r❡ ✹✳✶✻✳ ❚♦ r❡♠❛✐♥ ✐♥s✐❞❡ ❛ ❞✐✛❡r❡♥❝❡ ♦❢0.5 ➦C t♦ t❤❡ ❛✐r t❡♠♣❡r❛t✉r❡✱ ❞r♦♣❧❡ts ✇✐t❤ ❛ ♠❛①✐♠✉♠ ❞✐❛♠❡t❡r ♦❢ ❛❜♦✉t 85µm ❝❛♥ ❜❡t❡st❡❞✳ ❯s✐♥❣ t❤❡ ▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥✱ t❤✐s r❡s✉❧ts ✐♥ ❛ ♠❛①✐♠✉♠ ▼❱❉ ♦❢ ❛❜♦✉t38µm t❤❛t ❝❛♥ ❜❡ t❡st❡❞ ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ st✐❧❧ ❛❞❥✉st ❢❛st ❡♥♦✉❣❤ t♦ t❤❡ ❛✐rt❡♠♣❡r❛t✉r❡✳❚❤❡r❡❢♦r❡ ❞r♦♣❧❡ts ✇✐t❤ ▼❱❉s ♦❢ 38µm ❛r❡ t❤❡ ❜✐❣❣❡st ❞r♦♣❧❡ts t♦ ❜❡ t❡st❡❞ ✐♥s✐❞❡

t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ st✐❧❧ ❢✉❧✜❧❧ ❡✈❡r② r❡q✉✐r❡♠❡♥t✳■❢ ❛ ❞❡s✐❣♥ ✐s ✇❛♥t❡❞ t❤❛t ✇♦r❦s ❢♦r ❤✐❣❤❡r ▼❱❉s✱ t❤❡ ❧❡♥❣t❤ ❜❡t✇❡❡♥ t❤❡ s♣r❛② s②st❡♠

❛♥❞ t❤❡ t❡st ♦❜❥❡❝t ♥❡❡❞s t♦ ❜❡ ❡♥❧❛r❣❡❞✳ ❖♥ t❤❡ ❝♦♥tr❛r②✱ t❤❡ ❧❡♥❣t❤ ❝❛♥ ❜❡ s❤♦rt❡r ✐❢

✺✵

✹ ❘❡s✉❧ts

0 20 40 60 80 100 120

droplet diameter [ m]

0

1

2

3

tem

pe

ratu

re

de

via

tio

n [

K] temperature deviation

maximum allowed deviation

❋✐❣✉r❡ ✹✳✶✻✿ ❚❡♠♣❡r❛t✉r❡ ❞❡✈✐❛t✐♦♥ ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t ❞✐❛♠❡t❡rs✳

t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s❤❛❧❧ ❜❡ ❞❡s✐❣♥❡❞ ❢♦r s♠❛❧❧❡r ❞r♦♣❧❡ts✳ ❖♥❡ ♦♣t✐♦♥ t♦ ❝❤❛♥❣❡ t❤❡❧❡♥❣t❤ ♦❢ t❤❡ ❞r♦♣❧❡ts✬ tr❛❥❡❝t♦r✐❡s ✐s t♦ ❥✉st ❝❤❛♥❣❡ t❤❡ ♥♦③③❧❡ ❧❡♥❣t❤✳ ❋✐❣✉r❡ ✹✳✶✼ s❤♦✇st❤❡ ❧❡♥❣t❤ t❤❡ ♥♦③③❧❡ ✇♦✉❧❞ ♥❡❡❞ t♦ ❤❛✈❡ ❢♦r ❞✐✛❡r❡♥t ❞✐❛♠❡t❡rs t♦ ❛❝❤✐❡✈❡ t❤❡ ❞r♦♣❧❡tt❡♠♣❡r❛t✉r❡ ❛♥❞ ✈❡❧♦❝✐t② ❛s ❢♦r♠✉❧❛t❡❞ ✐♥ t❤❡ r❡q✉✐r❡♠❡♥ts✳ ■t ✐s ❤♦✇❡✈❡r ✐♠♣♦rt❛♥t t♦st❛t❡ t❤❛t ♠✉❝❤ s❤♦rt❡r ♥♦③③❧❡ ❧❡♥❣t❤s ✐♥❝r❡❛s❡ t❤❡ r✐s❦ ♦❢ s❡♣❛r❛t✐♦♥ ❞r❛st✐❝❛❧❧②✳ ❋♦r❞r♦♣❧❡ts ✇✐t❤ ❛ ❞✐❛♠❡t❡r ♦❢ 35µm ♦r ❧❡ss✱ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡ ❝❛♥ ❜❡ ❛s s❤♦rt ❛s0.05m ❜❡❝❛✉s❡ t❤❡ ❧❡♥❣t❤s ❜❡t✇❡❡♥ t❤❡ s♣r❛② s②st❡♠ ❛♥❞ ♥♦③③❧❡ ❡♥tr② ❛♥❞ ❜❡t✇❡❡♥ t❤❡t❡st s❡❝t✐♦♥ ❡♥tr② ❛♥❞ t❤❡ t❡st ♦❜❥❡❝t ❛r❡ ❛❧r❡❛❞② ❧♦♥❣ ❡♥♦✉❣❤✳

0 50 100 150

droplet diameter [ m]

0

1

2

3

4

5

6

ne

ce

ssa

ry n

ozzle

le

ng

th [

m]

adaquate velocity adaption

adaquate temperature adaption

❋✐❣✉r❡ ✹✳✶✼✿ ◆❡❝❡ss❛r② ❧❡♥❣t❤ ♦❢ t❤❡ ♥♦③③❧❡ t♦ ❢✉❧✜❧❧ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r ❞✐✛❡r❡♥t ❞r♦♣❧❡t❞✐❛♠❡t❡rs✳

✺✶

✹ ❘❡s✉❧ts

❚❤❡ ♠❛①✐♠✉♠ ▼❱❉ ✐♥ t❤❡ ❊❆❙❆ ❝❡rt✐✜❝❛t✐♦♥s ✐s 50µm✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ ▲❛♥❣♠✉✐r❉ ❞✐str✐❜✉t✐♦♥✱ t❤❡ ❜✐❣❣❡st ❞r♦♣❧❡ts ✐♥ s✉❝❤ ❛ ❞r♦♣❧❡t ❝❧♦✉❞ ❤❛✈❡ ❛ ❞✐❛♠❡t❡r ♦❢ ❛❜♦✉t110µm✳ ❚❤❡ ♥❡❝❡ss❛r② ♥♦③③❧❡ ❧❡♥❣t❤ t♦ ❞♦ ❡①♣❡r✐♠❡♥ts ✇✐t❤ ❞r♦♣❧❡ts ✇✐t❤ ❛ ❞✐❛♠❡t❡r♦❢ 110µm ✐s 3.25m ❛❝❝♦r❞✐♥❣ t♦ ❋✐❣✉r❡ ✹✳✶✼✳ ❚❤❡r❡❢♦r❡ ❛ ♥♦③③❧❡ ✇✐t❤ ❛ ❧❡♥❣t❤ ♦❢ 3.25m✐s ♥❡❡❞❡❞ t♦ t❡st t❤❡ ✇❤♦❧❡ ❜❛♥❞✇✐❞t❤ ♦❢ t❤❡ ❊❆❙❆ ❝❡rt✐✜❝❛t✐♦♥s✳

✹✳✺ Pr❡ss✉r❡ ❧♦ss❡s ❛♥❞ ❢❛♥ s❡❧❡❝t✐♦♥

❆s ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ ❡✈❡r② ❝♦♠♣♦♥❡♥t ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐♥✢✉❡♥❝❡st❤❡ ♣r❡ss✉r❡ ❧♦ss✳ ❚❤❡ ✈❛❧✉❡s ♥❡❝❡ss❛r② t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss ♦❢ ❡❛❝❤ ❝♦♠♣♦♥❡♥t❛r❡ ❛❧r❡❛❞② ❣✐✈❡♥ ✐♥ t❤❡ r❡s♣❡❝t✐✈❡ s✉❜s❡❝t✐♦♥✳ ❚❤❡ r❡♠❛✐♥✐♥❣ ✈❛❧✉❡s ✇✐❧❧ ❜❡ ✐♥tr♦❞✉❝❡❞❛♥❞ ❡①♣❧❛✐♥❡❞ ✐♥ t❤✐s s✉❜s❡❝t✐♦♥✳❋♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❢r✐❝t✐♦♥ ❝♦❡✣❝✐❡♥t ❛❝❝♦r❞✐♥❣ t♦ ❡q✉❛t✐♦♥ ✸✳✸✵ t❤❡ ❘❡②♥♦❧❞s

♥✉♠❜❡r ✐s ♥❡❡❞❡❞✳ ❚❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r ✐s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ ❡q✉❛t✐♦♥ ✷✳✶✳ ❆s t❤❡ ❤②✲❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ♦❢ ❡✈❡r② ❝♦♠♣♦♥❡♥t ✐s ❣✐✈❡♥ ✐♥ t❤❡ r❡s♣❡❝t✐✈❡ s✉❜s❡❝t✐♦♥ ❛♥❞ t❤❡ ✈✐s✲❝♦s✐t② ✐♥ ❚❛❜❧❡ ✹✳✷✱ ❥✉st t❤❡ ❛✐r ✈❡❧♦❝✐t② ✐s ♠✐ss✐♥❣✳ ❚❤❡ ✈❡❧♦❝✐t② ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤t❤❡ ❝♦♥t✐♥✉✐t② ❡q✉❛t✐♦♥✳ ❚❤❡ ✈❡❧♦❝✐t✐❡s ❛t t❤❡ ✐♥❧❡t ❛♥❞ t❤❡ ❡①✐t ♦❢ t❤❡ ❞✐✛❡r❡♥t ♣❛rts ♦❢t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡ ✹✳✹✳ ❆s ❤✐❣❤❡r ✈❡❧♦❝✐t✐❡s ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ❧❡❛❞ t♦ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s✱ t❤❡ ♠❛①✐♠✉♠ ✈❡❧♦❝✐t② ♦❢ 35m s−1 ✐♥s✐❞❡ t❤❡t❡st s❡❝t✐♦♥ ✇❛s ✉s❡❞ ❛s t❤❡ ❞❡s✐❣♥ ♣♦✐♥t✳

❝♦♠♣♦♥❡♥t ✐♥❧❡t ✈❡❧♦❝✐t② [m s−1] ❡①✐t ✈❡❧♦❝✐t② [m s−1]

❢❛♥ ❞✉❝t 9.95 9.95✇✐❞❡✲❛♥❣❧❡✲❞✐✛✉s❡r 9.95 3.89

s❡tt❧✐♥❣ ❛r❡❛ 3.89 3.89♥♦③③❧❡ 3.89 35.00

t❡st s❡❝t✐♦♥ 35.00 35.00❞✐✛✉s❡r 35.00 14.00

❚❛❜❧❡ ✹✳✹✿ ❱❡❧♦❝✐t✐❡s ❛t t❤❡ ✐♥❧❡t ❛♥❞ ♦✉t❧❡t ♦❢ ❡✈❡r② ❝♦♠♣♦♥❡♥t✳

❲❤❡♥ ❝❛❧❝✉❧❛t✐♥❣ t❤❡ ♣r❡ss✉r❡ ❧♦ss ❞✉❡ t♦ t❤❡ ❞r❛❣ ♦❢ ❛ str✉❝t✉r❡ ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ✇✐t❤ ❡q✉❛t✐♦♥ ✸✳✹✼✱ t❤❡ ✈❛❧✉❡ ǫ ✐s ♥❡❡❞❡❞✳ ❚❤✐s ✈❛❧✉❡ ❛❝❝♦✉♥ts ❢♦r t❤❡ ✐♥✢✉❡♥❝❡ t❤❡str✉❝t✉r❡ ❤❛s ♦♥ t❤❡ ♣r❡ss✉r❡ ❧♦ss ✐♥ ❞♦✇♥str❡❛♠ s❡❝t✐♦♥s✳ ❚❤❡ t✇♦ str✉❝t✉r❡s ✐♥s✐❞❡ t❤❡✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ t❤❡ s♣r❛② s②st❡♠ ❛♥❞ t❤❡ t❡st ♦❜❥❡❝t✳ ❆s ❜♦t❤ ❛r❡ ❞❡s✐❣♥❡❞ ✇✐t❤❛♥ ❛❡r♦❞②♥❛♠✐❝ s❤❛♣❡✱ t❤❡ ❞♦✇♥str❡❛♠ ✐♥✢✉❡♥❝❡ ✐s s✉♣♣♦s❡❞ t♦ ❜❡ ♥❡❣❧✐❣✐❜❧❡✳ ❚❤❡r❡❢♦r❡ǫ ✐s ❛ss✉♠❡❞ t♦ ❜❡ t❤❡ ♠✐♥✐♠✉♠ ♣♦ss✐❜❧❡ ✈❛❧✉❡ ♦❢ 1✳❚❤❡ t❡st ♦❜❥❡❝t ✐ts❡❧❢ ♣r♦❞✉❝❡s ❞r❛❣✳ ❚❤✐s ❞r❛❣ r❡s✉❧ts ✐♥ ❛ ♣r❡ss✉r❡ ❧♦ss t❤❛t ❝❛♥ ❜❡

❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❡q✉❛t✐♦♥ ❢♦r ✐♥t❡r♥❛❧ str✉❝t✉r❡s✳ ❚♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss✱ t❤❡❞r❛❣ ❝♦❡✣❝✐❡♥t ✐s ♥❡❡❞❡❞✳ ❚❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t ✐s ❤✐❣❤❡r ❢♦r ❧♦✇❡r ❘❡②♥♦❧❞s ♥✉♠❜❡rs✳❆❝❝♦r❞✐♥❣ t♦ ❋✐❣✉r❡s ✹✳✶ ❛♥❞ ✹✳✷✱ t❤❡ ❧♦✇❡st ❘❡②♥♦❧❞s ♥✉♠❜❡rs ❢♦r ❯❆❱s ✇✐❧❧ ❜❡ ❢♦r✈❡❧♦❝✐t✐❡s ♦❢ ❛r♦✉♥❞ 10m s−1 ❛♥❞ ❝❤♦r❞ ❧❡♥❣t❤s ♦❢ 0.1m✳ ❚❤✐s ✇♦✉❧❞ r❡s✉❧t ✐♥ ❛ ❘❡②♥♦❧❞s♥✉♠❜❡r ♦❢ ❛❜♦✉t 80,000✳ ❚❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t ♦❢ t❤❡ ❘●✶✺ ❛✐r❢♦✐❧ ❢♦r ✈❛r✐♦✉s ❘❡②♥♦❧❞s♥✉♠❜❡rs ✐s ❧✐st❡❞ ❜② ❆✐r❢♦✐❧ ❚♦♦❧s ❬✺✵❪✳ ❆s ♥♦ ✈❛❧✉❡s ❛r❡ ❣✐✈❡♥ ❢♦r ❛ ❘❡②♥♦❧❞s ♥✉♠❜❡r ♦❢

✺✷

✹ ❘❡s✉❧ts

80,000✱ t❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t ✇✐❧❧ ❜❡ t❛❦❡♥ ❢♦r ❛ ❘❡②♥♦❧❞s ♥✉♠❜❡r ♦❢ 50,000✳ ❚❤❡ ❤✐❣❤❡st❞r❛❣ ❝♦❡✣❝✐❡♥t ❢♦r ❛ ❘❡②♥♦❧❞s ♥✉♠❜❡r ♦❢ 50,000 ✐♥s✐❞❡ t❤❡ ❧✐♥❡❛r r❡❣✐♦♥ ♦❢ t❤❡ cL✲α✲❝✉r✈❡ ✐s 0.039✳ ❚❤❡ r❡♠❛✐♥✐♥❣ ✉♥❦♥♦✇♥ ✐s t❤❡ r❛t✐♦ ♦❢ t❤❡ ❛r❡❛ ♦❢ t❤❡ ❞r❛❣ ✐t❡♠ t♦ t❤❡✢♦✇ ❛r❡❛✳ ❚❤❡ ❞r❛❣ ❛r❡❛ ♦❢ ❛♥ ❛✐r❢♦✐❧ ✐s ✐ts ❝❤♦r❞ ❧❡♥❣t❤ t✐♠❡s t❤❡ ✇✐❞t❤✳ ❚❤❡ ✢♦✇ ❛r❡❛✐s t❤❡ ♣❛rt ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ t❤❛t ✐s ♥♦t ❜❧♦❝❦❡❞✳ ❆s t❤❡ ❜❧♦❝❦❛❣❡ ✇✐❧❧ ❜❡ 10%♠❛①✐♠✉♠✱ t❤❡ ✢♦✇ ❛r❡❛ ✐s 90% ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❚❤❡ s♣r❛② s②st❡♠ ❛❧s♦ ♣r♦❞✉❝❡s ❞r❛❣ ❛♥❞ t❤❡r❡❢♦r❡ ❛ ♣r❡ss✉r❡ ❧♦ss✳ ❚❤❡ s❤❛♣❡ ♦❢ t❤❡

s♣r❛② s②st❡♠ s❤♦✉❧❞ ❜❡ ♦♥❡ ✇✐t❤ ❛ s♠❛❧❧ ❞r❛❣ ❝♦❡✣❝✐❡♥t t♦ r❡❞✉❝❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s❛♥❞ t❤❡ ❛❡r♦❞②♥❛♠✐❝ ❧♦ss❡s✳ ❍♦✇❡✈❡r✱ ❛s ♥♦ s♣r❛② s②st❡♠ ❝♦✉❧❞ ❜❡ s❡❧❡❝t❡❞✱ ❛❧s♦ t❤❡s❤❛♣❡ ♦❢ t❤❡ s♣r❛② s②st❡♠ ✐s ♥♦t ②❡t ❞❡t❡r♠✐♥❡❞✳ ❚♦ ♥♦t ✉♥❞❡r❡st✐♠❛t❡ t❤❡ ♣r❡ss✉r❡❧♦ss ♦❢ t❤❡ s♣r❛② s②st❡♠✱ t❤❡ ✇♦rst ❝❛s❡ ✇❛s ❝❛❧❝✉❧❛t❡❞✳ ❚♦ ❞♦ t❤✐s✱ t❤❡ s❤❛♣❡ ♦❢ t❤❡s♣r❛② s②st❡♠ ✐s s✐♠♣❧✐✜❡❞ t♦ ❛ ❝✐r❝✉❧❛r ♣✐♣❡ ✐♥ ❝r♦ss✢♦✇✳ ❚❤❡r❡❢♦r❡ t❤❡ ❞r❛❣ ❝♦❡✣❝✐❡♥t❜❡❝♦♠❡s 1✳ ❋♦r t❤❡ ❜❧♦❝❦❛❣❡ ♦❢ ❛ s♣r❛② s②st❡♠✱ ❛ ♠❛①✐♠✉♠ ♦❢ 17% ✐s r❡❝♦♠♠❡♥❞❡❞ ❜②▲❡♦♥❡ ❡t ❛❧✳ ❬✺✼❪✳ ❚❤❡ ❞r❛❣ ❛r❡❛ ♦❢ t❤❡ s♣r❛② s②st❡♠ ✐s ✐ts ♣r♦❥❡❝t❡❞ ❛r❡❛ ❛♥❞ t❤❡r❡❢♦r❡♠❛①✐♠✉♠ 17% ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛✱ ✇❤✐❧❡ t❤❡ ✢♦✇ ❛r❡❛ ✐s t❤❡ r❡♠❛✐♥✐♥❣ 83% ♦❢t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛✳❚❤❡ ♣r❡ss✉r❡ ❧♦ss ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ s❝r❡❡♥ ❝♦♥t❛✐♥s t❤❡ ♣❛r❛♠❡t❡r KRe✳ ❋♦r t❤❡

❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❘❡②♥♦❧❞s ♥✉♠❜❡r t❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ s❝r❡❡♥ ✇✐r❡ ♥❡❡❞s t♦ ❜❡ ❦♥♦✇♥✳❚❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ ✇✐r❡ ✇❛s ❛ss✉♠❡❞ t♦ ❜❡ 0.5mm ❛s ✇❛s ❛❧s♦ ❞♦♥❡ ❜② ❆r✐❢✉③③❛♠❛♥❛♥❞ ▼❛s❤✉❞ ❬✷✷❪✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♠❡s❤ ❝♦♥st❛♥t KMESH ♥❡❡❞s t♦ ❜❡ ✜①❡❞ t♦ ❝❛❧❝✉❧❛t❡t❤❡ ❧♦ss❡s✳ ❚❤❡ ✈❛❧✉❡ ❢♦r ❛✈❡r❛❣❡ ❝✐r❝✉❧❛r ♠❡t❛❧ ✇✐r❡s ✇❛s ✉s❡❞ ❛♥❞ t❤❡r❡❢♦r❡ KMESH

❜❡❝♦♠❡s 1.3✳ ❚❤❡ ♠✐ss✐♥❣ r❛t✐♦ ♦❢ t❤❡ ✢♦✇ ❛r❡❛ t♦ t❤❡ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❛r❡❛ ✐s ❡q✉✐✈❛❧❡♥tt♦ t❤❡ ♣♦r♦s✐t② ♦❢ t❤❡ s❝r❡❡♥✳❚❤❡ ❢r✐❝t✐♦♥ ❝♦❡✣❝✐❡♥t ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜s ❞❡♣❡♥❞s ♦♥ t❤❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ t❤❡

❤♦♥❡②❝♦♠❜s✳ ❆s ❞♦♥❡ ❜② ❆r✐❢✉③③❛♠❛♥ ❛♥❞ ▼❛s❤✉❞ ❬✷✷❪✱ ♣♦❧②✈✐♥②❧ ❝❤❧♦r✐❞❡ ✭P❱❈✮ ❝❛♥❜❡ ✉s❡❞ ❢♦r t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ t❤❡ ❤♦♥❡②❝♦♠❜s✳ ▼❡❛s✉r❡♠❡♥ts ❜② ❘♦❝❤❛ ❡t ❛❧✳ ❬✻✵❪s❤♦✇❡❞ t❤❛t t❤❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ P❱❈ ❝❛♥ ❜❡ ❛s ❤✐❣❤ ❛s 8µm✳❋♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♣r❡ss✉r❡ ❧♦ss ✐♥s✐❞❡ t❤❡ ❞✐✛✉s❡r✱ t❤❡ ✈❛❧✉❡ KEXP ♥❡❡❞s t♦

❜❡ ❦♥♦✇♥✳ ❚❤❡ ✈❛❧✉❡ ✇❛s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❡q✉❛t✐♦♥ ❢♦r sq✉❛r❡ ❝r♦ss✲s❡❝t✐♦♥s✳ ❚❤✐s ✐s❜❡❝❛✉s❡ ❛ sq✉❛r❡ ✐s ❝❧♦s❡r t♦ ❛ r❡❝t❛♥❣✉❧❛r s❤❛♣❡ t❤❛♥ ❛ ❝✐r❝❧❡ ❛♥❞ ❜❡❝❛✉s❡ t❤✐s ❧❡❛❞s t♦❛ ♠♦r❡ ❝♦♥s❡r✈❛t✐✈❡ ❝❛❧❝✉❧❛t✐♦♥✳❋♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❡①✐t ❧♦ss❡s✱ t❤❡ ▼❛❝❤ ♥✉♠❜❡r ❛t t❤❡ ❡①✐t ♥❡❡❞s t♦ ❜❡ ❝❛❧✲

❝✉❧❛t❡❞✳ ■t ✐s ❛ss✉♠❡❞ t❤❛t t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❛✐r st❛②s ❝♦♥st❛♥t ✐♥s✐❞❡ t❤❡ ✇❤♦❧❡✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ ▼❛❝❤ ♥✉♠❜❡r ❛♥❞ t❤❡r❡❢♦r❡ ❛❧s♦ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛r❡ ❤✐❣❤❡r❢♦r ❧♦✇❡r t❡♠♣❡r❛t✉r❡s✳ ❚❤❡r❡❢♦r❡ t❤❡ ✇♦rst✲❝❛s❡ t❡♠♣❡r❛t✉r❡ ♦❢ −15 ➦C ✇❛s ❝❤♦s❡♥✳❚❤❡ r❡s✉❧t✐♥❣ ♣r❡ss✉r❡ ❧♦ss❡s ❢♦r ❡✈❡r② ❝♦♠♣♦♥❡♥t ❛♥❞ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐♥ t♦t❛❧

❛r❡ st❛t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✺✳ ❆❧s♦ t❤❡ ♥✉♠❜❡r ♦❢ t❤❡ ❡q✉❛t✐♦♥ t❤❛t ✇❛s ✉s❡❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡♣r❡ss✉r❡ ❧♦ss ✐s ❣✐✈❡♥ ✐♥ t❤✐s t❛❜❧❡✳❚♦ ❝♦♠♣❡♥s❛t❡ ❢♦r ♣♦ss✐❜❧❡ s❤♦rt❝♦♠✐♥❣s ✐♥ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s✱ ❛ s❛❢❡t② ♠❛r❣✐♥ ✐s ✐♥✲

tr♦❞✉❝❡❞✳ ■t ✇❛s ❝❤♦s❡♥ t❤❛t t❤❡ s❡❧❡❝t❡❞ ❢❛♥ ❤❛s t♦ ❜❡ ❛❜❧❡ t♦ ❝♦♠♣❡♥s❛t❡ ❛❜♦✉t 1.5t✐♠❡s t❤❡ ❝❛❧❝✉❧❛t❡❞ ♣r❡ss✉r❡ ❧♦ss❡s✳ ❚❤✐s r❡s✉❧ts ✐♥ ❛ ♣r❡ss✉r❡ r✐s❡ ♦❢ ❛❜♦✉t 500Pa t❤❡❢❛♥ ❤❛s t♦ ❞❡❧✐✈❡r✳ ❆ ❢✉rt❤❡r ♦❜❥❡❝t✐✈❡ ❢♦r t❤❡ ❢❛♥ ✇❛s t♦ ❤❛✈❡ ❛ ❞✐❛♠❡t❡r ♦❢ ❛❜♦✉t 1.1mt♦ ❤❛✈❡ ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ ❛❜♦✉t 2.5 ♦✈❡r t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r✳ ❚❤❡ t❤✐r❞ ♣♦✐♥t ✐s t❤❡✈♦❧✉♠❡ ✢✉① t❤r♦✉❣❤ t❤❡ ❢❛♥✳ ❆ ♠❛①✐♠✉♠ ✈♦❧✉♠❡ ✢✉① ♦❢ 9.28m3 s−1 ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞✇✐t❤ ❡q✉❛t✐♦♥ ✸✳✽✳

✺✸

✹ ❘❡s✉❧ts

❝♦♠♣♦♥❡♥t ❡q✉❛t✐♦♥ ❑ ♣r❡ss✉r❡ ❧♦ss [Pa]

t❡st s❡❝t✐♦♥ ✸✳✷✽ 0.016 13.40t❡st ♦❜❥❡❝t ✸✳✹✼ 0.025 20.93♥♦③③❧❡ ✸✳✸✶ 0.014 11.72

s❡tt❧✐♥❣ ❛r❡❛ ✸✳✷✽ 0.011 0.11s♣r❛② s②st❡♠ ✸✳✹✼ 0.205 2.12

s❝r❡❡♥ ✸✳✹✽ 1.210 12.51❤♦♥❡②❝♦♠❜s ✸✳✹✹ 0.404 4.18

✇✐❞❡✲❛♥❣❧❡✲❞✐✛✉s❡r ✸✳✺✶ 1.360 91.41❢❛♥ ❞✉❝t ✸✳✷✽ 0.011 0.74❞✐✛✉s❡r ✸✳✸✷ 0.057 47.73

❡①✐t ❧♦ss❡s ✸✳✹✸ 1.000 133.97

t♦t❛❧ ❧♦ss❡s 338.82

❚❛❜❧❡ ✹✳✺✿ ❖✈❡r✈✐❡✇ ♦✈❡r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ ❡✈❡r② ❝♦♠♣♦♥❡♥t ❛♥❞ ✐♥ t♦t❛❧✳

❚❤❡ s❡❧❡❝t❡❞ ❢❛♥ ✐s t❤❡ ♠♦❞❡❧ ✹✸❲✼✷✻ ❜② ❆❡r♦✈❡♥t ❬✻✶❪✳ ■t ❤❛s ❛ ❞✐❛♠❡t❡r ♦❢ 1.09m❛♥❞ ❛ ❧❡♥❣t❤ ♦❢ 0.91m✳ ❚❤❡ ❢❛♥ ✐s ❛❜❧❡ t♦ ❞❡❧✐✈❡r ❛ ♣r❡ss✉r❡ r✐s❡ ♦❢ ❛❜♦✉t 500Pa ❢♦r ❛✈♦❧✉♠❡ ✢♦✇ ♦❢ 11.0m3 s−1✳ ❚❤❡r❡❢♦r❡ t❤❡ ❢❛♥ ✐s ♣❡r❢❡❝t❧② ❛❜❧❡ t♦ ❢✉❧✜❧❧ t❤❡ r❡q✉✐r❡♠❡♥ts✳❚❤❡ ✐♥♣✉t ♣♦✇❡r ♦❢ t❤✐s ❢❛♥ ✐♥ t❤❡ ✈✐❡✇❡❞ ♠♦❞❡ ✐s 8.024 kW✳ ❚❤✐s ♣❛r❛♠❡t❡r ✐s ✐♠♣♦rt❛♥tt♦ ❜❡ ❝♦♥s✐❞❡r❡❞ ❢♦r t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r✳

✹✳✻ ❈♦♦❧✐♥❣ ❝❤❛♠❜❡r

✹✳✻✳✶ ❈♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts

❚❤❡ ♥❡❝❡ss❛r② ❡q✉❛t✐♦♥s ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ ❤❡❛t r❡❧❡❛s❡❞ ❞✉r✐♥❣ t❤❡ r✉♥ ♦❢ t❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ✇❡r❡ ❣✐✈❡♥ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✳ ❚❤❡ r❡q✉✐r❡❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ❞❡♣❡♥❞s ♦♥t❤❡ ✇❛t❡r ❝♦♥t❡♥t ✐♥ t❤❡ ❛✐r ❛♥❞ ♦♥ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡❛♥❞ t❤❡ ❛✐r t❡♠♣❡r❛t✉r❡✳ ❚❤❡ ✇♦rst ❝❛s❡ ✐s ❛ss✉♠❡❞ ❢♦r ❜♦t❤ ♣❛r❛♠❡t❡rs✳ ❚❤❡r❡❢♦r❡ ❛▲❲❈ ♦❢ 2.9 gm−3 ❛♥❞ ❛♥ ❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −15 ➦C ❛r❡ ✉s❡❞✳❆s ❛❧r❡❛❞② ♠❡♥t✐♦♥❡❞✱ t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ✐s ❛ss✉♠❡❞ t♦ ❜❡ 15 ➦C✳ ❚❤❡r❡✲

❢♦r❡ t❤❡ ♠❛①✐♠✉♠ t❡♠♣❡r❛t✉r❡ ❞✐✛❡r❡♥❝❡ ✐s 30 ➦C✳ ❲✐t❤ ❛ ♠❛①✐♠✉♠ ▲❲❈ ♦❢ ❛❜♦✉t2.9 gm−3 ❛♥❞ t❤❡ ♠❛①✐♠✉♠ ❛✐r ♠❛ss ✢♦✇ ♦❢ 9.150m3 s−1✱ t❤❡ ♠❛①✐♠✉♠ ♠❛ss ✢♦✇ ♦❢t❤❡ ✇❛t❡r ✐s 0.0269 kg s−1✳ ❚❤✐s ✇♦✉❧❞ r❡s✉❧t ✐♥ ❛ s❡♥s✐❜❧❡ ❤❡❛t ♦❢ 3.510 kW ❛♥❞ ❛ ❧❛t❡♥t❤❡❛t ♦❢ 8.985 kW✳ ❈♦♠❜✐♥❡❞ ✇✐t❤ t❤❡ ❢❛♥ ✐♥♣✉t ♣♦✇❡r ♦❢ 8.024 kW✱ t❤❡ ♣r♦❞✉❝❡❞ ❤❡❛t❛❞❞s ✉♣ t♦ 20.520 kW✳ ❚❤✐s ✐s t❤❡ ♠❛①✐♠✉♠ ❛♠♦✉♥t ♦❢ ❤❡❛t t❤❡ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r ❤❛st♦ r❡♠♦✈❡ t♦ ❡♥s✉r❡ ❛ st❡❛❞② r✉♥✳❆ t②♣✐❝❛❧ t❡♠♣❡r❛t✉r❡ ❢♦r t❤❡ ❛✐r ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡ ❛r♦✉♥❞ −10 ➦C✳

❚❤❡ r❡s✉❧t✐♥❣ ❤❡❛t ❢♦r ❞✐✛❡r❡♥t ▲❲❈s ✐s ♣❧♦tt❡❞ ✐♥ ❋✐❣✉r❡ ✹✳✶✽✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ r❡❣✲✉❧❛t✐♦♥s ❜② t❤❡ ❊❆❙❆✱ t❤❡ ♠❛①✐♠✉♠ ▲❲❈ ❢♦r ❛ t❡♠♣❡r❛t✉r❡ ♦❢ −10 ➦C ✐s 2.5 gm−3✳❚❤❡r❡❢♦r❡ ❤✐❣❤❡r ▲❲❈s ❞♦ ♥♦t ♥❡❡❞ t♦ ❜❡ t❡st❡❞ ✐♥ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

✺✹

✹ ❘❡s✉❧ts

05101520250 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3heat [kW] LWC [g/m^3]fan power latent heat sensible heat

❋✐❣✉r❡ ✹✳✶✽✿ ❘❡q✉✐r❡❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ❢♦r t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t ▲❲❈s ❛♥❞❛♥ ❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −10 ➦C✳

✹✳✻✳✷ ❙♣❛❝❡ r❡q✉✐r❡♠❡♥ts

❆s ♠❡♥t✐♦♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s ❝❤❛♣t❡r✱ ●r❡❡♥✇❛② ❛♥❞ ❲♦♦❞ ❬✹✻❪ ❞✐❞ s✐♠✉❧❛t✐♦♥s ❢♦r ❛s✐♥❣❧❡ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ♥❡❝❡ss❛r② ❝❧❡❛r❛♥❝❡ ❛t t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐♥❧❡t✳❚❤❡② ❢♦✉♥❞ ♦✉t t❤❛t t❤❡ ✐♥✢♦✇ ❛r❡❛ ❤❛s t♦ ❜❡ ❛t ❧❡❛st 1.8 t✐♠❡s ❜✐❣❣❡r t❤❛♥ t❤❡ ✐♥❧❡t❛r❡❛✳ ❋♦r t❤❡ ❣✐✈❡♥ ❞❡s✐❣♥✱ t❤❡ ✐♥❧❡t ✐s ❛t t❤❡ ❢❛♥ s❡❝t✐♦♥✳ ❚❤❡ ❢❛♥ ❛r❡❛ ✐s 0.93m2✳❚❤❡r❡❢♦r❡ t❤❡ ❛r❡❛ ♦❢ t❤❡ ✐♥✢♦✇ ❤❛s t♦ ❜❡ ❛t ❧❡❛st 1.67m2✳ ❋✐❣✉r❡ ✹✳✶✾ s❤♦✇s ❞✐✛❡r❡♥t❝♦♠❜✐♥❛t✐♦♥s ♦❢ s✐❞❡ ❧❡♥❣t❤s ♦❢ ♣♦ss✐❜❧❡ ❝❤❛♠❜❡rs ❛♥❞ ❧❡♥❣t❤s ❜❡t✇❡❡♥ t❤❡ ✐♥❧❡t ❛♥❞ t❤❡✇❛❧❧✳ ❆s t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s 1.54m ✇✐❞❡ ❛♥❞ ❤✐❣❤ ❛t ✐ts ❜✐❣❣❡st ♣♦s✐t✐♦♥✱ s♠❛❧❧❡r❝❤❛♠❜❡rs ❛r❡ ♥♦t ♣♦ss✐❜❧❡ ❛t ❛❧❧✳

00.40.81.2 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9necessary clearance of the entry [m] hydraulic diameter of the cooling chamber [m]❋✐❣✉r❡ ✹✳✶✾✿ ◆❡❝❡ss❛r② ❝❧❡❛r❛♥❝❡ t♦ t❤❡ ❡♥tr② ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t ❤②✲

❞r❛✉❧✐❝ ❞✐❛♠❡t❡rs ♦❢ t❤❡ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r✳

✹✳✼ ❈♦sts

❚❤❡ ❝♦sts ♣❧❛② ❛♥ ✐♠♣♦rt❛♥t r♦❧❡ ✐♥ t❤❡ q✉❡st✐♦♥ ♦❢ ✇❤❡t❤❡r ❛ ♣r♦❥❡❝t ❝❛♥ ❜❡ r❡❛❧✐③❡❞✳❚❤❡r❡❢♦r❡ ❛ r♦✉❣❤ ❡st✐♠❛t❡ ♦❢ t❤❡ ❝♦sts ♦❢ t❤❡ ❜✉✐❧❞✐♥❣ ♦❢ t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✐s ♣r❡s❡♥t❡❞✳ ❆s t❤❡r❡ ✐s ♥♦ ❧✐t❡r❛t✉r❡ t❤❛t ♦✛❡rs ❢♦r♠✉❧❛s t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❝♦sts✱ t❤❡

✺✺

✹ ❘❡s✉❧ts

❡st✐♠❛t✐♦♥s ✇✐❧❧ ❜❡ r❡❛❧❧② ❝♦❛rs❡✳ ❚❤❡ ✜rst ♣♦✐♥t ✐s t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ♥❡❝❡ss❛r②♠❛t❡r✐❛❧ ✈♦❧✉♠❡ ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧ ♣❛rts✳ ❚❤❡ s✉r❢❛❝❡ ❛r❡❛ ♦❢ ❛❧❧ ❞❡s✐❣♥❡❞ ♣❛rts ❛❞❞s ✉♣t♦ 26.70m2✳ ❆ss✉♠✐♥❣ ❛ ✇❛❧❧ t❤✐❝❦♥❡ss ♦❢ 5mm✱ t❤❡ ♠❛t❡r✐❛❧ ✈♦❧✉♠❡ ❜❡❝♦♠❡s 0.134m3✳❲✐t❤ t❤❡ ❞❡♥s✐t② ♦❢ 2710 kgm−3 ♦❢ ❛❧✉♠✐♥✉♠✱ t❤❡ t♦t❛❧ ♠❛t❡r✐❛❧ ✇❡✐❣❤t ✐s 363.1 kg✳ ❚❤❡♣r✐❝❡ ♦❢ ❛❧✉♠✐♥✉♠ ✐s 3.06 $/kg ❛❝❝♦r❞✐♥❣ t♦ ▼❡t❛❧▼✐♥❡r ❬✻✷❪✳ ❚❤✐s r❡s✉❧ts ✐♥ ♠❛t❡r✐❛❧❝♦sts ♦❢ ❛❜♦✉t 1100 $✳ ❚❤❡ s❤❛r❡ ♦❢ ♠❛t❡r✐❛❧ ❝♦sts ♦♥ t❤❡ t♦t❛❧ ❝♦sts ✐s ❛❜♦✉t 15% ✐♥t❤❡ ♥♦r♠❛❧ ✐♥❞✉str② ❛❝❝♦r❞✐♥❣ t♦ ❲✐❧t✐♥❣ ❛♥❞ ❍❛♥❡♠❛❛✐❥❡r ❬✻✸❪✳ ❚❤❡r❡❢♦r❡ t❤❡ t♦t❛❧♠❛♥✉❢❛❝t✉r✐♥❣ ❝♦sts ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧ ♣❛rts ❛r❡ 7300 $✳ ❚❤✐s ❝❛❧❝✉❧❛t✐♦♥ ✐s ❤♦✇❡✈❡r❝♦❛rs❡ ❛♥❞ ♣r♦❜❛❜❧② t❤❡ r❡❛❧ ❝♦sts ❛r❡ ❤✐❣❤❡r✱ ❡✳❣✳ ❜❡❝❛✉s❡ ♦❢ s♣❡❝✐❛❧ ❛❧❧♦②s t❤❛t ♥❡❡❞ t♦❜❡ ✉s❡❞ ❜❡❝❛✉s❡ ♦❢ t❤❡ ❝♦❧❞ t❡♠♣❡r❛t✉r❡s ❛♥❞ t❤❡ ❤✐❣❤ ❤✉♠✐❞✐t② ✐♥s✐❞❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ s♣r❛② s②st❡♠ ❛♥❞ t❤❡ ❢❛♥ ♥❡❡❞ t♦ ❜❡ ❜♦✉❣❤t✳ ❆❝❝♦r❞✐♥❣ t♦ ❙♣r❛②✐♥❣

❙②st❡♠s ❈♦✳ ❬✻✹❪✱ t❤❡ ♣r✐❝❡ ❢♦r ❛♥ ❛✉t♦♠❛t❡❞ s②st❡♠ ❝❛♥ ❜❡ ❡st✐♠❛t❡❞ t♦ ❜❡ ✐♥ t❤❡ r❡❣✐♦♥♦❢ 35,000 $✳ P❛✐♥t ❇♦♦t❤ ❙✉♣♣❧② ❬✻✺❪ ❧✐sts t❤❡ ♣r✐❝❡ ♦❢ ❛♥ ❛①✐❛❧ ❢❛♥✱ ❝♦♠♣❛r❛❜❧❡ t♦ t❤❡s❡❧❡❝t❡❞ ♦♥❡✱ ❛t 3000 $✳❚❤❡r❡❢♦r❡ t❤❡ t♦t❛❧ ❝♦sts ✇♦✉❧❞ s✉♠ ✉♣ t♦ ❛❜♦✉t 45,300 $✳ ❚❤✐s ✐s ❤♦✇❡✈❡r ❥✉st ❛ ✈❡r②

❝♦❛rs❡ ❡st✐♠❛t✐♦♥✳ ❆❞❞✐t✐♦♥❛❧❧②✱ s❡♥s♦rs t♦ ♠❡❛s✉r❡ t❤❡ ♣r❡ss✉r❡ ♦r t❤❡ t❡♠♣❡r❛t✉r❡ ❢♦r❡①❛♠♣❧❡ ✇❡r❡ ♥♦t ❝♦♥s✐❞❡r❡❞ ②❡t✳

✹✳✽ ❍❡❛t ♠❛♣

❉✉r✐♥❣ t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❞✐✛❡r❡♥t ♦♣t✐♦♥s ✇❡r❡ ❝♦♥s✐❞❡r❡❞ ❛♥❞ t❤❡✧r❡s✉❧t✧ ✐s ✐♥ t❤❡ ❡♥❞ ♠♦r❡ ❛ r❡❝♦♠♠❡♥❞❛t✐♦♥ t❤❛♥ t❤❡ ♦♥❧② ♣♦ss✐❜❧❡ ❞❡s✐❣♥✳ ❚❤❡ ✜♥❛❧s♣❡❝✐✜❝❛t✐♦♥s ❢♦r t❤❡ ❝❤♦s❡♥ ❞❡s✐❣♥ ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡ ❆✳✶ ✐♥ t❤❡ ❆♣♣❡♥❞✐①✳ ❚♦s❤♦✇ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ s♦♠❡ ❝❤❛♥❣❡s ✐♥ ♣❛r❛♠❡t❡rs✱ ❛ ❤❡❛t ♠❛♣ ✇❛s ❝r❡❛t❡❞ t❤❛t ✐s♣r❡s❡♥t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✻✳ ❚❤❡ ❤❡❛t ♠❛♣ ♣r❡s❡♥ts t❤❡ q✉❛❧✐t❛t✐✈❡ ✐♥✢✉❡♥❝❡ ♦❢ ❛ ❝❤❛♥❣❡♦❢ s❡✈❡r❛❧ ♣❛r❛♠❡t❡r✳ ❊✈❡r② ❝❤❛♥❣❡ ✐♥ t❤❡ ♣❛r❛♠❡t❡r t❤❛t ❧❡❛❞s t♦ ❛♥ ✐♥❝r❡❛s❡ ✐♥ s✐③❡✱

♣❛r❛♠❡t❡r ♦❢ ❝❤❛♥❣❡ ❧❡♥❣t❤ ❞✐❛♠❡t❡r ∆pT ❢❛♥ ♣♦✇❡r ❝♦♦❧✐♥❣ ∆u ∆T

❝✉rr❡♥t ❞❡s✐❣♥ ✵ ✵ ✵ ✵ ✵ ✵ ✵❝❤♦r❞ ❧❡♥❣t❤ ✰✰ ✰ ✰ ✰ ✰✰ ✲ ✲

❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ✰ ✰ ✰ ✰ ✰✰ ✲ ✲

✇✐❞t❤ ✰✰ ✰ ✰ ✰ ✰✰ ✲ ✲

s♣❡❡❞ ✵ ✵ ✰✰ ✰✰ ✰✰ ✰✰ ✰✰

❆❘ ❞✐✛✉s❡r ✰✰ ✵ ✲ ✲ ✵ ✵ ✵❆❘ ♥♦③③❧❡ ✰ ✰ ✰ ✰ ✵ ✵ ✲ ✲

Tdrop,0 ✵ ✵ ✵ ✵ ✰ ✵ ✰

❛✐r t❡♠♣❡r❛t✉r❡ ✵ ✵ ✵ ✵ ✲ ✲ ✵ ✲

❚❛❜❧❡ ✹✳✻✿ ■♠♣❛❝t ♦❢ t❤❡ ✐♥❝r❡❛s❡ ♦❢ ❞✐✛❡r❡♥t ♣❛r❛♠❡t❡rs ♦♥ t❤❡ s✐③❡✱ t❤❡ t♦t❛❧ ♣r❡ss✉r❡❧♦ss❡s ❛♥❞ t❤❡ ♥❡❝❡ss❛r② ❢❛♥ ❛♥❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ ❛s ✇❡❧❧❛s ♦♥ t❤❡ ✜♥❛❧ ❞r♦♣❧❡t ❞❡✈✐❛t✐♦♥s ✐♥ t❡♠♣❡r❛t✉r❡ ❛♥❞ ✈❡❧♦❝✐t②✳ Tdrop,0 ✐s ✉s❡❞❢♦r t❤❡ ✐♥✐t✐❛❧ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡✳ ●r❡❡♥ ❝♦❧♦r ✐♥❞✐❝❛t❡ ♣♦s✐t✐✈❡ ❝❤❛♥❣❡s✱ r❡❞♥❡❣❛t✐✈❡ ❝❤❛♥❣❡s✳

✺✻

✹ ❘❡s✉❧ts

t②♣✐❝❛❧❧② ❧❡❛❞s t♦ s♠❛❧❧❡r ✜♥❛❧ ❞❡✈✐❛t✐♦♥s ✐♥ ❞r♦♣❧❡t t❡♠♣❡r❛t✉r❡ ❛♥❞ ✈❡❧♦❝✐t②✱ ❜✉t ❛❧s♦t♦ ❤✐❣❤❡r ❢❛♥ ❛♥❞ ❝♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts✳ ❆♥ ❡①❝❡♣t✐♦♥ ✐s t❤❡ ❛r❡❛ r❛t✐♦ ♦❢ t❤❡ ❞✐✛✉s❡rt❤❛t ❞❡❝r❡❛s❡s t❤❡ ❢❛♥ ❛♥❞ ❝♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts ❜❡❝❛✉s❡ ❛ ❤✐❣❤❡r ❛r❡❛ r❛t✐♦ ❧❡❛❞s t♦❢❡✇❡r ♣r❡ss✉r❡ ❧♦ss❡s ❛t t❤❡ ❡①✐t ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❍✐❣❤❡r ❛✐r s♣❡❡❞s ✐♥❝r❡❛s❡ ❡✈❡r②❛s♣❡❝t ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ s✐❣♥✐✜❝❛♥t❧②✳

✹✳✾ ❈❋❉ s✐♠✉❧❛t✐♦♥s

❆ ❧♦t ♦❢ t❤❡ ❡q✉❛t✐♦♥s ✉s❡❞ ❢♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥s ❛r❡ ❡✐t❤❡r ❡♠♣✐r✐❝❛❧❧② ♦r ✉s❡ ❛ss✉♠♣t✐♦♥st❤❛t ❝❛♥ ♥♦t ❛❧✇❛②s ❜❡ ❢✉❧❧② ❢✉❧✜❧❧❡❞✳ ❆❧s♦ s♦♠❡ ❜❛s✐❝ r✉❧❡s ♦❢ t❤✉♠❜ ✇❡r❡ ❝♦♥s✐❞❡r❡❞✇❤✐❧❡ ❞❡s✐❣♥✐♥❣ t❤❡ ❝♦♠♣♦♥❡♥ts✳ ❆s ❛ ✜rst ✐♠♣r❡ss✐♦♥ ♦❢ ✇❤❡t❤❡r t❤❡ ❞❡s✐❣♥ ♠✐❣❤t ❛❝t ❛s❝❛❧❝✉❧❛t❡❞✱ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❛r❡ ❤❡❧♣❢✉❧✳ ❈❋❉ r❡s✉❧ts ❢♦r t✇♦ ❞✐✛❡r❡♥t t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s✇❡r❡ ♣r♦❞✉❝❡❞ ✐♥ ✸❉ ❜② ❘✐❝❤❛r❞ ❍❛♥♥ ✇✐t❤ ❋❊◆❙❆P✲■❈❊✳ ❋❊◆❙❆P✲■❈❊ ✐s ❛ ♣❛rt ♦❢t❤❡ ❆♥s②s ❋❧✉✐❞ ❈❋❉ ♣r♦❣r❛♠✳ ■t ✐s s♣❡❝✐❛❧❧② ❞❡s✐❣♥❡❞ ❢♦r ✐♥✲✢✐❣❤t ✐❝✐♥❣ s✐♠✉❧❛t✐♦♥s✐♥ ✸❉✳ ❚❤❡ ✉s❡❞ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s ✇❡r❡ t❤❡ ❙♣❛❧❛rt✲❆❧❧♠❛r❛s ♠♦❞❡❧ ❛♥❞ t❤❡ ▼❡♥t❡rk − ω ❙❙❚✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ✇✐t❤ t❤❡ ❙♣❛❧❛rt✲❆❧❧♠❛r❛s ♠♦❞❡❧ ❛r❡ ♣r❡s❡♥t❡❞ ❤❡r❡✳❋♦r t❤❡ ❡❛s❡ ♦❢ t❤❡ s✐♠✉❧❛t✐♦♥✱ ❥✉st ♦♥❡ q✉❛rt❡r ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇❛s s✐♠✉❧❛t❡❞✳ ❚❤✐s✐s ♣♦ss✐❜❧❡ ❜❡❝❛✉s❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐s s②♠♠❡tr✐❝✳❋✐❣✉r❡ ✹✳✷✵ s❤♦✇s t❤❡ ✈❡❧♦❝✐t② ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❛✐r ♦✈❡r t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞

t✉♥♥❡❧✳ ❆s t❤❡ ❛✐r ✈❡❧♦❝✐t② ❛t t❤❡ t❡st s❡❝t✐♦♥ ✐s ❛❧♠♦st 35m s−1 t❤❡ ✐♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s❛r❡ ✈❛❧✐❞✳

❋✐❣✉r❡ ✹✳✷✵✿ P❧♦t ♦❢ t❤❡ ✈❡❧♦❝✐t② ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥✳

❆♥ ✐♠♣♦rt❛♥t q✉❡st✐♦♥ ✐s t♦ ❦♥♦✇ ✇❤❡t❤❡r s❡♣❛r❛t✐♦♥ ♦❝❝✉rs ✐♥s✐❞❡ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳❚❤✐s ✇♦✉❧❞ ❧❡❛❞ t♦ ✐♥❝r❡❛s❡❞ ♣r❡ss✉r❡ ❧♦ss❡s ❛♥❞ ❞❡❝r❡❛s❡❞ ✢♦✇ q✉❛❧✐t②✳ ❚❤❡r❡❢♦r❡ t❤❡q✉❛❧✐t② ♦❢ t❤❡ r❡s✉❧ts ✇♦✉❧❞ ❜❡ ✇♦rs❡✳ ❆ ❣♦♦❞ ✐♥❞✐❝❛t♦r ♦❢ s❡♣❛r❛t✐♦♥ ✐s ❛ s✉r❢❛❝❡ str❡ss♦❢ ✵✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ s✉r❢❛❝❡ str❡ss ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ✇❛❧❧✲♥♦r♠❛❧ ❣r❛❞✐❡♥t ♦❢t❤❡ ✈❡❧♦❝✐t②✳ ❆s ❡①♣❧❛✐♥❡❞ ✐♥ s✉❜s❡❝t✐♦♥ ✷✳✷✳✶✱ t❤❡ ♣♦s✐t✐♦♥ ✇❤❡r❡ t❤✐s ❣r❛❞✐❡♥t ❜❡❝♦♠❡s③❡r♦ ✐s t❤❡ ♣♦✐♥t ♦❢ s❡♣❛r❛t✐♦♥✳ ❚❤❡r❡❢♦r❡ t❤❡ ❈❋❉ r❡s✉❧ts ✇❡r❡ ❝♦♥tr♦❧❧❡❞ ❢♦r ❛r❡❛s ✇✐t❤s✉r❢❛❝❡ str❡ss❡s ♦❢ ✵✳ ❆s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ✹✳✷✶ s❡♣❛r❛t✐♦♥ ♠✐❣❤t ❡s♣❡❝✐❛❧❧② ♦❝❝✉r ✐♥ t❤❡❝♦r♥❡r ♦❢ t❤❡ ♥♦③③❧❡ ❛♥❞ ♦❢ t❤❡ ❞✐✛✉s❡r✱ ❜✉t ❛❧s♦ ✐♥ t❤❡ ❝♦r♥❡r ♦❢ t❤❡ t❡st s❡❝t✐♦♥✳❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✇❡r❡ ❝❛❧❝✉❧❛t❡❞✳ ❚♦ ❛♥❛❧②③❡ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥s✐❞❡

t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✱ t❤❡ t♦t❛❧ ♣r❡ss✉r❡ ✐s ❛✈❡r❛❣❡❞ ♦✈❡r t❤❡ ♣❧❛♥❡ ♦❢ ✐♥t❡r❡st ❛♥❞ t❤❡♥❝♦♠♣❛r❡❞ t♦ ♣r❡✈✐♦✉s ♣♦s✐t✐♦♥s✳ ❚❤❡ r❡s✉❧ts ❢♦r ❜♦t❤ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s ❛r❡ s❤♦✇♥ ✐♥❚❛❜❧❡ ✹✳✼✳ ❚❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s ✐♥❞✐❝❛t❡ ♠✉❝❤ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s ❢♦r ❡✈❡r② ❝♦♠♣♦✲♥❡♥t t❤❛♥ t❤❡ ❝❛❧❝✉❧❛t❡❞ ✈❛❧✉❡s✳ ❚❤❡ ♠♦st ♣r♦❜❛❜❧❡ r❡❛s♦♥ ✐s t❤❛t t❤❡ s❡♣❛r❛t✐♦♥ ❛r❡❛s

✺✼

✹ ❘❡s✉❧ts

❋✐❣✉r❡ ✹✳✷✶✿ P❧♦t ♦❢ t❤❡ s❡♣❛r❛t✐♦♥ ③♦♥❡s ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥✳

❧❡❛❞ t♦ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s t❤❛♥ ❡①♣❡❝t❡❞✳ ■❢ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s t❤❛t ✇❡r❡ ❛❝❤✐❡✈❡❞✇✐t❤ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥ ❛r❡ ❝❧♦s❡r t♦ t❤❡ r❡❛❧✐t② t❤❛♥ t❤❡ ✈❛❧✉❡s ❝❛❧❝✉❧❛t❡❞ ✐♥ s✉❜s❡❝✲t✐♦♥ ✹✳✺✱ ❛ ♠♦r❡ ♣♦✇❡r❢✉❧ ❢❛♥ ✇♦✉❧❞ ❜❡ ♥❡❡❞❡❞✳ ❚❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡❈❋❉ s✐♠✉❧❛t✐♦♥ ❛r❡ ❛❜♦✉t t❤r❡❡ t✐♠❡s ❤✐❣❤❡r t❤❛♥ t❤❡ ♦♥❡s ❝❛❧❝✉❧❛t❡❞ ✐♥ s✉❜s❡❝t✐♦♥✹✳✺✳ ❚❤❡r❡❢♦r❡ ❛ ❢❛♥ ✇♦✉❧❞ ❤❛✈❡ t♦ ❞❡❧✐✈❡r ❛t ❧❡❛st ❛ ♣r❡ss✉r❡ r✐s❡ ♦❢ ❛❜♦✉t 1000Pa✳❚❤❡ ✹✸❲✼✶✽ ❜② ❆❡r♦✈❡♥t ❬✻✶❪ ❤❛s t❤❡ s❛♠❡ ❞✐♠❡♥s✐♦♥s ❛s t❤❡ ❢❛♥ s❡❧❡❝t❡❞ ♣r❡✈✐♦✉s❧②❛♥❞ ✇♦✉❧❞ ❜❡ ❛❜❧❡ t♦ ❞❡❧✐✈❡r t❤❡ ♥❡❝❡ss❛r② ♣r❡ss✉r❡ r✐s❡ ✇✐t❤ ❛ ♣♦✇❡r ♥❡❡❞ ♦❢ 14.71 kW✇❤✐❝❤ ✐s ❛♥ ✐♥❝r❡❛s❡ ♦❢ 83%✳ ❚❤❡r❡❢♦r❡ ❛❧s♦ t❤❡ ❝♦♦❧✐♥❣ r❡q✉✐r❡♠❡♥ts ✇♦✉❧❞ ✐♥❝r❡❛s❡ t♦27.03 kW ❝♦♠♣❛r❡❞ t♦ 20.23 kW ❜❡❢♦r❡✳

❝♦♠♣♦♥❡♥t ❙♣❛❧❛rt✲❆❧❧♠❛r❛s ▼❡♥t❡r k − ω ❙❙❚ ❝❛❧❝✉❧❛t❡❞ ✈❛❧✉❡s

t❡st s❡❝t✐♦♥ 33 27 13♥♦③③❧❡ 60 92 12

s❡tt❧✐♥❣ ❛r❡❛ 2 1 0❞✐✛✉s❡r 125 156 48

t♦t❛❧ ❧♦ss❡s 220 276 73

❚❛❜❧❡ ✹✳✼✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❛♥❞ t❤❡✈❛❧✉❡s ❝❛❧❝✉❧❛t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✺✳ ❆❧❧ ✈❛❧✉❡s ✐♥ Pa✳

❚❤❡ r❡s✉❧ts ✇✐t❤ t❤❡ ▼❡♥t❡r k − ω ❙❙❚ ♠♦❞❡❧ ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❆♣♣❡♥❞✐① ❆✳✹✳ ❚❤❡✈❡❧♦❝✐t② ♣❧♦t ✐s ❛❧♠♦st ❡①❛❝t❧② t❤❡ s❛♠❡ ❛s ❢♦r t❤❡ ❙♣❛❧❛rt✲❆❧❧♠❛r❛s ♠♦❞❡❧✳ ❚❤❡ ♣❧♦t ♦❢t❤❡ s❡♣❛r❛t✐♦♥ ❛r❡❛ s❤♦✇s ♠♦r❡ s❡♣❛r❛t✐♦♥ ✐♥ t❤❡ r❡❣✐♦♥ ♦❢ t❤❡ ❞✐✛✉s❡r ❢♦r t❤❡ ▼❡♥t❡rk − ω ❙❙❚ ♠♦❞❡❧✱ ❜✉t ♦✈❡r❛❧❧ ❛ ❝♦♠♣❛r❛❜❧❡ r❡s✉❧t✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ t❤❡ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧t❤❡r❡❢♦r❡ ❥✉st ❤❛s ❛ ♠✐♥♦r ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s✳ ❇♦t❤ r❡s✉❧tss❤♦✇❡❞ ♣♦ss✐❜❧❡ s❡♣❛r❛t✐♦♥ ✐♥ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❛s ✇❡❧❧ ❛s ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s t❤❛♥❝❛❧❝✉❧❛t❡❞ ❜❡❢♦r❡✳ ❚❤❡ ❡①♣❧❛♥❛t✐♦♥ ❢♦r t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ❈❋❉ r❡s✉❧ts ❛♥❞ t❤❡❝❛❧❝✉❧❛t✐♦♥s ❝❛♥ ❜❡ ❝❛✉s❡❞ ❜② ❜♦t❤ s✐❞❡s✳ ❈❋❉ r❡s✉❧ts✱ ❡s♣❡❝✐❛❧❧② ✇✐t❤ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s✱tr② t♦ r❡♣❧✐❝❛t❡ t❤❡ r❡❛❧✐t②✱ ❜✉t ✉♥t✐❧ t♦❞❛② t❤❡r❡ ❛r❡ s❤♦rt❝♦♠✐♥❣s✳ ❚❤❡ ❝❛❧❝✉❧❛t✐♦♥s ❝❛♥❛❧s♦ ❧❡❛❞ t♦ ✇r♦♥❣ r❡s✉❧ts✱ ❛s s♦♠❡ ❛ss✉♠♣t✐♦♥s ♠✐❣❤t ❤❛✈❡ ❜❡❡♥ ✇r♦♥❣ ❛♥❞ ♠❛♥②❡q✉❛t✐♦♥s ✇❡r❡ ❞❡✈❡❧♦♣❡❞ ❡♠♣✐r✐❝❛❧❧② r❛t❤❡r t❤❛♥ ❜❡✐♥❣ str✐❝t❧② ♣❤②s✐❝❛❧✳

✺✽

✹ ❘❡s✉❧ts

✹✳✶✵ ❙♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧

❚❤❡ ◆❚◆❯ ♦✇♥s ❛ s♠❛❧❧ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r✳ ❚❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ t❤✐s ❝❤❛♠❜❡r ❛r❡ ❛♣✲♣r♦①✐♠❛t❡❧② 3.8m ① 3.3m✳ ❍♦✇❡✈❡r✱ ♥♦t ❡✈❡♥ t❤❡ ✇❤♦❧❡ s♣❛❝❡ ❝❛♥ ❜❡ ✉s❡❞✱ ❛s s♦♠❡✐♥str✉♠❡♥ts ❛r❡ st♦r❡❞ ✐♥s✐❞❡ t❤✐s r♦♦♠✳ ◆❡✈❡rt❤❡❧❡ss✱ t❤❡ ❛✈❛✐❧❛❜✐❧✐t② ♦❢ t❤✐s ❝♦♦❧✐♥❣❝❤❛♠❜❡r ❧❡❛❞ t♦ t❤❡ t❤♦✉❣❤t ♦❢ ❞❡s✐❣♥✐♥❣ ❛ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ t❤❛t ✇♦✉❧❞ ✜t ✐♥s✐❞❡t❤✐s ❝❤❛♠❜❡r ❜✉t ♦❢ ❝♦✉rs❡ ❤❛s s❤♦rt❝♦♠✐♥❣s ❝♦♠♣❛r❡❞ t♦ t❤❡ ❜✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧❞❡s✐❣♥✳❆s ❛ ✜rst st❡♣✱ ♥❡✇ r❡q✉✐r❡♠❡♥ts ❤❛✈❡ t♦ ❜❡ ❢♦✉♥❞✳ ❚❤❡② ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❚❛❜❧❡

✹✳✽✳ ❆s ♣r❡s❡♥t❡❞ ❡❛r❧✐❡r✱ t❤❡ s❝❛❧✐♥❣ ♦❢ ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ✐s ❞✐✣❝✉❧t✳ ❚❤✐s ✐s ✇❤②t❤❡ r❡q✉✐r❡♠❡♥ts ❝❛♥♥♦t ❜❡ r❡❞✉❝❡❞ ❛♥②♠♦r❡ ✇✐t❤♦✉t r❡❞✉❝✐♥❣ t❤❡ ✉s❛❜✐❧✐t② ❞r❛st✐❝❛❧❧②✳❖♥❡ ❝❤❛♥❣❡❞ s♣❡❝✐✜❝❛t✐♦♥ ❛r✐s❡s ❜❡❝❛✉s❡ t❤❡ ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r ❝❛♥ ❥✉st ❜❡ ❝♦♦❧❡❞ ❞♦✇♥t♦ −10 ➦C✳

r❡q✉✐r❡♠❡♥t ♦❧❞ ✈❛❧✉❡ ♥❡✇ ✈❛❧✉❡

❝❤♦r❞ ❧❡♥❣t❤ 0.4m 0.3m♠❛①✐♠✉♠ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ 8◦ 4◦

✉♥✐♠♣❡❞❡❞ ✇✐❞t❤ ♦❢ t❤❡ t❡st s❡❝t✐♦♥ 0.30m 0.18ms♣❡❡❞ 35m s−1 25m s−1

❢❛♥ ❞✉❝t ❧❡♥❣t❤ 0.10m 0.05m❛✐r t❡♠♣❡r❛t✉r❡ −15 ➦C −10 ➦C

❚❛❜❧❡ ✹✳✽✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ✭♦❧❞✮ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ❜✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡✭♥❡✇✮ s✐♠♣❧✐✜❡❞ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

❍♦✇❡✈❡r✱ ✐t ✇❛s ❛❣r❡❡❞ t♦ ❜❡ ❛❧❧ r✐❣❤t ✇✐t❤ ✇♦rs❡ ✢♦✇ ❝♦♥❞✐t✐♦♥s ✐♥s✐❞❡ t❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧✱ ❛s t❤❡ s♠❛❧❧ ✇✐♥❞ t✉♥♥❡❧ s❤♦✉❧❞ ♠❛✐♥❧② ❜❡ ❢♦r t❡st✐♥❣ ❡q✉✐♣♠❡♥t ❛♥❞❣❛✐♥✐♥❣ ❡①♣❡r✐❡♥❝❡✳ ❚❤❡r❡❢♦r❡ ❛❧s♦ s❧✐❣❤t❧② ❧❛r❣❡r ❞❡✈✐❛t✐♦♥s ♦❢ t❤❡ ❞r♦♣❧❡t ✈❡❧♦❝✐t② ❛♥❞t❡♠♣❡r❛t✉r❡ ❝❛♥ ❜❡ ❛❝❝❡♣t❡❞✳❆s t❤❡ ❞✐✛✉s❡r ❤❛s ❛ ❤✉❣❡ s❤❛r❡ ♦❢ t❤❡ ♦✈❡r❛❧❧ ❧❡♥❣t❤ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡

s♣❛❝❡ ✐s t✐❣❤t ✐♥s✐❞❡ t❤✐s ❝♦♦❧✐♥❣ ❝❤❛♠❜❡r✱ ✐t ✇❛s ❡❛r❧② ❞❡❝✐❞❡❞ t❤❛t t❤❡ ❛r❡❛ r❛t✐♦ ♦❢ t❤❡❞✐✛✉s❡r ❤❛s t♦ ❜❡ ❧♦✇❡r ❢♦r t❤✐s s♠❛❧❧ t✉♥♥❡❧ t❤❛♥ ❢♦r t❤❡ ❜✐❣ ♦♥❡✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ✇✐t❤❛ ❧♦✇❡r ❛r❡❛ r❛t✐♦ ❛❧s♦ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❞✐✛✉s❡r ✐s s❤♦rt❡r✳ ❚❤❡r❡❢♦r❡ ❛❧❧ ❝❛❧❝✉❧❛t✐♦♥s✇❡r❡ ❞♦♥❡ ✇✐t❤ ❛♥ ❛r❡❛ r❛t✐♦ ♦❢ ✷ ❢♦r t❤❡ ❞✐✛✉s❡r✳ ❆❧❧ t❤❡ ♦t❤❡r ✈❛❧✉❡s ✇❡r❡ ❝❛❧❝✉❧❛t❡❞

❱❡rs✐♦♥ ❞✐✛✉s❡r ❆❘ ♥♦③③❧❡ ❆❘ ■❲❚ ❧❡♥❣t❤ [m] ♣r❡ss✉r❡ ❧♦ss❡s [Pa]

✶ 2 9 4.22 216✷ 1.5 9 3.70 291✸ 1 9 3.10 517✹ 2 6 3.76 201✺ 1.5 6 3.24 277

❚❛❜❧❡ ✹✳✾✿ ❈♦♠♣❛r✐s♦♥ ♦❢ ❞✐✛❡r❡♥t ♦♣t✐♦♥s ❢♦r ❛ s❤♦rt❡r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✭■❲❚✮✳

✺✾

✹ ❘❡s✉❧ts

❛s ❢♦r t❤❡ ❜✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❍♦✇❡✈❡r✱ t❤✐s ❧❡❛❞ t♦ ❛ t♦♦ ❧♦♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❙♦♠❡❝♦♥s✐❞❡r❛t✐♦♥s ✇❡r❡ ♠❛❞❡ ❛❜♦✉t ❤♦✇ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❧❡♥❣t❤ ❝♦✉❧❞ ❜❡ r❡❞✉❝❡❞ ❡✈❡♥❢✉rt❤❡r✳ ❚❤❡② ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✾✳ ❱❡rs✐♦♥ ✶ ✐s t❤❡ ✈❡rs✐♦♥ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡✈❛❧✉❡s ❛s ❢♦r t❤❡ ❜✐❣ t✉♥♥❡❧ ❡①❝❡♣t ❢♦r t❤❡ ❛r❡❛ r❛t✐♦ ♦❢ ✷ ♦❢ t❤❡ ❞✐✛✉s❡r✳ ❱❡rs✐♦♥ ✷ ✐s❛ ✈❡rs✐♦♥ ✇✐t❤ ❛♥ ❡✈❡♥ ❧♦✇❡r ❛r❡❛ r❛t✐♦ ♦❢ t❤❡ ❞✐✛✉s❡r✱ ✇❤✐❧❡ ✈❡rs✐♦♥ ✸ ✐s ❛ ❝❛❧❝✉❧❛t✐♦♥✇✐t❤♦✉t ❛♥② ❞✐✛✉s❡r ❛t ❛❧❧✳ ❱❡rs✐♦♥s ✹ ❛♥❞ ✺ ❛r❡ ❝❛❧❝✉❧❛t✐♦♥s ✇✐t❤ ❛ s♠❛❧❧❡r ❛r❡❛ r❛t✐♦♦❢ t❤❡ ♥♦③③❧❡✱ ♦♥❝❡ ✇✐t❤ ❛ ❤✐❣❤ ❛♥❞ ♦♥❝❡ ✇✐t❤ ❛ ❧♦✇ ❛r❡❛ r❛t✐♦ ♦❢ t❤❡ ❞✐✛✉s❡r✳■t ✐s ♦❜✈✐♦✉s t❤❛t ❧♦✇❡r ❛r❡❛ r❛t✐♦s r❡❞✉❝❡ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s✐❣♥✐❢✲

✐❝❛♥t❧②✳ ❍♦✇❡✈❡r✱ r❡❞✉❝✐♥❣ t❤❡ ❛r❡❛ r❛t✐♦ ♦❢ t❤❡ ❞✐✛✉s❡r ❧❡❛❞s t♦ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s❛s t❤❡ ❦✐♥❡t✐❝ ❡♥❡r❣② ♦❢ t❤❡ ✢♦✇ ❛t t❤❡ ❡①✐t ✐s ❤✐❣❤❡r✳ ❚❤❡r❡❢♦r❡ t❤❡ ✈❡rs✐♦♥ ✇✐t❤♦✉t ❛❞✐✛✉s❡r ✐s ♥♦t ✉♥❞❡r ❢✉rt❤❡r ❝♦♥s✐❞❡r❛t✐♦♥✳ ❚❤✐s ✐s ✇❤② ✈❡rs✐♦♥ ✺ ✇❛s ❝❤♦s❡♥ ✐♥ t❤❡ ❡♥❞✳❚❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ t❤❡ s✐♥❣❧❡ ❝♦♠♣♦♥❡♥ts ❢♦r t❤✐s ❝❛s❡ ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❚❛❜❧❡ ✹✳✶✵✳

❈♦♠♣♦♥❡♥t ▲❡♥❣t❤❬m❪ ❉✐♠❡♥s✐♦♥s❬m❪

■♥❧❡t ❖✉t❧❡t

❢❛♥ ❞✉❝t 0.66 0.61 0.61✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r 0.16 0.61 0.70 ① 0.70 ✭0.70✮

s❡tt❧✐♥❣ ❛r❡❛ 0.56 0.70 ① 0.70 ✭0.70✮ 0.70 ① 0.70 ✭0.70✮♥♦③③❧❡ 0.79 0.70 ① 0.70 ✭0.70✮ 0.24 ① 0.34 ✭0.28✮

t❡st s❡❝t✐♦♥ 0.47 0.24 ① 0.34 ✭0.28✮ 0.24 ① 0.34 ✭0.28✮❞✐✛✉s❡r 0.60 0.24 ① 0.34 ✭0.28✮ 0.30 ① 0.40 ✭0.34✮

✇✐♥❞ t✉♥♥❡❧ 3.24 ♠❛① 0.70 ① 0.70 ✭0.70✮

❚❛❜❧❡ ✹✳✶✵✿ ❉✐♠❡♥s✐♦♥s ♦❢ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❝♦♠♣♦♥❡♥ts✳ ❚✇♦ ✈❛❧✉❡s ❛r❡ ❣✐✈❡♥✐♥ t❤❡ ❞✐♠❡♥s✐♦♥s ❝♦❧✉♠♥ ✐❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ♦♥❡ ✈❛❧✉❡ ✐❢ t❤❡ s❡❝t✐♦♥✐s r♦✉♥❞✳ ■❢ t❤❡ s❡❝t✐♦♥ ✐s r❡❝t❛♥❣✉❧❛r✱ ❛❧s♦ t❤❡ ❤②❞r❛✉❧✐❝ ❞✐❛♠❡t❡r ✐s ❣✐✈❡♥✐♥ ❜r❛❝❦❡ts✳

❱❡rs✐♦♥ ■❲❚ ❧❡♥❣t❤ [m] t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss❡s [Pa]

❱❡rs✐♦♥ ✶ ✭❚❛❜❧❡ ✹✳✾✮ 4.22 216❝❤♦r❞ ❧❡♥❣t❤ 0.25m 3.82 192❛♥❣❧❡ ♦❢ ❛tt❛❝❦ 3◦ 3.98 199

✉♥✐♠♣❡❞❡❞ ✇✐❞t❤ 0.15m 3.94 197❛❧❧ ♦♣t✐♦♥s ❝♦♠❜✐♥❡❞ 3.44 182

❚❛❜❧❡ ✹✳✶✶✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❝❤❛♥❣❡❞ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ s❤♦rt❡r ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ♦♥ t❤❡ ♦✈❡r❛❧❧ ❧❡♥❣t❤ ❛♥❞ t❤❡ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss❡s✳

■t ✇❛s ❛❧s♦ ✉♥❞❡r ❝♦♥s✐❞❡r❛t✐♦♥ t♦ r❡❞✉❝❡ t❤❡ r❡q✉✐r❡♠❡♥ts✳ ❙♦♠❡ ❡①❛♠♣❧❡s ❛r❡ ❧✐st❡❞✐♥ ❚❛❜❧❡ ✹✳✶✶✳ ❲❤✐❧❡ ❛ r❡❞✉❝t✐♦♥ ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ✇♦✉❧❞ ❛❧s♦ ♣❧❛② ❛ r♦❧❡ t♦ r❡❞✉❝❡ t❤❡✇✐♥❞ t✉♥♥❡❧ ❧❡♥❣t❤✱ t❤❡ ✉s❛❜✐❧✐t② ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇♦✉❧❞ s✉✛❡r ❜❛❞❧②✳ ❚❤✐s ✐s ❞✉❡

✻✵

✹ ❘❡s✉❧ts

t♦ t❤❡ ♠❡♥t✐♦♥❡❞ ♣r♦❜❧❡♠s ✇✐t❤ t❤❡ s❝❛❧✐♥❣ ♦❢ r❡s✉❧ts✳ ❆s t❤❡ ♦♣t✐♦♥ ❡①♣❧❛✐♥❡❞ ❜❡❢♦r❡s❡❡♠s t♦ ❜❡ ❛❜❧❡ t♦ ❢✉❧✜❧❧ t❤❡ r❡q✉✐r❡♠❡♥ts ✉♥❞❡r t❤❡ s♣❛❝❡ ❧✐♠✐t❛t✐♦♥s ♥❡✈❡rt❤❡❧❡ss✱ ❛r❡❞✉❝t✐♦♥ ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ✇❛s s❦✐♣♣❡❞✳❚❤❡ ♠❛①✐♠✉♠ ▼❱❉ t❤❛t ❝❛♥ ❜❡ t❡st❡❞ ✇❛s ❛❧s♦ ❝❛❧❝✉❧❛t❡❞ ❢♦r t❤✐s s♠❛❧❧ ✇✐♥❞ t✉♥♥❡❧✳

■♥ ❋✐❣✉r❡ ✹✳✷✷✭❛✮ t❤❡ ✜♥❛❧ ✈❡❧♦❝✐t② ❞❡✈✐❛t✐♦♥ ❢♦r ❞r♦♣❧❡ts ♦❢ ❞✐✛❡r❡♥t s✐③❡s ✐s ❣✐✈❡♥✳ ■♥❋✐❣✉r❡ ✹✳✷✷✭❜✮ t❤❡ s❛♠❡ ✐s ❞♦♥❡ ❢♦r t❤❡ t❡♠♣❡r❛t✉r❡✳ ❲✐t❤ t❤❡ ❞❡s✐❣♥❡❞ s♠❛❧❧ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧✱ ❛ ♠❛①✐♠✉♠ ❞✐❛♠❡t❡r ♦❢ s❧✐❣❤t❧② ❛❜♦✈❡ 50µm ❝❛♥ ❜❡ t❡st❡❞✳ ❇② t❛❦✐♥❣ t❤❡▲❛♥❣♠✉✐r ❉ ❞✐str✐❜✉t✐♦♥✱ t❤❡ ▼❱❉ ♦❢ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❞✐str✐❜✉t✐♦♥ ✐s ❛❜♦✉t 23µm✳❲❤✐❧❡ t❤✐s ✐s ♠✉❝❤ ❧❡ss t❤❛♥ t❤❡ ❤✐❣❤❡st ▼❱❉ ❣✐✈❡♥ ✐♥ t❤❡ ❊❆❙❆ r❡q✉✐r❡♠❡♥ts✱ t❤❡ ▼❱❉✐s st✐❧❧ ❤✐❣❤ ❡♥♦✉❣❤ t♦ ❞♦ r❡❛s♦♥❛❜❧❡ ❡①♣❡r✐♠❡♥ts ✇✐t❤ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

0 20 40 60 80 100 120

droplet diameter [ m]

0

2

4

ve

locity

de

via

tio

n [

m/s

]

velocity deviation

maximum allowed deviation

✭❛✮ ❋✐♥❛❧ ✈❡❧♦❝✐t② ❞❡✈✐❛t✐♦♥s✳

0 20 40 60 80 100 120

droplet diameter [ m]

0

5

tem

pe

ratu

re

de

via

tio

n [

K]

temperature deviation

maximum allowed deviation

✭❜✮ ❋✐♥❛❧ t❡♠♣❡r❛t✉r❡ ❞❡✈✐❛t✐♦♥s✳

❋✐❣✉r❡ ✹✳✷✷✿ ❚❤❡ ✜♥❛❧ ❞❡✈✐❛t✐♦♥s ✐♥ ✈❡❧♦❝✐t② ❛♥❞ t❡♠♣❡r❛t✉r❡ ❢♦r ❞r♦♣❧❡ts ✇✐t❤ ❞✐✛❡r✲❡♥t ❞✐❛♠❡t❡rs ❛♥❞ ❢♦r ❞✐✛❡r❡♥t ✇❛t❡r ♣r❡ss✉r❡s ✐♥s✐❞❡ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧✳

❚❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ❢♦r t❤❡ s✐♥❣❧❡ ❝♦♠♣♦♥❡♥ts ❛♥❞ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐♥ t♦t❛❧ ❝❛♥ ❜❡❝❛❧❝✉❧❛t❡❞ ✐♥ t❤❡ s❛♠❡ ✇❛② ❛s ❞♦♥❡ ❢♦r t❤❡ ❜✐❣ ♦♥❡✳ ❚❤❡ r❡s✉❧ts ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❚❛❜❧❡

❝♦♠♣♦♥❡♥t ❡q✉❛t✐♦♥ ❑ ♣r❡ss✉r❡ ❧♦ss [Pa]

t❡st s❡❝t✐♦♥ ✸✳✷✽ 0.022 9.40t❡st ♦❜❥❡❝t ✸✳✹✼ 0.038 16.23♥♦③③❧❡ ✸✳✸✶ 0.013 5.55

s❡tt❧✐♥❣ ❛r❡❛ ✸✳✷✽ 0.012 0.14s♣r❛② s②st❡♠ ✸✳✹✼ 0.205 2.44

s❝r❡❡♥ ✸✳✹✽ 1.198 14.24❤♦♥❡②❝♦♠❜s ✸✳✹✹ 0.523 6.22

✇✐❞❡✲❛♥❣❧❡✲❞✐✛✉s❡r ✸✳✺✶ 0.594 19.82❢❛♥ ❞✉❝t ✸✳✷✽ 0.015 0.50❞✐✛✉s❡r ✸✳✸✷ 0.028 11.96

❡①✐t ❧♦ss❡s ✸✳✹✸ 1.001 190.13

t♦t❛❧ ❧♦ss❡s 276.63

❚❛❜❧❡ ✹✳✶✷✿ ❖✈❡r✈✐❡✇ ♦✈❡r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ ❡✈❡r② ❝♦♠♣♦♥❡♥t ❛♥❞ ✐♥ t♦t❛❧ ❢♦r t❤❡s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

✻✶

✹ ❘❡s✉❧ts

✹✳✶✷✳ ❚♦ ❝♦✉♥t❡r t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s✱ t❤❡ ❢❛♥ ♠✉st ❜❡ ❛❜❧❡ t♦ ❞❡❧✐✈❡r ❛ ♣r❡ss✉r❡ r✐s❡ ♦❢❛❜♦✉t 415Pa t♦ ❤❛✈❡ ❛ s❛❢❡t② ♠❛r❣✐♥ ❢♦r s❤♦rt❝♦♠✐♥❣s ✐♥ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s✳ ❆❞❞✐t✐♦♥❛❧❧②✱t❤❡ ❢❛♥ ✇✐❧❧ s❡❡ ❛ ✈♦❧✉♠❡ ✢♦✇ ♦❢ ❛❜♦✉t 2.0m3 s−1✳ ❆♥ ❡①❛♠♣❧❡ ♦❢ ❛ ❢❛♥ t❤❛t ♠✐❣❤t ❜❡s✉✐t❛❜❧❡ t♦ ❢✉❧✜❧❧ t❤❡s❡ r❡q✉✐r❡♠❡♥ts ✐s t❤❡ ♠♦❞❡❧ ✷✹❲✼✷✷ ❜② ❆❡r♦✈❡♥t ❬✻✶❪✳ ■t ♦✛❡rs ❛♣r❡ss✉r❡ r✐s❡ ♦❢ ❛❜♦✉t 436Pa ❢♦r ❛ ✈♦❧✉♠❡ ✢♦✇ ♦❢ 2.1m3 s−1✳ ■❢ t❤❡ ❢❛♥ ✐s r✉♥ ✉♥❞❡rt❤❡s❡ ♠❛①✐♠✉♠ ❝♦♥❞✐t✐♦♥s✱ ✐t ✇✐❧❧ ♣r♦❞✉❝❡ ❛ ❤❡❛t ♦❢ 1.33 kW✳❆❧t❤♦✉❣❤ ♥♦ ❞❛t❛ ✐s ❣✐✈❡♥ ❢♦r t❤❡ ❝♦♦❧✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ❝❧✐♠❛t❡ ❝❤❛♠❜❡r ❛t t❤❡ ◆❚◆❯✱

t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ✐s ❝❛❧❝✉❧❛t❡❞✳ ❚❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ✐s ♣❧♦tt❡❞ ✐♥❋✐❣✉r❡ ✹✳✷✸✳ ❚❤❡ ♠❛①✐♠✉♠ ❝♦♦❧✐♥❣ ♣♦✇❡r ♥❡❝❡ss❛r② ❢♦r t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✐s 3.942 kW✳ ❆❧❧ s♣❡❝✐✜❝❛t✐♦♥s ❢♦r t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛r❡ ❛❧s♦ s✉♠♠❛r✐③❡❞ ✐♥❚❛❜❧❡ ❆✳✶ ✐♥ t❤❡ ❆♣♣❡♥❞✐①✳

012345

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3heat [kW] LWC [g/m^3]fan power latent heat sensible heat❋✐❣✉r❡ ✹✳✷✸✿ ❘❡q✉✐r❡❞ ❝♦♦❧✐♥❣ ♣♦✇❡r ❢♦r t❤❡ s♠❛❧❧ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❞✐✛❡r❡♥t ▲❲❈s ❛t ❛♥

❛✐r t❡♠♣❡r❛t✉r❡ ♦❢ −10 ➦C✳

✻✷

✺ ❉✐s❝✉ss✐♦♥

✺✳✶ ❈♦♥❝❧✉s✐♦♥ ❛♥❞ ❞✐s❝✉ss✐♦♥

❚❤❡ ✉s❛❣❡ ♦❢ ❯❆❱s ❝❛♥ ❜❡ s✐❣♥✐✜❝❛♥t❧② ✐♥✢✉❡♥❝❡❞ ❜② ✐❝❡ ❛❝❝r❡t✐♦♥s ♦♥ t❤❡ ❛✐r❝r❛❢t✳ ❚♦✐♥❝r❡❛s❡ t❤❡ ✉s❛❜✐❧✐t②✱ s②st❡♠s ♥❡❡❞ t♦ ❜❡ ❞❡s✐❣♥❡❞ t❤❛t ♣r♦t❡❝t t❤❡ ❛✐r❝r❛❢t ✐♥ ✐❝✐♥❣❝♦♥❞✐t✐♦♥s✳ ❚❤❡r❡❢♦r❡ ❛ ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ♣❤②s✐❝s ❜❡❤✐♥❞ t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥s ✐s♥❡❝❡ss❛r②✳ ❚♦ ❞♦ ❡①♣❡r✐♠❡♥ts✱ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ♦❢t❡♥ ✉s❡❞ ❛s t❡st ❢❛❝✐❧✐t✐❡s✳ ■❝✐♥❣✇✐♥❞ t✉♥♥❡❧s ❛❧s♦ ♦✛❡r t❤❡ ♦♣♣♦rt✉♥✐t② t♦ t❡st ❞❡s✐❣♥❡❞ ✐❝❡ ♣r♦t❡❝t✐♦♥ s②st❡♠s ✉♥❞❡rr❡❛❧✐st✐❝ ❝♦♥❞✐t✐♦♥s✳ ❚♦❞❛② t❤❡ ♥✉♠❜❡r ♦❢ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ✐s s♠❛❧❧✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ♠♦st♦❢ t❤❡ ❡①✐st✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❛r❡ ❞❡s✐❣♥❡❞ ❢♦r ♠❛♥♥❡❞ ❛✐r❝r❛❢t ❛♥❞ ♥♦t s✉✐t❛❜❧❡ ❢♦r❯❆❱s✳ ❚❤✐s ✐s ✇❤② t❤✐s t❤❡s✐s ✐s ❛❜♦✉t t❤❡ ❞❡s✐❣♥ ♦❢ ❛ ♥❡✇ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❢♦r ❯❆❱s✳❆♥ ♦❜❥❡❝t✐✈❡ ❢♦r ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ✐s t♦ ❞♦ t❤❡♠ ✇✐t❤ t❤❡ ❝♦♥❞✐t✐♦♥s t❤❛t ♦❝❝✉r ✐♥ r❡❛❧

❧✐❢❡✳ ❚❤✐s ✐s ✇❤② t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❝❛♥ ❝♦♥t❛✐♥ ❯❆❱ ❛✐r❢♦✐❧s ✇✐t❤ r❡❛❧✲❧✐❢❡❝❤♦r❞ ❧❡♥❣t❤s✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✇✐❧❧ ❜❡ ❛❜❧❡ t♦ ❛❝❝❡❧❡r❛t❡ t❤❡ ❛✐r t♦ 35m s−1

❛♥❞ t❤❡r❡❢♦r❡ ❣❡♥❡r❛t❡ r❡❛❧✲❧✐❢❡ ❛✐r ✢♦✇s✳❆s t❤❡ ♣✉r♣♦s❡ ♦❢ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s t♦ s✐♠✉❧❛t❡ t❤❡ ✐❝❡ ❛❝❝r❡t✐♦♥s ♦♥ t❤❡ t❡st

♦❜❥❡❝t✱ t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ✇❛s ❝❛❧❝✉❧❛t❡❞ ❢♦r t❤❡ ❞❡s✐❣♥❡❞ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡ r❡s✉❧tss❤♦✇ t❤❛t t❤❡ ❧❛r❣❡st ♣❛rt ♦❢ t❤❡ t②♣✐❝❛❧ ✐❝✐♥❣ ❡♥✈✐r♦♥♠❡♥t ❝❛♥ ❜❡ t❡st❡❞ ✐♥ t❤❡ ❞❡s✐❣♥❡❞✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♥❡❝❡ss❛r② ♥♦③③❧❡ ❧❡♥❣t❤ ✇❛s ❣✐✈❡♥ t❤❛t ✐s ♥❡❡❞❡❞ t♦❞♦ ❡①♣❡r✐♠❡♥ts ✇✐t❤ ❜✐❣❣❡r ❞r♦♣❧❡ts ❛s ✇❡❧❧✳❚♦ r✉♥ t❤❡ ✇✐♥❞ t✉♥♥❡❧✱ ♣♦✇❡r ✐s ♥❡❡❞❡❞✳ ❚❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ✐♥ ❡✈❡r② ❝♦♠♣♦♥❡♥t

✇❡r❡ ❝❛❧❝✉❧❛t❡❞✳ ❚❤❡ r❡s✉❧t✐♥❣ t♦t❛❧ ♣r❡ss✉r❡ ❧♦ss ✇✐❧❧ ❜❡ ❜❛❧❛♥❝❡❞ ❜② ❛♥ ❛①✐❛❧ ❢❛♥ s✐tt✐♥❣❛s t❤❡ ♠♦st ✉♣str❡❛♠ ♣❛rt ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ■♥ t❤✐s t❤❡s✐s ❛❧s♦ ❛ ❢❛♥ ✇❛s ♣r❡s❡♥t❡❞t❤❛t ❝❛♥ ♦✛❡r t❤❡ ♥❡❝❡ss❛r② ♣♦✇❡r ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧✳❲✐t❤♦✉t ♣r♦♣❡r ❝♦♦❧✐♥❣✱ ❛ r❡❛s♦♥❛❜❧❡ r✉♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐s ✐♠♣♦ss✐❜❧❡✳ ❚❤❡r❡❢♦r❡✱

t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ❝❧✐♠❛t❡ ❝❤❛♠❜❡r t❤❛t ✇✐❧❧ ❝♦♥t❛✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇❡r❡❢♦r♠✉❧❛t❡❞✳Pr❡❧✐♠✐♥❛r② ❈❋❉ s✐♠✉❧❛t✐♦♥s ✇❡r❡ ❞♦♥❡ t♦ ❝❤❡❝❦ t❤❡ ❝♦rr❡❝t♥❡ss ♦❢ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s

❛♥❞ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥✳ ❚❤❡ r❡s✉❧ts ✐♥❞✐❝❛t❡ t❤❡ ♦❝❝✉rr❡♥❝❡ ♦❢ ✢♦✇ s❡♣❛r❛t✐♦♥ ✐♥t❤❡ ❝♦r♥❡rs ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ♦❢ t❤❡ ❈❋❉ r❡s✉❧ts ❛r❡♠✉❝❤ ❤✐❣❤❡r t❤❛♥ t❤❡ ♦♥❡s ❝❛❧❝✉❧❛t❡❞ ❢♦r t❤❡ ✇✐♥❞ t✉♥♥❡❧✳ ❚❤❡r❡❢♦r❡ t❤❡ ❈❋❉ r❡s✉❧ts✐♥❞✐❝❛t❡ t❤❛t t❤❡ ❞❡s✐❣♥❡❞ ✇✐♥❞ t✉♥♥❡❧ ♥❡❡❞s ♠♦r❡ ❛tt❡♥t✐♦♥ ❜❡❢♦r❡ ✐t ❝❛♥ ❜❡ ❜✉✐❧t✳❚❤❡ ❧❛st ♣❛rt ♦❢ t❤❡ t❤❡s✐s ✇❛s ❝♦♥❝❡r♥❡❞ ✇✐t❤ t❤❡ ❞♦✇♥✲s❝❛❧✐♥❣ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧

❞❡s✐❣♥✳ ❚❤✐s ✇❛s ❞♦♥❡ ❛s t❤❡ ◆❚◆❯ ♦✇♥s ❛ s♠❛❧❧ ❝❧✐♠❛t❡ r♦♦♠ t❤❛t ❝♦✉❧❞ ❛❧s♦ ❜❡ ✉s❡❞❛s ❛ ❝❧✐♠❛t❡ ❝❤❛♠❜❡r ❢♦r ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳ ❍♦✇❡✈❡r✱ ✐ts ❞✐♠❡♥s✐♦♥s ❛r❡ t♦♦ s♠❛❧❧t♦ ❝♦♥t❛✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐t❤ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r♠✉❧❛t❡❞ ❢♦r ❣♦♦❞ s❝✐❡♥t✐✜❝t❡st✐♥❣✳ ❚❤❡r❡❢♦r❡ ❛ ♥❡✇ ❧✐st ♦❢ r❡q✉✐r❡♠❡♥ts ✇❛s ❢♦r♠✉❧❛t❡❞ t❤❛t ❝❛♥ ❜❡ ❤❡❧❞ ❜② ❛ ✇❛②s♠❛❧❧❡r ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ st✐❧❧ ❧❡❛❞ t♦ s♦♠❡ ❣❛✐♥ ✐♥ ❦♥♦✇❧❡❞❣❡✳ ❋♦r t❤✐s s♠❛❧❧❡r ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧✱ ❞✐✛❡r❡♥t ❞❡s✐❣♥ ✐❞❡❛s ✇❡r❡ ♣r❡s❡♥t❡❞ ❛♥❞ ❝♦♠♣❛r❡❞✳

✻✸

✺ ❉✐s❝✉ss✐♦♥

❖✈❡r❛❧❧✱ ❞✉r✐♥❣ t❤✐s t❤❡s✐s✱ t❤❡ ❜❛s✐❝ ❞❡s✐❣♥ ♦❢ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s♣❡❝✐✜❝❛❧❧② ❞❡s✐❣♥❡❞❢♦r ❯❆❱s ✐s ♣r❡s❡♥t❡❞✳ ❚❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s ❝♦♠♣❛r❛❜❧❡ ✐♥ t❡st s❡❝t✐♦♥ s✐③❡ ❛♥❞ ❛✐rs♣❡❡❞ t♦ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ✐♥ ❇r❛✉♥s❝❤✇❡✐❣ ✭s❡❡ ❇❛♥s♠❡r ❡t ❛❧✳ ❬✸✶❪✮ ❛♥❞ t❤❡ ❱❚❚✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✭s❡❡ ❚✐✐❤♦♥❡♥ ❡t ❛❧✳ ❬✷✻❪✮✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ r❡s✉❧ts✱ t❤❡ ❞❡s✐❣♥❡❞ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧ ✐s s✉✐t❛❜❧❡ ❛s t❡st ❢❛❝✐❧✐t② ❢♦r ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ✐❝✐♥❣ ❡①♣❡r✐♠❡♥ts ♦♥ ❯❆❱s✳❚❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❤♦✇❡✈❡r s❤♦✇❡❞ s♦♠❡ ✉♥s❡tt❧❡❞ t♦♣✐❝s ❧✐❦❡ s❡♣❛r❛t✐♦♥ ❛♥❞ ❤✐❣❤❡r

♣r❡ss✉r❡ ❧♦ss❡s✳ ❆s t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇❛s ❥✉st ❞❡s✐❣♥❡❞ ❜② ✉s✐♥❣ ❜❛s✐❝ ❡q✉❛t✐♦♥s t❤❛t♦❢t❡♥ ✉s❡ s✐♠♣❧✐✜❝❛t✐♦♥s✱ s♦♠❡ ✉♥❝❡rt❛✐♥t✐❡s r❡♠❛✐♥✳ ❊s♣❡❝✐❛❧❧② t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ✇❛s❥✉st ❝❛❧❝✉❧❛t❡❞ r♦✉❣❤❧② ❛♥❞ ✇✐t❤♦✉t t❛❦✐♥❣ t✉r❜✉❧❡♥❝❡ ✐♥t♦ ❛❝❝♦✉♥t✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡♣r❡ss✉r❡ ❧♦ss❡s ❞✐✛❡r ❜② t❤❡ ❢❛❝t♦r t❤r❡❡ ❜❡t✇❡❡♥ ❝❛❧❝✉❧❛t✐♦♥s ❛♥❞ t❤❡ ❈❋❉ r❡s✉❧ts✳ ❲✐t❤t❤❡ ✉♥❝❡rt❛✐♥t② ❜❡✐♥❣ s♦ ❤✐❣❤✱ ✐t ✐s ♥♦t s❡♥s✐❜❧❡ t♦ s❡❧❡❝t ❛ ❢❛♥✳ ❆ ❢✉rt❤❡r ✇❡❛❦♥❡ss ♦❢t❤❡ ✇♦r❦ ❞♦♥❡ s♦ ❢❛r ✐s✱ t❤❛t ✐t ✇❛s ♥♦t ♣♦ss✐❜❧❡ ②❡t t♦ s❡❧❡❝t ❛ s♣r❛② s②st❡♠ ❢♦r t❤❡ ✐❝✐♥❣✇✐♥❞ t✉♥♥❡❧✳◆❡✈❡rt❤❡❧❡ss✱ t❤❡ ❞❡s✐❣♥ ✐s ❛ ❣♦♦❞ st❛rt✐♥❣ ♣♦✐♥t ❢♦r ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ❛♥❛❧②s✐s✳ ❆s t❤❡r❡

✐s ❛ ♥❡❡❞ ❢♦r ♠♦r❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❢♦r ❯❆❱s✱ ✐t ✐s ❛❜s♦❧✉t❡❧② r❡❝♦♠♠❡♥❞❡❞ t♦ ❝♦♥t✐♥✉❡t❤❡ ✇♦r❦ ❛♥❞ ❡✈❡♥t✉❛❧❧② ❜✉✐❧❞ ❛♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❜❛s❡❞ ♦♥ t❤✐s ✇♦r❦✳

✺✳✷ ❋✉rt❤❡r ✇♦r❦

❚❤❡ ♠❡♥t✐♦♥❡❞ ❈❋❉ r❡s✉❧ts ❧❡❛❞ t♦ t❤❡ ♥❡❡❞ ❢♦r ❛♥ ♦✈❡rt❤✐♥❦✐♥❣ ♦❢ ❝❡rt❛✐♥ ♣❛rts ♦❢t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❞❡s✐❣♥✳ ❋✐rst✱ ❛ ❞❡❡♣❡r ❛♥❛❧②s✐s ♦❢ t❤❡ ❈❋❉ r❡s✉❧ts ✐s ♥❡❝❡ss❛r② t♦✉♥❞❡rst❛♥❞ t❤❡ r❡❛s♦♥ ❢♦r t❤❡ ✢♦✇ s❡♣❛r❛t✐♦♥ ❛♥❞ t❤❡ ❤✐❣❤❡r ♣r❡ss✉r❡ ❧♦ss❡s✳ ■❢ t❤✐s❦♥♦✇❧❡❞❣❡ ✐s ♣r❡s❡♥t✱ t❤❡ ❞❡s✐❣♥ ♦❢ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ❝❛♥ ❜❡ ❝❤❛♥❣❡❞ t♦ r❡❞✉❝❡ t❤❡s❡❡✛❡❝ts✳ ❆ ✜rst ✐❞❡❛ ✐s t♦ ✐♥s❡rt ✜❧❧❡ts ✐♥ t❤❡ ❝♦r♥❡rs ❛s r❡❝♦♠♠❡♥❞❡❞ ❜② ❇❛r❧♦✇ ❡t ❛❧✳❬✷✵❪✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ❛♥ ♦t❤❡r ♥♦③③❧❡ ❞❡s✐❣♥ ❝❛♥ ❜❡ ❝❤❡❝❦❡❞ t♦ s❡❡ ✐❢ ❛ ❝❤❛♥❣❡ ♦❢ t❤❡ ♥♦③③❧❡❝♦♥t♦✉r ❤❡❧♣s t♦ r❡❞✉❝❡ t❤❡ s❡♣❛r❛t✐♦♥ ❛r❡❛✳ ❖t❤❡r ♣♦ss✐❜✐❧✐t✐❡s ❛r❡ t♦ ♠❛❦❡ t❤❡ ♥♦③③❧❡❧♦♥❣❡r ♦r t♦ r❡❞✉❝❡ t❤❡ ♦♣❡♥✐♥❣ ❛♥❣❧❡ ♦❢ t❤❡ ❞✐✛✉s❡r✳❆ ❦❡② st❡♣ t❤❛t ♥❡❡❞s t♦ ❜❡ t❛❦❡♥ ♦♥ t❤❡ ✇❛② t♦ ❛ ✇♦r❦✐♥❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s t♦ s❡❧❡❝t

❛ s✉✐t❛❜❧❡ s♣r❛② s②st❡♠✳ ❙♦♠❡ ✐❞❡❛s ✇❡r❡ ♣r❡s❡♥t❡❞ ✐♥ s❡❝t✐♦♥ ✹✳✸✳✸✳✶✳ ■t ✇✐❧❧ ♣r♦❜❛❜❧②❜❡ ♥❡❝❡ss❛r② t♦ ❞♦ ❞❡t❛✐❧❡❞ ❈❋❉ s✐♠✉❧❛t✐♦♥s ♦❢ t❤❡ ❞r♦♣❧❡t ❜❡❤❛✈✐♦r ❢♦r ❞✐✛❡r❡♥t ❞❡s✐❣♥s♦❢ ❛ s♣r❛② s②st❡♠✳❆♥♦t❤❡r t♦♣✐❝ ❢♦r t❤❡ ❢✉t✉r❡ ✐s t♦ ♣r♦✈✐❞❡ t❤❡ ♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r ❢♦r t❤❡ ✐❝✐♥❣

✇✐♥❞ t✉♥♥❡❧✳ ❚❤✐s ❝♦✉❧❞ ❜❡ ❞♦♥❡ ❜② ♣❧❛❝✐♥❣ t❤❡ ✇✐♥❞ t✉♥♥❡❧ ✐♥ ❛ ❝❧✐♠❛t❡ ❝❤❛♠❜❡r✱ ❜②✐♥❥❡❝t✐♥❣ ❧✐q✉✐❞ ♥✐tr♦❣❡♥✱ ♦r ❜② ❝❤❛♥❣✐♥❣ t❤❡ ❞❡s✐❣♥ ✐♥t♦ ❛ ❝❧♦s❡❞ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✇✐t❤❛ ❤❡❛t ❡①❝❤❛♥❣❡r✳ ■❢ ❛ ❞❡❝✐s✐♦♥ ✐s ♠❛❞❡✱ ❛ ❈❋❉ s✐♠✉❧❛t✐♦♥ ♦❢ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞✐ts ❡♥✈✐r♦♥♠❡♥t ✐s ♥❡❝❡ss❛r② t♦ ❝❤❡❝❦ t❤❛t t❤❡ ✢♦✇ q✉❛❧✐t② ✐s s✉✣❝✐❡♥t✳ ❚❤✐s ✇♦✉❧❞ ❜❡❡s♣❡❝✐❛❧❧② ✐♠♣♦rt❛♥t ❢♦r t❤❡ ✐♥❧❡t ♦❢ ❛♥ ♦♣❡♥ r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧✳❖♥❝❡ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ✐s ❜✉✐❧❞✱ ❞✐✛❡r❡♥t ✐♥str✉♠❡♥ts ♥❡❡❞ t♦ ❜❡ ✐♥st❛❧❧❡❞✱ ❢♦r

❡①❛♠♣❧❡ t♦ ♠❡❛s✉r❡ t❤❡ t❡♠♣❡r❛t✉r❡✱ t❤❡ s♣❡❡❞ ♦r t❤❡ ✇❛t❡r ❝♦♥t❡♥t ✐♥ t❤❡ ✐❝✐♥❣ ✇✐♥❞t✉♥♥❡❧✳ ❆❢t❡r✇❛r❞s✱ t❤❡ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ ❛♥❞ t❤❡ ✐♥str✉♠❡♥ts ♥❡❡❞ t♦ ❜❡ ❝❛❧✐❜r❛t❡❞ ❛s❡①♣❧❛✐♥❡❞ ✐♥ ❙❆❊✲❆❘P ✺✾✵✺ ❬✻✻❪✳ ❆ t❤♦r♦✉❣❤ ❝❛❧✐❜r❛t✐♦♥ ✐s ✈❡r② ❤❡❧♣❢✉❧ t♦ ❤❛✈❡ tr✉st ✐♥t❤❡ r❡s✉❧ts ♦❢ ❡①♣❡r✐♠❡♥ts✳ ❊s♣❡❝✐❛❧❧② t❤❡ ✉♥✐❢♦r♠✐t② ♦❢ t❤❡ ❞r♦♣❧❡t ❝❧♦✉❞ ✐♥s✐❞❡ t❤❡ t❡sts❡❝t✐♦♥ s❤♦✉❧❞ ❜❡ ❝❤❡❝❦❡❞ t♦ ♠❛❦❡ s✉r❡ t❤❛t ♠✉❧t✐♣❧❡ ♠❡❛s✉r❡♠❡♥ts ♦❢ t❤❡ ✐❝❡ s❤❛♣❡s❛r❡ ❞♦♥❡ ❛t ♣♦s✐t✐♦♥s ✇✐t❤ ❝♦♠♣❛r❛❜❧❡ ❝♦♥❞✐t✐♦♥s✳

✻✹

❇✐❜❧✐♦❣r❛♣❤②

❬✶❪ ❇r❛❣❣✱ ▼✳✱ ❇r♦❡r❡♥✱ ❆✳✱ ❛♥❞ ❇❧✉♠❡♥t❤❛❧✱ ▲✳ ■❝❡❞✲❛✐r❢♦✐❧ ❛❡r♦❞②♥❛♠✐❝s✳ Pr♦❣r❡ss ✐♥❆❡r♦s♣❛❝❡ ❙❝✐❡♥❝❡s✱ ✹✶✭✺✮✿✸✷✸✕✸✻✷✱ ✷✵✵✺✳

❬✷❪ ❑✐♥❞✱ ❘✳✱ P♦t❛♣❝③✉❦✱ ▼✳✱ ❋❡♦✱ ❆✳✱ ●♦❧✐❛✱ ❈✳✱ ❛♥❞ ❙❤❛❤✱ ❆✳ ❊①♣❡r✐♠❡♥t❛❧ ❛♥❞ ❝♦♠✲♣✉t❛t✐♦♥❛❧ s✐♠✉❧❛t✐♦♥ ♦❢ ✐♥✲✢✐❣❤t ✐❝✐♥❣ ♣❤❡♥♦♠❡♥❛✳ Pr♦❣r❡ss ✐♥ ❆❡r♦s♣❛❝❡ ❙❝✐❡♥❝❡s✱✸✹✭✺✮✿✷✺✼ ✕ ✸✹✺✱ ✶✾✾✽✳

❬✸❪ P❡❝❦✱ ▲✳✱ ❘②❡rs♦♥✱ ❈✳✱ ❛♥❞ ▼❛rt❡❧✱ ❈✳ ❆r♠② ❆✐r❝r❛❢t ■❝✐♥❣✳ ❊❘❉❈✴❈❘❘❊▲ ❚❘✲✵✷✲✶✸✱ ❯❙ ❆r♠② ❈♦r♣s ♦❢ ❊♥❣✐♥❡❡rs✱ ✷✵✵✷✳

❬✹❪ ❙③✐❧❞❡r✱ ❑✳ ❛♥❞ ▼❝■❧✇❛✐♥✱ ❙✳ ■♥✲❋❧✐❣❤t ■❝✐♥❣ ♦❢ ❯❆❱s ✲ ❚❤❡ ■♥✢✉❡♥❝❡ ♦❢ ❘❡②♥♦❧❞s◆✉♠❜❡r ♦♥ t❤❡ ■❝❡ ❆❝❝r❡t✐♦♥ Pr♦❝❡ss✳ ■♥ ❙❆❊ ❚❡❝❤♥✐❝❛❧ P❛♣❡r✳ ❙❆❊ ■♥t❡r♥❛t✐♦♥❛❧✱✷✵✶✶✳

❬✺❪ ❍❛♥♥✱ ❘✳ ❆t♠♦s♣❤❡r✐❝ ■❝❡ ❆❝❝r❡t✐♦♥s✱ ❆❡r♦❞②♥❛♠✐❝ ■❝✐♥❣ P❡♥❛❧t✐❡s✱ ❛♥❞ ■❝❡ Pr♦✲t❡❝t✐♦♥ ❙②st❡♠s ♦♥ ❯♥♠❛♥♥❡❞ ❆❡r✐❛❧ ❱❡❤✐❝❧❡s✳ P❤❉ t❤❡s✐s✱ ◆♦r✇❡❣✐❛♥ ❯♥✐✈❡rs✐t②♦❢ ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤♥♦❧♦❣②✱ ✷✵✷✵✳

❬✻❪ ❍❛♥♥✱ ❘✳ ❛♥❞ ❏♦❤❛♥s❡♥✱ ❚✳ ❆✳ ❯♥s❡tt❧❡❞ ❚♦♣✐❝s ✐♥ ❯♥♠❛♥♥❡❞ ❆❡r✐❛❧ ❱❡❤✐❝❧❡ ■❝✐♥❣✳❙❆❊ ❊❉●❊ ❘❡s❡❛r❝❤ ❘❡♣♦rt ❊P❘✷✵✷✵✵✵✽✱ ❙❆❊ ■♥t❡r♥❛t✐♦♥❛❧✱ ✷✵✷✵✳

❬✼❪ ❊✉r♦♣❡❛♥ ❆✈✐❛t✐♦♥ ❙❛❢❡t② ❆❣❡♥❝②✳ ❈❡rt✐✜❝❛t✐♦♥ ❙♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ❆❝❝❡♣t❛❜❧❡▼❡❛♥s ♦❢ ❈♦♠♣❧✐❛♥❝❡ ❢♦r ▲❛r❣❡ ❆❡r♦♣❧❛♥❡s ❈❙✲✷✺✱ ❝❤❛♣t❡r ❆♣♣❡♥❞✐① ❈✳ ✷✵✶✻✳

❬✽❪ ❋❛❥t✱ ◆✳✱ ❍❛♥♥✱ ❘✳✱ ❛♥❞ ▲✉t③✱ ❚✳ ❚❤❡ ■♥✢✉❡♥❝❡ ♦❢ ▼❡t❡♦r♦❧♦❣✐❝❛❧ ❈♦♥❞✐t✐♦♥s ♦♥t❤❡ ■❝✐♥❣ P❡r❢♦r♠❛♥❝❡ P❡♥❛❧t✐❡s ♦♥ ❛ ❯❆❱ ❆✐r❢♦✐❧✳ ■♥ ✽t❤ ❊✉r♦♣❡❛♥ ❈♦♥❢❡r❡♥❝❡ ❢♦r❆❡r♦♥❛✉t✐❝s ❛♥❞ ❆❡r♦s♣❛❝❡ ❙❝✐❡♥❝❡s ✭❊❯❈❆❙❙✮✱ ✷✵✶✾✳

❬✾❪ ❍❛♥♥✱ ❘✳✱ ❍❡❛rst✱ ❘✳ ❏✳✱ ❙➹➛tr❛♥✱ ▲✳ ❘✳✱ ❛♥❞ ❇r❛❝❝❤✐✱ ❚✳ ❊①♣❡r✐♠❡♥t❛❧ ❛♥❞ ◆✉♠❡r✲✐❝❛❧ ■❝✐♥❣ P❡♥❛❧t✐❡s ♦❢ ❛♥ ❙✽✷✻ ❆✐r❢♦✐❧ ❛t ▲♦✇ ❘❡②♥♦❧❞s ◆✉♠❜❡rs✳ ❆❡r♦s♣❛❝❡✱ ✼✭✹✮✱✷✵✷✵✳

❬✶✵❪ ▲❛✇s♦♥✱ ❈✳ ❊❧❡❝tr✐❝❛❧❧② P♦✇❡r❡❞ ■❝❡ Pr♦t❡❝t✐♦♥ ❙②st❡♠s ❢♦r ▼❆▲❊ ❯❆❱s ✲ ❘❡✲q✉✐r❡♠❡♥ts ❛♥❞ ■♥t❡❣r❛t✐♦♥ ❈❤❛❧❧❡♥❣❡s✳ ■♥ ✷✺t❤ ❈♦♥❣r❡ss ♦❢ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦✉♥❝✐❧♦❢ ❆❡r♦♥❛✉t✐❝❛❧ ❙❝✐❡♥❝❡s✱ ✷✵✵✻✳

❬✶✶❪ ❍❛♥♥✱ ❘✳✱ ❊♥❛❝❤❡✱ ❆✳✱ ◆✐❡❧s❡♥✱ ▼✳ ❈✳✱ ❙t♦✈♥❡r✱ ❇✳ ◆✳✱ ✈❛♥ ❇❡❡❝❦✱ ❏✳✱ ❏♦❤❛♥s❡♥✱❚✳ ❆✳✱ ❛♥❞ ❇♦r✉♣✱ ❑✳ ❚✳ ❯❆❱ ■❝✐♥❣✿ ❊①♣❡r✐♠❡♥t❛❧ ❍❡❛t ▲♦❛❞s ❢♦r ❆♥t✐✲■❝✐♥❣ ❛♥❞❉❡✲■❝✐♥❣✳ ✷✵✷✵✳

❬✶✷❪ ❆♥❞❡rs♦♥✱ ❏✳ ❋✉♥❞❛♠❡♥t❛❧s ♦❢ ❆❡r♦❞②♥❛♠✐❝s✳ ▼❝●r❛✇✲❍✐❧❧ ❊❞✉❝❛t✐♦♥✱ ✷✵✶✵✳ ■❙❇◆✾✼✽✵✵✼✸✸✾✽✶✵✺✳

✻✺

❇✐❜❧✐♦❣r❛♣❤②

❬✶✸❪ ❱❡rst❡❡❣✱ ❍✳ ❛♥❞ ▼❛❧❛❧❛s❡❦❡r❛✱ ❲✳ ❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ❈♦♠♣✉t❛t✐♦♥❛❧ ❋❧✉✐❞ ❉②✲♥❛♠✐❝s✿ ❚❤❡ ❋✐♥✐t❡ ❱♦❧✉♠❡ ▼❡t❤♦❞✳ P❡❛rs♦♥ ❊❞✉❝❛t✐♦♥ ▲✐♠✐t❡❞✱ ✷✵✵✼✳ ■❙❇◆✾✼✽✵✶✸✶✷✼✹✾✽✸✳

❬✶✹❪ ●❛t❡s✱ ❊✳✱ ▲❛♠✱ ❲✳✱ ❛♥❞ ▲♦③♦✇s❦✐✱ ❊✳ ❙♣r❛② ❡✈♦❧✉t✐♦♥ ✐♥ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s✳ ❈♦❧❞❘❡❣✐♦♥s ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤♥♦❧♦❣②✱ ✶✺✭✶✮✿✻✺ ✕ ✼✹✱ ✶✾✽✽✳

❬✶✺❪ ▼❛r✐t✐♠❡ ❘♦❜♦t✐❝s✳ ❚❍❊ P❳✲✸✶ ❋❛❧❦✳ ❤tt♣s✿✴✴✇✇✇✳♠❛r✐t✐♠❡r♦❜♦t✐❝s✳❝♦♠✴♣①✲✸✶✱ ✷✵✶✾✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✺✳

❬✶✻❪ ❉❏■✳ ❆❣r❛s ❚✶✻ ✲ ❆❣r✐❝✉❧t✉r❛❧ ❙♣r❛②✐♥❣ ❉r♦♥❡✳ ❤tt♣s✿✴✴✇✇✇✳❞❥✐✳❝♦♠✴♥♦✴t✶✻✱✷✵✶✾✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✵✸✳

❬✶✼❪ ❉❡●❛r♠♦✱ ▼✳ ❚✳ ■ss✉❡s ❈♦♥❝❡r♥✐♥❣ ■♥t❡❣r❛t✐♦♥ ♦❢ ❯♥♠❛♥♥❡❞ ❆❡r✐❛❧ ❱❡❤✐❝❧❡s ✐♥❈✐✈✐❧ ❆✐rs♣❛❝❡✳ ✱ ▼■❚❘❊✱ ❈❡♥t❡r ❢♦r ❆❞✈❛♥❝❡❞ ❆✈✐❛t✐♦♥ ❙②st❡♠ ❉❡✈❡❧♦♣♠❡♥t✱▼❝▲❡❛♥✱ ❱✐r❣✐♥✐❛✱ ✷✵✵✹✳

❬✶✽❪ ●❡♥t✱ ❘✳ ❲✳✱ ❉❛rt✱ ◆✳✱ ❛♥❞ ❈❛♥s❞❛❧❡✱ ❏✳ ❚✳ ❆✐r❝r❛❢t ✐❝✐♥❣✳ P❤✐❧♦s♦♣❤✐❝❛❧ ❚r❛♥s❛❝✲t✐♦♥s ♦❢ t❤❡ ❘♦②❛❧ ❙♦❝✐❡t② ♦❢ ▲♦♥❞♦♥✳ ❙❡r✐❡s ❆✿ ▼❛t❤❡♠❛t✐❝❛❧✱ P❤②s✐❝❛❧ ❛♥❞ ❊♥❣✐✲♥❡❡r✐♥❣ ❙❝✐❡♥❝❡s✱ ✸✺✽✿✷✽✼✸ ✕ ✷✾✶✶✱ ✷✵✵✵✳

❬✶✾❪ ❍❛♥♥✱ ❘✳ ❛♥❞ ❏♦❤❛♥s❡♥✱ ❚✳ ❆✳ ❯❆❱ ■❝✐♥❣✿ ❚❤❡ ■♥✢✉❡♥❝❡ ♦❢ ❆✐rs♣❡❡❞ ❛♥❞ ❈❤♦r❞▲❡♥❣t❤ ♦♥ P❡r❢♦r♠❛♥❝❡ ❉❡❣r❛❞❛t✐♦♥✳ ❆✐r❝r❛❢t ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❆❡r♦s♣❛❝❡ ❚❡❝❤♥♦❧✲♦❣②✱ s✉❜♠✐tt❡❞ ✷✵✷✵✳

❬✷✵❪ ❇❛r❧♦✇✱ ❏✳✱ ❘❛❡✱ ❲✳✱ ❛♥❞ P♦♣❡✱ ❆✳ ▲♦✇✲❙♣❡❡❞ ❲✐♥❞ ❚✉♥♥❡❧ ❚❡st✐♥❣✳ ❆❡r♦s♣❛❝❡❡♥❣✐♥❡❡r✐♥❣✱ ♠❡❝❤❛♥✐❝❛❧ ❡♥❣✐♥❡❡r✐♥❣✳ ❲✐❧❡②✱ ✶✾✾✾✳ ■❙❇◆ ✾✼✽✵✹✼✶✺✺✼✼✹✻✳

❬✷✶❪ ❑✉❧❦❛r♥✐✱ ❱✳✱ ❙❛❤♦♦✱ ◆✳✱ ❛♥❞ ❈❤❛✈❛♥✱ ❙✳ ❉✳ ❙✐♠✉❧❛t✐♦♥ ♦❢ ❤♦♥❡②❝♦♠❜✲s❝r❡❡♥ ❝♦♠✲❜✐♥❛t✐♦♥s ❢♦r t✉r❜✉❧❡♥❝❡ ♠❛♥❛❣❡♠❡♥t ✐♥ ❛ s✉❜s♦♥✐❝ ✇✐♥❞ t✉♥♥❡❧✳ ❏♦✉r♥❛❧ ♦❢ ❲✐♥❞❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ■♥❞✉str✐❛❧ ❆❡r♦❞②♥❛♠✐❝s✱ ✾✾✭✶✮✿✸✼ ✕ ✹✺✱ ✷✵✶✶✳

❬✷✷❪ ❆r✐❢✉③③❛♠❛♥✱ ▼✳ ❛♥❞ ▼❛s❤✉❞✱ ▼✳ ❉❡s✐❣♥ ❈♦♥str✉❝t✐♦♥ ❛♥❞ P❡r❢♦r♠❛♥❝❡ ❚❡st ♦❢ ❛▲♦✇ ❈♦st ❙✉❜s♦♥✐❝ ❲✐♥❞ ❚✉♥♥❡❧✳ ■❖❙❘ ❏♦✉r♥❛❧ ♦❢ ❊♥❣✐♥❡❡r✐♥❣✱ ✵✷✿✽✸✕✾✷✱ ✷✵✶✷✳

❬✷✸❪ ■❊❆ ❲✐♥❞ ❚❛s❦ ✶✾✳ ❆✈❛✐❧❛❜❧❡ ❚❡❝❤♥♦❧♦❣✐❡s❢♦r ❲✐♥❞ ❊♥❡r❣② ✐♥ ❈♦❧❞ ❈❧✐♠❛t❡s✳❚❡❝❤♥✐❝❛❧ r❡♣♦rt✱ ✷✵✶✽✳

❬✷✹❪ ❈■❘❆✳ ■❝✐♥❣ ❲✐♥❞ ❚✉♥♥❡❧✳ ❤tt♣s✿✴✴✇✇✇✳❝✐r❛✳✐t✴❡♥✴r❡s❡❛r❝❤✲✐♥❢r❛str✉❝t✉r❡s✴✐❝✐♥❣✲✇✐♥❞✲t✉♥♥❡❧✲✭✐✇t✮✴■❝✐♥❣✪✷✵❲✐♥❞✪✷✵❚✉♥♥❡❧✱ ✷✵✶✼✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✾✳

❬✷✺❪ ◆❆❙❆ ●❧❡♥♥ ❘❡s❡❛r❝❤ ❈❡♥t❡r✳ ■❝✐♥❣ ❘❡s❡❛r❝❤ ❚✉♥♥❡❧✳ ❤tt♣s✿✴✴✇✇✇✶✳❣r❝✳♥❛s❛✳❣♦✈✴❢❛❝✐❧✐t✐❡s✴✐rt✴✱ ✷✵✷✵✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✾✳

❬✷✻❪ ❚✐✐❤♦♥❡♥✱ ▼✳✱ ❏♦❦❡❧❛✱ ❚✳✱ ▼❛❦❦♦♥❡♥✱ ▲✳✱ ❛♥❞ ❇❧✉❡♠✐♥❦✱ ●✳✲❏✳ ❱❚❚ ■❝✐♥❣ ✇✐♥❞t✉♥♥❡❧ ✷✳✵✳ ■♥ ❲✐♥t❡r✇✐♥❞ Pr❡s❡♥t❛t✐♦♥s ✷✵✶✻✱ ✷✵✶✻✳

❬✷✼❪ ❈r❛♥✜❡❧❞ ❯♥✐✈❡rs✐t②✳ ■❝✐♥❣ ❚✉♥♥❡❧✳ ❤tt♣s✿✴✴✇✇✇✳❝r❛♥❢✐❡❧❞✳❛❝✳✉❦✴❢❛❝✐❧✐t✐❡s✴✐❝✐♥❣✲t✉♥♥❡❧✱ ✷✵✷✵✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✾✳

✻✻

❇✐❜❧✐♦❣r❛♣❤②

❬✷✽❪ ❋❧❡♠♠✐♥❣✱ ❘✳✱ ❇♦♥❞✱ ❚✳✱ ❛♥❞ ❇r✐tt♦♥✱ ❘✳ ❘❡s✉❧ts ♦❢ ❛ s✉❜✲s❝❛❧❡ ♠♦❞❡❧ r♦t♦r ✐❝✐♥❣t❡st✳ ■♥ ✷✾t❤ ❆❡r♦s♣❛❝❡ ❙❝✐❡♥❝❡s ▼❡❡t✐♥❣✱ ✶✾✾✶✳

❬✷✾❪ ❇r♦✉✇❡rs✱ ❊✳✱ P❛❧❛❝✐♦s✱ ❏✳✱ ❙♠✐t❤✱ ❊✳✱ ❛♥❞ P❡t❡rs♦♥✱ ❆✳ ❚❤❡ ❡①♣❡r✐♠❡♥t❛❧ ✐♥✈❡st✐❣❛✲t✐♦♥ ♦❢ ❛ r♦t♦r ❤♦✈❡r ✐❝✐♥❣ ♠♦❞❡❧ ✇✐t❤ s❤❡❞❞✐♥❣✳ ❆♥♥✉❛❧ ❋♦r✉♠ Pr♦❝❡❡❞✐♥❣s ✲ ❆❍❙■♥t❡r♥❛t✐♦♥❛❧✱ ✹✿✷✻✶✾✕✷✻✸✺✱ ✷✵✶✵✳

❬✸✵❪ ❈❛♦✱ ❨✳ ❛♥❞ ❈❤❡♥✱ ❑✳ ❍❡❧✐❝♦♣t❡r ✐❝✐♥❣✳ ❚❤❡ ❆❡r♦♥❛✉t✐❝❛❧ ❏♦✉r♥❛❧ ✭✶✾✻✽✮✱ ✶✶✹✭✶✶✺✷✮✿✽✸✕✾✵✱ ✷✵✶✵✳

❬✸✶❪ ❇❛♥s♠❡r✱ ❙✳✱ ❇❛✉♠❡rt✱ ❆✳✱ ❙❛tt❧❡r✱ ❙✳✱ ❑♥♦♣✱ ■✳✱ ▲❡r♦②✱ ❉✳✱ ❙❝❤✇❛r③❡♥❜♦❡❝❦✱ ❆✳✱❏✉r❦❛t✲❲✐ts❝❤❛s✱ ❚✳✱ ❱♦✐❣t✱ ❈✳✱ P❡r✈✐❡r✱ ❍✳✱ ❛♥❞ ❊s♣♦s✐t♦✱ ❇✳ ❉❡s✐❣♥✱ ❈♦♥str✉❝✲t✐♦♥ ❛♥❞ ❈♦♠♠✐ss✐♦♥✐♥❣ ♦❢ t❤❡ ❇r❛✉♥s❝❤✇❡✐❣ ■❝✐♥❣ ❲✐♥❞ ❚✉♥♥❡❧✳ ❆t♠♦s♣❤❡r✐❝▼❡❛s✉r❡♠❡♥t ❚❡❝❤♥✐q✉❡s ❉✐s❝✉ss✐♦♥s✱ ♣❛❣❡s ✶✕✺✶✱ ✷✵✶✼✳

❬✸✷❪ ❊❝❦❡rt✱ ❲✳✱ ▼♦rt✱ ❑✳✱ ❛♥❞ ❏♦♣❡✱ ❏✳ ❆❡r♦❞②♥❛♠✐❝ ❞❡s✐❣♥ ❣✉✐❞❡❧✐♥❡s ❛♥❞ ❝♦♠♣✉t❡r♣r♦❣r❛♠ ❢♦r ❡st✐♠❛t✐♦♥ ♦❢ s✉❜s♦♥✐❝ ✇✐♥❞ t✉♥♥❡❧ ♣❡r❢♦r♠❛♥❝❡✳ ❚◆ ❉✲✽✷✹✸✱ ◆❆❙❆✱✶✾✼✻✳

❬✸✸❪ ❇❡❧❧✱ ❏✳ ❍✳ ❛♥❞ ▼❡❤t❛✱ ❘✳ ❉✳ ❈♦♥tr❛❝t✐♦♥ ❉❡s✐❣♥ ❢♦r ❙♠❛❧❧ ▲♦✇✲❙♣❡❡❞ ❲✐♥❞ ❚✉♥✲♥❡❧s✳ ❚❡❝❤✳ ❘❡♣✳ ❏■❆❆ ❚❘✲✽✹✱ ❙t❛♥❢♦r❞ ❯♥✐✈❡rs✐t②✱ ✶✾✽✽✳

❬✸✹❪ ❇r❛ss❛r❞✱ ❉✳ ❛♥❞ ❋❡r❝❤✐❝❤✐✱ ▼✳ ❚r❛♥s❢♦r♠❛t✐♦♥ ♦❢ ❛ P♦❧②♥♦♠✐❛❧ ❢♦r ❛ ❈♦♥tr❛❝t✐♦♥❲❛❧❧ Pr♦✜❧❡ ✳ ❏♦✉r♥❛❧ ♦❢ ❋❧✉✐❞s ❊♥❣✐♥❡❡r✐♥❣✱ ✶✷✼✭✶✮✿✶✽✸✕✶✽✺✱ ✷✵✵✺✳

❬✸✺❪ ▼♦r❡❧✱ ❚✳ ❈♦♠♣r❡❤❡♥s✐✈❡ ❉❡s✐❣♥ ♦❢ ❆①✐s②♠♠❡tr✐❝ ❲✐♥❞ ❚✉♥♥❡❧ ❈♦♥tr❛❝t✐♦♥s✳ ❏♦✉r✲♥❛❧ ♦❢ ❋❧✉✐❞s ❊♥❣✐♥❡❡r✐♥❣✱ ✾✼✭✷✮✿✷✷✺✕✷✸✸✱ ✶✾✼✺✳

❬✸✻❪ ▼❛rt✐♥✱ ❏✳ ❙✳ ◆♦③③❧❡ ❉❡s✐❣♥ ❢♦r ❛ s♠❛❧❧✱ ❧♦✇✲s♣❡❡❞✱ ❝❧♦s❡❞✲r❡t✉r♥ ✇✐♥❞ t✉♥♥❡❧✳❇❛❝❤❡❧♦r✬s t❤❡s✐s✱ ❍♦✉❣❤t♦♥ ❈♦❧❧❡❣❡✱ ✷✵✶✾✳

❬✸✼❪ ▼❡❤t❛✱ ❘✳ ❉✳ ❆s♣❡❝ts ♦❢ t❤❡ ❉❡s✐❣♥ ❛♥❞ P❡r❢♦r♠❛♥❝❡ ♦❢ ❇❧♦✇❡r ❲✐♥❞ ❚✉♥♥❡❧❈♦♠♣♦♥❡♥ts✳ P❤❉ t❤❡s✐s✱ ❉❡♣❛rt♠❡♥t ♦❢ ❆❡r♦♥❛✉t✐❝s✱ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡✱ ❯♥✐✈❡rs✐t②♦❢ ▲♦♥❞♦♥✱ ✶✾✼✽✳

❬✸✽❪ ❉♦✇♥✐❡✱ ❏✳✱ ❏♦r❞✐♥s♦♥✱ ❘✳✱ ❛♥❞ ❇❛r♥❡s✱ ❋✳ ❖♥ t❤❡ ❞❡s✐❣♥ ♦❢ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ✇✐♥❞t✉♥♥❡❧ ❝♦♥tr❛❝t✐♦♥s✳ ❆❡r♦♥❛✉t✐❝❛❧ ❏♦✉r♥❛❧✱ ✽✽✿✷✽✼✕✷✾✺✱ ✶✾✽✹✳

❬✸✾❪ ▼❡❤t❛✱ ❘✳ ❛♥❞ ❇r❛❞s❤❛✇✱ P✳ ❉❡s✐❣♥ r✉❧❡s ❢♦r s♠❛❧❧ ❧♦✇ s♣❡❡❞ ✇✐♥❞ t✉♥♥❡❧s✳ ❚❤❡❆❡r♦♥❛✉t✐❝❛❧ ❏♦✉r♥❛❧ ✭✶✾✻✽✮✱ ✽✸✭✽✷✼✮✿✹✹✸✕✹✺✸✱ ✶✾✼✾✳

❬✹✵❪ ❙❛✈✐♦ ❙r❧✳ ❆①✐❛❧ ❢❛♥s ❛♥❞ ❈❡♥tr✐❢✉❣❛❧ ❢❛♥s ❝♦♠♣❛r✐s♦♥✳ ❤tt♣s✿✴✴✇✇✇✳s❛✈✐♦❝❧✐♠❛✳❝♦♠✴❡♥✴❛①✐❛❧✲❢❛♥s✲❛♥❞✲❝❡♥tr✐❢✉❣❛❧✲❢❛♥s✲❝♦♠♣❛r✐s♦♥✴✱ ✷✵✶✻✳ ❆❝❝❡ss❡❞✿✷✵✷✵✲✵✼✲✵✷✳

❬✹✶❪ ❍❡r♥á♥❞❡③✱ ▼✳ ❆✳ ●✳✱ ▲ó♣❡③✱ ❆✳ ■✳ ▼✳✱ ❏❛r③❛❜❡❦✱ ❆✳ ❆✳✱ P❡r❛❧❡s✱ ❏✳ ▼✳ P✳✱ ❲✉✱❨✳✱ ❛♥❞ ❳✐❛♦①✐❛♦✱ ❙✳ ❉❡s✐❣♥ ▼❡t❤♦❞♦❧♦❣② ❢♦r ❛ ◗✉✐❝❦ ❛♥❞ ▲♦✇✲❈♦st ❲✐♥❞ ❚✉♥♥❡❧✳■♥ ❲✐♥❞ ❚✉♥♥❡❧ ❉❡s✐❣♥s ❛♥❞ ❚❤❡✐r ❉✐✈❡rs❡ ❊♥❣✐♥❡❡r✐♥❣ ❆♣♣❧✐❝❛t✐♦♥s✱ ❝❤❛♣t❡r ✶✳■♥t❡❝❤❖♣❡♥✱ ✷✵✶✸✳

✻✼

❇✐❜❧✐♦❣r❛♣❤②

❬✹✷❪ ▲❛♥❣♠✉✐r✱ ■✳ ❛♥❞ ❇❧♦❞❣❡tt✱ ❑✳ ❆ ▼❛t❤❡♠❛t✐❝❛❧ ■♥✈❡st✐❣❛t✐♦♥ ♦❢ ❲❛t❡r ❉r♦♣❧❡t❚r❛❥❡❝t♦r✐❡s✳ ❆r♠② ❆✐r ❋♦r❝❡s t❡❝❤♥✐❝❛❧ r❡♣♦rt✳ ❆r♠② ❆✐r ❋♦r❝❡s ❍❡❛❞q✉❛rt❡rs✱ ❆✐r❚❡❝❤♥✐❝❛❧ ❙❡r✈✐❝❡ ❈♦♠♠❛♥❞✱ ✶✾✹✻✳

❬✹✸❪ ▼♦rr✐s♦♥✱ ❋✳ ❆✳ ❉❛t❛ ❈♦rr❡❧❛t✐♦♥ ❢♦r ❉r❛❣ ❈♦❡✣❝✐❡♥t ❢♦r ❙♣❤❡r❡✳ ✱ ❉❡♣❛rt♠❡♥t ♦❢❈❤❡♠✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ▼✐❝❤✐❣❛♥ ❚❡❝❤♥♦❧♦❣✐❝❛❧ ❯♥✐✈❡rs✐t②✱ ✷✵✶✻✳

❬✹✹❪ P◆❘✳ ❙♣r❛② ❊♥❣✐♥❡❡r✐♥❣ ❍❛♥❞❜♦♦❦✳ ❤tt♣s✿✴✴✇✇✇✳♣♥r✲❢r❛♥❝❡✳❢r✴s✐t❡✲✇❡❜✴■▼●✴♣❞❢✴❊◆●■◆❊❊❘■◆●❴❍❆◆❉❇❖❖❑❴❈❚●❴❙❍✵✼❴❇❘✳♣❞❢✱ ✷✵✶✷✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✻✲✷✽✳

❬✹✺❪ ❑♥✉❞s❡♥✱ ❏✳ ●✳ ❛♥❞ ❑❛t③✱ ❉✳ ▲✳ ❱✳ ❋❧✉✐❞ ❞②♥❛♠✐❝s ❛♥❞ ❤❡❛t tr❛♥s❢❡r✳ ❍✉♥t✐♥❣t♦♥✱◆✳❨✳ ✿ ❘✳ ❊✳ ❑r✐❡❣❡r P✉❜✳ ❈♦✱ ✶✾✼✾✳ ■❙❇◆ ✾✼✽✲✵✲✽✽✷✼✺✲✾✶✼✲✸✳

❬✹✻❪ ●r❡❡♥✇❛②✱ ▼✳ ❛♥❞ ❲♦♦❞✱ ❈✳ ❚❤❡ ❖①❢♦r❞ ❯♥✐✈❡rs✐t② ✹ ♠ ① ✷ ♠ ■♥❞✉str✐❛❧ ❆❡r♦❞②✲♥❛♠✐❝s ❲✐♥❞ ❚✉♥♥❡❧✳ ❏♦✉r♥❛❧ ♦❢ ❲✐♥❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ■♥❞✉str✐❛❧ ❆❡r♦❞②♥❛♠✐❝s✱✹✭✶✮✿✹✸✕✼✵✱ ✶✾✼✾✳

❬✹✼❪ ❈❤♠✐❡❧❡✇s❦✐✱ ●✳ ❊✳ ❇♦✉♥❞❛r②✲▲❛②❡r ❈♦♥s✐❞❡r❛t✐♦♥s ✐♥ t❤❡ ❉❡s✐❣♥ ♦❢ ❆❡r♦❞②♥❛♠✐❝❈♦♥tr❛❝t✐♦♥s✳ ❏♦✉r♥❛❧ ♦❢ ❆✐r❝r❛❢t✱ ✶✶✭✽✮✿✹✸✺✕✹✸✽✱ ✶✾✼✹✳

❬✹✽❪ ❙❝❤❧✐❝❤t✐♥❣✱ ❍✳ ❇♦✉♥❞❛r②✲▲❛②❡r ❚❤❡♦r②✳ ▼❝●r❛✇✲❍✐❧❧✱ ✶✾✼✾✳

❬✹✾❪ ◆❛❣❡❧✱ ❆✳ ❛♥❞ ❙❤❡♣s❤❡❧♦✈✐❝❤✱ ▼✳ ❚❤❡ ❝♦♥❝❡♣t ♦❢ ❍✐❣❤✲▲✐❢t✱ ▼✐❧❞ ❙t❛❧❧ ❲✐♥❣✳ ■♥✷✹t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❣r❡ss ♦❢ t❤❡ ❆❡r♦♥❛✉t✐❝❛❧ ❙❝✐❡♥❝❡s✱ ✷✵✵✹✳

❬✺✵❪ ❆✐r❢♦✐❧ ❚♦♦❧s✳ ❘●✲✶✺ ✽✳✾✪ ✭r❣✶✺✲✐❧✮✳ ❤tt♣✿✴✴❛✐r❢♦✐❧t♦♦❧s✳❝♦♠✴❛✐r❢♦✐❧✴❞❡t❛✐❧s❄❛✐r❢♦✐❧❂r❣✶✺✲✐❧✱ ✷✵✶✷✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✵✺✳

❬✺✶❪ ❍❛♥♥✱ ❘✳ ❯❆❱ ■❝✐♥❣✿ ■❝❡ ❆❝❝r❡t✐♦♥ ❊①♣❡r✐♠❡♥ts ❛♥❞ ❱❛❧✐❞❛t✐♦♥✳ ■♥ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ■❝✐♥❣ ♦❢ ❆✐r❝r❛❢t✱ ❊♥❣✐♥❡s✱ ❛♥❞ ❙tr✉❝t✉r❡s✳ ❙❆❊ ■♥t❡r♥❛t✐♦♥❛❧✱ ✷✵✶✾✳

❬✺✷❪ ➬❡♥❣❡❧✱ ❨✳ ❆✳ ❛♥❞ ❈✐♠❜❛❧❛✱ ❏✳ ▼✳ ❋❧✉✐❞ ▼❡❝❤❛♥✐❝s✿ ❋✉♥❞❛♠❡♥t❛❧s ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s✳▼❝●r❛✇✲❍✐❧❧✱ ✷✵✶✹✳ ■❙❇◆ ✾✼✽✲✵✲✵✼✲✸✸✽✵✸✷✲✷✳

❬✺✸❪ ❍❛r❡✱ ❉✳ ❊✳ ❛♥❞ ❙♦r❡♥s❡♥✱ ❈✳ ▼✳ ❚❤❡ ❞❡♥s✐t② ♦❢ s✉♣❡r❝♦♦❧❡❞ ✇❛t❡r✳ ■■✳ ❇✉❧❦ s❛♠♣❧❡s❝♦♦❧❡❞ t♦ t❤❡ ❤♦♠♦❣❡♥❡♦✉s ♥✉❝❧❡❛t✐♦♥ ❧✐♠✐t✳ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❈❤❡♠✐❝❛❧ P❤②s✐❝s✱ ✽✼✭✽✮✿✹✽✹✵✕✹✽✹✺✱ ✶✾✽✼✳

❬✺✹❪ ❙t❡♣❛♥♦✈✱ ■✳ ❆♥♦♠❛❧♦✉s ❞❡♣❡♥❞❡♥❝❡ ♦❢ t❤❡ ❤❡❛t ❝❛♣❛❝✐t② ♦❢ s✉♣❡r❝♦♦❧❡❞ ✇❛t❡r ♦♥♣r❡ss✉r❡ ❛♥❞ t❡♠♣❡r❛t✉r❡✳ ❘❡s✉❧ts ✐♥ P❤②s✐❝s✱ ✹✿✷✽ ✕ ✸✵✱ ✷✵✶✹✳

❬✺✺❪ ❙③❡❞❧❛❦✱ ❆✳✱ ❇❧❛♥❝❤❛r❞✱ ❆✳✱ ❑♦st✐♥s❦✐✱ ❆✳✱ ❛♥❞ ❈❛♥tr❡❧❧✱ ❲✳ ❚❤❡ ❚❡♠♣❡r❛t✉r❡❉❡♣❡♥❞❡♥❝❡ ♦❢ ❲❛t❡r✬s ▲❛t❡♥t ❍❡❛t ♦❢ ❋r❡❡③✐♥❣✳ ❆●❯ ❋❛❧❧ ▼❡❡t✐♥❣ ❆❜str❛❝ts✱ ✷✵✵✾✳

❬✺✻❪ ❑r❡②s③✐❣✱ ❊✳✱ ❑r❡②s③✐❣✱ ❍✳✱ ❛♥❞ ◆♦r♠✐♥t♦♥✱ ❊✳ ❏✳ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ▼❛t❤❡♠❛t✲✐❝s✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✱ ✶✵t❤ ❡❞✐t✐♦♥✱ ✷✵✶✶✳ ■❙❇◆ ✾✼✽✲✵✲✹✼✵✲✹✺✽✸✻✲✺✳

❬✺✼❪ ▲❡♦♥❡✱ ●✳✱ ❱❡❝❝❤✐♦♥❡✱ ▲✳✱ ▼❛tt❡✐s✱ P✳ ❉✳✱ ❙③❡♠s❦❛t✱ ❱✳✱ ❛♥❞ ❘❡✐st❡r✱ ❆✳ ❚❤❡ ♥❡✇❈■❘❆ ■❝✐♥❣ ❲✐♥❞ ❚✉♥♥❡❧ ❙♣r❛② ❇❛r ❙②st❡♠ ❞❡✈❡❧♦♣♠❡♥t✳ ■♥ ✸✽t❤ ❆❡r♦s♣❛❝❡ ❙❝✐✲❡♥❝❡s ▼❡❡t✐♥❣ ❛♥❞ ❊①❤✐❜✐t✱ ✷✵✵✵✳

✻✽

❇✐❜❧✐♦❣r❛♣❤②

❬✺✽❪ ❙♣r❛②✐♥❣ ❙②st❡♠s ❈♦✳ ❆✉t♦❥❡t ♣r❡❝✐s✐♦♥ s♣r❛② ❝♦♥tr♦❧ s②st❡♠s✳ ❤tt♣s✿✴✴✇✇✇✳✉❦✳s♣r❛②✳❝♦♠✴▲✐t❡r❛t✉r❡❴P❉❋s✴❇✼✶✷❈❴■♥❞✉str✐❛❧❴P✉❧s❛❏❡t❴◆♦③③❧❡s✳♣❞❢✱ ✷✵✶✼✳❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✾✳

❬✺✾❪ ❙♣r❛②✐♥❣ ❙②st❡♠s ❈♦✳ ❆✉t♦♠❛t✐❝ s♣r❛② ♥♦③③❧❡s✳ ❤tt♣s✿✴✴✇✇✇✳s♣r❛②✳❝♦♠✴✲✴♠❡❞✐❛✴❉❆▼✴❙❛❧❡s✲▼❛t❡r✐❛❧s✴❝✴❝❛t✼✻❆❆❴✉s❴❆✉t♦♠❛t✐❝❴❇✳♣❞❢✱ ✷✵✶✼✳ ♣❛❣❡✿ ✶✵✳❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✾✳

❬✻✵❪ ❘♦❝❤❛✱ ❍✳ ❙✳ ❞✳✱ ▼❛rq✉❡s✱ P✳ ❆✳ ❆✳✱ ❈❛♠❛r❣♦✱ ❆✳ P✳ ❞✳✱ ❋r✐③③♦♥❡✱ ❏✳ ❆✳✱ ❛♥❞ ❙❛r❡tt❛✱❊✳ ■♥t❡r♥❛❧ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ ♣❧❛st✐❝ ♣✐♣❡s ❢♦r ✐rr✐❣❛t✐♦♥✳ ❘❡✈✐st❛ ❇r❛s✐❧❡✐r❛ ❞❡❊♥❣❡♥❤❛r✐❛ ❆❣rí❝♦❧❛ ❡ ❆♠❜✐❡♥t❛❧✱ ✷✶✿✶✹✸ ✕ ✶✹✾✱ ✷✵✶✼✳

❬✻✶❪ ❆❡r♦✈❡♥t✳ ❱❛♥❡❛①✐❛❧ ❋❛♥s✳ ❤tt♣s✿✴✴❛❡r♦✈❡♥t✳❝♦♠✴✇♣✲❝♦♥t❡♥t✴✉♣❧♦❛❞s✴✷✵✶✽✴✶✷✴❱❛♥❡❛①✐❛❧✲❋❛♥s✲❚②♣❡✲❲✲▼♦❞❡❧s✲❱❲❇❉✲❱❲✲❈❛t❛❧♦❣✲✹✺✻✳♣❞❢✱ ✷✵✶✽✳ ❆❝✲❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✵✺✳

❬✻✷❪ ▼❡t❛❧▼✐♥❡r✳ ▼❡t❛❧▼✐♥❡r Pr✐❝❡s✿ ❆❧✉♠✐♥✉♠ Pr✐❝❡s✳ ❤tt♣s✿✴✴❛❣♠❡t❛❧♠✐♥❡r✳❝♦♠✴♠❡t❛❧✲♣r✐❝❡s✴❛❧✉♠✐♥✉♠✴✱ ✷✵✷✵✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✸✳

❬✻✸❪ ❲✐❧t✐♥❣✱ ❍✳ ❈✳ ❛♥❞ ❍❛♥❡♠❛❛✐❥❡r✱ ❆✳ ❍✳ ❙❤❛r❡ ♦❢ r❛✇ ♠❛t❡r✐❛❧ ❝♦sts ✐♥ t♦t❛❧ ♣r♦❞✉❝✲t✐♦♥ ❝♦sts✳ ✱ P❇▲ ◆❡t❤❡r❧❛♥❞s ❊♥✈✐r♦♥♠❡♥t❛❧ ❆ss❡ss♠❡♥t ❆❣❡♥❝②✱ ✷✵✶✹✳

❬✻✹❪ ❙♣r❛②✐♥❣ ❙②st❡♠s ❈♦✳ ❲✐♥❞s❤✐❡❧❞ ▼❛♥✉❢❛❝t✉r❡r ❙❛✈❡s ❯❙✩ ✼✺✱✵✵✵ ✇✐t❤ ❆✉t♦♠❛t❡❞❙♣r❛② ❙②st❡♠✳ ❤tt♣s✿✴✴✇✇✇✳s♣r❛②✳❞❡✴❧✐t❡r❛t✉r❡❴♣❞❢s✴❈❙✷✷✺❴❲✐♥❞s❤✐❡❧❞❴▼❛♥✉❢❛❝t✉r❡r❴❙❛✈❡s❴✇✐t❤❴❆✉t♦❴❙♣r❛②❴❙②s✳♣❞❢✱ ✷✵✶✻✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✸✳

❬✻✺❪ P❛✐♥t ❇♦♦t❤ ❙✉♣♣❧②✳ ✹✷ ✧ ✧❆❡r♦✈❡♥t✧ ❚✉❜❡ ❆①✐❛❧ ❋❛♥ ▲❡ss ▼♦t♦r ✭❋♦r ❯s❡❲✐t❤ ✼✳✺❍P✮✳ ❤tt♣s✿✴✴✇✇✇✳♣❛✐♥t❜♦♦t❤s✉♣♣❧②✳❝♦♠✴♣r♦❞✉❝t❴♣✴❛t❛✲✹✷✲✵✼✺✳❤t♠✱ ✷✵✷✵✳ ❆❝❝❡ss❡❞✿ ✷✵✷✵✲✵✼✲✶✸✳

❬✻✻❪ ❙❆❊✲❆❘P ✺✾✵✺✳ ❈❛❧✐❜r❛t✐♦♥ ❛♥❞ ❆❝❝❡♣t❛♥❝❡ ♦❢ ■❝✐♥❣ ❲✐♥❞ ❚✉♥♥❡❧s✱ ✷✵✶✺✳

✻✾

❆ ❆♣♣❡♥❞✐①

❆✳✶ ❯❆❱ ❉❛t❛❜❛s❡

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References UAV Database [1] Northrop Grumman (2016): "RQ-4 Block 30 Global Hawk". URL: http://web.archive.org/web/ 20200112193929/https://www.northropgrumman.com/Capabilities/GlobalHawk/Documents/GH_Brochure_B30.pdf (access: 20.01.2020)

[2] U.S. Air Force (2014, October 27): "RQ-4 Global Hawk". URL: https://www.af.mil/About-Us/Fact-Sheets/Display/Article/104516/rq-4-global-hawk/ (access: 20.01.2020) [3] Zsolt Bottyán: "In-flight icing characteristics of unmanned aerial vehicles during special atmospheric condition over the carpathian-basin". Landscape & Environment 7 (2) 2013. 74-80 [4] Guy Norris (2001, January 30): "Unmanned Air Vehicles - Global leader". URL: https:// www.flightglobal.com/unmanned-air-vehicles-global-leader/35917.article (access: 20.01.2020) [5] U.S. Air Force (2015, September 23): "MQ-1B Predator". URL: https://www.af.mil/About-Us/Fact-Sheets/Display/Article/104469/mq-1b-predator/ (access: 20.01.2020) [6] David Lednicer (2010, September 15): "The Incomplete Guide to Airfoil Usage". URL: https://m-selig.ae.illinois.edu/ads/aircraft.html (access: 20.01.2020) [7] The Warfighter Encyclopedia (2001, January 27): "RQ-1 Predator". URL: https://web.archive.org/ web/20041105115728/https://wrc.navair-rdte.navy.mil/warfighter_enc/aircraft/UAVs/predator.htm (access: 20.01.2020) [8] Military Factory (2019, April 11): "AAI (Textron) RQ-7 Shadow". URL: https://www.militaryfactory.com/aircraft/detail.asp?aircraft_id=326 (access: 20.01.2020) [9] RCGroups (2011, March 30): "Shadow 200 UAV – research". URL: https://www.rcgroups.com/ forums/showthread.php?1415637-Shadow-200-UAV-research (access: 20.01.2020) [10] Insitu (2015): "RQ-21A Blackjack". URL: https://www.insitu.com/images/uploads/pdfs/RQ-21ABlackjack_v2_ProductCard_PR120115.pdf (access: 20.01.2020) [11] Hope Hodge Seck: "Marine Special Operators Fly New Surveillance Drone in Iraq". URL: https://www.military.com/daily-news/2016/10/08/marine-special-operators-fly-new-surveillance-drone-in-iraq.html?ERSC=todayinmil.sm (access: 20.01.2020) [12] Insitu: "ScanEagle System". URL: https://web.archive.org/web/20130126192751/http:// www.insitu.com/systems/scaneagle (access: 20.01.2020) [13] RCGroups (2006, July 31): "ScanEagle UAV Project". URL: https://www.rcgroups.com/forums/ showthread.php?549982-ScanEagle-UAV-Project (access: 20.01.2020)

[14] Maritime Robotics: "PX-31". URL: https://0257507f-59fc-4319-ab54-9d567d769b35. filesusr.com/ugd/a0d8a5_d4defc8e2e814a4dabeda68ee2b5cb74.pdf (access: 20.01.2020) [15] UAV Factory: "Penguin B UAV platform". URL: https://www.uavfactory.com/product/46 (access: 20.01.2020)

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❆ ❆♣♣❡♥❞✐①

❆✳✷ ❆❞❞✐t✐♦♥❛❧ ❋✐❣✉r❡s

❋✐❣✉r❡ ❆✳✶✿ ❉❡s✐❣♥ r✉❧❡s ❢♦r t❤❡ ❧❡♥❣t❤ ♦❢ ♥♦③③❧❡s ❢♦r ❞✐✛❡r❡♥t r❛t✐♦s ♦❢ ✐♥❧❡t t♦ ♦✉t❧❡t❞✐❛♠❡t❡r✳ ❆❞❛♣t❡❞ ❢r♦♠ ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪✳

✽✵

❆ ❆♣♣❡♥❞✐①

❋✐❣✉r❡ ❆✳✷✿ ◆❡❝❡ss❛r② ♥✉♠❜❡r ♦❢ s❝r❡❡♥s ✐♥ t❤❡ ✇✐❞❡✲❛♥❣❧❡ ❞✐✛✉s❡r ❢♦r ❝❡rt❛✐♥ ♦♣❡♥✐♥❣❛♥❣❧❡s ❛♥❞ ❛r❡❛ r❛t✐♦s✳ ❆❞❛♣t❡❞ ❢r♦♠ ▼❡❤t❛ ❛♥❞ ❇r❛❞s❤❛✇ ❬✸✾❪✳

✽✶

❆ ❆♣♣❡♥❞✐①

❆✳✸ ❚❤❡ ❘●✶✺ ❛✐r❢♦✐❧

❍❡r❡✱ t❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ s✉r❢❛❝❡ ♦❢ ❛♥ ❘● ✶✺ ❛✐r❢♦✐❧ ❛r❡ ♣❧♦tt❡❞✳ ❚❤❡ ①✲❛①✐s ✐s t❤❡ ❛①✐s✐♥ ✢♦✇ ❞✐r❡❝t✐♦♥✳ ❚❤❡ ③✲❛①✐s ✐s ♣❡r♣❡♥❞✐❝✉❧❛r t♦ t❤❡ ①✲❛①✐s✳ ❇♦t❤ ❛①❡s ❛r❡ ♥♦r♠❛❧✐③❡❞✇✐t❤ t❤❡ ❝❤♦r❞ ❧❡♥❣t❤ ♦❢ t❤❡ ❛✐r❢♦✐❧✳ ❚❤❡r❡❢♦r❡ t❤❡ ①✲❛①✐s ❤❛s ✈❛❧✉❡s ❜❡t✇❡❡♥ 0 ❛♥❞ 1✳

①✲♣♦s✐t✐♦♥ ③✲♣♦s✐t✐♦♥✶✳✵✵✵✵✵✵ ✵✳✵✵✵✵✵✵✵✳✾✾✻✼✶✵ ✵✳✵✵✵✺✹✵✵✳✾✽✼✷✻✵ ✵✳✵✵✷✷✾✵✵✳✾✼✷✸✼✵ ✵✳✵✵✺✶✹✵✵✳✾✺✷✹✽✵ ✵✳✵✵✽✻✺✵✵✳✾✷✼✻✹✵ ✵✳✵✶✷✺✹✵✵✳✽✾✽✶✵✵ ✵✳✵✶✻✽✺✵✵✳✽✻✹✷✼✵ ✵✳✵✷✶✺✷✵✵✳✽✷✻✻✵✵ ✵✳✵✷✻✹✹✵✵✳✼✽✺✺✼✵ ✵✳✵✸✶✹✾✵✵✳✼✹✶✻✺✵ ✵✳✵✸✻✺✹✵✵✳✻✾✺✸✼✵ ✵✳✵✹✶✹✻✵✵✳✻✹✼✷✸✵ ✵✳✵✹✻✶✷✵✵✳✺✾✼✼✽✵ ✵✳✵✺✵✸✾✵✵✳✺✹✼✺✸✵ ✵✳✵✺✹✶✹✵✵✳✹✾✼✵✷✵ ✵✳✵✺✼✷✼✵✵✳✹✹✻✼✻✵ ✵✳✵✺✾✻✻✵✵✳✸✾✼✷✼✵ ✵✳✵✻✶✷✸✵✵✳✸✹✾✵✷✵ ✵✳✵✻✶✾✵✵✵✳✸✵✷✹✽✵ ✵✳✵✻✶✻✷✵✵✳✷✺✽✵✾✵ ✵✳✵✻✵✸✻✵

✵✳✷✶✻✷✹✵ ✵✳✵✺✽✶✵✵✵✳✶✼✼✸✵✵ ✵✳✵✺✹✽✻✵✵✳✶✹✶✻✶✵ ✵✳✵✺✵✻✽✵✵✳✶✵✾✹✺✵ ✵✳✵✹✺✻✹✵✵✳✵✽✶✵✽✵ ✵✳✵✸✾✽✺✵✵✳✵✺✻✼✸✵ ✵✳✵✸✸✹✸✵✵✳✵✸✻✺✽✵ ✵✳✵✷✻✺✹✵✵✳✵✷✵✼✻✵ ✵✳✵✶✾✸✺✵✵✳✵✵✾✸✷✵ ✵✳✵✶✷✶✹✵✵✳✵✵✷✸✺✵ ✵✳✵✵✺✷✻✵✵✳✵✵✵✵✵✵ ✵✳✵✵✵✵✵✵✵✳✵✵✵✵✷✵ ✲✵✳✵✵✵✹✽✵✵✳✵✵✸✸✻✵ ✲✵✳✵✵✺✸✹✵✵✳✵✶✷✹✼✵ ✲✵✳✵✶✵✵✻✵✵✳✵✷✻✼✵✵ ✲✵✳✵✶✹✸✻✵✵✳✵✹✺✾✻✵ ✲✵✳✵✶✽✶✶✵✵✳✵✼✵✶✵✵ ✲✵✳✵✷✶✷✸✵✵✳✵✾✽✾✻✵ ✲✵✳✵✷✸✼✷✵✵✳✶✸✷✷✹✵ ✲✵✳✵✷✺✺✾✵✵✳✶✻✾✻✸✵ ✲✵✳✵✷✻✽✽✵✵✳✷✶✵✼✸✵ ✲✵✳✵✷✼✻✷✵✵✳✷✺✺✵✾✵ ✲✵✳✵✷✼✽✺✵

✵✳✸✵✷✷✶✵ ✲✵✳✵✷✼✻✷✵✵✳✸✺✶✺✻✵ ✲✵✳✵✷✻✾✻✵✵✳✹✵✷✺✼✵ ✲✵✳✵✷✺✾✵✵✵✳✹✺✹✻✸✵ ✲✵✳✵✷✹✹✻✵✵✳✺✵✼✶✸✵ ✲✵✳✵✷✷✻✷✵✵✳✺✺✾✹✹✵ ✲✵✳✵✷✵✷✺✵✵✳✻✶✶✷✽✵ ✲✵✳✵✶✼✶✼✵✵✳✻✻✷✹✹✵ ✲✵✳✵✶✸✻✻✵✵✳✼✶✷✸✼✵ ✲✵✳✵✶✵✶✺✵✵✳✼✻✵✸✼✵ ✲✵✳✵✵✻✾✶✵✵✳✽✵✺✼✺✵ ✲✵✳✵✵✹✶✸✵✵✳✽✹✼✼✾✵ ✲✵✳✵✵✶✾✷✵✵✳✽✽✺✽✸✵ ✲✵✳✵✵✵✸✹✵✵✳✾✶✾✷✺✵ ✵✳✵✵✵✻✷✵✵✳✾✹✼✹✽✵ ✵✳✵✵✶✵✶✵✵✳✾✼✵✵✸✵ ✵✳✵✵✵✾✼✵✵✳✾✽✻✺✷✵ ✵✳✵✵✵✻✹✵✵✳✾✾✻✻✵✵ ✵✳✵✵✵✷✶✵✶✳✵✵✵✵✵✵ ✵✳✵✵✵✵✵✵

❚❤❡ s❤❛♣❡ ♦❢ ❛♥ ❘●✶✺ ❛✐r❢♦✐❧ ✇✐t❤ ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 0◦ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ❆✳✸✳

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

z-coordinates

x-coordinates

❋✐❣✉r❡ ❆✳✸✿ ❚❤❡ ❘●✶✺ ❛✐r❢♦✐❧ ✇✐t❤ ❛♥ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ ♦❢ 0◦✳ ❆①❡s ❛r❡ ♥♦r♠❛❧✐③❡❞ ✇✐t❤t❤❡ ❝❤♦r❞ ❧❡♥❣t❤✳

✽✷

❆ ❆♣♣❡♥❞✐①

❆✳✹ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✉s✐♥❣ t❤❡ ▼❡♥t❡r k − ω ❙❙❚

♠♦❞❡❧

❆s ❡①♣❧❛✐♥❡❞ ✐♥ s✉❜s❡❝t✐♦♥ ✷✳✷✳✶✱ t❤❡ ✐♠♣❛❝t ♦❢ t✉r❜✉❧❡♥❝❡ ✐s ♠♦❞❡❧❡❞ ✐♥ ♦✉r ❈❋❉ s✐♠✲✉❧❛t✐♦♥s✳ ❇② ♠♦❞❡❧✐♥❣ t❤❡ t✉r❜✉❧❡♥❝❡✱ t❤❡ ❝❛❧❝✉❧❛t❡❞ ✢♦✇ ✜❡❧❞ ❝❛♥ ❞✐✛❡r ❢r♦♠ t❤❡ tr✉❡✢♦✇ ✜❡❧❞✳ ❚❤❡r❡❢♦r❡ ❞♦✐♥❣ ❛ ❝♦♠♣❛r✐s♦♥ ✇✐t❤ ❛t ❧❡❛st ❛ s❡❝♦♥❞ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧ ✐s❛❧✇❛②s r❡❛s♦♥❛❜❧❡✳ ❋♦r t❤✐s t❤❡s✐s✱ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥s ✇❡r❡ ❞♦♥❡ ✇✐t❤ t✇♦ ❞✐✛❡r❡♥tt✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤❡ ❙♣❛❧❛rt✲❆❧❧♠❛r❛s ♠♦❞❡❧ ✇❡r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤❡♠❛✐♥ ♣❛rt ♦❢ t❤❡ t❤❡s✐s✳ ❚❤❡ ✈❡❧♦❝✐t② ♣❧♦t ♦❢ t❤❡ s✐♠✉❧❛t✐♦♥ ✇✐t❤ t❤❡ ▼❡♥t❡r k − ω ❙❙❚♠♦❞❡❧ ✐s s❤♦✇♥ ✐♥ ❋✐❣✉r❡ ❆✳✹✳

❋✐❣✉r❡ ❆✳✹✿ ❱❡❧♦❝✐t② ♣❧♦t ♦❢ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✇✐t❤ ❛ s❡❝♦♥❞ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧✳

❚❤❡ ✢♦✇ ✜❡❧❞ ❧♦♦❦s s✐♠✐❧❛r t♦ t❤❡ ♦♥❡ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡ ❙♣❛❧❛rt✲❆❧❧♠❛r❛s t✉r❜✉❧❡♥❝❡♠♦❞❡❧✳ ❚❤❡ s❛♠❡ ✐s tr✉❡ ❢♦r t❤❡ s❡♣❛r❛t✐♦♥ ♣❧♦t ✐♥ ❋✐❣✉r❡ ❆✳✺✳ ❚❤❡ ♣r❡ss✉r❡ ❧♦ss❡s ♦❢❜♦t❤ ♠♦❞❡❧s ✇❡r❡ ❛❧r❡❛❞② ♣r❡s❡♥t❡❞ ✐♥ ❚❛❜❧❡ ✹✳✼✳ ❲❤✐❧❡ t❤❡ t✇♦ s✐♠✉❧❛t✐♦♥s s❤♦✇ s♠❛❧❧❞✐✛❡r❡♥❝❡s✱ t❤❡② ❛r❡ ♠✉❝❤ ❝❧♦s❡r t♦ ❡❛❝❤ ♦t❤❡r t❤❛♥ t✇♦ t❤❡ ✈❛❧✉❡s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ t❤❡❜❛s✐❝ ❡q✉❛t✐♦♥s ❣✐✈❡♥ ♠♦st❧② ❜② ❊❝❦❡rt ❡t ❛❧✳ ❬✸✷❪✳

❋✐❣✉r❡ ❆✳✺✿ P❧♦t ♦❢ t❤❡ s❡♣❛r❛t✐♦♥ ③♦♥❡s ✐♥ t❤❡ ❈❋❉ s✐♠✉❧❛t✐♦♥ ✇✐t❤ ❛ s❡❝♦♥❞ t✉r❜✉❧❡♥❝❡♠♦❞❡❧✳

❚❤❡ ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡ t✇♦ ❞✐✛❡r❡♥t t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧s s❤♦✇❡❞ ❥✉st ✈❡r② s♠❛❧❧ ❞✐❢✲❢❡r❡♥❝❡s✳ ❚❤❡r❡❢♦r❡ t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❈❋❉ s✐♠✉❧❛t✐♦♥s ❛♥❞ t❤❡ ✈❛❧✉❡s ❝❛❧❝✉❧❛t❡❞✇✐t❤ ❛❧❣❡❜r❛✐❝ ❡q✉❛t✐♦♥s ❞❡♣❡♥❞s ♥♦t ♦♥ t❤❡ ❝❤♦✐❝❡ ♦❢ t❤❡ t✉r❜✉❧❡♥❝❡ ♠♦❞❡❧✳

✽✸

❆ ❆♣♣❡♥❞✐①

❆✳✺ ■❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s♣❡❝✐✜❝❛t✐♦♥s

❚❤❡ ✜♥❛❧ s♣❡❝✐✜❝❛t✐♦♥s ♦❢ t❤❡ t✇♦ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧s ❞❡s✐❣♥❡❞ ✐♥ t❤✐s t❤❡s✐s ❛r❡ ❝♦♠♣❛r❡❞✐♥ ❚❛❜❧❡ ❆✳✶✳

♣❛r❛♠❡t❡r ❜✐❣ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧

♠❛①✐♠✉♠ s♣❡❡❞ ❛t t❡st s❡❝t✐♦♥ 35m s−1 25m s−1

♠❛①✐♠✉♠ ❝❤♦r❞ ❧❡♥❣t❤ 0.4m 0.3m♠❛①✐♠✉♠ ❛♥❣❧❡ ♦❢ ❛tt❛❝❦ 8◦ 4◦

✉♥✐♠♣❡❞❡❞ t❡st s❡❝t✐♦♥ ✇✐❞t❤ 0.30m 0.18m♠✐♥✐♠✉♠ ❛✐r t❡♠♣❡r❛t✉r❡ −15 ➦C −10 ➦C

♠❛①✐♠✉♠ ▼❱❉ 38µm 23µm✇✐♥❞ t✉♥♥❡❧ ❧❡♥❣t❤ 8.03m 3.24m

♠❛①✐♠✉♠ ❝r♦ss✲s❡❝t✐♦♥ 1.54m ① 1.54m 0.70m ① 0.70m❢❛♥ ♣♦✇❡r 8.024 kW 1.33 kW

♥❡❝❡ss❛r② ❝♦♦❧✐♥❣ ♣♦✇❡r 20.52 kW 3.942 kW

❚❛❜❧❡ ❆✳✶✿ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ s♣❡❝✐✜❝❛t✐♦♥s ♦❢ t❤❡ ❜✐❣ ❛♥❞ t❤❡ s♠❛❧❧ ✐❝✐♥❣ ✇✐♥❞ t✉♥♥❡❧✳

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