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UNIVERSITY OF GENOVA SCUOLA POLITECNICA MASTER OF SCIENCE THESIS IN MECHANICAL ENGINEERING Numerical simulation of a droplet icing on a cold surface Supervisors: Candidates: Prof.


  1. UNIVERSITY OF GENOVA SCUOLA POLITECNICA MASTER OF SCIENCE THESIS IN MECHANICAL ENGINEERING Numerical simulation of a droplet icing on a cold surface Supervisors: Candidates: Prof. Alessandro Bottaro Saverio Buccini Prof. Dominique Legendre Francesco Peccianti March 2017

  2. ❙✐♠✉❧❛③✐♦♥❡ ♥✉♠❡r✐❝❛ ❞❡❧ ❝♦♥❣❡❧❛♠❡♥t♦ ❞✐ ✉♥❛ ❣♦❝❝✐❛ s✉ ✉♥❛ s✉♣❡r✜❝✐❡ ❢r❡❞❞❛ ❙♦♠♠❛r✐♦ ▲✬♦❜❜✐❡tt✐✈♦ ❞❡❧ ♣r❡s❡♥t❡ ❧❛✈♦r♦ ❞✐ t❡s✐ ❝♦♥s✐st❡ ♥❡❧ s✐♠✉❧❛r❡ ♥✉♠❡r✐❝❛♠❡♥t❡ ✐❧ ❢❡♥♦♠❡♥♦ ❞❡❧ ❝♦♥❣❡❧❛♠❡♥t♦ ❞✐ ✉♥❛ ❣♦❝❝✐❛ ❞✬❛❝q✉❛ ♣♦st❛ ❛ ❝♦♥t❛tt♦ ❝♦♥ ✉♥❛ s✉♣❡r✜❝✐❡ ❢r❡❞❞❛✳ ■♥ ♣❛rt✐❝♦❧❛r❡✱ ✉♥♦ ❞❡❣❧✐ s❝♦♣✐ è s✐♠✉❧❛r❡ ❡ ❞❡t❡r♠✐♥❛r❡ ❧❛ ❝❛✉s❛ ♦ ❧❡ ❝❛✉s❡ ❝❤❡ ♣♦rt❛♥♦ ❛❧❧❛ ❢♦r♠❛③✐♦♥❡ ❞❡❧❧❛ ❝❛r❛tt❡r✐st✐❝❛ ♣✉♥t❛ ❝❤❡ ♣✉ò ❡ss❡r❡ ♦ss❡r✈❛t❛ ✐♥ ❝✐♠❛ ❛❧❧❛ ❣♦❝❝✐❛ st❡ss❛ ✉♥❛ ✈♦❧t❛ ❝❤❡ ❡ss❛ s✐ è ❝♦♥❣❡❧❛t❛✳ ❆ t❛❧❡ s❝♦♣♦✱ è st❛t♦ ✉t✐❧✐③③❛t♦ ✐❧ ❝♦❞✐❝❡ ❏❆✲ ❉■▼ s✈✐❧✉♣♣❛t♦ ❛❧❧✬ ■♥st✐t✉t ❞❡ ▼é❝❛♥✐q✉❡s ❞❡s ❋❧✉✐❞❡s ❞❡ ❚♦✉❧♦✉s❡ ✳ ❈♦♥ ❧✬♦❜❜✐❡tt✐✈♦ ❞✐ s✐♠✉❧❛r❡ ❧✬❡s♣❛♥s✐♦♥❡ ❞❡❧❧✬❛❝q✉❛ ♥❡❧ ❝♦rs♦ ❞❡❧ ♣❛ss❛❣❣✐♦ ❞❛❧ s✉♦ st❛t♦ ❧✐q✉✐❞♦ ❛ q✉❡❧❧♦ s♦❧✐❞♦✱ ♥❡❧ ❝♦❞✐❝❡ ✐♥ ♦❣❣❡tt♦ è st❛t❛ ✐♠♣❧❡♠❡♥t❛t❛ ✉♥❛ ❢♦r♠✉❧❛③✐♦♥❡ ♦r✐❣✐♥❛❧❡ ❝❤❡ ❛❝✲ ❝♦♣♣✐❛ ✐❧ ❝❛❧❝♦❧♦ t❡r♠♦❞✐♥❛♠✐❝♦✱ ✐❧ ♠❡t♦❞♦ ■♠♠❡rs❡❞ ❇♦✉♥❞❛r② ❡ ❧❛ ❢♦r♠✉❧❛③✐♦♥❡ ❞❡tt❛ ❱♦❧✉♠❡ ♦❢ ❋❧✉✐❞ ✭❱♦❋✮ ✳ ■♥✜♥❡✱ è st❛t❛ s✈♦❧t❛ ✉♥✬❛♥❛❧✐s✐ s✉✐ ♣❛r❛♠❡tr✐ ❝❤❡ ♠❛❣❣✐♦r♠❡♥t❡ ✐♥✢✉❡♥③❛♥♦ ❧❛ ✈❡❧♦❝✐tà ❞✐ ❝♦♥❣❡❧❛♠❡♥t♦✱ ❛❧ ✜♥❡ ❞✐ ❞❡t❡r♠✐♥❛r❡ s♦❧✉③✐♦♥✐ t❡❝♥✐❝❤❡ ❝❤❡ ♣♦ss❛♥♦ ♣❡r♠❡tt❡r❡ ❞✐ r✐t❛r❞❛r❡ ❧❛ ❢♦r♠❛③✐♦♥❡ ❞✐ ❣❤✐❛❝❝✐♦ s✉ ✉♥❛ s✉♣❡r✜❝✐❡✳ ✐

  3. ◆✉♠❡r✐❝❛❧ s✐♠✉❧❛t✐♦♥ ♦❢ ❛ ❞r♦♣❧❡t ✐❝✐♥❣ ♦♥ ❛ ❝♦❧❞ s✉r❢❛❝❡ ❆❜str❛❝t ❚❤❡ ♦❜❥❡❝t✐✈❡ ♦❢ t❤❡ ♣r❡s❡♥t ✇♦r❦ ✐s t♦ ♥✉♠❡r✐❝❛❧❧② s✐♠✉❧❛t❡ t❤❡ ✐❝✐♥❣ ♣❤❡♥♦♠❡♥♦♥ ♦❢ ❛ ✇❛t❡r ❞r♦♣❧❡t ✇❤❡♥ ❞❡♣♦s❡❞ ♦♥ ❛ ❝♦❧❞ s✉r❢❛❝❡✳ ■♥ ♣❛rt✐❝✉❧❛r✱ ♦♥❡ ♦❢ t❤❡ ♦❜❥❡❝t✐✈❡ ✐s t♦ s✐♠✉❧❛t❡ ❛♥❞ ❞❡t❡r♠✐♥❡ t❤❡ ❝❛✉s❡✭s✮ ❢♦r t❤❡ ❝❤❛r❛❝t❡r✐st✐❝ ♣♦✐♥t② t✐♣ t❤❛t ❛♣♣❡❛rs ♦♥ t❤❡ t♦♣ ♦❢ t❤❡ ❢r♦③❡♥ ❞r♦♣ ♦♥❝❡ t❤❡ s♦❧✐❞✐✜❝❛t✐♦♥ ❤❛s ❝♦♠♣❧❡t❡❞✳ ■♥ ♦r❞❡r t♦ ❛❝❝♦♠♣❧✐s❤ t❤✐s t❛s❦ t❤❡ r❡s❡❛r❝❤ ❝♦❞❡ ❏❆❉■▼ ❞❡✈❡❧♦♣♣❡❞ ❛t t❤❡ ■♥st✐t✉t ❞❡ ▼é❝❛♥✐q✉❡s ❞❡s ❋❧✉✐❞❡s ❞❡ ❚♦✉❧♦✉s❡ ❤❛s ❜❡❡♥ ✉s❡❞✳ ❲✐t❤ t❤❡ ❛✐♠ t♦ s✐♠✉❧❛t❡ t❤❡ ❡①♣❛♥s✐♦♥ ❡①♣❡r✐❡♥❝❡❞ ❜② t❤❡ ✇❛t❡r ❞✉r✐♥❣ t❤❡ tr❛♥s✐t✐♦♥ ❢r♦♠ ✐ts ❧✐q✉✐❞ t♦ ✐ts s♦❧✐❞ st❛t❡ ✐♥ t❤❡ ❝♦❞❡ ❛♥ ♦r✐❣✐♥❛❧ ❢♦r♠✉❧❛t✐♦♥ ❤❛s ❜❡❡♥ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ✇❤✐❝❤ t❤❡ t❤❡r♠❛❧ ❝♦♠♣✉t❛t✐♦♥✱ t❤❡ ■♠♠❡rs❡❞ ❇♦✉♥❞❛r② ▼❡t❤♦❞ ✭■❇▼✮ ❛♥❞ t❤❡ ❱♦❧✉♠❡ ♦❢ ❋❧✉✐❞ ✭❱♦❋✮ ❛♣♣r♦❛❝❤ ❤❛✈❡ ❜❡❡♥ ❝♦✉♣❧❡❞✳ ❋✉rt❤❡r♠♦r❡✱ ❛♥ ❛♥❛❧②s✐s ♦♥ t❤❡ ♠❛✐♥ ♣❛r❛♠❡t❡rs ✇❤✐❝❤ ❛✛❡❝t t❤❡ ✐❝✐♥❣ ✈❡❧♦❝✐t② ❤❛s ❜❡❡♥ ♣❡r❢♦r♠❡❞ ✐♥ ♦r❞❡r t♦ ❞❡t❡r♠✐♥❡ ♣♦ss✐❜❧❡ t❡❝❤♥♦❧♦❣✐❝❛❧ s♦❧✉t✐♦♥s t♦ ❞❡❧❛② t❤❡ ❛❝❝r❡t✐♦♥ ♦❢ ✐❝❡ ♦♥ t❤❡ s✉r❢❛❝❡s✳ ✐✐

  4. ❘✐♥❣r❛③✐❛♠❡♥t✐ ❱♦❣❧✐♦ r✐♥❣r❛③✐❛r❡ ✐❧ ♣r♦❢❡ss♦r ❆❧❡ss❛♥❞r♦ ❇♦tt❛r♦ ♣❡r ❧✬♦♣♣♦rt✉♥✐tà ❞❛t❛♠✐ ❞✐ s✈♦❧✲ ❣❡r❡ q✉❡st❛ t❡s✐ ❛❧❧✬ ■♥st✐t✉t ❞❡ ▼é❝❛♥✐q✉❡s ❞❡s ❋❧✉✐❞❡s ❞❡ ❚♦✉❧♦✉s❡ ❡ ♣❡r ✐ s✉♦✐ ❝♦♥s✐❣❧✐✱ ❝♦sì ❝♦♠❡ ✐❧ ♣r♦❢❡ss♦r ❉♦♠✐♥✐q✉❡ ▲❡❣❡♥❞r❡ ❝❤❡ ♠✐ ❤❛ ❛❝❝♦❧t♦ ❡ ❛✐✉t❛t♦ ♥❡❧ ❝♦rs♦ ❞❡❧ ❧❛✈♦r♦✳ ❚r❛ ✐ ♠✐❡✐ ❝♦♠♣❛❣♥✐ ❞✐ st✉❞✐✱ ✈♦❣❧✐♦ r✐❝♦r❞❛r❡ ✐♥ ♣❛rt✐❝♦❧❛r ♠♦❞♦ ❙❛✈❡r✐♦ ❝♦♥ ❝✉✐ ❤♦ ❝♦♥❞✐✈✐s♦ ❧✬❡s♣❡r✐❡♥③❛ ❞✐ ❚♦❧♦s❛ ♠❛ ❛♥❝❤❡ ▼❡r❧♦✱ ❆♥♥❛✱ ▼✐r♦✱ ❊♠❛✱ ❘✐❝❤✐✱ P❡rr✐✱ ❋r❛✱ ❇❛③③✉ ❡ ▲♦r❡ ❝♦♥ ✐ q✉❛❧✐ ❤♦ tr❛s❝♦rs♦ ❣r❛♥ ♣❛rt❡ ❞❡❧ ♠✐♦ t❡♠♣♦ ❞✉r❛♥t❡ q✉❡st✐ ❝✐♥q✉❡ ❡ ♣✐ù ❛♥♥✐ ❞✐ st✉❞✐✳ ◗✉✐♥❞✐ ✈♦❣❧✐♦ r✐♥❣r❛③✐❛r❡ ✐ ♠✐❡✐ ❛♠✐❝✐ ❝♦✐ q✉❛❧✐ ❤♦ tr❛s❝♦rs♦ ❧❛ ♠❛❣❣✐♦r ♣❛rt❡ ❞❡❧ t❡♠♣♦ ❛❧ ❞✐ ❢✉♦r✐ ❞❡❧❧✬✉♥✐✈❡rs✐tà ▼❛♥❣✐✱ ❆❧❜✐✱ P✐♣♣✐✱ ❋♦①✱ ❊❣✱ ●❛❣❣✐♦✫■❧❡✱ ❉❡❝❝❡✱ ●❛✐❛✱ ❈❡❧✐✱ ❙✐❧✈✐❛✱ ❋✉♠❛✱ ❉♦❝✱ ●✐❛♥ ❡ ❳✳ ❉❡❧❧❛ ♠✐❛ ❡s♣❡r✐❡♥③❛ t♦❧♦s✐❛♥❛ r✐❝♦r❞❡rò s❡♠♣r❡ ❝♦♥ ♣✐❛❝❡r❡ ❧❡ ♣❡rs♦♥❡ ❝❤❡ ❧ì ❤♦ ❝♦♥♦s❝✐✉t♦✳ P❡r ♣r✐♠✐✱ ✐♥ ♦r❞✐♥❡ ❞✐ ❝♦♥♦s❝❡♥③❛✱ ❞❡❧ ❣r✉♣♣♦ ■♥t❡r❢❛❝❡ ♦✈✈❡r♦ ✐♥ ♣❛r✲ t✐❝♦❧❛r❡ ❙❡❜✱ ❋❧♦✱ ▼✐❝❤❡❛❧✱ ❊s❧✐✱ ❈❧é♠❡♥t✱ ❱❛❧❡♥t✐♥✱ ❊♠❡r②❦✱ ❏❇✱ P❛✉❧✱ ❘❛❢✱ ❘♦♠❛✐♥✱ ❩❤❡♥❣ ❡ ❆❧❡①✐s ❡ q✉✐♥❞✐ ❝♦❧♦r♦ ❝❤❡ ❤♦ ❝♦♥♦s❝✐✉t♦ ✐♥ ❣✐r♦ ♣❡r ❧❛ ❝✐ttà✱ ❝♦♠❡ ❘❡❧❧♦✱ ❋❡❞❡ ❡ P❛♦❧♦✳ ❚r❛ ✐ ♠✐❡✐ ❛♠✐❝✐ ❞✐ s❡♠♣r❡ ❝❤❡ s♦♥♦ ♣r❛t✐❝❛♠❡♥t❡ ♣❛rt❡ ❞❡❧❧❛ ❢❛♠✐❣❧✐❛ ❛♥❝❤❡ s❡ ♥♦♥ ❝✐ ✈❡❞✐❛♠♦ ❝♦sì s♣❡ss♦✱ ✈♦❣❧✐♦ r✐♥❣r❛③✐❛r❡ ●✐♦r❣✐♦✱ ❋r❛♥❝❡s❝♦ ❡ ▼❛rt❛✳ P❡r ❝♦♥❝❧✉❞❡r❡✱ ✉♥ ❣r❛♥❞❡ ❣r❛③✐❡ ❛✐ ♠✐❡✐ ❣❡♥✐t♦r✐ ♣❡r ✐❧ ❧♦r♦ s✉♣♣♦rt♦ ✐♥ q✉❡st✐ ❛♥♥✐ ❡ ♣❡r ❛✈❡r♠✐ s❡♠♣r❡ ❛♣♣♦❣❣✐❛t♦ ♥❡❧❧❡ ♠✐❡ s❝❡❧t❡✳ ✐✐✐

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