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❯ P
❯ ❯
❯ ❯❯
ssrtçã♦ ♣rs♥t ♦ Pr♦r♠
Pósrçã♦ ♠ ♥♥r â♥ ♦
♥tr♦ ê♥s ♥♦ós ❯♥r
s ♦ st♦ ♥t tr♥ ♦♠♦
rqst♦ ♣r ♣r ♦t♥çã♦ ♦ ít♦
str ♠ ♥♥r â♥
r♥t♦r Pr♦ r ❱③ r
♦♦r♥t♦r Pr♦ r P♦ ér♦ r
♥ ❩♥s
❱
Ficha catalográfica elaborada pelo(a) autor(a), com auxílio do programa de geração automática da
Biblioteca Setorial do CCT/UDESC
Perão, Leandro Henrique Simulação numérica da transferência de calorconjugada de escoamentos turbulentos em canaisaletados / Leandro Henrique Perão. - Joinville ,2017. 156 p.
Orientador: Miguel Vaz Jr Co-orientador: Paulo Sérgio Berving Zdanski Dissertação (Mestrado) - Universidade do Estadode Santa Catarina, Centro de Ciências Tecnológicas, Programa de Pós-Graduação em Engenharia Mecânica,Joinville, 2017.
1. Troca térmica conjugada. 2. Escoamentoturbulento. 3. Canais de placas paralelas aletadas.I. Vaz Jr, Miguel. II. Zdanski, Paulo SérgioBerving. , .III. Universidade do Estado de SantaCatarina, Centro de Ciências Tecnológicas, Programade Pós-Graduação em Engenharia Mecânica. IV. Título.
♦s ♣r♦ss♦rs ♦ PP ♣♦r ♥trr ♠s ♦ q ♣rt ♦ ♦♥♠♥t♦
♣♦r s♥r♠ çã♦ ♦ ♣r♦ss♦♥s♠♦ rç♦ s♣♠♥t ♦ Pr♦
t♠é♠ ♦ Pr♦ ❩♥s ♣ ♦♣♦rt♥ ♣♦ t♠♣♦ ♦ ♣r s rçõs
st ♦tr♦s tr♦s
♦s q ♦r♠ ♣rr♦s ♥♥t♦rs ♦♦r♦rs ♦s r ♣
ss♦ ♠r ♥r ♦sé r♦s ♥r ♦♥③③ ♦s P♦♥ts ♦ã♦ ♦rt♦
♥③ ♦♠r ❲③② r ♦♠♣r♥
P ♦♦r♥çã♦ ♣rç♦♠♥t♦ Pss♦ í ♣r♦r ♣♦
♥♠♥t s♣♦rt ♥♥r♦ ♠♥t ♦s st♦s r♥t ♦ ♣r♦r♠
♦s ♥♦♥ár♦s ♦♥trt♦s ❯ ♣ ss♥ ♦♦rçã♦ ♣rtr s
rs♣ts ♥çõs srtr ♦t ♠♣③ â♥ t
rs tt rs tt ♦♥ tr
♦t② ♥ tt rs ssr rs ♥
s♦ ♦♥ t♦ s♦st②s r② rs♦♥
①st ♥tr ♦ês é♠ q s sá♦
♥t♥t P♦s ♥tã♦ q ♣r♦ ss♦ ♣♦
s ♦♠ ♦♠♣♦rt♠♥t♦ ♣s ss çõs
♣rts ♦♠ ♠ s♦r♦
❯
s♦♠♥t♦ tr♥t♦ ♣r♠♥♥t ♠é♦ ♠ ♦ ♥t♦♥♥♦ ♠ ♥s ♦
r③♦♥ts ♠♥s♦♥s ♦♠ ts ♣♥s tr♥srs♠♥t ♥♥s s♣♦sts
♦r♠ ♥ ♦ s♥ ♦ st♦ trés s♠çã♦ ♥♠ér ♥t♦ s
♣rs ♦s ♥s q♥t♦ s ts s qs ♦♠♣õ♠ ♦ ♦♠í♥♦ só♦ ♣♦ss♠ s♣s
sr sã♦ ♦♥t♦rs ♦r st ♦r♠ ♦s ♠ ♦♥srçã♦ tr♦ tér♠
♦♥ ♥tr ♦ só♦ ♦ ♦ s ♦t♦s ♣r♥♣s sã♦ ♦ st♦ ♥ê♥
rçã♦ ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s s♦r tr♥srê♥ ♦r
♣r r s rçõs ♦♠étrs ♦r♥♠s ♦s rr♥♦s ts
♥♦ s♥♦ ♥♦ â♥♦s ♥♥çã♦ s ts 90 té 0 ♥♦ s♥t♦
♦ s♦♠♥t♦ té três r③õs ♦q♦ t ♦s s♣ç♠♥t♦s ♥tr ts
t♦t s♦s ♦♠♥ s rçõs ♦♠étrs ♦♠ três r♥ts ♦♥çõs r♦♥â
♠s ♦♠♥t s♦r s ♣rs ♥ çã♦ é t trés ♦ ♦♥t
trt♦ s♣r Cfx ♦ ♥ú♠r♦ sst Nux çã♦ ♦ é r③
♦♠ s ♥♦ ♦♥t ♣rssã♦ Cp ♥♦ ♥ú♠r♦ sst ♠é♦ ♠♦♦ Nu
♦r♠çã♦ ♠ ♦♥srçã♦ ♦ ♦r tr♦♦ ♣s ts ♥s ♦r♠
r ♥ê♥ ♠s s♥t ♦s ♣râ♠tr♦s ♦♠étr♦s é r③ã♦ ♦q♦
t s ♣ ♥♥çã♦ ♣♦r ♠ ♣♦ s♣ç♠♥t♦ ♥tr s ts ♦r♦
♦♠ ♦s rst♦s tr♦ tér♠ ♦ é t ♣ ♦r♠çã♦ ③♦♥s rrçã♦
①♦s r♥ts t♠♣rtr ♣s rõs r♦♠♥t♦ t♦s r♥ts
t♠♣rtr s ♣rs ♦s ♥r ♦ s♦♠♥t♦ ♣r♥♣ ♦♦rr♠ ♣♦r s
♠♥t♦ ♦♠ ♦s órts Cfx ♥t♦ ♣♦r s♠♥t♦ ♦♠ s s♣rís s ♣rs
♦ ♥ Cfx ♣♦st♦ ♣r♥♣♠♥t s ♠♦rs rçõs ♦s s s♦r s
♣rs ♦ ♥ ♦♦rr♠ ♣r ♦ rr♥♦ s♥♦ ♦♥sr♥♦ ♠ ♠s♠ r③ã♦
♦q♦ ts ♦ rr♥♦ ♥♦ ♣rs♥t ♦rs s♣r♦rs ♣r s q♥ts
♦s ♥ás tr♦ tér♠ ♦♥ ♣r♠t ♥tr q tr♦ ♦r
trés s ts é r ♠♦r ♥♦ rr♥♦ ♥♦ ♦♠ s rçõs s ♦♥
çõs r♦♥â♠s ♥ ♥tr ♦ ♥ ♦ ♣♦ssí ♦tr ♠♥t♦ té ♣r ♦
sst ♦
Prs r♦ tér♠ ♦♥ s♦♠♥t♦ tr♥t♦ ♥s ♣s
♣rs ts
t♦♠♥s♦♥ st②stt ♦ ♥ ♣r♣t ♥♥s t tr♥srs ♣♥
♥s s ssss s♥ ♥♠r s♠t♦♥ t♠r qt♦♥s ♥ ♦♥♥t♦♥
t t s♦tr♦♣ tr♥t s♦st② ②♣♦tss r s♦ s♥ t s♦tr
t♦♦ CFX s♦ ♦♠♥ ♦♠♣rss t ♦♥t♥ ♥♥ s ♥ t♦ sts
♦ q②s♣ ♥s ♥ rs t♦ ♦♥t t tr♥sr ♣r♦♠ s ♦r
♥stts t ♥♥ ♦ sr ♦♠tr② ♦♠♥t♦♥s t r♥t ②r♦②♥♠
♦♣rt♥ ♦♥t♦♥s ♦♥ t ♠♥ ♥r② ♦ss ♥ t tr♥sr ♦♠tr
♠♦ ♦♥ts ♦r t♦ ♥ rr♥♠♥ts str ♥ ♥♥ ♥ ♥♥t♦♥s r♦♠
90 t♦ 0 str♠s ♣ t♦ tr ♥s ♦ rt♦ ♥ t♦ r♥t ♥ s♣♥
t♦t ♥♠r ♦ ss ♥s t ♦♠♥t♦♥ ♦ ♦♠tr stt♥s t tr
②r♦②♥♠ ♦♥t♦♥s tr r♥t ♥t ♦ts s♥ rt♦♥ Cfx ♥
♦ sst ♥♠r Nux r ♦♠♣t ♦r ♥♥ s ♠♦ sst ♥♠r
Nu ♥ t ♣rssr ♦♥t Cp r s s ♦ ♣r♦r♠♥ ♠srs s♦ tt
t t ♦ ♥s r s♦ t t s ♦♥ tt ♥ ♥r t ♠♦st s♥♥t
♥♥ ♦ t ♦♠tr ♣r♠trs s t ♥ ♦ rt♦ ♦♦ ② ♥♥t♦♥
♥ ♥ s♣♥ ♦r♥ t♦ t rsts t ♦ t tr♥sr s rt② t ②
rrt♥ ③♦♥s ♦ t♠♣rtr r♥ts ♥ ♦ rtt♠♥t t♠♣rtr
r♥ts ♦ r♥t ♠♥s♠s ♦ ♠♥ ♥r② ♦ss s ♣rt ② t s♥
rt♦♥ ♦♥t ♦rt① s♥ ♥t s ♦ Cfx ♦r sr strss ♣♦st
s ♦ Cfx ♠♥② str ♦♥rt♦♥ ♣rs♥t t st ♦st♦♥ ♦r
♦ q♥tts r ♦♠♣t ♦♥ t ♥♥ s ♦♥sr♥ ♥ q ♥
♦ rt♦ t rr s ♦r t ♦ q♥tts rst ♠♦st② ♦r t ♥♥
♦♥rt♦♥ rtss t st s ♦ sst Nu ♦r ♦r t str
♦♥rt♦♥ ♦♥t t tr♥sr s♦s tt t ♥♥ rr♥♠♥t ♣rs♥t
t rt♦♥ ♦ t ①♥ ② ♥s r t♥ t str ♦♥rt♦♥ ♦r
t r♥ ♦ ②r♦②♥♠ ♦♥t♦♥s ♥stt t s ♦♥ ♥ ♠♥tt♦♥ ♦r t
♦ sst ♣ t♦
②♦rs ♦♥t t tr♥sr r♥t ♦s ♥♥ ♣r♣t ♥♥s
❯Õ
①♠♣♦ ♣r♦♠ ♦♠ tr♦ ♦r ♦♥
strçã♦ ♥t♥s tr♥t ♥ rã♦ s♦♠♥t♦ ♣ró♦
❱rçã♦ ♦ ♥ú♠r♦ sst ♠é♦ ♦♠ ♦ ♥ú♠r♦ ②♥♦s ♣r
r♥ts r③õs tr ♥
t♦ tr t s♦r strçã♦ t♠♣rtr ♣r L/H = 4Pr = 0,71 Re = 200
❱t♦rs ♦ ♣r r♥ts r③õs ♦q♦ Pr
♥s ♦rr♥t ♣r r♥ts t♠♥♦s s♣ç♠♥t♦s ♥s
t ♠ ♥ã♦ strtr ♣r s♠çã♦ ♦ s♦♠♥t♦ tr
♥t♦ s♦r ♠ ♣ q ♦♠ ♥s sq♠át♦ ♦ ♦♠í♥♦
♦♠♣t♦♥
s♦s ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♠♥s♦♥ r♣rs♥t♥♦ ♣rt s
♣r♦r ♦ t♦ tr♦♦r ♦r
sq♠ ♠♦str♥♦ s ♦♠trs ♦ ①♣r♠♥t♦ ♦ ♣r♠♥t♦ ♦
s♦♠♥t♦ s♥ár♦
♦♠tr ♦ ♥ ♦♠í♥♦ ♦♠♣t♦♥ ♦ s♦♠♥t♦ ♣ró♦
♥s ♦♠ ♦♠tr ♥♦ ♦r♠t♦
sq♠át♦ ♠ strtr í ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♥♦ ♥
♣♥ê♥ t① tr♦ tér♠ ♠♥s♦♥ ♦♠ r③ã♦ s♣t♦
t ♦♠ r③ã♦ ♥tr s ♦♥ts tér♠s
♣r r♥ts ♥ú♠r♦s ②♥♦s
ú♠r♦ sst ♦ ♣r ♣r s♣r♦r ♥r♦r ♦ rr♥♦
s♥♦ ♣r ♦ rr♥♦ ♥♦
tí♣ rtrísts ♠♥s♦♥s t③s ♣r s ♦♠trs
♦♠ ①♣♥sã♦ r♣t
♥♣♥ê♥ ♠ ♣r ♦ s♦ ♦♠♣rt♦ ♦ ♣r ♦
♥tr três r♥ts ♠s
Pr ♦ ♠ x/d = 5,33 ♣r ♦♠tr ♥ ♦♠ r③ã♦
①♣♥sã♦ r♣t Hs/He
st♦ ♥♣♥ê♥ ♠ ♣r ♦ ♥ú♠r♦ t♥t♦♥ s♣rí
♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦
r♣t Hs/He
ú♠r♦ t♥t♦♥ ♦ ♣r s♣rí ♥r♦r sçã♦ ①♣♥
♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He
♦♠tr ♦♠ ts ♠ tí♣ t③ ♣r s♦çã♦ ♥r
♥ét tr♥t s♦
♥♣♥ê♥ ♠ ♣r ♦ ♣r ♥r ♥ét tr♥t ♥♠
sçã♦ ♥ ♣♥♦
❱rçã♦ ♦ ♣r ♥r ♥ét tr♥t ♥♠ sçã♦ ♥
♣♥♦
rtrísts ♠♥s♦♥s s ♦♠trs áss ♣r ♠♦s ♦s rr♥♦s
♥s t♦s ♥♦ s♣r♦r s♥♦ ♥r♦r
♦♠tr t ♦♠♦ ♥çã♦ ♦s r♥ts â♥♦s ♥♥çã♦ β ♣r
♠ ♠s♠ r③ã♦ ♦q♦
s ♦s s♣ç♠♥t♦s ♥tr ts b s rçõs r③ã♦ ♦q♦
t rba ♣r ♠♦s ♦s rr♥♦s ♥ t♦
①♠♣♦ ♠s ♣r♦③s r♥t ♦ st♦ ♥♣♥ê♥ ♠
t ♥♦ ♥t♦r♥♦ ♠ t ♦♠ β = 90
st♦ ♥♣♥ê♥ ♠ rst♦s ♣r s ♠s ♠♦strs
♥ r
♥s ♦rr♥t ♦♦rs ♦♠ ♦ ♣r r♥ts ♥♥çõs
t ♠♦s ♦s rr♥♦s ♥♦ ♦♥ sqr s♥♦ ♦
♥ rt ♥♦ s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠
ue = 9 m/s
♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦
♥ rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr
s♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba = 0,4
♦♥çã♦ r♦♥â♠ ue = 3 m/s
♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦
♥ rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr
s♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba = 0,4
♦♥çã♦ r♦♥â♠ ue = 3 m/s
❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦
t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç
♠♥t♦ ♥tr ts b = 2H
❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦
t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç
♠♥t♦ ♥tr ts b = 3H
♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba
s♣ç♠♥t♦ ♥tr ts b = 2H
♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba
s♣ç♠♥t♦ ♥tr ts b = 2H
♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba
s♣ç♠♥t♦ ♥tr ts b = 2H
strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦
q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 3 m/s
strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦
q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 3 m/s
❱rçã♦ ♦ ♣r ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦
♦q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 3 m/s
❱rçã♦ ♦ Cp ♣r s r♥ts r③õs ♦q♦ s ♦♠trs
♥ ♦♠ b = 2H ♦ rr♥♦ ♥♦ b = 2H ♦ rr♥♦ s♥♦
b = 3H ♦ rr♥♦ ♥♦ b = 3H ♦ rr♥♦ s♥♦ ♥s
três ♦♥çõs r♦♥â♠s s♠s
♦♠♣rt♦ ♦ Cp ♥tr ♦s ♦s rr♥♦s r♥ts r③õs ♦q♦
s♣ç♠♥t♦ ♥tr ts b = 2H ♥s três ♦♥çõs r♦♥â♠s ue
❱♦rs Cp/Cp0 ♣r ♦ rr♥♦ s♥♦ r♥ts s♣ç♠♥t♦
♥tr ts ♥s três ♦♥çõs r♦♥â♠s ue
t rçã♦ ♦ s♦♠♥t♦ ♦ à rstrçã♦ ár rst♥t
♣r ♦ â♥♦ ♥♥çã♦ t β = 18 ♣r ♦♠tr ♦♠ rba = 0,6 b = 2a t♦♣♦♦ ♦ s♦♠♥t♦ ♥ ♣rt ♥r♦r ♦ ♥
♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr
♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s
♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba ♦♥çã♦
r♦♥â♠ ue = 3 m/s
♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr
♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s
♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba ♦♥çã♦
r♦♥â♠ ue = 3 m/s
♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♥♥çã♦
t rr♥♦ ♥♦ ♦♥ sqr rr♥♦ s♥♦ ♦♥
rt ♣r ♦♠trs ♦♠ b = 2H rba = 0,4 ♦ rrê♥
ue = 3 m/s
♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦
rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦
s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦
t rba = 0,4 ♥♥çã♦ β = 18
♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦
rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦
s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦
t rba = 0,4 ♥♥çã♦ β = 54
♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦
rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦
s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦
t rba = 0,4 ♥♥çã♦ β = 90
❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦
t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s
♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H
❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦
t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s
♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 3H
♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba = 0,4
s♣ç♠♥t♦ ♥tr ts b = 2H
♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba = 0,4
s♣ç♠♥t♦ ♥tr ts b = 2H
♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦
rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba = 0,4
s♣ç♠♥t♦ ♥tr ts b = 2H
strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦
q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 9 m/s
strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦
q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 9 m/s
strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦
q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H
♦ rrê♥ ue = 9 m/s
ú♠r♦ sst ♦ ♠♦s ♦s rr♥♦s t ♣r s ♦♠trs
♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♦♥ sqr b = 3H ♦♥
rt
r♥srê♥ ♦r ♥ ♥tr rçã♦ ♦ ①♦ ♦r t♦t
♠♥s♦♥ ♣r ♦ ♦r tr♦ trés s ts ♦♠ ♦ â♥♦
♥♥çã♦ t β ♣r ♦s r♥ts s♣ç♠♥t♦s t b = 2H♦♥ sqr b = 3H ♦♥ rt
❱rçã♦ rçã♦ ♦ ♦r tr♦♦ trés ♥tr ♦♠ ♦ â♥♦
♥♥çã♦ t β ♣r ♦s s♦s ♦ s♣ç♠♥t♦ t b = 2H
♦ rrê♥ ue = 9 m/s
♥ê♥ ♦ rrê♥ ue ♥ strçã♦ tr♦ tér
♠ trés ♥tr ♥♦ ♦r tr♥sr♦ t♦t ♠♥s♦♥ ♣r ♦s
rr♥♦s t s♥♦ s♣r♦r ♥♦ ♥r♦r
t♦ r③ã♦ ♦q♦ t rba s♦r ♣r ♦r tr♦
trés s ts s♦r ♦ ♦r tr♥sr♦ t♦t ♠♥s♦♥ ♣r ♠♦s
♦s rr♥♦s ♦♠trs ♦♠ b = 2H
s ♦♠étrs r♥ts ♣r ♦ CFX rs ♥ts ①
çã♦ ♦ ó♦ ♥♠ s♠çã♦ ♥♠ér
♦♥strçã♦ ♦ ♦♠ ♦♥tr♦ ❱ s♥♦ ♦r♠çã♦ ❱
r♥s♦r♠çã♦ ♥tr s ♦♦r♥s ♦s ♦ sst♠ s ♦♦r♥s
♦s t③s ♣s ♥çõs ♦r♠
Pr ♦ tí♣♦ ♠ ♠t tr♥t
❱rçõs ♦♠étrs ♦♥rçã♦ ts ♥s ♣r ♠ s♣
ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t
rba ♦♥ ♦♥
❱rçõs ♦♠étrs ♦♥rçã♦ ts s♥s ♣r ♠ s
♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t
rba ♦♥ ♦♥ ♦♥
♦♠♥çã♦ s rçõs ♦♠étrs b rba ♦♠ s rçõs s ♦♥
çõs ♦♥t♦r♥♦ r♦♥â♠s ue ♦ Re ♣r ♦ ♠ ♥♥çã♦
t β
st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r
♠♥t
Pr♦♣rs íss t③s ♥ t♣ çã♦ rçã♦ ♦ ó♦
♥♠ér♦
♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥♦ s♦ t♣
rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥
♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥ s♦çã♦ tér♠ s♦
t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥
♦s s ♠s t③s ♣r ♦ st♦ r♥♦ ♠ ♣r
çã♦ rçã♦ ♥r ♥ét tr♥t κ
❱rçã♦ r③ã♦ ♥tr rr s t w s s♣ssr
t ♠ ♥çã♦ ♦ s â♥♦ ♥♥çã♦
Prâ♠tr♦s ♦♠étr♦s r♦s ♦♥rçã♦ ♣á r♥ts
s♣çã♦ ♦s ♣râ♠tr♦s ♦♠étr♦s ♥rss
Pr♦♣rs íss t③s ♣r rtr③çã♦ ♦s ♦♠í♥♦s ♦♠♣
t♦♥s ♦s s♦s st♦s
❱♦rs ♦ ♦♥t ♣rssã♦ ♣r ♦ ♥ s♠ ts
ú♠r♦ sst ♦ ♦ ♥ s♠ ts ♣r s três r♥ts ♦♥
çõs r♦♥â♠s
♥t ♦r tr♥sr ♣r ♦ ♦ ♥♦ ♥ s♠ ts ♣r s
três r♥ts ♦♥çõs r♦♥â♠s
③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é
♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H
③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é
♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H
③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é
♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H
③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é
♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H
❱❯
♦♠♣tçã♦ ssst ♣♦r ♦♠♣t♦r ♦ ♥ês ♦♠♣tr ♥♥r♥
♥â♠ ♦s ♦s ♦♠♣t♦♥ ♦ ♥ês ♦♠♣tt♦♥
②♥♠s
CFX ♣r♦r♠ ♦♠r
s♠çã♦ ♥♠ér rt ♦ ♥ês rt ♥♠r s♠t♦♥
❱ ♠ét♦♦ ♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês
♠♥ts ♥t ♦♠ ♠t♦
♠ét♦♦ ♠♥t♦s ♥t♦s ♦ ♥ês ♥t ♠♥t ♠t♦
qçõs rt♦s ♦♠ ♠é ②♥♦s ♦ ♥ês
②♥♦s r rt♦s
♠é qrát ♦ ♥ês r♦♦t ♠♥ sqr
tr♥s♣♦rt s t♥sõs tr♥ts ♦ ♥ês sr strss
tr♥s♣♦rt
❱ ♦♠ ♦♥tr♦
❮
A ár
Ai t♦r ár ♥♦r♠
b s♣ç♠♥t♦ ♥tr ts ssss ♠ ♠s♠ ♣r
Bi ♦ rt♦ ♦ ♠tr③ ♦♥t♥♦ s♦çã♦ ♦ sst♠ ♥r s qçõs
srt③s
C ♦♥st♥t ♠♦♠ ♦ ♣ró①♠ à ♣r
c ♦r s♣í♦ ♣rssã♦ ♦♥st♥t
ci t♦r q ♦s ♥trós ♠♥t♦s ♥ts
cpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦
Cfx ♦♥t trt♦ ♦
Cp ♦♥t ♣rssã♦
d tr ♦ r ♣r ♠ ♥ ♦♠ ①♣♥sã♦ r♣t ár
Dh â♠tr♦ rá♦
Dij t♥s♦r t① ♦r♠çã♦
D′
ij t♥s♦r t① ♦r♠çã♦ s♦r
dmin dmax stâ♥s t③s ♣♦ CFX♣r ♦ á♦ ♦ t♦r ①♣♥sã♦
♠
dpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦
e s♣ssr ♣r ♦ ♥ t♦
F1 F2 ♥çõs ♦ ♠♦♦ trê♥
fi t♦r q ♦ ♥tró ♦ ♠♥t♦ ♦ ♥tró ♠ ss
s
FU ①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r
fpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦
h ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦
H tr ♠ sçã♦ ♦♠étr
Ha ♠á①♠ tr rt t
hx ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦
I ♥t♥s tr♥t
J ♠tr③ ♦♥
K ♦♥st♥t ♦♥ ár♠á♥
k ♦♥t tér♠ ♦ ♠♦
kt ♦♥t tér♠ tr♥t
L ♦♠♣r♠♥t♦ ♠ sçã♦ ♦♠étr
lt ♦♠♣r♠♥t♦ rtríst♦ s tr♥t
mpi ①♦ ♠áss♦ trés s♣rí ♠ ♦♠ ♦♥tr♦
M ♥ú♠r♦ ts ♥ ♠s♠ ♣r ♦ ♥
m ③ã♦ ♠áss
Ni ♥çõs ♦r♠
Nu ♥ú♠r♦ sst ♦
Nux ♥ú♠r♦ sst ♦
p ♣rssã♦ ♦
pi ♣♦♥t♦ ♥trçã♦
Pr ♥ú♠r♦ Pr♥t
q ①♦ ♦r
ri t♦r ♣rtr ♦ ♥ó ♠♦♥t♥t té ♦ ♣♦♥t♦ ♥trçã♦ ♦♥sr♦
rba r③ã♦ ♦q♦ t
Re ♥ú♠r♦ ②♥♦s
sij t♥s♦r t♥sã♦ s♦r
Stx ♥ú♠r♦ t♥t♦♥ ♦
T t♠♣rtr ♦
t t♠♣♦ ♦ s♣ssr t
T + t♠♣rtr ♠♥s♦♥ ♥ rã♦ ♣r
Tm t♠♣rtr ♠é ♦rít♠
ui ♦♠♣♦♥♥t ♦ rts♥
uτ ♦ trt♦
Uref ♦ ♠é rrê♥
vt ♦ rtríst s tr♥t
w rr s t
Wij t♥s♦r t① r♦tçã♦
xi, x, y ♦♦r♥ rts♥ ♦
y+ stâ♥ ♠♥s♦♥
trs rs
α α∗ ♦♥st♥ts ♦ ♠♦♦ trê♥
β â♥♦ ♥♥çã♦ t
Γ rá tér♠ ♣r
γ ♦♥st♥t ♦ ♠♦♦ trê♥
∆ rçã♦ ♣r♦♣r
δij ♦♣r♦r r♦♥r
ǫRMS ♠é qrát
ε t① ss♣çã♦ ♥r ♥ét tr♥t
ϑ tr♠♦ ♦rrçã♦ ♥♠ér t ♥♦ sq♠ t rs♦çã♦
κ ♥ ♥ét tr♥t
Λ rá ♥ér
µ s♦s ♥â♠ ♠♦r
µt s♦s ♥â♠ tr♥t
ν s♦s ♥♠át ♠♦r
νt s♦s ♥♠át tr♥t
ξ, η ♦♦r♥s ♦s t③s ♣s ♥çõs ♦r♠
ρ ♠ss s♣í
σκ σω σω2 ♦♥st♥ts ♦ ♠♦♦ trê♥
ς ς1 ς2 ♦♥st♥ts ♦ ♠♦♦ trê♥
τij t♥s♦r ②♥♦s
τint,x t♥sã♦ s♥t ♦ ♦ ♦ ♦♠ ♣r ♥ ♥ ♥tr só♦
♦
φ φ′ ♣rs ♠é t♥t ♦♠♣♦sçã♦ ②♥♦s
ψ rá tér♠ ♣r
Ω ♦rt
ω t① ss♣çã♦ s♣í
í♥s
0 rr♥t ♦ ♥ s♠ ts
a rr♥t às ts
e t q é♠ s♦♠ ♥tr s ♣rs ♦ ♦ ♠♦rs ♦
s♦♠♥t♦ tr♥ts
esp s♣♦
f ♦
i ♥ú♠r♦ q ♥t ♦ ♦♠ ♦♥tr♦ ♦ ♥ó ♦ qçõs ♦
sst♠ ♦♣♦ qçõs ssçã♦
i, j, k ♦♠♣♦♥♥ts r♦♥s ♥társ s♦r ♦s ①♦s ♦ sst♠ rts♥♦
int rr♥t à ♥tr só♦♦ ♥♦s ♥s t♦s
Λ rá ♥ér
max ♠á①♠
min ♠í♥♠
w ♣r
ref rrê♥
s só♦
t tr♥t
tan t♥♥
up ♠♦♥t♥t
x ♦ ♦ ♦♥♦ rçã♦ rts♥ x
♣rí♥s
∗ ♠♥s♦♥
o ♣ss♦ t♠♣♦ ♥tr♦r
e ♥tr
nb ③♥♦s
s sí
❯
❯
t♦s st tr♦
strtr st tr♦
❱ ❯
❯Õ Ó Õ
qçõs ♦♥srçã♦
♠♦♦ s qçõs ♦♥srçã♦
♦♠ trê♥
çã♦ ♣r r
çã♦ r♥srê♥ ♦r
❯ ❯Õ
❱rçã♦ çã♦ ♠♦♠ ♠t♠át s♦çã♦ ♥♠ér
♦ CFX
s♦ s♦çã♦ ♦
♦♠tr
♦♥çõs ♦♥t♦r♥♦
st♦s
s♦ s♦çã♦ tér♠
♦♠tr
♦♥çõs ♦♥t♦r♥♦
st♦s
s♦ s♦çã♦ ♥r ♥ét tr♥t
♦♠tr
♦♥çõs ♦♥t♦r♥♦
st♦s
Pr♦♠ ♦ s♦♠♥t♦ ♠ ♥s t♦s
♦♦ ♦♠étr♦ ♦ ♥ t♦
♣♦ st♦ r♥♦ ♠
♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs
Pr♥♣s rtrísts ♦ s♦♠♥t♦ ♥♦s s♦s ♦s ♥s t♦s
st♦s ♣r ♣r r
♥s ♦rr♥t t♦♣♦♦ ♦ s♦♠♥t♦
♦♥t trt♦ ♦ Cfx
r♥ç ♣rssã♦ ∆p ♦♥t ♣rssã♦ Cp
r♥srê♥ ♦r ♥tr ♦ ♦♠í♥♦ só♦ ♦ ♦♠í♥♦ ♦
strçã♦ t♠♣rtr t♦♣♦♦ ♦ s♦♠♥t♦
ú♠r♦ sst ♦ Nux
ú♠r♦ sst ♦ Nu
♦r t♦t ♠♥s♦♥ qtotal/q0 ♣r ♦r tr♦
♦ trés s ts
♦♠♣rt♦s s q♥ts ♦s
❯Õ PP❱ ❯❯
P
s♣t♦s ♥â♠ ♦s ♦♠♣t♦♥
rçã♦ ♠ ♥♠ér
ét♦♦ ♥♠ér♦ ♦r♠ ❱
♥çõs ♦r♠
r♠♦s s♦s
r♠♦s ♦♥t♦s
♦♣♠♥t♦ ♣rssã♦♦
sst♠ ♦♣♦ qçõs
♦♥çõs ♦♥t♦r♥♦
♦♦ trê♥
rt♠♥t♦ ♥t♦ à ♥tr só♦♦ ♥çõs ♣r s
ás ① ♦r♠çã♦ ①♦ ②♥♦s
①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r
①♦ ♦r ♥ rã♦ ♣r
rr♥♦ ♥♦
rr♥♦ s♥♦
r♦r s♦s
❯
st♦ ♣r♦ss♦s ♥♦♥♦ tr♥srê♥ ♦r é r♥t ♠ ár♦s
s♠♥t♦s ♥strs ♣♦rt♥t♦ ♠ ♠♣ ♠ ♣sqss t♠ s♦ ♦♥t♥♠♥t
r③ s♥♦ ♠♦r ♥ ê♥ t♥t♦ ♥ t♣ ♣r♦t♦ q♥t♦ ♥ ♦♣r
çã♦ ♦s sst♠s tér♠♦s ♠♦r sts sst♠s ♦ à ♣rs♥ç ♦♥çã♦
♦rç ♦ r♠ s♦♠♥t♦ é ♦ tr♥t♦ é♠ ♦ r♠ s♦♠♥t♦ s
♣r♦♣rs íss ♦s ♦s ♦s ♠trs ♦♥strçã♦ ♦s ♦♠♣♦♥♥ts sts
sst♠s s rtrísts ♦♠étrs t♠é♠ ♥♥♠ rt♠♥t ♥♦ ♣r♦ss♦
tr♥srê♥ ♦r s ♣r♦ss♦s tr♥srê♥ ♦r ♣♦♠ sr st♦s
♦r♠ ①♣r♠♥t ♣♦ré♠ ♥s út♠s és s ♦sr ♠ ♦çã♦ ♥♦ s♦ r
r♠♥ts ♦♠♣t♦♥s ♦ts ♣r r③çã♦ ♣sqs s♥♦♠♥t♦
t♠s ♦♠♦ st
Pr s ♦tr ♠♦rs t①s tr♥srê♥ ♦r ♥tr ♠ s♣rí só
♠ ♦ ♦ s♦ ts stá ♥tr s té♥s ♠s t③s ♥tr♦çã♦ ts
é♠ ♣r♦♣♦r♦♥r ♠♥t♦ ár tr♦ tér♠ ♥tr ♣♦ tr ♦ ♣rã♦
s♦♠♥t♦ t tr♥srê♥ ♦r ♦♥ ♥ q
s♦çã♦ tér♠ ♦ só♦ ♦ ♦ é trt ♦r♠ ♦♣ ♣♦ sr t③ ♣r
str st t♣♦ ♣r♦♠ ss♠ s ♦♥srr ♥ê♥ s ♣r♦♣rs ♦
só♦ ♥ás ♣rã♦ ♥sts s♦s ♦♥sst ♥♦♥trr ♦♥rçã♦ q ♦rç
♦ ♠♦r ♥ç♦ ♥tr q ♣rssã♦ ♦ à ♦strçã♦ s ♣s ts ♦
♥♦ ♠ tr♥srê♥ ♦r q sts ♣r♦♣♦r♦♥♠ é♠ ♦ ♠♥t♦ ár
♥tr tr♦ tér♠ ♣rs♥ç s ts ♣♦ ♠♥tr ♦ ♥í trê♥ ♦
s♦♠♥t♦
♦s ♣r♦ss♦s ♥strs ♦♦rr ♦ ♣r♦♠í♥♦ s♦♠♥t♦s tr♥t♦s ♦s qs
♣rs♥t♠ s s♥ts rtrísts t♦s ♥ú♠r♦s ②♥♦s rrr ♦
t♦r s tçõs tr♠♥s♦♥s ♦rt ss♣çã♦ s
s♦♠♥t♦s tr♥t♦s sã♦ ♥ô♠♥♦s q ♦♦rr♠ ♥ s ♦ ♦♥tí♥♦ é ♠
rtríst ♦ s♦♠♥t♦ ♥ã♦ ♦ ♦ s♦ s♦♠♥t♦ ❯❨
♦♥sr♥♦s q á st ♣çã♦ st t♣♦ s♦♠♥t♦ ①st♠ qs q
♠♥♠ s♣ t♥çã♦ ♦♠♦ ♦s s♦♠♥t♦s tr♥t♦s ♦♠ s♣rçã♦ ♠
♠t t♦s sts ♦♦rr♠ ♦♠ ♣♦str♦r r♦♠♥t♦ ♠ ♠t ♥t♦ à ♠
s♣rí só st stçã♦ ♥ q á s♣rçã♦ r♦♠♥t♦ ♦ s♦♠♥t♦
♦r♥ ♥ ♠ ♠♦r ás ♥ q t♦rs ♠♦♦s trê♥ sã♦ tst♦s
♣♦ss♠♥t ♠♦r♦s t
s ♠♦♦s trê♥ q rs♥t♠ s♠♣çõs s♦r ís ♦s s♦
♠♥t♦s sr♠ ♦♠♦ tr♥t ♣r ③r ♦ s♦ rr♠♥ts ♥â♠
♦s ♦♠♣t♦♥ ♦ ♦ ♥ês ♦♠♣tt♦♥ ②♥♠s st s♥
t♦ ♠♦çã♦ s qçõs rt♦s ♦♠ ♠é ②♥♦s ♦ ♥ês
②♥♦sr rt♦s t♦r♥♦s ♦r♠ ♠s t③ ♣r
r s♦♠♥t♦s tr♥t♦s ♦ s♦ ♦s s♦♠♥t♦s tr♥t♦s st♦♥ár♦s ♦s qs
r♣rs♥t♠ ♠♦r s ♣çõs ♥♥r ♦♠♣♦sçã♦ ②♥♦s ♣r
s ♣r♦♣rs tr♥s♣♦rt é trt ♦r♠ sttíst ♦♠ ♠ ♠é ♥♦ t♠♣♦
❲❳ t
♦r♠ q ♦r♥ ♠♦r rá ♣r s♠çã♦ trê♥ ♣♦
ré♠ é q ♠ q s qçõs rt♦s sã♦ rs♦s s♠ ♦♥srr ♥♥♠
♣r♦♠♥t♦ ♠é ♦ ♣r♦①♠çã♦ é♠ ♦ ♣r♦ss♦ srt③çã♦ st t♣♦
s♠çã♦ é ♦♥ ♦♠♦ s♠çã♦ ♥♠ér rt ♦ ♥ês rt
♠r ♠t♦♥ ❩ P srs q ♦ s♦ s♠çõs
♠♣ ♣♦r ①♠♣♦ ♥♠ t♦ st♦ ♦♠♣t♦♥ é♠ rr ♠ q♥t
♦s s♥ssár ♣r ♣çõs ♥♥r ♥ ♣sr ♦s s♦rç♦s ♠ ♦
s s♦ ♠ s♦♠♥t♦s ♥trss rt♦ ♥ ♥♥r stá ♠ ♦♥♦ ♠♥♦ s
t♦r♥r ♣rát♦ ♠♦r q s ♣♦ ♥çr té ♥tã♦ sã♦ s♠çõs ♠♦r♦s ♥ú
♠r♦s ②♥♦s ♠ ♦♠trs ①tr♠♠♥t s♠♣s ♣♦r ①♠♣♦ ♦s ♣ró♦s
❱
♣rtr ♦ ①♣♦st♦ s♦r ♦ ♦♥t♦ ♦ s♦ s rr♠♥ts rts ♦
♥ês ♦♠♣t ♥♥r♥ ♥♦ ♥♠♥t♠♥t ♥á
s tér♠ ♦ s s♦ ♠♦r ③ ♠s rq♥t r♥t ♦ s♦ ♦s
♠♦s ♣r♦tót♣♦s rts P ❯ ♥sst ♦ ♦♠♣♠♥t♦
①♣r♠♥t ♦çã♦ ♠ ♣rt stá ♥ ♦ s♥♦♠♥t♦ ♦s
rrs♦s ♦♠♣t♦♥s ♣r♦ss♠♥t♦ r♠③♥♠♥t♦ ♦s ♣r♦r♠s ♦♠♣
t♦♥s ♦♠ rçã♦ ♦ s♥♦♠♥t♦ ♦s ♣r♦r♠s ①st♠ árs tr♥ts
s♥♦ q rsõs strís ♦r♠ ♦♠r sã♦ ♦♥srs ♦♠♦ s t♥♦♦s
♣♦♥t
♠♦r s rr♠♥ts ♦♠rs FLUENT CFX1 STAR −CD STAR −CCM+ s s ♥ ♦r♠ ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s ♣
♥♦ ♣r♦ss♦ srt③çã♦ s qçõs r♥s st ♠ét♦♦ s s ♥
♦r♠ ♥tr s qçõs ♦♥srçã♦ ♦♠♦ ♣♦♥t♦ ♣rt s♥♦ ♦ ♦♠í♥♦
s♦çã♦ s♦ ♠ ♠ ♥ú♠r♦ ♥t♦ ♦♠s ♦♥tr♦ ❱ trés ♠
♠❩ P ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s áss♦ ♦ ♦♠ ♦♥
tr♦ ♦♥ ♦♠ ♦ ♠♥t♦ ♠ s♥♦♦ ♠s r♥t♠♥t ♦ ♠ét♦♦ ♦s
♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês ❱ ♠♥ts ♥t ❱♦♠
t♦ r ♠ ❱ q é ♦♠♣♦st♦ ♣♦r s♦♠s ♦r♥♦s ♦ ♣r♦ss♦ sã♦
Pr♦r♠ s♠çã♦ ♥â♠ ♦s ♦s ♦♠ tr♥srê♥ ♦r rçõs qí♠s ♦♠r③♦ ♣ ❨
Pr♦r♠ ♥ás ♦♥â♠ ♦♠♣t♦♥ ♦♠r③♦ ♣ ♣♦Pt♦r♠ ♠ts♣♥r ♣r s♠çã♦ ♦♠r③♦ ♣ ♠♥s
♦s ♠♥t♦s ♠ st♥t ♣r♦♣r♦ q♥♦ s t③ ♠s ♥ã♦strtrs
st t♣♦ ♠ t♠é♠ é q ♣r s t③r ♦♠ ♦tr ♦r♠çã♦ ♦
♠ét♦♦ ♦s ♠♥t♦s ♥t♦s ♦ ♦ ♥ês ♥t ♠♥t t♦
♦r♦ ♦♠ rs ♦ é ♥tr♠♥t ♣r♦♣r♦ ♣r ♠s
♥ã♦strtrs ♦r♠ ♣rtr ♣r ♦r♠çõs ss ♥♦s érts ♦s
♠♥t♦s ♠ ♥♦ ♦ ♠s♠♦ t♦r ♥ ♠ ♦s ♣ss♦s ♦ ♠ét♦♦
♦♥sst ♥r ♠ ♠♥t♦ ♠ ♠ r♣rs♥tçã♦ ♣r♠étr s rá
s ♣♥♥ts ♦♠ s ♥♠ ♠í ♥çõs ♦r♠ ss♦ à ♠♥t♦
srs q ♥♦ ♣r♦r♠ t③♦ ♥st tr♦ ♦ CFX stá ♠♣♠♥t♦ ♦
♠ét♦♦ ❱ q t♠é♠ t③ s ♥♦♠♥s ♥çõs ♦r♠ ♦s ♣ê♥s
st tr♦ ♥♦♥tr♠s ♥♦r♠çõs ♠s s♣ís s♦r ♦ ♣r♦r♠ ♥t♠♥t
♦♠ ♦tr♦s s♣t♦s
❱
♣r♥♣ ♦t♦ st tr♦ é ♦ st♦ ♥ê♥ ♦ ♣♦s♦♥♠♥t♦
ts ♦♥t♦rs tr♥srss ♦ s♦♠♥t♦ ♠ ♠ ♥ sçã♦ rt s♦r
tr♥srê♥ ♦r ♦♥ s♦r ♣r r ♣♦s♦♥♠♥t♦ s ts
trá s ♦♥rçõs áss ♥ s♥ ♦♥♦r♠ str♦ ♥ r
stçã♦ ♠♦♥str ♥st r t♥t♦ ♣r ♦ ♥ q♥t♦ s ts
♣♦ss♠ s♣ssr ♦♥③♠ ♥r st♦ rtr③ ♠ ♣r♦♠ ♥♦ q ♠s s
♦r♠s tr♦ ♦r ♠ sr trts ♠♥r ♦♥ ♦♥çã♦ ♥♦ só♦
♦♥çã♦ ♥♦ ♦ ♣♦r ♠♦ ♠ ♥tr só♦♦ q sr st
♥tr é ♦ t♣♦ ♦♥srt st♦ ♠♣ q t♦♦ ♦ ♦r q ① ♦ ♦♠í♥♦ só♦
é ♦♥t③♦ ♣r ♦ ♦♠í♥♦ ♦ ❨
♦♠tr ♦♥sr ♥ r ♣rs♥t árs ♣♦sss q♥t♦ ♦s
♣râ♠tr♦s ♦♠étr♦s st♦ Pr st tr♦ ♦r♠ s♦s rçã♦ ♦
â♥♦ ♥♥çã♦ s ts r③ã♦ ♦q♦ t ♦ s♣ç♠♥t♦ ♥tr ts
sts ♣râ♠tr♦s ♦r♠ ♦s ♠ ♠s s ♦♥rçõs r ♦♥
♠♥t ♣r ♠ ♥ás ♦ t♦ rçã♦ ♦ rrê♥ ♦ s♦♠♥t♦
♦r♠ rs♥ts três ♦♥çõs ♦♥t♦r♥♦ r♥ts ♦ st♦
Pr ♥çr ♦s ♦t♦s ♣r♥♣s ♦s s♥ts t♥s sã♦ ♦♥sr♦s
❼ ❱çã♦ rçã♦ ♦ ♣r♦r♠ ♦♠r CFX ♣r s♦s ♦♥t♥♦
íss s♠♥ts às q srã♦ ♥♦♥trs ♥st tr♦
❼ ♥tçã♦ s ♣rs ♦r tr♥srs ♣r ♦ ♦ ♣♦r ♠♦ s ts
♣♦r ♠♦ s ♣rs ♦ ♥
❼ çã♦ ♦ ♠♣♦ t♠♣rtrs ♦s ♦♠í♥♦s só♦ ♣rs ♦ ♥ ts
♦
❼ çã♦ t♦♣♦♦ ♦ s♦♠♥t♦ ♣r ♦s s♦s ♦ ♣r♦♠♦
❼ çã♦ ♣r r trés ♦ ♦♥t ♣rssã♦ t♠é♠ ♦ ♦♥t
trt♦ ♦♠♥t
❼ çã♦ tr♥srê♥ ♦r trés ♦ ♥ú♠r♦ sst ♦ ♦
t♠ ♣rt♥♥t ♦ ♦♥♥t♦ s♦s st♦s ♥st tr♦ srá ♦
q♥t♦ à ♥ê♥ ♦s ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s
r ①♠♣♦ ♣r♦♠ ♦♠ tr♦ ♦r ♦♥
20 H
b /2
b/2
♥ ♦♠ ts s♥s
H
l
β
b b/2 L
w
e
20 H
x
y
♥ ♦♠ ts ♥s
♦♥t ♣t♦ P t
❯❯
♣rs♥t ssrtçã♦ é strtr ♦ ♦♥♦ sçõs sss♠♥t ♥tr♦
çã♦ sã♦ trtr ♦r♠çõs órs ♦♥srçõs st♦s s
ssõs ♦♥sõs Prs♣ts trs
sã♦ trtr ♣rs♥t ♠ rs s♦s ♥♦♥♦ ♦ s♦
ts ss♠♦s ♣r ♥r♠♥t♦ tr♦ tér♠ rsst♥♦ ♦s ♣r♥♣s s♣t♦s
♦♥sr♦s ♦ ♦♥í♦s ♣♦s ss t♦rs sçã♦ s ♦r♠çõs órs
♦♥srçõs sã♦ ♣rs♥ts s s♠♣çõs ♣ótss ♦s ♠♦♦s ♠t♠át♦s
rst♥ts ♣r ♦ ♣r♦♠ ♦s ♥s t♦s s t♣s çã♦ rçã♦
♠ ♦♠♦ ♦ s♥♦♠♥t♦ ♣rs♥tçã♦ ♦s rst♦s s s♠çõs ♥♠érs ♦s
s♦s ♣r♦♣♦st♦s ♥♦ ♣rs♥t tr♦ ♦♠♣õ sçã♦ ♦s st♦s sssõs s
♦♥sõs Prs♣ts trs sã♦ rstr♦s ♦s stqs ♦s st♦s t♦s
♥♠♥t ♠s r♦♠♥çõs tr♦s tr♦s
❱ ❯
té♥ ♠♥t♦ tr♥srê♥ ♦r r é ♦♠♠♥t t③
♠ s♦♠♥t♦s ♠♦♥♦ás♦s ♣r ár♦s t♣♦s ♣çõs ♥strs ♣♦s♦♥♥♦s
ts ♦r♠ ♣ró ♠ ♥s q♠♥t♦ ♦ rsr♠♥t♦ ♥s ①♠♣♦s
♣♦s à ♥♥r sã♦ ♦s tr♦♦rs ♦r ♦ t♣♦ s♦t♦ ♦♠ ♥s s
♠♥ts ♦t♦rs s♦rs rsr♠♥t♦ ♥tr♥♦ ♣ás tr♥s ♥s t♣♦s ①♦
♦♠ r♥t♦ s♠ ♦r♠ ♣rtr ♦ s♦ ♣r♦♠♦t♦r trê♥ ♥♦ s♦
♠♥t♦ é st♥t ♦♠♠ ♦ ♦ ①♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r
♣rs♥t♦ ♣ ♠♦r ♦s ss sr ♣rs♥ts ♠ rs♠♦ árs ♣sqss
r tr♥srê♥ ♦r s qs ♣rs♥t♠ s♠♥ç ♦♠ s ♣r♦♣♦sts st
tr♦
st♦ ♦ s♦ ts ♣r ♣r♦♠♦r ♦ ♠♥t♦ ár tr♦ tér♠
♦ ♣r♦ss♦ ♠str t♠ s♦ r③♦ t♥t♦ ♠♥r ①♣r♠♥t q♥t♦
♠♥r ♥♠ér ♦♥sr♥♦ ♦ s♦ ♥♠ér♦ s s♠çõs tê♠ s♦ ♦♥③s
♠♣♠♥t ♣r s♦s ♠♥s♦♥s ♦ ♦♠ ♣r♦♣rs ♦♥st♥ts ♠ ♠t♦s
s♦s ♣♥♦s ♦♥çõs ♣r♦ ♥t♦ à ♦♠tr ♥♦ s♦ ♥s
♦♠ ts tr♥srss ♦ s♦♠♥t♦ á s ♣♦sss ♣r ♦ rr♥♦ s ts
t③s ♠ ♠s s ♣rs ♥♦ s♥♦ ♥tr ♠ ♠s♠♦ rr♥♦ é
♦♠♠ ♥çã♦ ♠♥sõs ♣r♠tr③s ♦r♠ q s stç♠ r③õs
s♣t♦ ♦♠étrs é♠ ss♦ s ♣rs ♦ ♥ sã♦ rq♥t♠♥t ssttís
♣♦r ♠ ♦♥çã♦ ♦♥t♦r♥♦ s q ♦ ♥trss ♠♦r s ♦ ♦♠í♥♦ ♦ ♦
♠♦str ♥s ♦s ①♠♣♦s ♦s tr♦s r③♦s ♣r ♥stçã♦
♦ s♦♠♥t♦ tr♥srê♥ ♦r ♠ ♥s t♦s
st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t
t♦rs ♠
t r♦ tér♠ ♦♥ s♦♠♥t♦ ♠♥r ♠
♥s ♦♠ ts ♥♥s
P t r♦ tér♠ ♦♥ s♦♠♥t♦ ♠♥r ♠
♥s ♦♠ ts ♥♥s
P ❲
s♦♠♥t♦ ♥tr s ♥s ♦♠ r♥ts ♦♠♣r
♠♥t♦s r♥ts s♣ç♠♥t♦s
❩ ❯
r♥srê♥ ♦r q ♣rssã♦ ♠ ♠ ♥
♠♥s♦♥ ♦♠ ♥s r♥ts trs
st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t
t♦rs ♠
t ♠çã♦ ♥♠ér tr♥srê♥ ♦r ♠ ♥
♦♠ ts ♦♥t♥s ♦♥sr♥♦ ♦♥çã♦ ♠st
♠ s♦ tr♥srê♥ ♦r ♦♥♦
❨ t st♦ ♥♠ér♦ ♦ rsr♠♥t♦ ♠ t tr♥s
rs ♠ ♠ ♥ ♣s ♣rs s♦ ♥ê♥
rçã♦ ♦ ♥ú♠r♦ r③ã♦ s ♦♥ts
tér♠s r③ã♦ s♣t♦ t
♠çã♦ tr♦ ♦r ♦ s♦♠♥t♦ tr♥t♦
♠ ♥ ♦♠ rr♥♦ s♥♦ ♣r♦trâ♥s r
♦ss r ♣ss ♣r r♥ts ♠♦♦s tr
ê♥
❱❯
♥stçã♦ ①♣r♠♥t tr♥srê♥ ♦r ♦♥
t ♠st ♠ ts ♦♥t♥s ♠ ♥ rt♥
r ♦r③♦♥t
❩ t st♦ ♥♠ér♦ ♦ s♦♠♥t♦ tr♥t♦ ♠ ♥
t♦ ♦♠♣rt♦ ♥tr ts rt♥rs ts tr
♣③♦s
PPP
P❱
♥ás ♥♠ér s♦♠♥t♦ ♠♥r ♣ró♦ ♠
♥ ♦♠ t ♠ ♦r♠t♦ ♠♥t
❯ t ♥ás ♥♠ér ♥ê♥ s♦r tr♥srê♥
♦r ♦rr♥t ♥srçã♦ ♠ t tr♥srs ♦
s♦♠♥t♦
❨❯ t st♦ ①♣r♠♥t ♥♠ér♦ ts ♥♥s ♦♥
t♥♠♥t ♦ s♦♠♥t♦ ♣r r♥ts â♥♦s
r♥ts t♠♥♦s ♥ ♠ ♠ ① tr♥t
♦ ♥ú♠r♦ ②♥♦s
♥stçã♦ ♥♠ér ♦ s♦♠♥t♦ ♠♥r ♠ ♥s
♦♠ ts ♣♦r♦ss
❯❱
♠çã♦ ♥♠ér tr♦ tér♠ ♦ s♦♠♥t♦
♠♥r r♥ts Pr ♦♥sr♥♦ rã♦ ♥tr
♠ ♥ ♦♠ ts s♥s ♣rs s♦tér♠s
st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t
t♦rs ♠
❨ ❲ tr♠♥çã♦ tr♦ tér♠ ♦ s♦♠♥t♦ tr
♥t♦ ♠ ♥ ♦♠ ts ♣♦r♦ss s♥s
t Prsõs ♥♠érs tr♥srê♥ ♦r ♦♥
♠ ♣ss♥s ♦♠ r♦s t③♥♦ ♦ FLUENT
çã♦ ♦ t♦ s ♦♥çõs ♦♥t♦r♥♦ tér♠s
♣r ♠ ♠ó♦ ♣ró♦ ♦ ♥
t ①♣r♠♥t♦s s♦r ♦ t♦ ♦ rr♥♦ ♣r♦trâ♥s
r♦ss s♦r tr♥srê♥ ♦r ♦♠♣♦rt♠♥t♦
♦ s♦♠♥t♦ ♠ ♣ss♥s rt♥rs rr♦♥
♣sss
❨❯ çã♦ ♥♠ér ♥ê♥ tr t ♣r
s♦♠♥t♦ tr♥t♦ ♠ ♥ ♦♠ rr♥♦ ♥♦
P❩ t ♠çã♦ ♥♠ér ♠ ♥ tr♠♥s♦♥ ♦♠
çã♦ tr♥srê♥ ♦r ♦ s♦♠♥t♦
t ①♣r♠♥t♦ tr♦ tér♠ s♦♠♥t♦ tr♥t♦
s♦r ♥s r♥ts trs
❲
❯
st♦ ♥♠ér♦ ♦♥çã♦ ♠♥r ♦rç ♠
♥s ♣s ♣rs ♦♠ ts tr♥srss r
çã♦ ♦ rr♥♦ ♥tr ♥♦ s♥♦ ♦♥sr♥♦
♣r♦
t ♥stçã♦ ①♣r♠♥t s ♣r♥♣s rtrísts
♦ s♦♠♥t♦ tr♥t♦ ♠ tr♦♦rs ♦r ♦ t♣♦
s♦t♦ ♣r r♥ts trs ♥s
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r♥r t ♣rs♥tr♠ s ♣r♥♣s rtrísts ♦ s♦♠♥t♦ tr
♥t♦ ♥♠ ♥ ♠♥s♦♥ ♦r♠ t③s r♥ts trs ♥s té
♥s s③çã♦ ♦♠ ♦ ♦t♦ ♥t♥r ♦ s♦♠♥t♦ ♠ tr♦♦rs ♦ t♣♦
s♦t♦ st tr♦ ♦ sr♦ q ♦ r♠ ♠♥r ♣r ♦s s♦s ♦s
♦♦rr ♣r Re ≤ 600 P♦r ♠♦ ♥♠♦♠tr sr♦♣♣r sr♦♣♣r ♥♠♦
♠tr② ♦s t♦rs ♠r♠ ♦s ♦rs s tçõs ♦s ♥ rçã♦
rt s♥♦ ♣♦ssí ss♠ tr♠♥r strçã♦ ♥t♥s tr♥t ♥tr
s ssss ♥s ♥ rã♦ s♦♠♥t♦ ♣ró♦ ♦♥♦r♠ r
r strçã♦ ♥t♥s tr♥t ♥ rã♦ s♦♠♥t♦ ♣ró♦
2
1
0 0,5 1x/s
chicana 7chicana 6
Res=9440
y/D0,280,430,510,580,660,73
2(v')
(Vs)
♦♥t ♣t♦ t
♦r♦ ♦♠ ♦s ①♣r♠♥t♦s t ♠ t♦ rt♥r ♦♠
ts s♥s ♣r r ♠♥t ♦♠ ♦ ♠♥t♦ tr s ts
é♠ ss♦ ♦s rst♦s ①♣r♠♥ts ♣♦♥t♠ q ♦s ♣râ♠tr♦s ♦ ♠é♦
tr♥srê♥ ♦r ♠♥t♠ ♦♠ ♦ ♠♥t♦ ♦ ♥ú♠r♦ ②♥♦s ♦♠ tr
s ts ♦♠♦ str r ♥ t ♦♥sttr♠ q ♣r
r ss♦ ♦ ♠t♦ ♠♦r ♦ q ♦ ♠♥t♦ ♥ tr♥srê♥ ♦r
❯♠ st♦ ♥♠ér♦ ♦ s♦♠♥t♦ tr♥t♦ ♣ró♦ ♥♠ ♥ ♦♠ rr♥♦
♥♦ ts t③♥♦ ♦ ♠♦♦ trê♥ κ− ǫ r♦ q ♣r ♠s♠ ♣♦
tê♥ ♦♠♠♥t♦ ♠♥♦r tr t t ♠♦r ♥ê♥ s♦r ♦ s♠♣
♥♦ tér♠♦ ❨❯ st ♦♠♣♦rt♠♥t♦ á s♦ r♦ ♣♦r ♥s♥
❲♥s♥ q♥♦ ♦ st♦ ♠ s♦♠♥t♦ ♠♥r ♥♠ ♥ ♣s
♣rs ts tr♥srss ♥sts ♣r r♥ts s♣ç♠♥t♦s st út♠♦
♦s t♦rs trír♠ ♥ê♥ ♦ rr♥♦ ♥♦ à r♥s rrçõs ♦r♠s
♥s rõs ♦ s♣ç♠♥t♦ ♥tr ts s ♦♥t♦r♥♦s t♠♣rtr ♦♠ tr s
ts ♣♦ sr s③♦ ♥ r
♦ s tr♦ ♦s ♦♦♠♥ s♠r♠ ♥♠r♠♥t ♦ s♦
♠♥t♦ ♠♥r ♦♥sr♥♦ rã♦ ♥tr ♥♠ ♥ ♦♠ ts s♥s
♣rs s♦tér♠s ♦♥stt♥♦ q tr♥srê♥ ♦r ♠♥t ♦♠ ♦ ♠♥t♦
tr s ts ♦♠ ♠♥çã♦ ♦ ♣ss♦ s ts ♦sã♦ ♦s t♦rs t♠é♠
r♠ ♥ê♥ ♦ ♥ú♠r♦ Pr♥t st s♥t♦ ♦srr♠ q ♦ s♦♠♥t♦
♣♦ s t♦r♥r ♣r♦♠♥t s♥♦♦ ♠t♦ ♥ts ♣r ♦s ♣rs ♦ ♦
q ♣r ♦s ♣rs t♠♣rtr tr♦ t♦r ♥trss ①♣♦r♦ ♣♦s t♦rs
r ❱rçã♦ ♦ ♥ú♠r♦ sst ♠é♦ ♦♠ ♦ ♥ú♠r♦ ②♥♦s ♣rr♥ts r③õs tr ♥
F/D duto liso0,7 madeira0,7 alumínio0,5 alumínio0,3 alumínio
200
160
120
80
40
0 4 8 12 16
Re x 10-3
Nu
Nu0
♦♥t ♣t♦ t
♦ ♥ê♥ tr s ts ♥ r♦♥â♠ ♦ s♦♠♥t♦ á ♠ ♠♥ç
s♥t ♥♦ ♣rã♦ ♦ s♦♠♥t♦ ♦♠♦ s ê ♥ r
Prr♥ ♦ r③r♠ ♠ st♦ ♥♠ér♦ ♣r ♦ s♦ s
♦♠♥t♦ ♥♦♠♣rssí tr♥t♦ ♠ ♠ ♥ rt♥r ♦♠ s ♥s s
rst♦s ♦r♠ ♦t♦s ♣r ♦♠♥çã♦ s s ♥s ♠♦♥ts ♥ ♠s♠ s
♣rí ♦♠ r♥ts ♦♠♣r♠♥t♦s r♥ts s♣ç♠♥t♦s s♣ç♠♥t♦ ♥tr
s ♥s ♦ r♦ ③s tr ♦ ♥ s t♦rs t③r♠ ♦ ♠♦♦
trê♥ ♦♥sttr♠ q ♦ ♦♠♣r♠♥t♦ r♦♠♥t♦ s♥t út♠
♥ ♦ ♣r♦①♠♥♠♥t ♦♥st♥t ♥♦ s♦ ♠ q st é ♠♥♦r q t ♥t
r t♦ tr t s♦r strçã♦ t♠♣rtr ♣r L/H = 4Pr = 0,71 Re = 200
(a) e/H=0,5 (b) e/H=0,3
(c) e/H=0,4 (d) e/H=0,2
♦♥t ♣t♦ ❲❯
r ❱t♦rs ♦ ♣r r♥ts r③õs ♦q♦ Pr
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
0
0
0
0
0
0
y/H
y/H
y/H
x/H
x/H
x/H
♦♥t ♣t♦ ❯❱
r♦r ♥♦ ♦s t♦rs st♦ ♦♦rr ♣♦s út♠ ♥ s ♦③ ♠rs ♥ rã♦
rrçã♦ r ♣ ♥ ♥tr♦r r stã♦ strs s ♥s
♦rr♥t ♣r três s♦s ♣r♦③♦s ♣♦r sts t♦rs ts ♠s♠♦ ♦♠♣r♠♥t♦
♣r♠r t ♠♦r q s♥ ♣r♠r t ♠♥♦r q s♥
r ♥s ♦rr♥t ♣r r♥ts t♠♥♦s s♣ç♠♥t♦s ♥s
(a)
(b)
(c)
♦♥t ♣t♦ P ❲
st♦ ♦♠♥çã♦ rçã♦ tr ♥ t♠é♠ ♦ st♦ ♣♦r
❩ ❯ ♣r ♠ ♥ ♦♠ ♥s sq♥s ♠♦♥ts s♦r
♠ ♣ q r stá ♠ s♦ç♦ ♦ ♦♠í♥♦ ♦♠♣t♦♥ t♠é♠ ♦
t r♥♠♥t♦ ♠ t③♦ s t♦rs t③r♠ ♠ ♣r♦r♠ ♦♠r
FLUENT ♦ ♠♦♦ trê♥ κε s ♦♥ír♠ q ♦ s♦ ♠
♥ ♠♥♦r ♥ ♣r♠r ♣♦sçã♦ ♠ ♥ ♠♦r ♥ út♠ ♠♥ r♥ç
♥tr ♠á①♠ ♠í♥♠ t♠♣rtr ♣ q ♦r♥♦ t♠♣rtrs
♠s ♦♠♦ê♥s
♦♥r st♦ ♥♠r♠♥t ♦ t♦ ♣r♦trâ♥s r♦ss
sçã♦ rt rr♥♦ s♥♦ ♥ tr♥srê♥ ♦r ♠ s♦♠♥t♦ tr♥t♦ ♥♦
r t ♠ ♥ã♦ strtr ♣r s♠çã♦ ♦ s♦♠♥t♦ tr♥t♦s♦r ♠ ♣ q ♦♠ ♥s sq♠át♦ ♦ ♦♠í♥♦ ♦♠♣t♦♥
Seção de entrada
Placa aquecida
Seção de teste
yx
EntradaSaída
Chicanas
♦♥t ♣t♦ ❩ ❯
♥tr♦r ♠ ♥ t♦r t③♦ ár♦s ♠♦♦s trê♥ ♦♥stt♦ q
♣rçã♦ s♦r ♦ s♦♠♥t♦ ♦ ♠s r q tr♦ tér♠ ♥ ♦
♥st♦ ♦ t♦ ♦ ♥ú♠r♦ Pr♥t tr♥t♦ s♦r ♠ ① ♦♠
t♦ s♥♥t s♦r ♦s rst♦s s♦çã♦ tér♠
♠♦r ♥♦ ♣r♦ss♦ tr♥srê♥ ♦r trés ♥srçã♦ ♠ ú♥
t ♦ ♥st ♣♦r q t t♦ ♠♥sã♦ t t♠é♠
s ♦r♥tçã♦ ♦ st♦ ♠ ts trés s♠çã♦ ♥♠ér ♠ ♦♠í♥♦
♠♥s♦♥ ♦♥♦r♠ r s rst♦s ♣♦♥t♠ ♣r ♠ s♥♥t ♠♦
r ♥ tr♦ tér♠ ♦ q♣♠♥t♦ ♣♦r ♠♦ ♥tr♦çã♦ ♠ t ♥♥ ♥
rçã♦ ♦ s♦♠♥t♦ ♦♠ ♠♥♦r ♣r r
♥stçã♦ ①♣r♠♥t ♣ss♥s ♦♠ ♣r♦trâ♥s r♦ss ♥♥s
♦♠ rçã♦ ♦ s♦♠♥t♦ ♦ r③ ♣♦r ♠ t st st♦ ♦s t♦rs
s♠ r ♦s t♦s ♦ rr♥♦ ♦s ♠♥t♦s r♦s s♦r ♦ s♦♠♥t♦
tr♥srê♥ ♦r s♥♦ ♣çã♦ ♥♦ rr♠♥t♦ s ♣ás ♠ tr♥ ás
r stá ♠ sq♠ ♠♦str♥♦ ♠ ♥ô♠♥♦ q ♦♦rr ♦♠ rqê♥ ♥♦
s♦♠♥t♦ ♠ ♥s sçã♦ ♥ã♦rr ♦ s♦♠♥t♦ s♥ár♦
♠♦r s s♠çõs ♥♠érs ♥♦♥♦ ♦ tó♣♦ ♠ qstã♦ é r③
♣r ♦ s♦ ♠♥s♦♥ ♥trt♥t♦ ♦♥♦r♠ á ♠♥♦♥♦ trê♥ é ♠
♥ô♠♥♦ tr♠♥s♦♥ st s♠♣çã♦ ♠♣ ♥ ♣r ♥♦r♠çã♦ ♦ st♦
♥♦♠♥t ♥tr♦çã♦ ♦stá♦s ♥♦ s♦♠♥t♦ ♣♦ rstr ♠ t♦s tr
♠♥s♦♥s ♠s♠♦ ♣r ♦ s♦ ♠♥r ♦♣③ t str♠ tr♥srê♥
♦r ♠ ♠ ♥ tr♠♥s♦♥ ♦♠ ♥s ♠♦♥str♥♦ ♣rs♥ç ♦rts
t♦s tr♠♥s♦♥s P♦r ♠♦ ♦ ♦♠♣rt♦ ♦♠ ♠ s♦ ♠♥s♦♥ s
♠♦♥strr♠ q ♣rsã♦ ♦ t♦r trt♦ ♣r ♦ s♦ é s♠♣r ♠♦r ♣r qs
rtrísts ♦♠étrs
♣rsã♦ ♥♠ér ♣r tr♥srê♥ ♦r ♦♥ ♥♠ ♥ ♠♥
s♦♥ ♦♠ r♦s r ♣ss ♦ r③ ♥♦ ♠ ♦♥srçã♦ ♦s t♦s
r♥ts ♦♥çõs ♦♥t♦r♥♦ r♥♦ t ♦♠♣rr♠ ♦s rst♦s
♥tr tr♦ tér♠ ♦♥ ♦♠ ♦ s♦ ♠ ♣r ♦ ♥ ♦♠ ①♦ ♦r
r s♦s ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♠♥s♦♥ r♣rs♥t♥♦ ♣rt s♣r♦r ♦ t♦ tr♦♦r ♦r
Parede
saídaentrada
Y
Xlinha de centro
h50 cm
D/2
(a)
saídaentrada
Y
X
50 cm
(b)
saídaentrada
Y
X
50 cm
(c)
saídaentrada
Y
X(d)
♦♥t ♣t♦ ❯ t
♦♥st♥t P♦r ♠♦ rst♦s ①♣r♠♥ts s ♣rsõs ♥♠érs ♦s t♦rs
♠♦strr♠ q ♣rsã♦ tr♥srê♥ ♦r é st♥t s♥sí ♦ t♣♦ ♦♥çã♦
♦♥t♦r♥♦ t③ ♥♦ ♠♦♦ ♥♠ér♦ st s♥s é ♠s ♥t q♥♦
é t ♣rsã♦ ♦ ♥ã♦ s♥♦ s♥t ♥ ♠é ♥ ♦ ♦♥stt♦ q
♠s sr♣â♥s ♥tr ♣rsã♦ ♥♠ér ♦ ①♣r♠♥t♦ ♣♦♠ sr ♠♥ís
♦♥sr♥♦ ♦♥çã♦ ♦r ♥s ♣r♦trâ♥s r♦ss rs st♦ é tr♥srê♥
♦r ♦♥
t♦ ♣♦r♦s ♠ ts t♠é♠ ♦ ♦t♦ st♦s ♥♠ér♦s P♦r
①♠♣♦ ♦ rr♥♦ s♥♦ ts sós ♣♦r♦ss ♦ ♥st♦ ♣r s♦♠♥t♦
tr♥t♦ ♠ ♠ ♥ rt♥r ❨ ❲ s t♦rs ♦♥sttr♠ q
tr♥srê♥ ♦r ♣r ♠s ♠♥t ♦♠ ♦ ♠♥t♦ tr s ts ♦ ♦
t♦ rçã♦ ♦ s♦♠♥t♦ ♦♠♦ ♣♦r♦s ♠♥ ♦ ♦q♦ ♦ s♦♠♥t♦
st t♣♦ ts ♣r♦♣♦r♦♥♦ ♠♥♦r ♣r r ♥t♦s ♠♦s t♠é♠
str♠ ♦ t♦ ts ♣♦r♦ss ♥ã♦ ♥♦♥tr♥♦ ♥t♥s ♥♦ s♦ ♠trs ♦♠
① ♣♦r♦s ♣r ♦ s♦♠♥t♦ ♠♥r ♥st♦
❱rçõs ♦♠étrs ts q ♦♠ ♦ ♦r♠t♦ ♣♥♦ áss♦ á ♦r♠
♦rs ♥♠r♠♥t r♣tt♥♣♣t Pr♦♠♦♥ ♥sr♠ ♦ s♦
♠♥t♦ ♠♥r ♣ró♦ ♠ ♠ ♥ sçã♦ rt ♦♠ ts ♠ ♦r♠t♦ ♠♥t
r ♦r♠ ♦ts ♠♦rs ♥ tr♥srê♥ ♦r ♦♠ rçã♦ às tr♦
r sq♠ ♠♦str♥♦ s ♦♠trs ♦ ①♣r♠♥t♦ ♦ ♣r♠♥t♦ ♦s♦♠♥t♦ s♥ár♦
Padrã
o de
esc
oam
ento
secu
ndár
io
Fundo Recolamento do
escoamento
45°Obstáculo
Separação do
escoamento
Lateral direita Linhas de
trajetória
Local da conexão do "obstáculo" com a parede superior
Topo
♦♥t ♣t♦ t
♥s ts ♣♥s ♣♦ré♠ ♦♥♦♥s ♠♥♦rs â♥♦s rtr tr♦ ①♠♣♦
♦ ♦ st♦ ♥③♥♥ t ♥♦ q ♦r♠ ♦♥③s s♠çõs ♥♠érs
♦ s♦♠♥t♦ tr♥t♦ ♠ ♥ ♣♥♦ ♣r ♦s ♦r♠t♦s ♥ ♦ rt♥r
áss♦ ♠ tr♣③♦ st s♦ ♦s t♦rs ♦♥sttr♠ ♠ ♦♥srá ♠♥t♦
♦s ♥♦ s♦ s ts tr♣③♦s ♦♠ rçã♦ ♦ ♦r♠t♦ tr♥r t♥♦
♦♠♦ ♦♥sqê♥ ♠ ♣rá ♠♥♦ ♦ ♦♥t trt♦ ♥♥ t
str♠ ♥♠r♠♥t ts ♦♠ ♦r♠t♦ ♠ ♦♥♦r♠ r s
t♦rs t③r♠ ♦ ó♦ ♦♠r FLUENT ♦♠ ♦ ♠♦♦ trê♥ s
♦♥sttr♠ q ♦ ♠♥t♦ ♥♦ ♥ú♠r♦ ②♥♦s ♣r♦♦ ♠ ♠♥t♦ sst♥ ♥♦
♥ú♠r♦ sst ♣♦ré♠ ♦♠ ♠♥t♦ ♥t♦ ♥ q ♣rssã♦
r ♦♠tr ♦ ♥ ♦♠í♥♦ ♦♠♣t♦♥ ♦ s♦♠♥t♦ ♣ró♦
H
b
s=H
L=2H
fronteiras periódicas
♦♥t ♣t♦ PPP P❱
r♥ts ♣♦s♦♥♠♥t♦s s ts ♥♦ ♥tr♦r ♦ s♦♠♥t♦ t♠é♠ ♦r♠
st♦s ❨♥ t str♠ ♦ t♦ ♥♥çã♦ s ts ♥♦ s♥t♦ ♦
s♦♠♥t♦ ❯♠ ♣r♦tót♣♦ rt ♦ s♠♦ ♥♠r♠♥t ♦ q stá str♦
♥ r
r ♥s ♦♠ ♦♠tr ♥♦ ♦r♠t♦
Le
s
chicanas em "L"
Lout
L
H
♦♥t ♣t♦ t
r sq♠át♦ ♠ strtr í ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♥♦ ♥
30
6
h1
1parede
aleta inclinada
parede711,5
domínio
numérico
2H
fluido
y
x
♦♥t ♣t♦ ❨❯ t
ss♠ ♦♠♦ s rtrísts ♦♠étrs r③ã♦ ♥tr s ♣r♦♣rs ♦ só♦
♦ ♦ t rt♠♥t tr♥srê♥ ♦r ❨ t t
♦♠♣rt♦ ♥tr s r♥ts r③õs ♥tr s ♦♥ts tér♠s
♦ só♦ ♦ ♦ ♣♦ sr s③♦ ♥ r Prs ♣♦ ♦
♠á①♠ q ♠♥t♥♦ r③ã♦ ♠ ③s t① tr♥srê♥ ♦r
♠♥s♦♥ ♣rs♥t ♠ ♠♥t♦ ♣r♦①♠♠♥t qr♣♦
♠ét♦♦ ♦♠s ♥t♦s t♠é♠ é t③♦ ♣r ♦♠í♥♦s ♦♠♣t♦♥s q
r♣rs♥t♠ ♠ só♦ ♦ tr♦ r③♦ ♣♦r t ♦♥çã♦ ♠st
♠ s♦♠♥t♦ tr♥t♦ ♠ ♥ ♦r③♦♥t rt♥r ♦♠ ts ♦♥t♥s ♦
❯♠ ♦s s♦s t③♦s ♣♦s t♦rs ♥♦ çã♦ tr♦ ♦r
♦♥ ♥ q ♦ ♦♠í♥♦ só♦ ts ♦ ♠♥t srt③♦ trés ♦ ♠ét♦♦
♦s ♦♠s ♥t♦s
♥ê♥ ♥♥çã♦ ts tr♥srss s♦r tr♦ ♦r ♦♥
♠ ♥s sçã♦ rt ♦ r♥t♠♥t st ♣r s♦♠♥t♦ ♠♥r P t
t③♥♦ ♦ CFX ♦sã♦ ♦s t♦rs ♦♥ír♠ q ♦ ♠♥t♦
r ♣♥ê♥ t① tr♦ tér♠ ♠♥s♦♥ ♦♠ r③ã♦ s♣t♦ t ♦♠ r③ã♦ ♥tr s ♦♥ts tér♠s ♣r r♥ts♥ú♠r♦s ②♥♦s
K=10Pr=0,7
(a)(b)
40
30
20
10
00 2 4 6 8 10 12 14 16 18 20 22
Local de máximo
Re=2000Re=1500Re=1000Re= 700Re= 500Re= 200Re= 100
Q
80
60
40
20
0
100
0 2 4 6 8 10 12 14 16 18 20 22
Local de K=200Pr=0,7
Re=2000Re=1500Re=1000Re= 700Re= 500Re= 200Re= 100
máximo
Q
♦♥t ♣t♦ ❨ t
ár tr♦ tér♠ ♣♦r ♠♦ s ts ♥ã♦ ♦ s♥t ♣r ♦♠♣♥sr s rõs
① tr♦ tér♠ ♦ às ③♦♥s rrçã♦ ♦ ♦ ♥t♦ à s s ts
é♠ ss♦ ♦s t♦rs ♦♥sttr♠ q ♦ ♦♥trár♦ ♦ rr♥♦ s♥♦ ♦ rr♥♦
♥♦ ♣rs♥t♦ ♠♥çã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ â♥♦
♥♥çã♦ s ts ♦♥♦r♠ s r ♥ r sts q ♦ st♦ ♦
r③♦ ♦♠♦ tr♦ ♣r♠♥r ♥ ♦rçã♦ ♦s s♦s ♣r♦♣♦st♦s ♣r ssrtçã♦
r ú♠r♦ sst ♦ ♣r ♣r s♣r♦r ♥r♦r ♦ rr♥♦s♥♦ ♣r ♦ rr♥♦ ♥♦
0,0
2,0
4,0
6,0
8,0
10,0
0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0
Nu
x
x*/a*
0° 23° 45° 68° 90° posição da aleta (a)
0,0
2,0
4,0
6,0
8,0
10,0
0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0
Nu
x
x*/a*
0° 23° 45° 68° 90° posição da aleta (b)
0,0
2,0
4,0
6,0
8,0
10,0
0,0 2,0 4,0 6,0 8,0 10,0
Nu
x
x*/a*
0° 23° 45° 68° 90° posição da aleta (c)
♦♥t ♣t♦ P t
❯Õ Ó Õ
st ♣ít♦ srã♦ ♣rs♥ts s ♦r♠çõs rst♥ts ♠♦♠ ♦ ♣r♦
♠ tr♥srê♥ ♦r ♦♥ ♦ s♦♠♥t♦ ♠ ♠ ♥ tr♥srs♠♥t
t♦ sçã♦ rt sts ♦r♠çõs ♦♥sr♠ ♠s s♠♣çõs ♥ q
♣óts ♠♥s♦♥ s ss♠ ♠♦♠ é ♣rs♥t ♣r ♦ s♦ tr♠♥
s♦♥ Pr♠r♠♥t sã♦ srts s qçõs ♦♥srçã♦ ásss ♣r ♠ss
q♥t ♠♦♠♥t♦ ♥r st út♠ t♠é♠ é ①♣rss ♣r ♦ s♦ ♦
só♦ sqê♥ s qçõs ♦♥srçã♦ ♦ ♦ sã♦ ♠♦s t③♥♦s
♠s♠ ♦r♠ q rst♠ s qçõs ♦♠ ♠é ♥♦ t♠♣♦ ♦ q á
♦r♠ ♦ ♣r♦♠ áss♦ ♦ ♠♥t♦ trê♥ sr ♣rs♥t♠s s
qçõs ♦♥srçã♦ ♠ tr♠♦s q♥ts ♠és q♥ts ts q
♥♠ ♦s t♦s ♦ ♦ r♠ s♦♠♥t♦ ♥♠♥t ♠ ③ q ♣óts
♦ss♥sq ♦ t③ ♣r ①♣rssr ♦ t♥s♦r ②♥♦s sts r♠♥t
♦r♠ ♣r s qçõs s♦s tr♥t ♣♦ ♠♦♦
♠ rtr③r rr♠♥t s♠çã♦ t③ ♥♦ ♣ê♥ stã♦
♣rs♥ts ♥♦r♠çõs r ♦ ♠ét♦♦ srt③çã♦ t♠é♠ s♦r strté
s♦çã♦ ♥♠ér
❯Õ ❱
r♦t♥ ♥♥r t♠é♠ r♥t r③çã♦ ♣sqss é ♦♠♠
♦çã♦ strtés ♠♦♦ rstr♥r ♦♠♣① ♦ t♠ ♠ qstã♦ st
st♦ ♦ ♣r♦♠♥t♦ é t♦ ♠♥t ♦♥srçã♦ s s♥ts s♠♣çõs
♦ t♦♥♥♦ Pr♦♣rs íss ♦♥st♥ts ss♣çã♦ s♦s ♦rçs
♦r♣♦ rçã♦ s♣r③ís ã♦ á rsstê♥ tér♠ ♦♥tt♦ ♥tr s ss s
ts s s♣rís ♥tr♥s s ♣rs ♦ ♥ ã♦ á ♦♥t rçã♦ ♥r
s♦♠♥t♦ ♥♦♠♣rssí ♠♥s♦♥ r♠ ♣r♠♥♥t ♦r♠
♠é ②♥♦s ♥♦ t♠♣♦ ♣r rs♦r s qçõs tr♥s♣♦rt
♦r♦ ♦♠ s s♠♣çõs ss♠s ♦r♠çã♦ ♦♥srt ♣r ís
♦ ♣r♦♠ ♥ ♦r♠ ♥ é r♣rs♥t ♣s qçõs q s♠
Pr ♦♥srçã♦ ♠ss
∂ρf
∂t+ ∂(ρui)
∂xi= 0, i = 1,2,3
♥ q ρf é ♠ss s♣í ♦ ♦ t r♣rs♥t ♦ t♠♣♦ xi sã♦ s ♦♦r♥s ♦
sst♠ ♦ ui sã♦ s ♦♠♣♦♥♥ts ♦
Pr ♦♥srçã♦ q♥t ♠♦♠♥t♦
∂(ρfui)∂t
+ ∂(ρfujui)∂xj
= − ∂p∂xi+ ∂sij∂xj
, i, j = 1,2,3
♥ q p é ♣rssã♦ ♦ sij é ♦ t♥s♦r t♥sã♦ s♦r
sij = 2µfD′
ij, i, j = 1,2,3
s♥♦ µ s♦s ♠♦r D′
ij ♦ t♥s♦r t① ♦r♠çã♦ s♦r
D′
ij =Dij − 1
3Dkkδij, i, j, k = 1,2,3
♥ q δij é ♦ ♦♣r♦r r♦♥r ♦ t♥s♦r t① ♦r♠çã♦ Dij é ♦t♦
♣rtr
Dij = 1
2(∂ui∂xj+ ∂uj∂xi) , i, j = 1,2,3
♦ts q ♣rtr ♣óts ♥♦♠♣rss ♣ qçã♦ ♦
s♥♦ tr♠♦ ♦ t♥s♦r t① ♦r♠çã♦ s♦r sr ♥♦ s qçõs
s t♦r♥♠ q♥ts
Pr ♦♥srçã♦ ♥r ♥♦ ♦
∂(ρfcfT )∂t
+ ∂(uiρfcfT )∂xi
= ∂
∂xi(kf ∂T
∂xi) , i = 1,2,3
♥ q T é t♠♣rtr cf é ♦ ♦r s♣í♦ ♣rssã♦ ♦♥st♥t ♦ ♦ kf é
♦♥t tér♠ ♠♦r ♦ ♦ Pr ♦♥srçã♦ ♥r ♥♦ só♦
∂(ρscsT )∂t
= ∂
∂xj(ks ∂T
∂xj) , j = 1,2,3
♥ q ρs é ♠ss s♣í ♦ só♦ cs é ♦ ♦r s♣í♦ ♣rssã♦ ♦♥st♥t ♦
só♦ ks é ♦♥t tér♠ ♦ só♦
❯Õ ❱
s ♠ét♦♦s ♥♠ér♦s ♦♠♣t♦♥s sã♦ t③♦s ♦♠♦ ♠ tr♥t ♣r
♣r♦①♠r s♦çã♦ s qçõs ♦♥srçã♦ ♦♥s ♦♠♦ qçõs r
t♦s ♦♠♦ tr♥t ♣r s♦çã♦ s♦♠♥t♦s ♦♠♣①♦s sã♦ ♣s ♦r♠
çõs sttísts ♦♠♦ t③ ♥st tr♦ ♦r♠ ②♥♦sr
r t♦s
♦r♠ ♦r♠ s á ♣♦r ♦t q♥♦ ②♥♦s ♣♦
s ♣sqs s♦r s♦♠♥t♦s tr♥t♦s ss♥♠♥t s qçõs rs
♣r♦♠çã♦ ②♥♦s sã♦ ss ♥ ♦♠♣♦sçã♦ ♠ q♥t ♠ ♠
♣r ♦r ♠é♦ φ ♠ ♣r ♦r t♥t φ′ ♦♠♦
φ = φ + φ′
♦♠♦ ♣rt t♥t é ♥tr③ tór ♠ trt♠♥t♦ sttíst♦ ♠é
♥♦ t♠♣♦ é ♣♦ st s♦ é ♣r♦♣r ♣r trê♥ st♦♥ár ♦ s
♣r ♠ s♦♠♥t♦ tr♥t♦ q ♥ ♠é ♥ã♦ r ♦♠ ♦ t♠♣♦ s ts
s♦r st ♣r♦♠♥t♦ ♣♦ sr ♥♦♥tr♦ ♠ ❲♦① t ♣ós ♣r st
♠t♦♦♦ às qçõs ♦♥srçã♦ ♦ ♦ t♠s qçã♦ ♦♥srçã♦
♠ss
∂ρf
∂t+ ∂(ρfui)
∂xi= 0, i = 1,2,3
s♥♦ q i = 1,2,3 r♣rs♥t♠ s rçõs ♦s ①♦s s ♦♦r♥s qçã♦
♦♥srçã♦ q♥t ♠♦♠♥t♦ s t♦r♥
∂(ρfui)∂t
+ ∂(ρfui uj)∂xj
= − ∂p∂xi+ ∂(sij − ρfu′iu′j)
∂xj, i, j = 1,2,3
♥ q ♦ tr♠♦ q ♥ tçã♦ s ♦s ♦ ♣♦ t♥s♦r ②♥♦s
τij = −ρfu′iu′j, i, j = 1,2,3
♥ q u′
i sã♦ s tçõs s ♦♠♣♦♥♥ts ♦ rçã♦ ♦♥sttt é
sij = 2µfD′
ij, i, j = 1,2,3
s♥♦
D′
ij =Dij − 1
3Dkkδij, i, j, k = 1,2,3
♦♠
Dij = 1
2(∂ui∂xj+ ∂uj∂xi) , i, j = 1,2,3
ssts q ♦ tr♠♦ τij á ♦r♠ ♠ t♥s♦r ♣r♥t ♦rrs♣♦♥♥♦ ♠
t① tr♥srê♥ q♥t ♠♦♠♥t♦ ♥♦s s tçõs ♦
♦ ♦ st tr♠♦ é ♦♥♦ ♦♠♦ t♥s♦r ②♥♦s ♥sst sr ①♣rss♦
♦r♦ ♦♠ ♠ ♠♦♦ trê♥ sr st♦ ♥♦ t♠ st ♣r♦♠ é
♦♥♦ ♦♠♦ ♦ ♣r♦♠ ♦ ♠♥t♦ trê♥ ♣r ♦r♠ st
♦r♠ q é ♣r♦♠♥♥t♠♥t t③ ♠ t t♠é♠ r♣rs♥tçã♦
ís ♦ ♣r♦♠
Pr qçã♦ ♥r t♠s t
∂(ρfcfT )∂t
+ ∂ρfcfuiT∂xi
= ∂
∂xi(kf ∂T
∂xi− ρfcfu′iT ′) , i = 1,2,3
♥ q ♦ tr♠♦ −ρfcfu′iT ′ rst ♦ ①♦ ♦r ♥♦ s tçõs tr♥ts
❯❯
♣r♦♠ ♥♠♥t ♦ á♦ s♦♠♥t♦s tr♥t♦s stá ♥ tr♠
♥çã♦ ♦s tr♠♦s ♦ t♥s♦r ②♥♦s qçã♦ s ①♣rssõs ♥♦♥♦ s
tçõs ♦ q sr♠ ♦♠♦ ♦♥sqê♥ ♦ ♣r♦ss♦ ♠é ②
♥♦s r♣rs♥t♠ ♥♦s ♥ó♥ts ♥çã♦ ♠♦♠ trê♥ é ♣♦rt♥t♦
s♥♦r ♣r♦①♠çõs ♣r sts ♦rrçõs s♦♥s ❲❳ t
①st♠ s ♦r♥s st♥ts ♣r ♠♦r ♦ t♥s♦r ②♥♦s ♦s ♠♦♦s
s♦s tr♥t ♦s ♠♦♦s t♥sõs ②♥♦s sts út♠♦s ♦♠♣t♠
t♦ ♦s t♥s♦rs ♣r♥ts ♦ t♥sõs ♣r♦③s ♣rtr ♦ t♥s♦r ②♥♦s
♥q♥t♦ q ♦s ♣r♠r♦s s s♠ ♥ ♣óts ♦ss♥sq sr s♠ s
♦♥srçõs ♣óts ♦ss♥sq
−ρfu′iu′j = µt (∂ui∂xj+ ∂uj∂xi) − 2
3ρfκδij, i, j = 1,2,3
♥ q µt é s♦s tr♥t δij é ♦ t r♦♥r κ é ♥r ♥ét
tr♥t ①♣rss ♣♦r
κ = 1
2u′
iu′
i, i = 1,2,3
stt♥♦ s qçõs ♥ qçã♦ t♠s
∂(ρfui)∂t
+ ∂(ρfui uj)∂xj
= −∂pe∂xi+ ∂
∂xj[µe (∂ui
∂xj+ ∂uj∂xi)] , i, j = 1,2,3
♥ q s♦s t µe é s♦♠ s ♣rs ♠♦r tr♥t
µe = µf + µt
pe é ♣rssã♦ t
pe = p + 2
3ρfκ .
♥♦♠♥t ♣r ♦♥srçã♦ ♥r t♠s
∂(ρfcfT )∂t
+ ∂(ρfcfuiT )∂xi
= ∂
∂xi(ke ∂T
∂xi) , i = 1,2,3
♥ q ♦ ①♦ ♦r s tçõs tr♥ts é ♠♦♦ ♣♦r
−ρfcfu′iT ′ = kt ∂T∂xi , i = 1,2,3
ke é ♦♥t tér♠ t ♦rrs♣♦♥ à s♦♠ ♥tr ♣r ♠♦r
♣r tr♥t
ke = kf + kt .
tr♠♥çã♦ ♦♥t tér♠ tr♥t s s ♥♦ ♥ú♠r♦
Pr♥t tr♥t♦
kt = cfµt
Prt
srs q ♦ ♥ú♠r♦ Pr♥t tr♥t♦ ♥ã♦ é ♣r♦♣r ♦ ♦ ♠s
ss♠ ♠ ♦r ♦♥st♥t ♦♠ s ♠ ①♣r♠♥t♦s ♥áss ♦♥stt♦s q Prts st ♣ró①♠♦ q é ♦ ♦r t③♦ ♥st ♦r♠çã♦ ❱ t
♥♠♥t é ♥ssár tr♠♥çã♦ q♥t µt q srá ♦t ♣♦r ♠♦
♠ ♠♦♦ trê♥
♦♥♦r♠ ♠♥♦♥♦ ♥ sçã♦ s♦r ♦ ♠♦♦ trê♥ ♦ à ís
♣rs♥t ♥♦ s♦♠♥t♦ ♦s s♦s st♦s ♥s ♦ s♦ ♦ ♠♦♦ ③♦♥
♥tr ♦r♦ ♦♠ ♣çã♦ ♦ t♦r t♠s qçã♦ ♣r ♥r
♥ét tr♥t κ
Dρfκ
Dt= τij ∂ui
∂xj− α∗ρfωκ + ∂
∂xj[(µf + σκµt) ∂κ
∂xj] , i, j = 1,2,3
❯♠ s♥ qçã♦ ♥♦ ♠♦♦ ♦r♥ t① ss♣çã♦ s♣í ω
Dρfω
Dt= γνtτij∂ui
∂xj−αρfω2+ ∂
∂xj[(µf + σωµt) ∂ω
∂xj]+2(1−F1)ρfσω2 1
ω
∂κ
∂xj
∂ω
∂xj, i, j = 1,2,3
s ♦rs s ♦♥st♥ts s qçõs tr♥s♣♦rt κ ω sã♦ tr♠♥s
trés ♠ ♦r♠çã♦ q ♠str ♦s ♦rs s rs♣ts ♦♥st♥ts ♥tr ♦rs
♦ ♠♦♦ ♣rt ♥tr♥ ♦ ♠♦♦ κ − ε ♣rã♦ ♣rt ①tr♥ ♦r♠çã♦
♠str é ♣♦r
ς = F1ς1 + (1 − F1)ς2
♥ q ♦s ♦rs s ♦♥st♥ts t③s ς1 ς2 ♣r ♦t♥çã♦ ♦ ♥♦♦ ♦♥♥t♦
♦♥st♥ts ♦ ♠♦♦ ♣♦♠ sr ♥♦♥trs ♠ ♥çã♦ ♠str
F1 é ♥ ♣♦ ♦♥♥t♦ qçõs q s
F1 = tanh(arg41),arg41 =min [max(
√κ
0,09ωy;500ν
y2ω) ; 4ρfσω2κCDκωy2
] ,CDκω =max(2ρfσω2 1
ω
∂κ
∂xj
∂ω
∂xj; 10−20) , j = 1,2,3
♥♦ q y é stâ♥ ♣r s♣rí ♠s ♣ró①♠ CDκω é ♣rt ♣♦st ♦ tr♠♦
sã♦ r③ qçã♦
♥çã♦ s♦s tr♥t é ♣♦r
µt = ρa1κ
max(a1ω;ΩF2) , Ω = √2WijWij e Wij = 1
2(∂ui∂xj− ∂uj∂xi) , i, j = 1,2,3
♥ q Ω é ♦ ♦r s♦t♦ ♦rt W é ♦ t♥s♦r t① r♦tçã♦ ♥çã♦ F2
é ♥ ♦♠♦
F2 = tanh(arg22),arg2 =max(2
√κ
0,09ωy;500ν
y2ω)
❱ P
❯♠ çã♦ ♠♣♦rt♥t ♥♦ ♣r♦t♦ q♣♠♥t♦s ♥♦♥♦ s♦♠♥t♦
♦rç♦ é ♣r r r♣rs♥t ♣ q ♣rssã♦ ∆p ❯♠ ♦s ♣r♥♣s
♠♦t♦s é ♦ st♦ ♦♣r♦♥ q s t♦r♥ ♠♦r q♥t♦ ♠♦r ♣r r
♦r♠ ♦ ♦ ♦ ♦ ♦♥t rçã♦ ♦ trt♦ s♣r Cfx
♦ ♦♥♦ s ♣rs ♦ ♥ ss♠ s rõs ♦♥srs ♥ çã♦ st ♦
♥t ♥ã♦ r♣rs♥t♠ ♦ trt♦ ♦ ♦ ♦♠ s ts ♠s s♦♠♥t ♦ trt♦ ♦ ♦ ♦♠
♥tr só♦♦ ♥s rõs ♣r ♠♦r ♥ã♦ ♦r♥ç ♠ ♠ rt
♦ t♦ ♦ rrst♦ s♦s♦ s♦r s ts ♦ ♦♠♣♦rt♠♥t♦ ♦ Cfx é ♥tr♥s♠♥t
tr♦ ♦s ♣râ♠tr♦s ♦♠étr♦s qs ♥ ♦ ♦♥t é ♠ ♣râ♠tr♦
♠ ♠t r♦♥â♠ st ♦r♠ é ♠ ♥♦r ♥♠♥t ♣r ♥t♥
r s rçõs ♥st rã♦ ♦ s♦♠♥t♦ ss♠ t♠s q ♦ ♦♥t trt♦
s♣r é ♦r♥♦ ♣♦r ❳ t
Cfx = τint,x∣y=±H/21
2ρfU
2
ref
♥ q τint,x é t♥sã♦ s♥t ♦ ♦ ♦ ♦♠ s s♣rís ♣r ♥ ♥tr
só♦♦ Uref é ♦ rrê♥ ss♠ ♦♠♦ ♦ ♥ ♥tr
♦ ♥
Pr ♠ çã♦ ♦ ♠ ♣r r ∆p é ♠♥s♦♥③
trés r③ã♦ ♦♠ ♣rssã♦ às ♦rçs ♥rs ♦ s♦♠♥t♦ ♥♠ sçã♦
rrê♥ ♥tr ♦ ♥ ♦♥♦r♠ qçã♦ ss♠ sã♦ ♦s ♠
♦♥srçã♦ ♦s t♦s ♦ trt♦ ♦ s♦♠♥t♦ ♦♠ s ♣rs ♦♠ s ts é♠
ss♣çã♦ ♥r ♠â♥ ♣♦s órts q sr♠ ♦ às ts ♦ trt♦
♥tr♥♦ q ♦♦rr ♥♦ ♦ st r③ã♦ é ♦♥ ♣♦r ♦♥t ♣rssã♦ Cp
♥ sr ❳ t
Cp = ∆p1
2ρfU
2
ref
♥ q ∆p é r♥ç ♣rssã♦ ♥tr ♣rssã♦ ♦ ♠é ♥♠ ♣♥♦ ♦③♦ ♠
x = 30H ♣rssã♦ ♠é ♥ sçã♦ ♥tr ♦ ♥ srs q ♣r
t♦♦s ♦s s♦s ♦ ♣♦♥t♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣ós ♦ tr♦ t♦ ♥
♦♦rr ♠ ♣♦sçõs ♠♦t♥t x = 30H
❱
tr♥srê♥ ♦r ♥tr ♦s ♦♠í♥♦s s♠♦s ♦♦rr ♠♥r ♦♥
♥ ♣♦r ♠ ♥tr ♦♥srt st♦ é t♦♦ ♦ ♦r q trss ♦ ♦♠í♥♦ só♦
é ♦♠♣t♦ ♣r ♦ ♦♠í♥♦ ♦
♦r♠ ♦ tr♦ tér♠ ♦ trés ♦ ♥ú♠r♦ sst ♦ q
r♦♥ tr♥srê♥ ♦r ♦♥t ♦♠ tr♥srê♥ ♦r ♦♥t
Nux = hxDh
kf
♥ q Nux é ♦ ♥ú♠r♦ sst ♦ Dh é ♦ â♠tr♦ rá♦ hx r♣rs♥t
♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦ kf ♦♥t tér♠ ♦
♦
♦♥t tr♥srê♥ ♦r ♦♥t♦ ♦ é ♥♦ ♣ ♦♠♥çã♦
♥tr q♥t ♦r tr♦ trés ♥tr ♠ r♥ç t♠♣rtrs
ss♠ t♠s
hx = qint,x∣y=±H/2Tint,x∣y=±H/2 − T e
s♥♦ qint,x Tint,x ♦ ①♦ ♦r t♠♣rtr ♦ ♦♥♦ ♥tr só♦♦
♥s ♣♦sçõs y = ±H/2 T e é t♠♣rtr rrê♥ ♥♦r♠ ♦♠♦ ♦♥çã♦
♦♥t♦r♥♦ ♥ ♥tr ♦ s♦♠♥t♦
srs q ♥çã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♥♦r♠ qçã♦
r♣rs♥t s rõs ♥tr ♥tr ts ♦ s ♥ rã♦ s ♣rs ♦
♥ st♦ ♦♥t ♣♦s s rrê♥s t③s y = ±H/2 ♦♥♠ ♦♠ s ss
s ts ♥s ss rs♣ts ♣♦sçõs sts ♦s ♣♦rt♥t♦ ♥çã♦ ♦ ♥ú♠r♦
sst ♥ã♦ s ♣ ♠ ③ q ú♥ ♦r♠ tr♥srê♥ ♦r ♦♦rr ♣♦r
♦♥çã♦ ♥tr ♣r ♦ ♥ s t
♦ts t♠é♠ ♥ qçã♦ ♠s ♠♣çõs tr♦ ♦r ♦♥
♦ ♥♠r♦r t♠s ♠♦r ♥ê♥ ♦ s♦♠♥t♦ ♠ ③ q st ♣♦ rr
r♠ ♥ís ♥t♥s tr♥t s♥ q♥t ♥♦ ♥♦♠♥♦r
é ♠t ♣ ♣ ♦ só♦ tr♥srr ♦r s r♦♥tr ①tr♥ ♦♠
rás s♣s té ♥tr só♦♦
♣r ♦sr♦ ♦ ♥ú♠r♦ sst ♦ ♥ rã♦ ♥tr s ts rst
♦r♠çã♦ ③♦♥s rrçã♦ ♣ró①♠s s ts ♥s ♠♥r ①♣r♠♥
t ❱♦ t♦♥ str♠ ♦♠tr ♠ ♥ ♦♠ ①♣♥sã♦ r♣t ♦♥
s ♦r♠ ♠ ③♦♥ rrçã♦ s♥t ♦ r s t♦rs ♦srr♠ q ①st
♠ ① t① tr♥srê♥ ♦r ♥ ③♦♥ rrçã♦ s ♠ ♠♥t♦
♥t♦ té t♥r ♠á①♠ t① q ♦♦rr ♣ró①♠ ♦ ♣♦♥t♦ r♦♠♥t♦ st
srçã♦ ①♣ ♦ ♦♠♣♦rt♠♥t♦ ♣rst♦ ♣s s♠çõs ♥♠érs st tr♦
♥♦ q ♦ s♦♠♥t♦ ♦ s♦♠♥t♦ ♦♦rr ♣rtr ♣♦♥t s ts ♦♠♦ srá
st♦ sr
Pr ♦♥srr ♦ t♦ ♦ tr♦ tér♠ st♦ é s sçã♦ ♥tr
té stâ♥ rrê♥ x = 30H ♦ t③♦ ♠ ♥ú♠r♦ sst ♠é♦ ♦
♦ ♥çã♦ ♦ s ♥♦ tr♦ ♦ srs q st
tr♥t s ③ ♥ssár ♠ ③ q ♦ ♥ú♠r♦ sst ♠é♦ áss♦ Nu ♦t♦
♥trçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♥ã♦ ♠ ♦♥t ♦ t♦ s ts
s♦r tr♥srê♥ ♦r ss♠ ♦ ♥ú♠r♦ sst ♦ é ♦ ♣♦r
Nu = hDh
kf
♥ q
h = mcf(T e − T x=30H)2Lx=30H∆Tm
,
s♥♦
∆Tm = T e − T x=30H
ln( T x=30Hint − T e
T x=30Hint − T x=30H
)
T x=30Hint = T x=30H
int ∣y=H/2
+ T x=30Hint ∣
y=−H/2
2
s♥♦ h ♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦ m ③ã♦ ♠áss ♦
♦ T x=30H Lx=30H sã♦ t♠♣rtr ♠é ♠str ♦ ♦♠♣r♠♥t♦
♦s ♥ ♣♦sçã♦ rr♥t x = 30H ∆Tm é r♥ç t♠♣rtr ♦rít♠
srs q ♠é rt♠ét s t♠♣rtrs ♠és ♥s ♥trs ♦ ♥ s
♥tr té stâ♥ rrê♥ x = 30H T x=30Hint ♦♥sr s♦♠♥t ♥tr
s rõs ♣r
♠♥r ♦♠♣♠♥tr ♦ ♥ú♠r♦ sst ♦ ♦ ♦r♠ r③s
♠s çõs tr♦ ♦r ♣r ♦ tr♦ s ♥tr té sçã♦ ♥ ♣♦sçã♦
x = 30H ♦r♠ tr♠♥r ♦ ♦r s ts st ♥ás s t♦r♥ ♠♣♦rt♥t
t♥♦ ♠ st ♦s ♦♠♣♦rt♠♥t♦s ♦♥trst♥ts ♣r ♦ ♥ú♠r♦ sst ♦ ♠é♦
♦♥♦r♠ ♣rs♥t♦ sr
♦r s ts qa ♦ q♥t♦ ♣♦ s♦♠tór♦ ♦ ♣r♦t♦ ♥tr ♦ ①♦
♦r trés s ts s ár s♣r
qa = 2N ∫Aa
qintdAa
♥ q 2N é ♦ ♥ú♠r♦ t♦t ts Aa r♣rs♥t ár s♣r ♠ ú♥
t
♦r t♦t qtotal tr♥sr♦ ♣r ♦ ♦ t♠é♠ ♦ q♥t♦ ♣r ♦
tr♦ ♥ s ♥tr té ♣♦sçã♦ x = 30H Pr ♦tr ss q♥t
rs♥ts ♦ ♦r tr♥sr♦ trés s ♣rs ♦ ♥ ♦ ♦r tr♦♦ trés s
ts qa
qtotal = ∫Aint
qintdAint
♥ q qint Aint ♦rrs♣♦♥♠ ♦ ♦r à ár t♦t ♥tr só♦♦ s
♥tr té ♣♦sçã♦ x = 30H
sr sã♦ ♣rs♥t♦s ♦s rst♦s st tr♦ s ♦♥srçõs s♦r
♦r♠ ♥♠ér ♣♦♠ sr ♦♥sts ♥♦s t♥s ♦ ♣ê♥ ♥♦ q sã♦
♦r♦s ♦s ♣r♥♣s s♣t♦s ♠
❯ ❯Õ
st ♣ít♦ é ♥♦ ♦♠ ♣rs♥tçã♦ s t♣s rçã♦ çã♦
♣r ♠s ♠s ♣rt♥♥ts ♦♠♦ ♦ ♥ú♠r♦ t♥t♦♥ ♥r ♥é
t tr♥t sts t♣s sã♦ ♠♣♦rt♥ts ♣♦s ♣r♠t♠ r ♣ ♦
♣r♦r♠ ♦♠r ♦rrt ♦♥strçã♦ ♦s s♦s ♣ss♥♦ ♣ ♦♠tr
♠ ♠ét♦♦ ♥♠ér♦
♣ós ♦s s♦s t♣ çã♦ rçã♦ stã♦ ♣rs♥t♦s ♦s t♥s q
♠♦tr♠ r③çã♦ st tr♦ st♦ é ♦ st♦ ♦ s♦♠♥t♦ tr♥t♦ ♥♦s
♥s t♦s ♥tr♦ sçã♦ sã♦ ♣rs♥ts s rçõs ♣r♦♣♦sts ♦♠étr
s r♦♥â♠s s t♣s ♦♥strçã♦ s ♠s s ♦♥çõs ♦♥t♦r♥♦
♣r♦♣rs íss sssã♦ ♦s rst♦s ♦t♦s
❱ ❱
❯ ❯ CFX
♠ rçã♦ çã♦ sã♦ ♦s ♦s ♣r♥♣s ♦♥t♦s ♠♣♠♥t
t③♦s ♣r rr ♦♥ rá s♦çã♦ ♠♥r rs♠
rçã♦ é çã♦ rá s♦çã♦ ♣r ♠ ♠♦♦ ♦♠♣t♦♥ P♦r
s ③ çã♦ stá r♦♥ à çã♦ rá ♠ s♠çã♦ trés
s ♦♠♣rçã♦ ♦♠ ♦s ①♣r♠♥ts ♦♦♦ ♠♦♦ r♥t rçã♦
é ♠ qstã♦ ♠t♠át ♥q♥t♦ q çã♦ é ♠ qstã♦ ís P
❯
s s♦çõs ♣r s qçõs ♦♥srçã♦ q♥t ♠♦♠♥t♦
♥r ♦r♠ rs ♣r ♦ s♦ ♠ ①♣♥sã♦ r♣t ♦♥♦r♠ rst♦s
♦t♦s ♣♦r ❩♥s t ♥s♦r t ♠ t ❱♦
t♦♥ Pr t♥t♦ ♦s s♦s ♦r♠ ♦r♥♦s stã♦ ♣rs♥t♦s ♥s ssçõs
s♦çã♦ ♦ s♦çã♦ tér♠ ♦♠tr ♣r s♦ é
rtr③ ♣♦s ♦♠♣r♠♥t♦s sçã♦ ♥tr sçã♦ ①♣♥ ♣ tr
♦ r q ♥ r③ã♦ ①♣♥sã♦
♦r♠ ♦♠♣♠♥tr s♦çã♦ qçã♦ tr♥s♣♦rt ♥r ♥ét
tr♥t κ ♦ ♦♠♣r ♦♠ ♣rsã♦ ♥♠ér ❩♥s t ♦♠
♦s ♦s ♥s♦r t st út♠♦ s♦ q stá ♣rs♥t♦ ♥
ssçã♦ s♦çã♦ ♥r ♥ét tr♥t ♦♠tr t③ ♦ ♠
♥ ♦r③♦♥t
♠ t♦♦s ♦s s♦s rçã♦ çã♦ t③♦s ♦ r t♠♦sér♦ ♦♠♦
♦ s s♠çõs ♥♠érs s ♣r♦♣rs íss ♣♦♠ sr ♦♥sts ♥
Pr♦♣rs íss t③s ♥ t♣ çã♦ rçã♦ ♦ ó♦♥♠ér♦
Pr♦♣r ❱♦r
❱s♦s ♥â♠ ♠♦r µf 1,831 × 10−5 Pa ⋅ sss s♣í ρf 1,185 kg/m3
♣ ♦rí ♣rssã♦ ♦♥st♥t cf 1004,4 J/kgK♦♥t tér♠ ♠♦r kf 0,0261 W /mK
♦♥t ♦t ♣r♦♣rs ♦ ♣r♦r♠ CFX
s♦ s♦çã♦ ♦
st st♣ rçã♦ çã♦ ♦ t③ ♦♠tr ♦rrs♣♦♥♥t
♠ ♥ ♦♠ ①♣♥sã♦ r♣t ❯♠ ♣r ♦s rtríst♦ ♦t♦ ♥ sçã♦
①♣♥ é ♦♠♣r♦ ♦♠ ♦s ①♣r♠♥ts ♦tr♦s ♠♦♦s ♦♠♣t♦♥s
♦♠tr
stã♦ ♣rs♥ts s ♠♥sõs ♣r♠tr③s ♦♠tr t
③ ♥♦ s♦ q ♣♦♠ sr s③s ♥ r
♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥♦ s♦ t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥
srçã♦ ♠♥sã♦
tr sçã♦ ♥tr He 2d
tr sçã♦ ①♣♥ Hs 3d
♦♠♣r♠♥t♦ sçã♦ ♥tr Le 3d
♦♠♣r♠♥t♦ sçã♦ ①♣♥ Ls 20d
tr ♦ r d (m)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♥♣♥ê♥ s♦çã♦ ♥♠ér ♦♠ rçã♦ à ♠ ♦ trés ♦
st♦ ♦ r♥♦ ♠ Pr t♥t♦ ♦ r③ ♠ sqê♥ s♦s ♦♠ rçã♦
♦ ♥ú♠r♦ ♦s ♠♥t♦s ♠♥t♦ ♦ r♥♦ ♠ t♣♦ ♠♥t♦ t③♦ ♥
rçã♦ s ♠s ♦ qrtr
r ♠♦str ♠ ♠ tí♣ t③ ♥st t♣ rçã♦
çã♦ ♣r s ♦♠trs ♦♠ ①♣♥sã♦ r♣t
r tí♣ rtrísts ♠♥s♦♥s t③s ♣r s ♦♠trs ♦♠①♣♥sã♦ r♣t
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♦♥çõs ♦♥t♦r♥♦
♦ s♦ s♦çã♦ ♦ t③♦s s s♥ts ♦♥çõs ♦♥t♦r♥♦
❼ çã♦ ♥tr ♣r ♦s ♠ ♠t tr♥t ♣♥♠♥t
s♥♦ ♦♠ ♥t♥s tr♥t ♦ rrê♥ st
s♦ ♦ Uref = 18,2 m/s❼ ♣rís ♦rrs♣♦♥♥ts às trs ♦♠étrs ♦♥çã♦ ♣♥♦ s♠tr
❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦ ♦ ♦ ③r♦ ♥ts q ♦
s♦ ♠ ♣r ♠♣ q ♥ã♦ á ①♦ ♠ss trés q r♦♥tr
♣♦rt♥t♦ é t♠é♠ ♦♥sr ♠♣r♠á
❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦
st♦s
♦♠♦ rst♦ ♣r ♦ st♦ r♥♦ ♠ ♣rs ♣r♦①♠
s s♦çõs ♦ts ♣r s três r♥ts ♠s ♠♥t♦s
♠♥t♦s ♠♥t♦s ♣rs♥ts ♥ r ♣r ♦s
♠♥s♦♥ ♦ ♦t♦ ♥♠ sçã♦ ♦③ x/d = 5,33 ♣r ♦♠tr ♥
♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He s rst♦s ♣r r③ã♦ u/u∞
r ♥♣♥ê♥ ♠ ♣r ♦ s♦ ♦♠♣rt♦ ♦ ♣r ♦♥tr três r♥ts ♠s
−0,4 −0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,20,0
0,5
1,0
1,5
2,0
2,5
①♦rrs♦
u/Uref
(y+d)/d
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♣rs♥tr♠ ♠ rçã♦ ♥♦ ♦r ♠á①♠♦ st r③ã♦ ♥♦ ♦r
♠í♥♠♦ st r③ã♦ ♥tr s ♠s
Pr ♥s rçã♦ çã♦ st s♦ t③♦s ♦♥♦r♠ ♣r
s♥t♦ ♥ r Prs q ♦s rst♦s r♦s ♥st tr♦ ♣rs♥tr♠
♠ ♦ ♣r♦①♠çã♦ ♠ rçã♦ ♦s ♦rs ①♣r♠♥ts trtr ①t♦ ♣ r
ã♦ ♣ró①♠ à ♣r st rã♦ ♦♥t♦ s ♠♥ts ♦srs ♦ ♦
①♦ rrs♦ r♠ ♥tr♦ ① rt ♣♦s t♦rs ♦ tr♦ ①♣r♠♥t
♦ rrê♥ 18,2 ms−1 srs ♥ q ♦ ♠♦♦
♣rs♥t rst♦ ♠s ♣ró①♠♦ ♦ ①♣r♠♥t q♥♦ ♦♠♣r♦ ♦♠ ♦s ♠♦♦s
κ − ε ♦♠ stq ♣r rã♦ ①♦ rrs♦
str ♥ q ♦♥çã♦ ♦♥t♦r♥♦ t③ ♥ sçã♦ ♥tr
♠♣♦ ♥ r③♦á r♥ç ♥tr ♦ ♠♦♦ κ − ε ❩ t ♦ ♠♦♦
♣rs♥t tr♦ ♠ ❩♥s t ♦s t♦rs t③r♠ ♠ ①♣rssã♦
♣r ♦ ♣r tr♥t♦ ♦s ♥ sçã♦ ♥tr P♦ré♠ ♥st tr♦
♦♥♦r♠ ♠♥♦♥♦ t③♦s ♠ ♣r tr♥t♦ ♣♥♠♥t s♥♦♦ ♦ q
♦ ①♣♦rt♦ ♣rtr sçã♦ sí ♠ ♥ sçã♦ rt ♠s♠ tr
♠ q ♦s sçã♦ ♥tr ♦♠tr srt ♥ r♥ç ♠
qstã♦ é q ♦sr ♣r rã♦ ♠s st ♣r (y + d)/d > 1,0 ♦♥
♦ ♠♦♦ ♣r ♦♠ ♠♦r rá ♦ q ♦ ♠♦♦ κ − ε ❩ t
♦ ♦r♠t♦ t♦ ♦ ♣r ♦s
r Pr ♦ ♠ x/d = 5,33 ♣r ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He
−0,4 −0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,20,0
0,5
1,0
1,5
2,0
2,5
①♦rrs♦
u/Uref
(y+d)/d
❱♦rs ①♣r♠♥ts t ♦♦ κ − ε ♣rã♦ ❯ t ♦♦ κ − ε ❩ t ♦♦ SST st tr♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
s♦ s♦çã♦ tér♠
st s♦ s♦çã♦ tér♠ ♦ ♣r ♠ ♦♠tr ♥ ♦♠ ①
♣♥sã♦ r♣t s rst♦s sã♦ ♦♠♣r♦s ♦s trtr s♥♦ ♦♥r♦♥t♦s ♦♠
♦s ①♣r♠♥ts ♠ ♦♠♦ ♦♠ ♣rsõs ♥♠érs ♦tr♦s t♦rs
♦♠tr
♦♠tr t③ ♥ s♦çã♦ st s♦ é s♠r àq ♦ s♦ ♠
♠ q ♠s ③♠ s♦ ♠ ①♣♥sã♦ r♣t ♠ ♥s ♣r♥♣ r♥ç é
r③ã♦ ①♣♥sã♦ Hs/He q ♥st s♦ é sã♦ ♣rs♥ts s
♠♥sõs ♦♠étrs ♣r st s♦
♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥ s♦çã♦ tér♠ s♦ t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥
srçã♦ ♠♥sã♦
tr sçã♦ ♥tr He 4d
tr sçã♦ ①♣♥ Hs 5d
♦♠♣r♠♥t♦ sçã♦ ♥tr Le 3d
♦♠♣r♠♥t♦ sçã♦ ①♣♥ Ls 20d
tr ♦ r d (m)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
rst♦ ♥stçã♦ ♥♣♥ê♥ s♦çã♦ ♣r r♥ts t♠
♥♦s ♠s ♦♠ ♠♥t♦s qrtrs ♣ ♠♥t♦s t
♠♥t♦s ♠♠ ♠♥t♦s stá ♣rs♥t♦ ♥ r ♥ q stá
♠♦str strçã♦ ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♦♥♦ s♣rí ♥r♦r sçã♦
①♣♥ tr Hs ♦ ♥ strçã♦ ♦ ♥ú♠r♦ t♥t♦♥ é ♣♦r
Stx = hx
ρfUrefcf
♥ q ♦ ♦♥t ♦♥t♦ tr♦ tér♠ ♦ ♦ ♦t♦ ♦♥♦r♠ sr
hx = qesp
Tw,x − Tref
♦♠ t♠♣rtr rrê♥ Tref s♥♦ ♣ró♣r t♠♣rtr ♥♦r♠ t③
♦♠♦ ♦♥çã♦ ♦♥t♦r♥♦ ♥ sçã♦ ♥tr ♦ ♥ qesp ♦ ①♦ ♦r s♣
♦ ♥ s♣rí ♦♥sr
♦♥çõs ♦♥t♦r♥♦
çã♦ rçã♦ s♦çã♦ tér♠ ♦r♠ t③s s s♥ts ♦♥
çõs ♦♥t♦r♥♦
❼ çã♦ ♥tr ♣r ♥♦r♠ t♠♣rtr 300 K ♣r ♦
s ♠ ♠t tr♥t ♣♥♠♥t s♥♦ ♦♠ ♥t♥s
tr♥t srs q ♦ ♣r♦♠♥t♦ ♣r ♦tr ♦ ♣r ♦s ♦ ♦
♠s♠♦ ♣♦ ♥♦ s♦ ♦ rrê♥ st s♦ ♦ Uref = 16 m/s❼ ♣rí ♥r♦r sçã♦ ①♣♥ sçã♦ tr Hs ①♦ ♦r ♦♥st♥t
qesp = 270 W /m2
❼ ♣rís trs ♦♠tr ♦♥çã♦ ♣♥♦ s♠tr
r st♦ ♥♣♥ê♥ ♠ ♣r ♦ ♥ú♠r♦ t♥t♦♥ s♣rí♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He
0 2 4 6 8 10 12 14 16 18 200
0,5
1
1,5
2
2,5
3
3,5
4
x/d
St×10
3
♣
t
♠♠
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦
❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦
st♦s
Pr ♦ st♦ ♥♣♥ê♥ s ♠s ♣rs♥ts ♥ r r♥ç
♥tr ♦ ♠á①♠♦ ♦r ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♥tr s ♠s ♠♠ t
♥tr ♠ t ♠ ♣ ss♠ ♦ s♦ ♠ t
♣r s ③r ♦ ♦♠♣rt♦ ♦♠ ♦s ♦s ①♣r♠♥ts ♦♠ s s♦çõs ♥♠érs
trtr
r ♣rs♥t ♦ ♦♠♣rt♦ ♠ t ♦♠ s ♣rsõs ♥♠érs
t③♥♦ ♠♦♦ κ−ǫ ts ♣♦r ❩ t t③♥♦ ♦ ♠ét♦♦ s r♥çs
♥ts ♣♦r ❩ t t③♥♦ ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s ♦♠ ♦s
rst♦s ①♣r♠♥ts ❱
r ♦srs q ♥q♥t♦ s s♠çõs ♥♠érs ♦♠ ♠♦♦ κ−ǫ♣rs♥t♠ ♦rs ♠♦rs q ♦s ①♣r♠♥ts ♠ ♣rt♠♥t t♦♦s ♦s ♣♦♥t♦s é♠
♠ s♦♠♥t♦ ♦r③♦♥t ♥♦ ♣♦ ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♠♦♦ é ♣③
r ú♠r♦ t♥t♦♥ ♦ ♣r s♣rí ♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He
0 2 4 6 8 10 12 14 16 18 200
0,5
1
1,5
2
2,5
3
3,5
4
♦sçõs ♦ ♦sórts ♥t♦
x/d
St×10
3
❱♦rs ①♣r♠♥ts ❱ ♦♦ κ − ε ❩ t ♦♦ κ − ε ❩ t ♦♦ SST t
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♣rr ♦③çã♦ st ♣♦ ♠ ♦♥tr♣rt ♣r st út♠♦ ♠♦♦ á ♠
q ♠s ♥t ♣r ♦ ♥ú♠r♦ t♥t♦♥ ♥ rã♦ ♣ós ③♦♥ rrçã♦
♦ ♣ós ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♠s♠ r ♥ á ♠ ♦srçã♦
♣r s ♦sçõs ♦ ♥ú♠r♦ t♥t♦♥ ♥t♦ ♦ r q s rr à ♣rs♥ç ♦s
órts ♦♥trr♦tt♦s ❯♠ ③ q ♦ ♥í r♥♦ ♠ ①♦ ♣r ♦ ♠♦♦
é t♦ sts strtrs sã♦ ♣trs ♦♠♦ rtrísts ♦ s♦♠♥t♦ ♠é♦
s♦ s♦çã♦ ♥r ♥ét tr♥t
♦ s♦ s♦çã♦ ♥r ♥ét tr♥t ♦♠tr t③ ♦ ♠
♥ sçã♦ ♥♦r♠ rst♦ ♥♠ér♦ ♦t♦ ♣r ♥r ♥ét tr
♥t ♠♥s♦♥ ♥♠ sçã♦ ♥ t③♥♦s ♦ ♠♦♦ trê♥ ♦
♦♠♣r♦ ♦♠ ♦trs s ♣rsõs ♥♠érs
♦♠tr
♠♥r s♠r à ♦♠tr ♦s s♦s ♥tr♦rs r ♣rs♥t
♦♠tr t③ ♥♦ s♦ ♥t♠♥t ♦♠ ts ♠ ♦♥♠♥t
r ♣rs♥t s rtrísts ♦♠étrs ♠♥s♦♥s ♥çã♦ ♣♦sçã♦
sçã♦ ♦♥ ♦s rst♦s ♦r♠ ♠♦str♦s tr ♦ ♥ ♦ s♣ ♦♠♦
H = 0,011m
r ♦♠tr ♦♠ ts ♠ tí♣ t③ ♣r s♦çã♦ ♥r♥ét tr♥t s♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
s ♠s t③s ♥♦ st♦ r♥♦ stã♦ r♦♥s ♥ ♦s
s ♠s ♦r♠ ♦♥strís ♦♠ ♠♥t♦s qrtrs r stã♦ ♠♦str♦s
♦s rst♦s ♣r s três ♠s
♦s s ♠s t③s ♣r ♦ st♦ r♥♦ ♠ ♣r çã♦ rçã♦ ♥r ♥ét tr♥t κ
sõs ♠♥t♦s y+ κmax(Jkg−1) κ/u2τ ① ① ①
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥♣♥ê♥ ♠ ♣r ♦ ♣r ♥r ♥ét tr♥t ♥♠sçã♦ ♥ ♣♥♦
0,0 0,5 1,0 1,5 2,0 2,5 3,00,0
0,2
0,4
0,6
0,8
1,0
κ/(u2τ)
y/(H/2)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
srs q t♥t♦ ♦♠tr ♦ ♥ ♦♠ sçã♦ ①♣♥ r
q♥t♦ ♦♠tr ♦ ♥ ♦♠ sçã♦ ♦♥st♥t r ♦r♠ ♦ s♦ ♠
♦ t♣♦ strtr ♦ à t♦♣♦r sts ♦♠trs ♦r♠ r♦s ♣♥s
♠♥t♦s qrtrs ♣r t♦s s ♠s sts ♠♥t♦s ♠s stã♦ s♠♣r
♦rt♦♦♥s ♥s ♦♠ rçã♦ ♦s ♦tr♦s t♥♦ ♦ ♥♠♥t♦ ♠ ♦♠ rçã♦
♣r♥♣ ♦ s♦♠♥t♦
♦♥çõs ♦♥t♦r♥♦
Pr s♦çã♦ ♥r ♥ét tr♥t ♦r♠ t③s s ♦♥çõs
♦♥t♦r♥♦ sr
❼ çã♦ ♥tr ♣r ♥♦r♠ ♦ ue = 19,3 m/s ♥t♥s tr
♥t
❼ ♣rís trs ♦ ♥ sçã♦ ♦♥st♥t ♦♥çã♦ ♣♥♦ s♠tr
❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦
❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦
st♦s
s ♣rs ♥r ♥ét tr♥t ♦ ♦♥♦ sçã♦ ♥ ♦r♠ ♠♦s
tr♦s ♠ ♠ stçã♦ ♦③ ♠ stâ♥ x/H = 45 q stá ♥ ♥ r
srs q st é ♠s♠ stâ♥ q ♦ t③ ♣♦r ❩♥s t
r ♠♦str q ♦s ♣rs ♦t♦s ♣rtr s ♠s rs r♠ st♥t
s♠♥ts ♥tr s st ♦r♠ ♠ ♥tr♠ár ♦ s♦ ♣r ♦ ♦♠♣rt♦
♦♠ ♦s ♦s trtr ♣rs♥t♦ ♥ r
r ❱rçã♦ ♦ ♣r ♥r ♥ét tr♥t ♥♠ sçã♦ ♥♣♥♦
0,0 1,0 2,0 3,0 4,0 5,00,0
0,2
0,4
0,6
0,8
1,0
κ/(u2τ)
y/(H/2)
❯ t ❩ t κ − ε st tr♦ SST
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
❯♠ ③ q ♦ ♠♦♦ trê♥ ♦t♦ é ♠ ♠♦♦ ♠♦ ①♦
②♥♦s ♦ ♥ s♦ ♠ ω ♥♦ts q é ♣♦ssí ♦tr s♦çã♦ ♣r κ s
♣r y = 0 ♠♦♦ trê♥ κ − ε t③♦ ♥ ♦♠♣rçã♦ ♦r♥ ♠
♠♦r ♣rsã♦ ♣r ♣r♦♣r ♦♥t♦ ♣♦r sr ♠ ♠♦♦ t♦ ②♥♦s
♥ã♦ é ♣③ ♦r♥r ♣rsã♦ ♥ rã♦ ♦rrs♣♦♥♥t à ③♦♥ ♠s ♥tr♥
♠ ♠t s rõs ♣ró①♠s à ♣r ♦ ♠♦♦ trê♥ t③♦s ♥s
s♠çõs ♦ ♣rs♥t tr♦ ♣rs♥t ♦ rá ♥ ♦♠♣rçã♦ ♦♠ s♠çã♦
rt
P ❱
st sçã♦ srã♦ ♣rs♥t♦s st♦s ♦s s♦s ♣r♦③♦s ♥st tr♦
♦♥sr♥♦ rs♦s s♣t♦s ♦♠étr♦s r♥ts ♦♥çõs r♦♥â♠s
sqê♥ ♠ sts t♥s é ♣rs♥t♦ st♦ ♠♥r ♣ré ♦s rst♦s
♦t♦s
♦♦ ♦♠étr♦ ♦ ♥ t♦
s ♦♠trs áss ♦ ♥ st♦ ♦♠ ♦s ♣r♥♣s ♣râ♠tr♦s ♣♦♠
sr sts ♥ r ♦♥rçã♦ ts s♥s é ♦t trés ♦ s
♦♠♥t♦ r ts ♦③s ♥ ♣r s♣r♦r ♦ ♥ ♦♥rçã♦
♥ ♠♦♦ q ♣r♠r t s♣r♦r st ♦③ ♥ stâ♥ ♦r③♦♥t
♦rrs♣♦♥♥t à ♣♦sçã♦ ♠é ♥tr s s ♣r♠rs ts r ♥r♦r st
trçã♦ ③ ♦♠ q ♦ t♠♥♦ ♦ ♥ ♣r s ts s♥s s ♠♦r ♣♦s
stâ♥ ♠í♥♠ s♣ s♥t út♠ t ♣r♠♥ ③s
tr ♦ ♥ Ls = 20H â♥♦ β ♥♥çã♦ s ts ♦ r♦ ♥tr 0
90 s♥♦ q ♦ ♣r♠r♦ ♦rrs♣♦♥ ♠ ♥ s♠ ts ♦ s♥♦ é ♦♥sr♦
♦ s♦ áss♦
s rtrísts ♠♥s♦♥s t sã♦ ♥s ♠ ♥çã♦ três s♣
çõs s♣ssr t ♦ â♥♦ ♥♥çã♦ s ts β r③ã♦ ♦q♦
t rba s s út♠s ♦r♠ rs r♥t ♦ st♦ ♥q♥t♦ q s♣ssr
s♣ t ♦ ♠♥t ♠s♠ ♣r t♦♦s ♦s s♦s srs q ♥♥çã♦
t ♠♣ ♥♠ rr s rá s rçõs q ♥♠ r③ã♦ ♦
q♦ t rba rr s t w sã♦ s ♥s qçõs
rs♣t♠♥t s ♦rs s t st st♦ s ♥♦♥tr♠ ♥
♦♠♣♠♥tr♠♥t ♦ t♦ ♦ ♠♥t♦ s ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥
çã♦ ♣♦♠ sr st♦s ♦r♠ qtt s♠ s ♥ r ss♠ r③ã♦
♦q♦ é
rba = Ha
H,
♥ q Ha é ♠á①♠ tr rt t H é tr ♦ ♥ t♠♥♦
s t é
w = t
sen(β) ,
r rtrísts ♠♥s♦♥s s ♦♠trs áss ♣r ♠♦s ♦s rr♥♦s ♥s t♦s ♥♦ s♣r♦r s♥♦ ♥r♦r
L
LsLe
Ha t
b
H
e
e
w
L
LsLe b
H
e
e
y
x
y
x
aletas:
direção do escoamento
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
s♥♦ t β s♣ssr ♦ â♥♦ ♥♥çã♦ t rs♣t♠♥t
tr♦ ♣râ♠tr♦ ♦♠étr♦ r♦ r♥t ♦ st♦ ♦ ♦ s♣ç♠♥t♦ ♥tr
ts b ♦s r♥ts ♦rs ♦r♠ ♥st♦s ♦ ♦r♦ ♦ tr♣♦ rtr
♦ ♥ b = 2H b = 3H st rçã♦ ♦ t③ ♠ ♠s s ♦♥rçõs
t ♥ s♥ Pr strr st rtríst r ♣rs♥t
♦♠♣rçã♦ s♠ s ♥tr ♦s ♦s s♣ç♠♥t♦s ♥tr ts st ♠s♠ r
stã♦ ♣rs♥ts s r③õs ♦q♦ t rba rs ♣r ♦♥rçã♦
♥ t♦ ♦♥♦r♠ s ♦sr ♥♦s s♦s r♦s ♦ rr♥♦ ♥♦ s♦♠♥t
s r③õs ♦q♦ t ♦r♠ ♣s ♥q♥t♦ q três r③õs
♦q♦ ♦r♠ ♣s ♣r ♦ rr♥♦ s♥♦
s ♦♠trs q r♠ ♠ ♠s♠♦ s♣ç♠♥t♦ ♥tr ts b ♣♦♠
sr sts s♠ s ♥s rs ♦s ♣ê♥s sts strçõs stã♦
♠♦♥str♦s ♦s tr♦s s♠♦s ♥ s ♥tr té s♥ t s♣r♦r
❱rçã♦ r③ã♦ ♥tr rr s t w s s♣ssr t♠ ♥çã♦ ♦ s â♥♦ ♥♥çã♦
β w/t90 72 54 36 18
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♠tr t ♦♠♦ ♥çã♦ ♦s r♥ts â♥♦s ♥♥çã♦ β ♣r♠ ♠s♠ r③ã♦ ♦q♦
72°
54°
36°
18°
Ha
90°
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
rú♥ ♦s ♣râ♠tr♦s ♦♠étr♦s q ♦r♠ r♦s ♥st st♦
♠ ♦♠♦ q♥t rçõs ♦♥rçã♦ t à q sts s ♣♠
ss♠ ♦s ♣râ♠tr♦s q sr♠ s ♠s rtrísts ♦♠étrs ♦ ♦r♠
s♣♦s ♦♠♦ ♦♥st♥ts ♦ sã♦ r♦s qs ♠♦str♦s ♥st t s
♣r♠r♦s á♦s ♣r t♦s s s♠çõs ①ts ♣♦r ss♦ ♥♦♠♦s ♥rss
♣♦♠ sr ♥♦♥tr♦s ♥
♣♦ st♦ r♥♦ ♠
Pr ♦ s♦ ♦♠trs ♦♠♣①s é ♣r♦♠♥♥t ♦ s♦ ♠s ♦ t♣♦
♥ã♦ strtrs s ♠s ♦s s♦s ♣r♦③♦s ♥st tr♦ ♦r♠ rs ♦♠
♠♥t♦s ♦ t♣♦ ①r♦s ♦♠ r♥♠♥t♦ ♥s rõs ♣ró①♠s às s♣rís ♦
♥ ts r♥♠♥t♦ ♦ ♣♦ ♦r♠ ♦r ♦ rqst♦ ♦ ♠♦♦
trê♥ y+ < 1 r stã♦ ♣rs♥t♦s ts qtr♦ ♠s
t③s ♥♦ st♦ ♦♥rê♥ ♠ ♣r ♠ ♦s s♦s st tr♦
r s ♦s s♣ç♠♥t♦s ♥tr ts b s rçõs r③ã♦ ♦q♦ t rba ♣r ♠♦s ♦s rr♥♦s ♥ t♦
b=3H
H
H
b=2H
0,20,4
0,6rba
0,2
rba0,4
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
Prâ♠tr♦s ♦♠étr♦s r♦s ♦♥rçã♦ ♣á r♥ts
Prâ♠tr♦ ♦♥rçã♦ ♣á ❱r♥ts
b ♠s 2H 3H
rba ts ♥s 0,2 0,4
rba ts s♥s 0,2 0,4 0,6
β ♠s 0 18 36 54 72 90
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
s ♣râ♠tr♦s s♦s t③♦s ♣r ♦ st♦ ♥♣♥ê♥ ♠ ♦♠♦
s r ♦r♠ ♦s ♦rs t♠♣rtr ♣rssã♦ s♥♦ q ♦ ♦r y+
t♠é♠ ♦ ♠♦♥t♦r♦ s ♠çõs s rás st♦ ♦r♠ ♦ts s♥t
út♠ t ♣ós ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ x = 30H ♦ q s ♦ ♦ ♦r
♠é♦ ♣r ♠s ♦ s♦ ♦ y+ ♦ t③♦ ♦ ♠á①♠♦ ♦r tr♠♥♦ ♣r st
q♥t ♠ t♦♦ ♦ ♦♠í♥♦ ♦
r ♠♦str ♦s rst♦s ♦ st♦ ♦ r♥♦ ♠ ♣r ♦ s♦
â♥♦ ♥♥çã♦ t β = 90 r③ã♦ ♦q♦ t rba = 0,2
s♣ç♠♥t♦ ♥tr ts b = 2H ♥ú♠r♦ ②♥♦s ue = 9 m/s ♣r ♦♥rçã♦ ♥ ts ♠s♠♦ ♣r♦♠♥t♦ ♦ s♥♦♦ ♣r
♠♦çã♦ r③ ♥ ♦♠tr ♦ ♥ ♦♥çã♦ ♥tr ♦ rrê♥
♦♥rçã♦ ♥ sr ♦s ♠s♠♦s ♣râ♠tr♦s ♦r♠ ♣♦s ♣r
♦♥rçã♦ s♥ ♦♠♦ ♣r♠r st♠t ♠
s♣çã♦ ♦s ♣râ♠tr♦s ♦♠étr♦s ♥rss
Prâ♠tr♦ srçã♦ s♣çã♦
M ♥ú♠r♦ ts ♥ ♠s♠ ♣r ♦ ♥ 5
t (mm) s♣ssr t 3H/20Le (mm) stâ♥ ♥tr ♥tr ♦ ♥ ♣r♠r t 2H
Ls (mm) stâ♥ ♥tr út♠ t sí ♦ ♥ 20H
e (mm) s♣ssr ♣r ♦ ♥ H/2H (mm) tr sçã♦ ♥tr ♦ ♥ 20
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ①♠♣♦ ♠s ♣r♦③s r♥t ♦ st♦ ♥♣♥ê♥ ♠t ♥♦ ♥t♦r♥♦ ♠ t ♦♠ β = 90
♠♥t♦s ♠♥t♦s
♠♥t♦s ♠♥t♦s
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs
s♠♥t ♦s t♣♦s ♦♥çõs ♦♥t♦r♥♦ ♦r♠ t③s ♦ ♦♥♦ s
r♦♥trs ♠♦s ♦s ♦♠í♥♦s só♦ ♦ rt ♦ ♠♥♥
r st♦ ♥♣♥ê♥ ♠ rst♦s ♣r s ♠s ♠♦strs♥ r
3 4 5 6 7 80,50
0,55
0,60
0,65
0,70
0,75
y+
P
ú♠r♦ ♠♥t♦s × 105
y+P
Pa
319,0
319,2
319,4
319,6
319,8
320,0
T K
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♦♥sr♥♦ r q ♣rs♥t s rtrísts áss ♣r s r
çõs ♦s s♦s ♠♦s ♦s rr♥♦s s ♥♦r♠çõs ♦ts ❨ s♠
s s♣çõs ♣r s ♦♥çõs ♦♥t♦r♥♦
❼ çã♦ ♥tr ♣rs ♥♦r♠s t♠♣rtr 298,15K ♦s r
ssçã♦ ♦♥♠♥t ♦ s♣♦ ♦ ♦r ♥t♥s tr♥t
I = 10%
❼ çã♦ sí ♣rssã♦ stát ③r♦ ♦s s ♠s q♥ts sã♦ ①
tr♣♦s ♣rtr ♦ ♥tr♦r st♦ é ♣r q♥ts srs ♦ ó♦ ♥♠ér♦
♠♣õ ♠ rstrçã♦ r♥t ♦♥st♥t ♥ r♦♥tr sí
❼ s s♣rí s ♣rs trs ♦ ♥ ♦♥çã♦ át sts s♣rís
sã♦ ♦♥srs s♦s ♣♦rt♥t♦ ♦ ①♦ ♦r trés s sr ♥♦
❼ ♣rí ①tr♦rs s ♣rs s♣r♦r ♥r♦r ♦ ♥ t♠♣rtr ♦♥st♥t
358,15K
❼ ♥tr ♦só♦ ♦♥çã♦ ♥ã♦s③♠♥t♦ ♣r ♦ ♦♥çã♦
♦♥srt ♣r ♥r ♥r q s ♦ ♦♠í♥♦ só♦ ♥r q ♥tr
♥♦ ♦♠í♥♦ ♦
❼ P♥♦s trs ♦ ♥ ♥♦r♠s ♦ ♣♥♦ s♦♠♥t♦ xy ♦♥çã♦ s♠
tr
❼ Pr ♦s s♦s ♥♦♥♦ ♦♥rçã♦ ♥ ts ♣♥s ♠t s♣
r♦r ♦ ♥ ♦ s♠ ♣♥♦s ♠ ♣♥♦ s♠tr ♦ ♦♥♦ ♦ ①♦ x ♠
y = 0s ♣r♦♣rs íss t③s ♣r ♦s s♦s st♦s ♥st tr♦ sã♦ ♣r
s♥ts ♥ sã♦ ♦rrs♣♦♥♥ts ♦ r
Pr♦♣rs íss t③s ♣r rtr③çã♦ ♦s ♦♠í♥♦s ♦♠♣t♦♥s ♦s s♦s st♦s
Pr♦♣r♦♠í♥♦
♦ ó♦
♦♥t tér♠ k Wm−1K−1 ♣ ♦rí c Jkg−1K−1 ss s♣í ρ kgm−3 ❱s♦s ♥â♠ µ Pas 1,846 × 10−5
♦♥t t
❱rçõs s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s
Pr s♦ ♦♠étr♦ ♦♥♦r♠ srt♦ ♦ ♦♥♦ ssçã♦ ♦r♠
t③s três rçõs ♦♥çã♦ ♦♥t♦r♥♦ r♦♥â♠ ♦ rrê♥
♥ ♥tr ♦ ♥ st♦ ♣♦sst♦ ♦ st♦ ♥ê♥ ♠ ① ♦ ♥ú♠r♦
②♥♦s s♦r tr♦ tér♠ ♦♥ ♥♦s ♥s t♦s s r♥ts ♦♥çõs
♦♥t♦r♥♦ t③s ♣r s ♦s rrê♥ ♥ ♦r♠ ♣rs ♥♦r♠s
♦ ♦r♠ ue1= 1 m/s (Re1 = 2517) ue2 = 3 m/s (Re2 = 7550) ue3 = 9 m/s (Re3 =
22649) ♦ ♥ú♠r♦ ②♥♦s ♦ ♦ ♦♠ s ♥♦ â♠tr♦ rá♦ Dh =2H
♦♠♥çã♦ rst♥t s rs ♦♠étrs ♦♠ s rs ♦♥
çõs ♦♥t♦r♥♦ r♦♥â♠s ♣♦ sr ♠♦r s③ ♥ r ♦ ♣ê♥
srs q â♥♦ ♥♥çã♦ t β á ♦r♠ ♠ ①♦r♠ ♦♠♦
♦ ♣rs♥t♦ ♥st ♣ê♥
Pr♥♣s rtrísts ♦ s♦♠♥t♦ ♥♦s s♦s ♦s
♥s t♦s
r ♣rs♥t s ♠♦çõs ♦rr♥ts ♣rs♥ç s ts ♥
t♦♣♦♦ ♦ s♦♠♥t♦ r♣rs♥t ♣s ♥s ♦rr♥t ♦ s♦♠♥t♦ ♠é♦ ♥♦
t♠♣♦ s ♥t♦s str♦s ♣r três r♥ts â♥♦s ♥♥çã♦ ♣r ♠♦s ♦s
rr♥♦s t sã♦ r♣rs♥tt♦s t♦♦s ♦s ♠s s♦s ♥st♦s ♥st tr
♦ ♥♦ ss♠ s ♣r♥♣s rtrísts ♥♦♥trs ♥♦s s♦♠♥t♦s st♦s
♦♥t♥♦ ts tr♥srss sã♦ s rõs rrçã♦ r♦♠♥t♦ ♥♦ tr♦
♦♠♣r♥♦ ♥tr ♦s ♦stá♦s ts ♠s ♦♦rr♠ ♠ ♥çã♦ ♦ s♦♠♥t♦ ♦
s♦♠♥t♦ ♦ ♠ ♠t ♦ à ①stê♥ r♥ts ♣rssã♦ rs♦s
s ♠♣çõs s rrçõs ♦ r♦♠♥t♦ s♦r ♦ s♠♣♥♦ ♦s tr♦♦rs
♦r t♦s srã♦ st♦s sr ♥♦s tó♣♦s ♣rt♥♥ts
s rs ♦ rr♥♦ ♥♦ é ♣♦ssí ♦srr q ♣r
t♦s s ♥♥çõs ♦♦rr ♦r♠çã♦ rrçã♦ s♦r t♦♦ ♦ tr♦ ♥tr s
ts ♦♠♦ ♦♥sqê♥ ♦srs q r♥ç ♦s ♥♦ tr♦ t♦ é
s♥t ❯♠ ♦tr♦ s♣t♦ stq ♣r sts rs é s♠tr ①st♥t ♥♦
s♦♠♥t♦
s s♦s ♦ rr♥♦ s♥♦ ♣rs♥t♦s ♥s rs
♣rs♥t♠ s♠♥t s rõs st♥ts ♥♦ tr♦ ♥tr ts rrçã♦
♦ r♦♠♥t♦ ♠ ♠ q ♦ â♥♦ t ♠♥ β → 0 ♥♦ts ♦
♠♥t♦ ③♦♥ rrçã♦ st♦ ♦♥t♥ té q ♣r ♦ ♠♥♦r â♥♦ ts
β = 18 ③♦♥ rrçã♦ s♦ ♣♦sçã♦ rã♦ r♦♠♥t♦ ♣r
s♣rí t s♥t ♦♣♥♦ t♦♦ ♦ tr♦ ♥tr s ts
Pr ♠♦s ♦s rr♥♦s ♥t♦ às s s ts ♣♦♠ sr ♦sr♦s ♦s ♠
♦s órts ♥t♦ q ♥♦ s♦♠♥t♦ ♠é♦ ♦ ♣rs♥t st♦ sr♠ ♦♠♦ ♣q♥s
rrçõs srs q ♥ r s ♥s ♦rr♥t stã♦ ♦♦rs ♣
♦ ♦ s é ♣♦r
U∗ = U −Umin
Umax −Umin
,
s♥♦ U Umin Umax s ♦s ♦s ♠í♥♠ ♠á①♠ rs♣t♠♥t ♠s
q Umax = 66,6 m/s ♣ ♦♥çã♦ ♥ã♦s③♠♥t♦ Umin = 0 m/s st♦s ♣r ♣r r
ss♣çã♦ ♥r ♠â♥ ♦ ♦r♠ ♦ t♠é♠ ♦r♠
♦ s q♥ts t③s ♣r tr♠♥r sts ♠s ♦r♠ rs♣t♠♥t
♦ ♦♥t trt♦ Cfx ♦ ♦♥t ♣rssã♦ Cp sr ♣rs♥ts ♦s
♦♥t♦r♥♦s ♦ ♠♣♦ ♦s rst♥t ♠s rçõs ♦♠étrs ♣r
♠♦s ♦s rr♥♦s sts rst♦s qtt♦s s♠ r s♣♦rt ♣r s çõs
q♥ttts q ♦s s♠
r ♥s ♦rr♥t ♦♦rs ♦♠ ♦ ♣r r♥ts ♥♥çõs t ♠♦s ♦s rr♥♦s ♥♦ ♦♥ sqr s♥♦ ♦♥ rt ♥♦s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠ ue = 9 m/s
β = 18 β = 18
β = 54 β = 54
β = 90 β = 90
0,000
0,069
0,138
0,207
0,276
0,345
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
1,000
U*
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♥s ♦rr♥t t♦♣♦♦ ♦ s♦♠♥t♦
s rs ♠♦str♠ ♦ t♦ rçã♦ ♦ â♥♦ ♥♥çã♦ β
s♦r ♦s ♠♣♦s ♦ t♦♣♦♦ ♦ s♦♠♥t♦ ♣r ♠ ♠s♠ r③ã♦
♦q♦ t rba ♠♦s ♦s rr♥♦s r ♦♥té♠ ♦s rs♣t♦s s♦s
♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H r ♣rs♥t sts s♦s ♣r ♦
s♣ç♠♥t♦ b = 3H s ♦rs ♦rrs♣♦♥♥t ♦s ♦♥t♦r♥♦s ♦ ♠♣♦ ♦
s ①♦ r ♦ ♠♥s♦♥③ ♦r♦ ♦♠ qçã♦ Pr
♠♥s♦♥③çã♦ t♠s q Umax = 21,9 m/s ♣ ♦♥çã♦ ♥ã♦s③♠♥t♦
Umin = 0 m/s♦ ♦ t♦ rr♥♦ é ♣♦ssí ♥tr ③♦♥s rçã♦ s
rçã♦ ♦ s♦♠♥t♦ ♣r♥♣ ♣r ♦ rr♥♦ ♥♦ st♦ q á ♠ rçã♦
♦♦rçã♦ rã♦ ♥tr ♦ ♥ rstrçã♦ ár ♠♣♦st ♣ r③ã♦ ♦q♦
ts rba ♦rç à rçã♦ ♦ s♦♠♥t♦ ♥ sçã♦ ár ♥tr s ♣♦♥ts s
ts Pr st rr♥♦ ♣♦s ♥ ♥rr ♦♠ s ♥sts rs q s ♣rs
♥r ♠â♥ ♦ s♦♠♥t♦ ♣r♥♣ ♦♦rr♠ ♥ sçã♦ ár ♥tr s ♣♦♥ts s
ts ♥♦ s♠♥t♦ ♦♠ ♦s órts s♠♥t
♦s s♦s ♦ rr♥♦ s♥♦ ár s♦♠♥t♦ é r ♦♠ ♠s rqê♥
♦ ♦♥♦ ♦ ♥ sr♠ rõs rçã♦ s à ①ã♦ ♦ s♦♠♥t♦
♥s ♦r♠ s♣ ①ã♦ ss♠étr é rtríst ♠s ♥♥t
♣r rçã♦ ♦ s♦♠♥t♦ ♦♠ s ♥ t♦♣♦♦ ♦ s♦♠♥t♦ é ♣♦ssí ♥
rr q ♥r ♠â♥ é ss♣ ♦ s♦♠♥t♦ ♣r♥♣ ♥♦ rrst♦ trt♦ ♦♠
s ♣rs ts é♠ ♦ s♠♥t♦ ♦♠ ♦s órts ♦ trt♦ ♥tr♥♦ ♦ ♦
♦♥t trt♦ ♦ Cfx
s rs rst♥ts tr♠♥çã♦ ♦ ♦♥t trt♦ s♣r sã♦ ♣r
s♥ts ♣r ♠ tr♦ r♣rs♥tt♦ ♥ t♦ ♣r ♠♦s ♦s rr♥♦s sr
s q ♦ à s♠tr ♦♠étr s♦♠♥t ♦s rst♦s ♣rt♥♥ts ♦s tr♦s
♣r s♣r♦r srã♦ ♣rs♥t♦s ♣r ♦ rr♥♦ ♥♦ ts ♦♠ ss♦ ♦r♥r
s ♣r♥♣s rtrísts ♦s ♣rs Cfx rst♥ts ♦s s♦s ♦r♦s ♥ê♥
♦s ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s ♥s s♦r ts rtrísts é
st sr
♥ê♥ ♦ â♥♦ ♥♥çã♦ t
s rs str♠ s rtrísts ♦ ♣r Cfx rst♥ts ♣r
rçã♦ ♦ â♥♦ ♥♥çã♦ t β s s♦s ♦r♠ ♦♥strí♦s ♣r
♦ rrê♥ ue = 3 m/s ♣r ♠s♠ r③ã♦ ♦q♦ t rba
t♣♦ rr♥♦ ♦ts ♥ q á ♥çã♦ ♣♦sçã♦ sq♥ s ts
♦rrs♣♦♥♥ts ♦ s♦ β = 18 ♠ ♣r
s rs ♦♥rçã♦ s♥ ♠♦strs t♥ê♥
♦ ♠♥t♦ ♠♥t ♦ ♦♥t trt♦ ♦ ♦♠ ♦ â♥♦ ♥♥çã♦
t rçã♦ r♣t ár s♦♠♥t♦ ♣r ♥♥çã♦ ♦rt♦♦♥ rst ♠
♠♦r rçã♦ ♣♦rt♥t♦ ♠♦rs ♦s ♥ts à ♣r Pr ♦ ♠♥♦r
â♥♦ ♥♥çã♦ β = 18 ♥♦ q s ♣rs ♥tr ts ♠ ♠♥♦s ①♣♦sts ♦
s♦♠♥t♦ ♣r♥♣ ♥♦ts q ♦ s♦♠♥t♦ ♠é♦ ♣rs♥t ♠ r♥ rã♦
r♥ç ♦s ♠t♦ ♣ró①♠ ③r♦ ♥t♦ à ♣r
❯♠ r♥ç ♠r♥t ♥tr s rs é q ♣r st út♠
á ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ t♠é♠ ♣r ♦ s♦ ♦ ♠♥♦r â♥♦ ♥♥çã♦
t β = 18 t♦ ♦♥♦r♠ s ♣♦ ♦srr ♥ r ♥st ♥♥çã♦
①ã♦ ♦ s♦♠♥t♦ ♣r♥♣ rst ♥ s ♥ê♥ s♦r s s s ssss
ts ♣rs ♦♣♦sts ♦tr ♦r♠ ♥ t♦♣♦♦ ♦ s♦♠♥t♦ ♠♦str
q á ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ ♥ rã♦ ♣r ♠ q
①ã♦ ♦ s♦♠♥t♦ ♠♥t β → 90 ♦ s♦♠♥t♦ ♣r♥♣ ♥ s♦r rã♦
♣r ♦♥♦r♠ s rs
♦♠ rçã♦ à ♥ê♥ ♥♥çã♦ ♥♦s ♦s r♥ts s♣ç♠♥t♦s ♥tr ts
♣r ♦ rr♥♦ s♥♦ ♥ ♦♦rr♠ stçõs ♦♥trst♥ts ♦ s♣ç♠♥t♦
♦rrs♣♦♥♥t b = 3H ♦sr♠s ♠♥♦rs ♠♥ts ♦ ♦♥t trt♦ ♣r ♦s
♦s ♠♦rs â♥♦s ♥♥çã♦ β = 72 β = 90 ♣♦ré♠ ♦♦rr ♠♥t♦ ♦ Cfx ♣r
♦s ♠s â♥♦s ♥st♦s P♦r ①♠♣♦ ♥♦ts q r ♣r ♦ â♥♦ β = 36 ♥♦ s♣ç♠♥t♦ b = 2H r rs q ♦t ♣r ♦ s♣ç♠♥t♦
b = 3H r st út♠♦ b = 3H ♣rs q á ♠ rã♦
r♦♠♥t♦ ♦ s♦♠♥t♦ ♥♦ tr♦ ♥tr ts ♠ ③ q r ♦ ♦♥t
trt♦ ♣rs♥t ♠ ♥rsã♦ ♠ ♥ s♥ r♦♠♥t♦ st s♦ ♣♦ sr
r♦ ♣ t♦♣♦♦ ♦ s♦♠♥t♦ ♦♥♦r♠ r
Pr ♦ rr♥♦ ♥♦ ♥s rs t♠é♠ ♦srs ♠
r♥ç s♥t ♥♦ ♣r ♦ ♦♥t trt♦ ♣r ♦ s♦ s ts ♠♥♦r
â♥♦ ♥♥çã♦ β = 18 st ♥♥çã♦ ①♠♣♦ ♦ q ♦♦rr ♥♦ rr♥♦
s♥♦ ♦ rrst♦ ♣♦r trt♦ ♥ rã♦ ♣r ♦♦rr ♦r♠ s♥t s♦♠♥t
♣r ♠ tr♦ rt♦ rã♦ ♥tr ts ♦③♦ ♣ró①♠♦ à s s ts r s
♣♦sçõs s ss t ♥s ♥ rs♣t r Pr ♠♦s ♦s s♣ç♠♥t♦s
♥tr ts b = 2H r b = 3H r ♣r♦♠♥♠ ♦s ♦rs
Cfx ♥t♦s ♣♦ssí ♦srr ♦ t♦ t♦♣♦♦ s♦r sts rst♦s ♥s
rs ♣r b = 2H b = 3H rs♣t♠♥t sts
rs ♠♦str♠ ①stê♥ rrçã♦ ♦ s♦♠♥t♦ ♠é♦ s♦r ♣rt♠♥t
t♦ rã♦ ♣r ♥tr ts
♦♠♦ rst♦ rçã♦ ♦ â♥♦ ♥♥çã♦ ♣r ♦ rr♥♦ s♥♦
t♠s q ♦ ♦r ♦ Cfx ♣r β = 90 é ③s ♠♦r q ♣r β = 18 b = 2H
③s ♠♦r ♥♦ s♦ b = 3H s rst♦s ♣r ♦ rr♥♦ ♥♦ ♦r♠ ♠s
♦♠♦ê♥♦s ♠ tr♠♦s ♠♥ts s♥♦ ♠♦r r♥ç rt ♥tr β = 90
β = 18 b = 2H ♦ b = 3H
♥ê♥ ♦ rrê♥
rs♣♦st ♦ ♦♥t trt♦ ♦ ♣r rçã♦ ♦ rrê♥
stá ①♠♣ ♥s rs ♥ê♥ ♦ ♠♥t♦ s ♦rçs
♥rs ♥ ♥tr ♦ ♥ é str ♣r três ♥♥çõs s♣ç♠♥t♦ ♥tr ts
b = 2H ♠♦s ♦s rr♥♦s t♥ê♥ ♦sr é ♠♥çã♦ ♠♣t s
rs ♦ ♦♥t trt♦ ♠ ♥çã♦ ♦ ♠♥t♦ s ♦rçs ♥rs ♥ ♥tr ♦
♥
♠é ♦♠ rçã♦ ♦ ♥tr 1 m/s ♣r 9m/s ♦s ♦rs ♣♦ ♦ Cfx sã♦ ♣♦r ♦t ③s ♠♥♦r ♠ ♠♥t ♣r ♠♦s ♦s rr♥♦s P♦r
♦tr♦ ♦ t♥sã♦ s♠♥t♦ ♥ ♣r t♠ ♠♥t♦ ♠é♦ s♥t♦ té
③s ♣r ♦ rr♥♦ ♥♦ té ③s ♣r ♦ rr♥♦ s♥♦ srs q
♦ ♠♥t♦ t♥sã♦ s♥t é ♦♥sqê♥ ♥t♥sçã♦ ♦ tr♥s♣♦rt ♦♥t♦
q♥t ♠♦♠♥t♦ ♦r♠ ♣r♦♠♥♥t ♥ rçã♦ x ♥t♥sçã♦
♦s tr♠♦s ♦♥t♦s ♦♦rr s ♦r♠s ♠♥r rt trés ♦ ♠♥t♦
♦ rrê♥ ♥ ♥tr ♦ ♥ ♦♠♦ ♦♥sqê♥ ♦ ♠♥t♦ ♦
tr♥s♣♦rt ♠♦♠♥t♦ ♦ às tçõs ♦s trê♥ ♦ts q ♦
♣r strçã♦ ♦ ♦♥t trt♦ s♣r é ♣rt♠♥t ♦♥sr♦
♥ê♥ r③ã♦ ♦q♦
Pr strr ♥ê♥ r③ã♦ ♦q♦ ♥♦ ♦♥t trt♦ ♦
t③♦s ♦s ♠s♠♦s s♦s ♦ t♠ ♥tr♦r P♦rt♥t♦ ♦ t♦ rçã♦ s três
r③õs ♦q♦ ♣r ♦ rr♥♦ s♥♦ s s ♦ rr♥♦ ♥♦ ♦r♠ ♥
sts ♣r s ♥♥çõs β = 18 β = 54 β = 90 ♦ rrê♥
ue = 3 m/s s rst♦s stã♦ ♣rs♥t♦s rs♣t♠♥t ♥s rs
t♥ê♥ ♦sr ♦ ♠♥t♦ ♦ ♦♥t trt♦ ♦♠ r③ã♦ ♦q♦
t é ♠ ♦♥sttçã♦ rt rstrçã♦ ár s♦♠♥t♦ s ♦strçõs
ss ♣ ♣rs♥ç s ts ♥♦ rs♦ ♦ s♦♠♥t♦ s♠ ♦ sr♠♥t♦ rõs
♦♠ rçõs ♦s ♦ q ③ ♠♥tr s ♦s ♥t♦ às ♣rs ♦♥sq♥
t♠♥t t① s♠♥t♦ τint,x
Pr ♦ rr♥♦ s♥♦ ♠é ♦ ♠♥t♦ ♦s ♦rs ♣♦ ♦ Cfx ♣♦
rr té ③s ♥tr rba = 0,6 rba = 0,2 β = 90 ♥q♥t♦ q ♣r ♦ rr♥♦
♥♦ s rçõs ♠és ♦♦rr♠ ♣♦r ♦t ③s ♥tr rba = 0,4 rba = 0,2♦♥sr♥♦ ♠s♠ rçã♦ r③ã♦ ♦q♦ ♣r ♦♥rçã♦ s♥
rba = 0,2 rba = 0,4 rçã♦ ♠é ♦s ♦rs ♣♦ Cfx r♠ ♥tr
③s
♥ê♥ ♦ rr♥♦ t
s r♥çs ♥♦♥trs ♥♦ ♣r s rs ♦ ♦♥t trt♦ s♣r
♣r ♠♦s ♦s rr♥♦s sã♦ ♠ s♥ts ♦♠♦ ♦♥sqê♥ ♦ ♥♠♥t♦ ♥tr
s ts ♥♦ rr♥♦ ♥♦ ♦ s♦♠♥t♦ ♣rs♥t ♦s ♥ts ♥t♦ à ♣r
♣r ♣rt♠♥t t♦ rã♦ ♥tr ♥tr s ts s ♦rs ♣♦st♦s ♦
♦♥t ♥st rr♥♦ ♦♦rr♠ ♣r ♥tr♦s ♠t♦ ♣q♥♦s ♥♦s tr♦s ♥tr ts
♦s s♦s ♦♥rçã♦ s♥ sã♦ ♦srs rõs s♥s ♦♣♦st♦s
♣r ♦ ♦♥t rçã♦ ♦ ♠ ♠s s ♣rs s♥t s ts r ♦
Cfx ♣rs♥t ♦rs ♥t♦s ♠ q ♦ s♦♠♥t♦ ♥ç ♣rs ♠
♥rsã♦ ♠ ♥ ♦ s♥ ♦ ♥t♦ à ♣r rã♦ ♥tr ts
♣♦sçã♦ ♦♥ ♦ ♦r Cfx ♣ss ♣♦ ③r♦ ♦ ♦♥♦ st ♥rsã♦ s♥s ♥t
rã♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ s ③♥♥çs st ♣♦♥t♦ ♥♦
♥ r ♦ s♦♠♥t♦ s ♠ ♣rt rr ♥♦ ♦r♠ ♦s ♦rs
♥t♦s ♦ ♦♥t trt♦ s♥t ♦ r♦♠♥t♦ ♣♦rt♥t♦ ♦s ♦rs ♦
♦♥t trt♦ s t♦r♥♠ ♣♦st♦s
♦♠♦ ♦♥sqê♥ ♦ r♦♠♥t♦ ♥s rõs ♣r ♥tr ts s ♠♦
rs ♠♥ts ♣♦ ♦ Cfx sã♦ ♥♦♥trs ♠♥r ♣r♦♠♥♥t ♥♦ rr♥♦
s♥♦
r♥ç ♣rssã♦ ∆p ♦♥t ♣rssã♦ Cp
♦r♠ ♦ çã♦ ♣r r ♥s ♦♠trs ♣r♦♣♦sts ♦ r
③ ♣♦r ♠♦ ♦ ♦♥t ♣rssã♦ Cp t♠é♠ r♥ç ♣rssã♦ ∆p
ss♦ sts s q♥ts sã♦ r♦♥s ♦r♦ ♦♠ qçã♦ ♣r
s♥t ♥♦ ♥í♦ st sçã♦
r stã♦ ♣rs♥t♦s ♦s ♦♥ts ♣rssã♦ ♦t♦s ♣r t♦♦s ♦s
♥ár♦s rst♥ts ♦♠♥çã♦ ♥tr ♦s r♥ts s♣ç♠♥t♦s t s
r③õs ♦q♦ t ♦ s♦ ♦ rr♥♦ s♥♦ rs ♦
♥ú♠r♦ r③õs ♦q♦ é três s rst♦s stã♦ ♣rs♥t♦s ♥ ♦r♠
r③ã♦ s♥♦ q ♦s ♦rs t③♦s ♦♠♦ rrê♥ ♦r♠ ♦s rs♣t♦s ♦♥ts
♣rssã♦ ♦ ♥ s♠ ts ♠♥♦♥♦s ♥ st r ♥ ♥♦ts
①stê♥ r♥ts ♣t♠rs ♠r♦s ♣♦r sts sts ♣t♠rs ♦rrs♣♦♥♠
às rçõs s três ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠ ue ♣r s st♥ts r③õs
♦q♦ t rba ♥s s♦r r
❱♦rs ♦ ♦♥t ♣rssã♦ ♣r ♦ ♥ s♠ ts
♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue ♦♥t ♣rssã♦ Cp0
①1,0 m/s 3,0 m/s 9,0 m/s
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
t♥ê♥ ♦sr ♣r ♣t♠r é ♠♥çã♦ ♦ ♦r Cp/Cp0♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ t β → 0 ♣r t♦s s r♥ts
♦s rrê♥ ♦♥t♦ é ♣r♣tí ♥s rs q st
t♥ê♥ ♥ã♦ s r ♥♦s s♦s ♦♠♣r♥♦s ♣ r③ã♦ ♦q♦ t rba = 0,6♦ rr♥♦ s♥♦ sts s♦s ♦ ♦r ♠é♦ ♦Cp ♣r ♦ ♠♥♦r â♥♦ 18 é
♣r♦①♠♠♥t 54% b = 2H 22% b = 3H ♦ ♦r ♦ Cp ♣r ♦ ♠á①♠♦ â♥♦
♥♥çã♦ 90 rts ♠ ①♣rss ♥rsã♦ ♥ t♥ê♥ q ♣♦s ③♥♦
♦ ♠s♠♦ ♦♠♣rt♦ ♣r ♦ â♥♦ 36 t♠é♠ ♦♠ rçã♦ ♦ ♠á①♠♦ â♥♦
♥♥çã♦ 90 ♦s ♦rs sã♦ 29% b = 2H 19% b = 3H rs♣t♠♥t s t♦rs
q ♦♦r♠ ♣r ♦ sr♠♥t♦ st ♥rsã♦ srã♦ ♠♦♥str♦s ♥ sqê♥ ♦
tr♦
sr ♦s r♥ts t♣♦s ♥ê♥ s♦r ♦s rst♦s ♦t♦s ♣r ♦ ♦
♥t ♣rssã♦ srã♦ st♦s ♦r♠ ♥ s t♦rs ♥ê♥ ♦♥sr♦s
♣♦♠ sr t♥t♦ ♥tr③ ♦♠étr q♥t♦ r♦♥â♠
♥ê♥ ♦ rr♥♦ t
♠ t♦♦s ♦s s♦s s♠♦s ♦ rr♥♦ ♥♦ ♦ ♦ q rst♦ ♥♦s ♠♦rs
♦rs Cp ♣r ♠ ♠s♠ r③ã♦ ♦q♦ t r ♠♦str r③ã♦
Cp/Cp0 ♣r ♠♦s ♦s rr♥♦s Pr str ♦ s♣t♦ ♦♠♣rçã♦ s♦♠♥t s
r③õs ♦q♦ rba = 0,2 rba = 0,4 sã♦ ♣rs♥ts Prs q ♠ ♠s♠
r③ã♦ ♦q♦ t rba ♦♥té♠ ♠ r♣♦ rs q r♣rs♥t♠ s r♥ts
♦♥çõs r♦♥â♠s ue sts r♣♦s rs r ♣♦ss♠ ss
♦rrs♣♦♥♥ts ♣t♠rs ♥ r
s rst♦s ♦t♦s ♠♦str♠ q ♠é ♦ ♦r r③ã♦ ♥tr ♦ ♦♥t
♣rssã♦ ♣r ♦♥rçã♦ ♥ ♦ ♦♥rçã♦ s♥ Cpalinhado/Cpdesalinhado rba = 0,2 b = 2H té rba = 0,4 b = 3H ♦ts q ♣♦r t♦
♦ rr♥♦ ♠♦r s ♠♦rs ♣rs r sã♦ ♦ts ♣r ♦♥rçã♦ ♥
s ♠♦rs rçõs ♣r ♠ ♠s♠ ♦♥çã♦ r♦♥â♠ ♦♦rr♠ ♥ ♦♥rçã♦
s♥ ♦♥♦r♠ r
♥ê♥ ♦ â♥♦ ♥♥çã♦ t
♦♥♦r♠ á ♦♠♥t♦ ♠♦str♦ ♥ r á ♠ t♥ê♥ ♠♥
çã♦ ♦ Cp ♦♠ ♦ â♥♦ ♥♥çã♦ s ts ♥♦ ♠ st q♥t ♥
ssçã♦ ♥tr♦r Cpalinhado/Cpdesalinhado é ♥trss♥t ♥♦tr q st r③ã♦ ♠♥t
♠♥r ♥rs ♦ â♥♦ ♥♥çã♦ ss♠ ♦ r r③ã♦ Cpalinhado/Cpdesalinhado♣rs q ♦♦rr ♠ ♠♥t♦ ♠é♦ s rba = 0,2 b = 3H té ♣r♦①♠
♠♥t rba = 0,4 b = 2H ♦ s♦♠♥t à rçã♦ ♦ â♥♦ ♥♥çã♦
β = 90 ♣r β = 18 st♦ é ♣r♣tí q♥♦ s ♦sr♠ ♦s ♦♠♣♦rt♠♥t♦s ♦
♦♥t ♣rssã♦ ♣r sts ♦s rr♥♦s t ♦♥♦r♠ r á
♠ ♠♦r rçã♦ ♥♦ Cp ♣r ♦ rr♥♦ s♥♦ ♠♥r ♠s ♥t ♣r
♠♦r r③ã♦ ♦q♦
♠♥t♦ ♦ â♥♦ t β → 90 ♣r♦♠♦ ♠♦r q ♣rssã♦ ∆p ♦
♦♥♦ ♦ tr♦ ♥ ♦ ss♠ ♠♦r q ♣rssã♦ ♦♦rr ♣r ♦s s♦s
♦♠ ♥♥çã♦ t 90 ♠♥♦r q ♣rssã♦ é ♥♦♥tr ♦♠ ♠♦r
rqê♥ ♣r ♥♥çã♦ 18 ♦♥rçã♦ ♥ r♥ç ∆p
♥♥çã♦ 90 é r ♠♦r ♦ q r♥ç ♥♥çã♦ 18 ♥♦s
s♦s ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H r ♠♦r ♥♦s s♦s ♦♠ s♣ç♠♥t♦
b = 3H ♦♥rçã♦ s♥ ♦ ∆p ♥♥çã♦ 90 é r
♠♦r b = 2H rba = 0,2 ♠♦r b = 3H rba = 0,4 ♦♠♣r♦s à ♥♥çã♦
18
♥ê♥ r③ã♦ ♦q♦
♦♥♦r♠ s ♦sr ♥ r ♦ ♣r♥♣ t♦ r③ã♦ ♦q♦
t rba s♦r q♥t Cp/Cp0 é ♣r♦♠♦r ♦ s ♠♥t♦ ♦♥t♦ ♠s
r♥çs sã♦ ♦srs ♣r rr♥♦ ❯♠ rtríst ♥trss♥t ♣r ♦
rr♥♦ s♥♦ é q ♠ ♠ q rba é ♠♥t ♥t♥ss rçã♦
Cp/Cp0 ♣r ♠ ♠s♠ ♦♥çã♦ r♦♥â♠ ue st t♦ ♥ã♦ é ♦sr♦ ♥♦
rr♥♦ ♥♦ s♠tr ♦♠étr
❯t③♥♦ s rs ♠s♠ ♦ r ♣♦s str ♠
t♦r ♣r♦♣♦r♦♥ ♣r r ♦ t♦ s s r③õs ♦q♦ t
♣rs♥ts s ♠ r③ã♦ ♥tr s q♥ts (Cp/Cp0)β rba=0,4 (Cp/Cp0)β rba=0,2♦♠♥♦ ♦s ♦s ①tr♠♦s ♣r ♦ â♥♦ ♥♥çã♦ t ♦ t♦r ♣r♦♣♦r♦
♥ é ♣r♦①♠♠♥t t♥t♦ ♣r β = 90 q♥t♦ ♣r β = 18 ♠
t♦s s ♦s ♦ rr♥♦ ♥♦ ♦ rr♥♦ s♥♦ ♦ ♣r♥♣♠♥t
à rçã♦ ♦sr ♣r rba = 0,4 ♦ t♦r ♣r♦♣♦r♦♥ é ♣ró①♠♦ q♥♦
β = 90 r③ ♦♥sr♠♥t ♣r ♥ ♥♥çã♦ β = 18 ♦♠ ♦ ♠♥t♦ ♦
s♣ç♠♥t♦ ts ♣r b = 3H ♦ t♦r ♣r♦♣♦r♦♥ ♠ t♦r♥♦
♣r ♠♦s ♦s â♥♦s β = 90 β = 18 ♦ rr♥♦ s♥♦ á ♠ t♦ ♠♦r
♦ s♣ç♠♥t♦ ♦ t♦r ♣r♦♣♦r♦♥ é r q♥♦ β = 90 ♥
♥♥çã♦ β = 18 r q ♣rs♥t r③ã♦ ♦ Cp/Cp0 ♣r t♦♦s ♦s s♦s ♦ rr♥♦
s♥♦ ♠♦str ♠ ♥rsã♦ ♥♦ ♦r Cp ♠♥r ♣r♦♣♦r♦♥ st♦ r♣r
s♥t q ∆p ♠♥t ♣r ♦ ♠♥♦r â♥♦ r♥t♠♥t ♦ ♥♦♥tr♦ ♥s ♠s
r③õs ♦q♦ t s rst♦s ♠♦str♠ ♠ ♠♥t♦ ♦ ∆p b = 2H
b = 3H ♣r ♦ â♥♦ 18 ♦♠ rçã♦ ♦ â♥♦ 36
r ♠♦str q ♣r st s♦ s♣í♦ rst♥t ♦♠♥çã♦ ♦
♠étr ♥tr β = 18 rba = 0,6 rstrçã♦ ár ♣ss♠ é ♠í♥♠ ♥tr ♣♦♥t
♠ t ♠♦♥t♥t t ssq♥t ♣r ♦♣♦st r é
♠♦str♦ ♥ ♦s ♦♥t♦r♥♦s ♦ ♣r ♠ rã♦ ♦ tr♦ t♦ ts
t♦♣♦♦ ♦ s♦♠♥t♦ ♠é♦ ♥t♦ à ♣r ♥r♦r s rõs ♦♥t♦r♥♦s ♠
r♠♦ r♣rs♥t♠ s ♠♦rs ♦s q ♦♦rr♠ ♦ ♦s t♦rs rs
trçã♦ ár s♦♠♥t♦ t♠é♠ ♦ à ♣rs♥ç rõs rrçã♦ q
♣r♦♦♠ ♦ s♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦♥♠♥t ♦s r♥s órts ♦r♠
♦s s♥t s ts ♣r♦♠♦♠ ♦ ♠♥t♦ q ♣rssã♦ ♦♥sq♥t♠♥t
♦ ♦ t♥ ♦s qs ③s ♦ ♥tr ♥♦ ♥ ue
♥ê♥ ♦ rrê♥ ♥ú♠r♦ ②♥♦s
t♦ rçã♦ s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s ♦ s♦♠♥t♦ ♦
♦ ♣r três r♥ts ♦s ♥tr ue = 1 m/s ue = 3 m/s ue =9 m/s ♦♠♦ ♦♥sqê♥ ♥♦♠♣rss ♦ ♦ ♣r♥♣♠♥t ♦♦rr ♦
s♠♣s s♦♠♥t♦ r ♦ Cp/Cp0 ♦♥♦r♠ ♠♦str♦ ♥s rs
sts rs s ♣r q ♦ ♣r Cp/Cp0 ♣r ♠ ♠s♠ ♦ ♥tr
ue s ♠♥té♠ ♣r♦①♠♠♥t ♥♣♥♥t r③ã♦ ♦q♦ ♣ ♦
s♦♠♥t♦ ♠♥t♦ ♦ rrê♥ ue = 1 m/s ♣r ue = 3 m/s rst♥♠ ♠♥t♦ ♦ ∆p ♣r♦①♠♠♥t ③s ♥♦ ♦ é ♠♥t
♣r ue = 9 m/s ♦ ♠♥t♦ ♦ ∆p é ♣r♦①♠♠♥t ③s rçã♦ qrát
q ♣rssã♦ ♦♠ ♦ ♦♦rr ♣r ♠s s ♦♥rçõs t ♦♠
rçã♦ ♠ t♦r♥♦ ♥tr rr♥♦s rba = 0,2 rba = 0,4 r♥srê♥ ♦r ♥tr ♦ ♦♠í♥♦ só♦ ♦ ♦♠í♥♦
♦
Pr ①r ♥s çõs s q♥ts ♦s ♦s sã♦ ♣rs♥t♦s ♥♦s
♣ró①♠♦s t♥s sr ♦s ♦♥t♦r♥♦s t♠♣rtrs ♣r ♠♦s ♦s ♦♠í♥♦s s ♥s
♦rr♥t ♣r rçã♦ ♦♠étr
strçã♦ t♠♣rtr t♦♣♦♦ ♦ s♦♠♥t♦
sts t♥s tr♥srê♥ ♦r é ♦r♠ qtt s♥♦ ♥r
qr ♥ás tr♥srê♥ ♦r ♣♦str♦r Pr t♥t♦ t③♠s strçã♦
t♠♣rtr ♥s ♦rr♥t ♠♦strs ♣♥s ♥t♦ à ♣r ♥r♦r ♦ ♥
strçã♦ t♠♣rtr ♥ ♦s t♦s tr♥srê♥ ♦r ♦♥
s ♥s ♦rr♥t ①♠ ♦ ♥t♥♠♥t♦ ♦s ♥ô♠♥♦s tr♥s♣♦rt ♥♦♦s
♥ê♥ ♥♥çã♦ t
s ♠♣♦s t♠♣rtr ♠ ♠♦s ♦s ♦♠í♥♦s só♦ ♦ rst♥ts ♦
t♦ ♥♥çã♦ stã♦ ♣rs♥t♦s ♥s rs srs q ♦ à
r③ã♦ ♦♥t tér♠ t③ ♥s s♠çõs ks/kf ♦ ♦♠í♥♦ só♦
♣rs ♦ ♥ ts ♥ s ♣ ♣r r ♥ã♦ ♣rs♥t rçã♦
♣r♣tí ♣r ♠♦r ♦s s♦s
sr s ♦rs ♦ ♠♥s♦♥③ s♥t ♦r♠
T ∗ = T − Tmin
Tmax − Tmin
s♥♦ T Tmin Tmax s t♠♣rtrs ♦s ♠í♥♠ Tmin = 298,15 K ♠á①♠ Tmax =358,15 K rs♣t♠♥t
♦s s♦s ♣rs♥t♦s t♦♣♦♦ ♦ s♦♠♥t♦ é s♣♠♥t ♥♥
♣ ♥♥çã♦ s ts ♣r ♦ rr♥♦ s♥♦ rs
♠ q ♦ â♥♦ ♥♥çã♦ ♠♥ β → 0 ①ã♦ s ♥s
♦rr♥t ♠♥ s♦♥♦ ♦ ♣♦♥t♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♦♠♦ ♦♥sqê♥
♣r tr♦ tér♠ st♦ t r♠♦çã♦ ♦r ♥ rã♦ ♣r ♥tr ts ♦t
s ♦ sr♠♥t♦ rõs qs s♦ s ts q♥t♦ ♠♥♦r ♦ â♥♦ ♥♥çã♦
β → 0 P♦r ♦tr♦ ♦ tr♦ tér♠ ♥ r♦♥t t ♠♥t ♦♠ s
♥♥çã♦ ♦ à ♣r♦①♠ ♦ s♦♠♥t♦ ♣r♥♣ s♣rí t ♦ q
♣r♦♠♦ ♠♦rs r♥ts t♠♣rtr
♦ rr♥♦ ♥♦ rs ①st ♦r♠çã♦
rrçã♦ rtríst ♣r t♦s s ♥♥çõs ♦ts q rã♦ rrçã♦
♥ç s♦r ♠♦♥t♥t s ts ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦
♦ às rrçõs ♦ s♦♠♥t♦ ♣r♥♣ é st♦ s ♣rs s♦ ♣rr♥
♠♥t ♣ ♣rt ♥tr ♦ ♥ ♣r♥♦ tr♦ tér♠ ♥ rã♦ s ♣rs
♥tr ts s rs ♠♦str♠ q ♦ ♦ ♠♦r s♣ç
♠♥t♦ ♥tr ts b = 3H ♦ s♦♠♥t♦ ♣r♥♣ s ♣r♦①♠ ♣r ♦ ♥ ♥
rã♦ ♥tr ts ♦ q ♠♥t tr♦ tér♠ ♦
♦♠ ♦s ♦♥t♦r♥♦s t♠♣rtr ♣♦s ♦r♠ rstrt ♦ só♦ ♣rs
ts ♥♦ts ♦ t♦ tr♦ tér♠ ♦♥ s rs
♠♦str♠ q ♣r ♦ rr♥♦ ♥♦ r♠♦çã♦ ♦ ♦r ♥ rã♦ ♣r é ♣r
♣ ①stê♥ rrçõs ♥t♦ à s♣rí ♣r P♦rt♥t♦ rçã♦
t♠♣rtr ♥s ♣rs ♦♦rr qs q ①s♠♥t ♥ rã♦ ♣ró①♠ s ss
s ts P♦r ♦tr♦ ♦ ♥♦ rr♥♦ s♥♦ rs é
♣♦ssí ♦tr ♠ ♠♦r r♠♦çã♦ ♦r s ♣rs ♦ só♦ st♦ ♦♦rr ♥♦ s♥t♦
♠♥t♦ ♦ â♥♦ ♥♥çã♦ s ts β → 90 ♦ s q♥t♦ ♠s ♦ s♦♠♥t♦
é t♦ ♣s ts ♠ rçã♦ às ♣rs st♦ t strçã♦ t♠♣rtrs
♦ ♦♥♦ s ♣rs ♦ tr♦ t♦ ♥ t♦r♥♥♦ ♠s ♦♠♦ê♥
srs q ♥ r s t♠♣rtrs t③ ♠s♠ ór♠
qçã♦ ♦♠ Tmin = 355,294 K Tmax = 358,15 K s ♦♠ st ①
♦rs ♦ ♦♥strí ♣r ♣rs s♦ ♠ ♦s s♦s st r st♦ é t③♥♦
s s ♦♦rrê♥s ♠í♥♠ ♠á①♠ t♠♣rtr ♥tr qs ♦♠trs ♣r
♦♥çã♦ ♦ rrê♥ ♥
♥ê♥ ♦ rrê♥
t♦ rst♥t ♦ rrê♥ ♥ ♦r♠ ♦♥t♦r♥♦s t♠♣
rtr srá str♦ ♣r ♦ ♦♠í♥♦ só♦ ♣rs ts ♣♥s Pr t♥t♦ ♦s
rst♦s s três ♦♥çõs ♦ rrê♥ sã♦ ♠♦strs ♣r três r♥
ts ♥♥çõs ♥s rs β = 18 β = 54 β = 90 sts rs
s t♠♣rtrs é ♠s♠ q t♠é♠ ♦ ♦♥strí s♦ ♠ ♣rtr
qçã♦ t③♥♦s Tmin = 351,79 K Tmax = 358,15 K
Pr sts três rs ♣rs ♠ ♠♦r rçã♦ ♦ ♠♣♦
t♠♣rtrs ♥♦ só♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ♦ q ♥
rs♥t tr♦ tér♠ ♥tr ♦s ♦♠í♥♦s ♦♠♣t♦♥s ♦ts q é♠ rstr
♠ ♠♥♦rs t♠♣rtrs ♥s ts ♦ ♠♥t♦ ♦ rrê♥ tr
♦r♠ ♦♥srá ♦ ♠♣♦ t♠♣rtrs s ♣rs ♦ ♥
s ♣ró①♠s sçõs stã♦ ♣rs♥ts s q♥tçõs tr♦ tér♠ sts
q♥tçõs ♦r♠ tr♠♥s ♦♠♥t s♦r s ♣rs ♦ ♥ trés ♦ Nux
♦r♠ ♦ ♣♦r ♠♦ ♦ Nu ♦ qtotal
ú♠r♦ sst ♦ Nux
sqê♥ srã♦ st♦s ♠♥r ♥ ♦r♠ ♦♠♦ ♦s ♣râ♠tr♦s
r♦s t♠ strçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦ q tr♠♥
q♥t ♦r tr♦ trés s ♣rs ♥
♥ê♥ ♦ â♥♦ ♥♥çã♦ t
Pr strr rçã♦ ♦ ♥ú♠r♦ sst ♦ ♥ rã♦ ♣r ♦♠ s
ts ♥♥s ♦r♠ s♦♥♦s ♦s ♠s♠♦s s♦s çã♦ ♦ Cfx st♦ é r③ã♦
♦q♦ t rba = 0,4 ♦ rrê♥ ♥tr♠ár ue = 3 m/s r ♣rs♥t s rtrísts rst♥ts ♣r ♦ ♥ú♠r♦ sst ♦
♦♠♦ ♦♥sqê♥ rçã♦ ♦ â♥♦ ♥♥çã♦ t ♥s ♦♠trs ♦♠
s♣ç♠♥t♦ ♥tr ts b = 2H Pr ♦ rr♥♦ ♥♦ r s♦♠♥t é
♠♦str♦ ♦ Nux ♥ ♣r s♣r♦r ♦ à s♠tr ♦♠étr ♦ts ♥ q
á ♥çã♦ ♣♦sçã♦ sq♥ s ts ♦rrs♣♦♥♥ts ♦ s♦ β = 18 ♠
♣r ♣r ♠♦s ♦s rr♥♦s st♦ ♥ q s rs ♣rs♥ts r♣rs♥t♠
s♦♠♥t ♦ ♥ú♠r♦ sst ♥s rõs ♣r st♦ é ♥trts ♦♥♦r♠ ♥çã♦
♦ Nux
s rtrísts rst♥ts ♣r s rs s ♦♠trs ♦♠ s♣ç♠♥t♦ b =3H sã♦ st♥t s♠♥ts às q ♦rrs♣♦♥♠ ♦ s♣ç♠♥t♦ ♣rs♥t♦ b = 2H
♦♥♦r♠ s ♦sr ♥ r st r ♠♦str q ♦s ♣rs ♣r strçã♦
♦ ♥ú♠r♦ sst ♦ sã♦ ♠t♦ s♠♥ts ♦s ♥♦♥tr♦s ♥s ♦♠trs
♠♥♦r s♣ç♠♥t♦ ♥tr ts
Prs ♥s rs q ♠♦str♠ ♦ rr♥♦ ♥♦ q
♠♦r r♥ç ♥♦ Nux é ♣r ♥♥çã♦ ♦ â♥♦ β = 18 ♣sr ♣rs♥tr
♦ ♠s♠♦ ♣r s ♠s rs ♦s ♦rs sst ♦ ♦♥♦ ♣r ♦r♠
♠♦♦ r ♦s ♠♥♦rs ♥tr t♦♦s ♦s s♦s ♠ ♦♠♣rçã♦ ♣r ♦ ♠á①♠♦ Nux
♥tr s ♥♥çõs β = 18 β = 90 st út♠ é s♣r♦r ♠ ♠♦s ♦s s♣ç♠♥t♦s
t ♠♦r ♣r b = 3H ♠♦r ♣r b = 2H srs q st♦ é
♠ ♦♥sqê♥ rt r♥ç ♦sr ♥♦s ♠♣♦s t♠♣rtrs ♦ ♦♠í♥♦
só♦ s rs ♥♠ q t♠♣rtr ♦ ♦♥♦ ♥tr
s ♣rs é ♠s ♦♠♦ê♥ t♠é♠ ♠s t ♣♦ s♦♠♥t♦ ♥♦ s♦ β = 90 s rs ♣r ♦ rr♥♦ s♥♦ r♥ç ♦Nux ♥tr
s ♥♥çõs é ♠s s♥t Prs q r♥ç ♥tr s ♥♥çõs ①tr♠s é
♦♥srá ♦ ♠♥♦r â♥♦ ♥♥çã♦ β = 18 ♦ sst rã♦ ♣r é
♥r♦r ♦s ♠s s♦s é♠ ♣♦ssr ♠ ♣r ♥♦t♠♥t st♥t♦ ♦s ♠s
â♥♦s β = 36 té β = 90 ♦ ♣r ♣r Nux é ♣rt♠♥t ♦ ♠s♠♦ ♦♠ ♠
♣q♥ r♥ç ♥s rõs ♣ró①♠s às ss t à ♣rs♥ç ♦s órts
♥t♦ ♦ ♥ês ♦r♥r s ♦r♠ q♥ttt ♦♦rr ♠♥çã♦ ♣r♦rss
♦ ♦r ♦ ♠á①♠♦ sst ♦ ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ β → 18
rçã♦ ♦s ♦rs ♠á①♠♦s Nux ♥tr β = 90 β = 72 é r ♣ss
♣r q♥♦ s ♦♠♣r ♦s ♦rs rçã♦ ♥tr β = 90 β = 18 ♥ ♠é
♣r ♠s s ♣rs ♦ s♣ç♠♥t♦ ♥tr ts b = 2H Pr ♦s s♦s ♦ s♣ç♠♥t♦
b = 3H s rs♣ts rçõs sã♦ q♥ts
♥ê♥ ♦ rrê♥ ♦ ♥ú♠r♦ ②♥♦s
♠♥t♦ ♦ rrê♥ ue ♦ ♦ ♥ú♠r♦ ②♥♦s ♦ s♦
♠♥t♦ ReDh ♣r♦♠♦ ♥t♥sçã♦ ♦ tr♥s♣♦rt ♦♥t♦ ♥r ♦♥
♠♥t s ♣r♦♣rs ♦ s♦♠♥t♦ trê♥ ♦♠♦ ♦♥sqê♥ st ♠♥t♦
♣r♦♦ ♦ s♦♠♥t♦ rt ♥s rs ♦ ♥ú♠r♦ sst ♦ s♠ trçã♦ ♦
s ♣r s rs str♠ st t♦ ♣r três r♥ts ♥♥çõs
β = 18 β = 54 β = 90 ♠♦s ♦s rr♥♦s t s s♦s ♣rs♥t♠ s
♠s♠s rtrísts ♦♠étrs b = 2H rba = 0,4 ♥s três r♥ts ♦♥çõs
♦♥t♦r♥♦ r♦♥â♠s st tr♦
çã♦ ♦ Nux ♦ rr♥♦ ♥♦ ♠♦str ♦ ♠♥t♦ ♥♦ sst ♦ ♦
♦r ♣♦ rr r ③s ♦ s ♠♥tr ♦ rrê♥ ♣rtr
ue = 1m/s ♣r ue = 3m/s ue = 9m/s rs♣t♠♥t ♦ s♦ ♦ rr♥♦ s♥♦
♦ ♦r ♦ ♠á①♠♦ ♥ú♠r♦ sst ♦ é ♣r♦①♠♠♥t ue = 3 m/s
ue = 9 m/s ③s ♠♦r ♦ s ♠♥tr ♦ rrê♥ ♣rtr ue = 1 m/s♥ê♥ r③ã♦ ♦q♦ t
Pr strr st t♦ ♦r♠ ♠♥t♦s ♦s três â♥♦s ♥♥çã♦ t
♥ás ♣ré β = 18 β = 54 β = 90 ♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H
♦♥çã♦ r♦♥â♠ ue = 9 m/s ♦ t③ s rst♦s ♣r ♠♦s ♦s
rr♥♦s sã♦ ♠♦str♦s ♠ sqê♥ ♣s rs
♥s♥♦ ♥♠♥t s rs ♣rs q ♥♣♥♥t ♦ â♥♦
♥♥çã♦ ♦♦rr ♦ ♠♥t♦ ♦ ♠á①♠♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦
♦q♦ t ♣r ♠♦s ♦s rr♥♦s ♦ts ♥ ♠ r♥ r♥ç ♥♦ ♣r
r strçã♦ ♦ Nux ♥ ♠♥♦r r③ã♦ ♦q♦ ♦ rr♥♦ s♥♦ ♣r
β = 18 r
Pr ♦ rr♥♦ ♥♦ ♦ ♠♥t♦ ♥♦ ♦r ♠á①♠♦ sst ♠ ♦rrê♥
rçã♦ ♥ r③ã♦ ♦q♦ é ♣ró①♠♦ Pr ♦ rr♥♦ s♥♦ st t♦r
é rá ♥s ♥♥çõs s s t♥ê♥ ♠♥r ♦ t♦r ♥♦ s♥t♦
♦ ♠♥♦r â♥♦ ♥♥çã♦ β → 18 ❱r♥♦s r③ã♦ ♦q♦ t
♣rtr ♣r ♦té♠s ♦ t♦r ♠♥t♦ ♦ ♦r ♦ sst ♦ ♠á①♠♦
♣r ♦s â♥♦s β = 90 β = 54 β = 18 rs♣t♠♥t s♦
s ♦♠♣r♦ ♦ t♦ ♦ ♠s♠♦ ♠♥t♦ r③ã♦ ♦q♦ q ♥♦ rr♥♦ ♥♦
st♦ é rba = 0,2 ♣r rba = 0,4 ♦ t♦r ♠♥t♦ ♦ ♦r ♣♦ ♦ Nux é ♠s
♦♠♦ê♥♦ s♥♦ ♣r ♦s â♥♦s β = 18 β = 54 β = 90 rs♣t♠♥t
♥ê♥ ♦ rr♥♦ t
♠ ♠♦s ♦s rr♥♦s ♦ ♣r ♦ sst ♦ ♣rs♥t rtrísts ♠♥t♦
s♥t ♠♥çã♦ ♠t♠♥t ♠♦♥t♥t s t ♦♥♦r♠ ♠♦str♦
♥ r ♣♦r ①♠♣♦ ♦r♦ ♦♠ ①♣r♠♥t♦s trtr ❱
♦ rés♠♦ é ♦♥sqê♥ ①stê♥ rrçã♦ ♥q♥t♦ q ♦ ♠♥t♦
sút♦ ♦♦rr ♦♠♦ ♦♥sqê♥ ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣
s rõs ♦ s♦♠♥t♦ ♥♦ q ①st♠ rrçõs s ♣r♦♣rs t♥♠
sr ♠s ♦♠♦ê♥s ♠♣♥♦ ♥♠ ① r♥ç t♠♣rtrs ♦ q t
rt♠♥t tr♥srê♥ ♦r P♦r ♦tr♦ ♦ q♥♦ ♦ s♦♠♥t♦ ♣r♥♣ r♦
♥ s♣rí ♦ ♥ ♦ r♥t tér♠♦ é ♣r♦♠♦♦ ♣♦r ss♦ ♦♦rr ♦ ♠♥t♦
tr♥srê♥ ♦r ♥♦ ♥t♦r♥♦ rã♦ r♦♠♥t♦
srs q á ♠ r♥ç ♠r♥t ♦ ♣r ♦ sst ♦ rst♥t
♦s ♦s rr♥♦s st♦s Pr ♦♥rçã♦ ♥ ♦ ♣r r Nux♣rs♥t ♠ s♣é ♣tô ♥ rã♦ ♠á①♠♦ Nux ♥q♥t♦ q ♥ ♦♥rçã♦
s♥ st rã♦ é ♠♦r srt ♣♦r ♠ ♣♦ ♦♥t♦ st♦ é r♦ ♥♦s
s♦s r③ã♦ ♦q♦ ♣r ♦ rr♥♦ s♥♦ s♦♠♥t sts s♦s
①ã♦ ♦ s♦♠♥t♦ é ♠s ♣r♦♥♥ q ♣r r③ã♦ ♦q♦ ♥♦ ♠s♠♦
rr♥♦ s ♠♦rs ①õs ♣r♦♦♠ ♦ s♦ ♦ s♦♠♥t♦ ♣r♥♣ ♣r rõs
♠s ♣ró①♠s ♣r ♦♣♦st rst♥♦ ♥♠ ♠♦r r♥t t♠♣rtrs ♠♦r
sst ♦
ú♠r♦ sst ♦ Nu
é♠ s ♦r♠çã♦ ♦ ♠ ♥ú♠r♦ sst ♦ t♠é♠ ♦ t③♦
♥s çõs r ♣rs♥t ♦s ♦rs sst ♦ ♣r t♦s s r③õs
♦q♦ ♦s rrê♥ â♥♦s ♥♥çã♦ ♠♦s ♦s rr♥♦s ♦t
s q ♦ sst ♦ Nu é ♣rs♥t♦ ♥ ♦r♠ r③ã♦ ♣r ♦ sst ♦ ♦
♥ s♠ ts Nu0 ♦s rs♣t♦s ♦rs stã♦ ♥
ú♠r♦ sst ♦ ♦ ♥ s♠ ts ♣r s três r♥ts ♦♥çõs r♦♥â♠s
♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue ú♠r♦ sst ♦ Nu0
①1 m/s 3 m/s 9 m/s
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
sqê♥ srã♦ st♦s ♠♥r ♥ q ♦r♠ ♦s ♦s r♥
ts ♣râ♠tr♦s ♦♠étr♦s s r♥ts ③õs ♥sts t♠ strçã♦ ♦
♥ú♠r♦ sst ♦
♥ê♥ ♦ â♥♦ ♥♥çã♦ t
♥ê♥ ♥♥çã♦ t s♦r ♦ sst ♦ é ♠s s♥t ♣r
♦ rr♥♦ s♥♦ rs st rr♥♦ rs ♠ t♥ê♥
q ♦ sst ♦ ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ t β → 0 Pr
♦s s♦s ♦ rr♥♦ ♥♦ rs ♥♥çã♦ t ♥ã♦ ♣rs♥t♦
♥ê♥ ♥♦tá s♦r Nu
♠é ♣r ♠s s r③õs ♦q♦ ♦ rr♥♦ ♥♦ rçã♦ ♦
sst ♦ é ♠♥♦r ♦ q ♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H ❯♠ r♦
♠♥t♦ ♦♦rr ♥♦ s♣ç♠♥t♦ b = 3H ♥♦ q rçã♦ ♠é ♠ t♦r♥♦
Pr ♦ rr♥♦ s♥♦ ♠♥♦r r③ã♦ ♦q♦ t ♣rs♥t rçã♦
♠é ♥tr b = 2H b = 3H Pr s ♦trs s r③õs ♦q♦
t rba = 0,4 rba = 0,6 s rçõs ♠és sã♦ t♦s ♠♦rs q ♥♦
rba = 0,6 b = 2H
♥ê♥ ♦ rrê♥
t♦ rçã♦ ♦ rrê♥ s♦r ♦ ♥ú♠r♦ sst ♠é♦
Nu é s♠r ♦ q ♦ ♦sr♦ ♣r ♦ ♥ú♠r♦ sst ♦ ♦ s ♦ ♠♥t♦
♦ rrê♥ ♠♣ ♥♦ ♠♥t♦ ♦ Nu ♠♥s♠♦ ♥t♥sçã♦ é
♦ ♠s♠♦ t♠é♠ á st♦
♠♥r r ♦ ♠♥t♦ ♠é♦ ♦ sst ♦ stá ♥tr ♦ s
♠♥tr ♦ rrê♥ ♣rtr 1 m/s ♣r 3 m/s ♠s♠♦ ♣r♥t
rés♠♦ é r♦ ♣r ♦ ♥r♠♥t♦ ♦ rrê♥ ♣rtr 3 m/s♣r 9 m/s♥ê♥ r③ã♦ ♦q♦ t
♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ t á ♦ rés♠♦ ár tr♦
tér♠ é♠ ♦s t♦s q ♠♦r rstrçã♦ ár ♠♣õ à ♥â♠ ♦ s♦♠♥t♦
♦♥♦r♠ á ♦♠♥t♦ Pr ♠♦s ♦s rr♥♦s q♥t♦ ♠♦r r③ã♦ ♦q♦
t ♠♦r ♦ ♥ú♠r♦ sst ♠é♦ ♦ s rst♦s ♠♥♦♥♦s sr
sã♦ ♦♠♥s ♦s ♦s s♣ç♠♥t♦s ♥tr ts b = 2H b = 3H
Pr ♦ ♠♥t♦ r③ã♦ ♦q♦ t rba = 0,2 ♣r rba = 0,4 ♦ t♦r
♠♥t♦ ♠é♦ ♦ sst ♦ é r ♦♥sr♥♦ t♦s s ♥♥çõs st
t♦r ♠♥t♦ ♦ ♦ ♠ ♠♦s ♦s rr♥♦s t
♦r♠ s♣í ♣r ♦ rr♥♦ s♥♦ r③ã♦ ♦q♦ t é
♠♥t rba = 0,4 ♣r rba = 0,6 rst♥♦ ♠ ♠ t♦r ♠♥t♦ ♠é♦ ♠
t♦r♥♦
♥ê♥ ♦ rr♥♦ t
♦♠ s ♥♦s rst♦s ♣rs♥t♦s ♣ r t♠s q ♦ rr♥♦
ts ♥s rs ♥ã♦ ♣rs♥t ♥ê♥ ♦♥srá s♦r ♦
sst ♦ ♦ts q st♦ é á♦ ♣r s s r③õs ♦q♦ ♣rs♥ts
rr♥♦ ts s♥s rs ♣♦ tr ♦r♠
s♥t ♦ sst ♦ q♥t♦ ♠♦r r③ã♦ ♦q♦ é♠ ss♦ ♠♦str♦s
q ①♠♣♦ ♦ q ♦♦rr ♣r ♦ ♦♥t ♣rssã♦ ♥ ♠♦r r③ã♦ ♦q♦
rba = 0,6 ♦ sst ♦ ♣rs♥t ♠ ♦♠♣♦rt♠♥t♦ s♣ ♣r ♦ ♠♥♦r â♥♦
♥♥çã♦ β = 18 ♦ à rstrçã♦ ár ♣ss♠ ♦ s♦♠♥t♦ r
♦r t♦t ♠♥s♦♥ qtotal/q0 ♣r ♦r tr♦♦ tr
és s ts
♦♠♦ ♥t♠ ♦ st♦ tr♥srê♥ ♦r ♦♥ ♣♦s r ♦
♦r t♦t tr♥sr♦ ♣r ♦ ♦ ♠ s ♣rs ♠ ♦rrs♣♦♥♥t à tr♦ tér♠
q ♦♦rr trés s♣rí s ts ♦tr q ♦rrs♣♦♥ à tr♦ tér♠
trés s♣rí s ♣rs ♦ ♥ ♠♥r ♦♠♣♠♥tr às çõs ♦s
♥ú♠r♦s sst ♦ ♦ q♥t♦s sts ♣rs ♠ s♣r♦ ♥
♦s ♥ê♥ ♦s ♣r♥♣s ♣râ♠tr♦s st♦s s♦r ts ♣rs
♥ê♥ ♥♥çã♦ t
r ♦srs ♦ t♦ ♥♥çã♦ s♦r ♣r tr♥srê♥
♦r trés s♣rí s ts t♠é♠ s♦r q♥t ♠♥s♦♥ qtotal/q0q r♣rs♥t ♦ t♦r ♠♥t♦ tr♥srê♥ ♦r ♦ à ♣rs♥ç s ts
♦♠ rçã♦ ♦ rs♣t♦ s♦ ♦ ♥ s♠ ts ♣r ♦ tr♦ L = 30H s ♦rs
t③♦s ♦♠♦ rrê♥ ♣r q♥t qtotal/q0 sã♦ ♠♦str♦s ♥
srs q ♦s s♦s r r♣rs♥t♠ ♦s rst♦s ♣r ♦♥çã♦
♦♥t♦r♥♦ ue = 3 m/sPr ♦ rr♥♦ ♥♦ rs q♥t qtotal/q0 ♣rs♥t♦
rçã♦ ♠♥♦r q ♦♠ ♦ â♥♦ ♥♥çã♦ s ts rçã♦ st q♥t
♥♦ rr♥♦ s♥♦ ♦♥t♦ é s♥t ♠ b = 3H ♥ ♥♦ts
q ♣r ♠ ♠s♠♦ s♣ç♠♥t♦ ♥tr ts ♦ rr♥♦ ♥♦ ♣rs♥t ♦s ♠♦rs
t♦rs ♠♥t♦ ♥ tr♥srê♥ ♦r ♣r t♦s s ♥♥çõs t q♥♦
♥t ♦r tr♥sr ♣r ♦ ♦ ♥♦ ♥ s♠ ts ♣r strês r♥ts ♦♥çõs r♦♥â♠s
♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue q♥t ♦r q0
①1 m/s 0,5745 W
3 m/s 1,287 W
9 m/s 3,051 W
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
b = 3H r ① r P♦ré♠ ♣r ♦ ♠♥♦r s♣ç♠♥t♦ ♥tr
ts b = 2H st♦ só é r♦ ♣r s ♠♦rs ♥♥çõs r ① r
♥ssár♦ ♥♦tr rçã♦ ♦♠♣♠♥tr ♦s rst♦s r ♦♠
strçã♦ Nux r ♦♥♦r♠ ♦♥stt♦ ♣r ♥♥çã♦ β = 18 ♦♥ú♠r♦ sst ♦ ♥ rã♦ ♣r s st ♣♦r sr ♦♥sr♠♥t ♠♥♦r
q ♣r ♦s ♠s â♥♦s ♥♥♦ q tr♦ ♦r ♣r♦♠♥r ♥s ts
st s♣♦sçã♦ é r ♣♦s ♦s rst♦s ♣r ♥♥çã♦ β = 18 r♠ q
♠♦r ♣rt tr♦ ♦r ♦♦rr t♦ trés s♣rí s ts ♣r ♠♦s
♦s rr♥♦s ♣r♥t ♦r tr♦♦ trés s ts té ♦ t♦t
β = 18 rba = 0,6♥ ♦s rst♦s ♣rs♥t♦s ♣r ♦ sst ♦ r sr♠ q
tr♦ tér♠ ♠♥ ♥ rã♦ ♣r ♣r ♦s ♥s ♦♠ ts q ♣rs♥t♠
♠♥♦r â♥♦ ♥♥çã♦ β → 0 t♦ r ♠♦str ss t♥ê♥
♣♦s st q ♠♦rs ♥♥çõs t♥♠ ♣rs♥tr ♠♦rs tr♦s ♦r trés
s♣rí t r ♠♦str q á ♠s♠ t♥ê♥ ♣r ♠♦s ♦s
rr♥♦s ♥t♦ ♥ r q♥t♦ ♥ r ♦srs q ①st
♠ ♥♥çã♦ ♣rtr q s rçõs ♦r sã♦ trs ♥tr ♦s â♥♦s
♥st♦s ♣rs q ♣r s ♥♥çõs té β = 54 q♥t♦ ♠♥♦r ♦ â♥♦
♥♥çã♦ t ♠♦r rçã♦ ♦r tr♦ trés s ts Pr ♥♥çõs
t ♠ ♦ â♥♦ st♦ ♣♦ré♠ ♥ã♦ ♦♦rr rçã♦ ♦♥srá sts
q♥ts
♦r♠ ♦♠♣♠♥tr st♦ ♣♦ sr s③♦ ♥ r q ♠♦str s
rçõs ♦ ♠♣♦ t♠♣rtrs ♥♦ ♦♠í♥♦ só♦ ♣rs ts st r
♥♦ts q s ♠♦rs rçõs sã♦ ♦③s s♦r s ts ♠♦r ♥♥çã♦
♥ê♥ ♦ rrê♥
Pr r ♥ê♥ ♦ rrê♥ ue s♦r ♣r ♦ ♦r
tr♥sr♦ ♣r ♦ ♦ trés s ts ♦r♠ t③♦s ♦s ♠s♠♦s s♦s s rs
♦♠ st♦ ♥♦♠♥t é ♣♦ssí ③r ♦ ♦♠♣rt♦ ♥tr s ♣rsõs
♦ ♥ú♠r♦ sst ♦ tr♦ ♦r ♥tr ♥ s♣rí s ♣rs s
ts ❯♠ ③ q ♦ Nux ♠♥t ♦♠ ♦ rrê♥ ♠ ♠♦r ♣r
♦r é tr♥sr ♣r ♦ ♦ trés s ♣rs ♦ ♥ P♦rt♥t♦ ♠♥çã♦
♣r ♦ ♦r trés s ts ♠♦str ♥ r é ♦r♥t ♦♠ ♣rsã♦
♥♠ér ís ♦ s♦♠♥t♦ ♣r ♠♦s ♦s rr♥♦s ♦ts ♦♥t♦ q á ♦
♠♥t♦ ♥ tr♦ ♦r t♦t ♠♥s♦♥ qtotal/q0 ♦♠ ♦ rrê♥
♦s ♠♦t♦s á ♦r♠ ♣r♠♥t st♦s
♠á①♠ rçã♦ ♦ ♦r t♦t ♠♥s♦♥ ♦♦rr ♣r ♦ rr♥♦ s♥♦
♦♠ β = 90 r Pr st ♦♥rçã♦ ♦ ♠♥t♦ ♦ ♦r
t♦t ♠♥s♦♥ ♦ ♠♥tr ♦ rrê♥ ♣rtr ue = 1 m/s ♣r
ue = 9 m/s st ♠s♠ ① rçã♦ ♦ rrê♥ ♥ê♥ ♥
strçã♦ ♦ ♦r ♦ ♠♦r ♣r ♦ rr♥♦ ♥♦ ♦♠ β = 18 r ♥♦
q s ♦sr ♠ ♠♥çã♦ ♦ ♦r trés s ts
♠♥r ♦♠♣♠♥tr ♦s rst♦s ♣r ♥ê♥ ♦ s♦r ♦
♠♣♦ t♠♣rtrs ♥♦ ♦♠í♥♦ só♦ ♣♦♠ sr st♦s ♥s rs
♣r ♦s â♥♦s ♥♥çã♦ t β = 18 β = 54 β = 90 rs♣t♠♥t
r ♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦ ♥rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠ue = 3 m/s
β = 18 β = 18
β = 36 β = 36
β = 54 β = 54
β = 72 β = 72
β = 90 β = 90
0,000
0,069
0,138
0,207
0,276
0,345
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
1,000
U*
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦ ♥rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba = 0,4 ♦♥çã♦ r♦♥â♠ue = 3 m/s
β = 18 β = 18
β = 36 β = 36
β = 54 β = 54
β = 72 β = 72
β = 90 β = 90
0,000
0,069
0,138
0,207
0,276
0,345
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
1,000
U*
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr tsb = 2H
-0.5
0.0
0.5
1.018° 36° 54° 72° 90°
-0.5
0.0
0.5
1.0
Parede superior
Parede inferior
Cf x
4 5 6 7 8 9 10
x/H
4 5 6 7 8 9 10
x/H
# posição das aletas para β=18°
#2 #3
Cf x
(β)
#2 #3 #4
recolamento do
escoamento
rr♥♦ s♥♦
-0.3
-0.1
0.1
0.318° 36° 54° 72° 90°Parede superior
Cf x
4 5 6 7 8 9 10
x/H
(β)
#3#2 #4
# posição das aletas para β=18°
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr tsb = 3H
-0.3
-0.1
0.1
0.318° 36° 54° 72° 90°
-0.3
-0.1
0.1
0.3
Parede superior
Parede inferior
Cf x
4 5 6 7 8 9 10
x/H
4 5 6 7 8 9 10
x/H
# posição das aletas para β=18°
Cf x
(β)
#2
#3
#2
recolamento do
escoamento
rr♥♦ s♥♦
-0.3
-0.1
0.1
0.318° 36° 54° 72° 90°Parede superior
Cf x
4 5 6 7 8 9 10
x/H
(β)
#3#2
# posição das aletas para β=18°
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H
-0.2
-0.1
0.0
0.1
0.29 m/s 3 m/s 1 m/s
-0.2
-0.1
0.0
0.1
0.2
aleta n° 2
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 2 aleta n° 3
aleta n° 3
aleta n° 4
rr♥♦ s♥♦
-0.5
-0.3
0.0
0.3
0.59 m/s 3 m/s 1 m/sParede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 3aleta n° 2
aleta n° 4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H
-0.5
-0.3
0.0
0.3
0.59 m/s 3 m/s 1 m/s
-0.5
-0.3
0.0
0.3
0.5
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 2 aleta n° 3 aleta n° 4
aleta n° 2 aleta n° 3 aleta n° 4
rr♥♦ s♥♦
-0.5
-0.3
0.0
0.3
0.59 m/s 3 m/s 1 m/sParede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 2 aleta n° 3 aleta n° 4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H
-1.0
-0.5
0.0
0.5
1.09 m/s 3 m/s 1 m/s
-1.0
-0.5
0.0
0.5
1.0
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 2 aleta n° 3 aleta n° 4
aleta n° 2 aleta n° 3 aleta n° 4
rr♥♦ s♥♦
-0.5
-0.3
0.0
0.3
0.59 m/s 3 m/s 1 m/sParede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 2 aleta n° 3 aleta n° 4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s
-0.2
-0.1
0.0
0.1
0.2Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 3 aleta n° 4
aleta n° 2 aleta n° 3
aleta n° 2
-0.2
-0.1
0.0
0.1
0.2rba=0,6 rba=0,4 rba=0,2rba=0,6 rba=0,4 rba=0,2
aleta n° 2 aleta n° 3
Parede superior
rr♥♦ s♥♦
-0.2
-0.1
0.0
0.1
0.2rba=0,4 rba=0,2Parede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 3aleta n° 2
aleta n° 4
rba=0,4 rba=0,2
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s
-1.0
-0.5
0.0
0.5
1.0rba=0,6 rba=0,4 rba=0,2
-1.0
-0.5
0.0
0.5
1.0
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 2 aleta n° 3 aleta n° 4
aleta n° 2 aleta n° 3 aleta n° 4
rba=0,6 rba=0,4 rba=0,2
rr♥♦ s♥♦
-0.5
-0.3
-0.1
0.1
0.3
0.5rba=0,4 rba=0,2Parede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 4aleta n° 2 aleta n° 3
rba=0,4 rba=0,2
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ ♣r ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0rba=0,6 rba=0,4 rba=0,2
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
Cf x
aleta n° 4aleta n° 3aleta n° 2
aleta n° 4aleta n° 3aleta n° 2
rba=0,6 rba=0,4 rba=0,2
rr♥♦ s♥♦
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3rba=0,4 rba=0,2Parede superior
Cf x
4 5 6 7 8 9 10
x/H
aleta n° 2aleta n° 3
aleta n° 4
rba=0,4 rba=0,2
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ Cp ♣r s r♥ts r③õs ♦q♦ s ♦♠trs ♥ ♦♠ b = 2H ♦ rr♥♦ ♥♦ b = 2H ♦ rr♥♦ s♥♦ b = 3H♦ rr♥♦ ♥♦ b = 3H ♦ rr♥♦ s♥♦ ♥s três ♦♥çõs r♦♥â♠ss♠s
18 36 54 72 90
1
10
100
1.000
rba = 0,2
rba = 0,4
β ( )ue (m/s)
Cp/Cp
0
18 36 54 72 90
1
10
100
1.000
rba = 0,2
rba = 0,4
rba = 0,6
β ( )ue (m/s)
Cp/Cp
0
18 36 54 72 90
1
10
100
1.000
rba = 0,2
rba = 0,4
β ( )ue (m/s)
Cp/Cp
0
18 36 54 72 90
1
10
100
1.000
rba = 0,2
rba = 0,4rba = 0,6
β ( )ue (m/s)
Cp/Cp
0
100 101 102 103Cp/Cp0
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♠♣rt♦ ♦ Cp ♥tr ♦s ♦s rr♥♦s r♥ts r③õs ♦q♦ s♣ç♠♥t♦ ♥tr ts b = 2H ♥s três ♦♥çõs r♦♥â♠s ue
ue = 1m/s ue = 3m/s ue = 9m/s
1
10
100
1.000
♥♦rba = 0,4
rba = 0,2
β( )
Cp/Cp
0
1
10
100
1.000
s♥♦
rba = 0,4
rba = 0,2
β( )
Cp/Cp
0
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱♦rs Cp/Cp0 ♣r ♦ rr♥♦ s♥♦ r♥ts s♣ç♠♥t♦♥tr ts ♥s três ♦♥çõs r♦♥â♠s ue
ue = 1m/s ue = 3m/s ue = 9m/s
1
10
100
1.000
b = 2H rba
β( )
Cp/Cp
0
1
10
100
1.000
b = 3H rba
β( )
Cp/Cp
0
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r t rçã♦ ♦ s♦♠♥t♦ ♦ à rstrçã♦ ár rst♥t♣r ♦ â♥♦ ♥♥çã♦ t β = 18 ♣r ♦♠tr ♦♠ rba = 0,6 b = 2a t♦♣♦♦ ♦ s♦♠♥t♦ ♥ ♣rt ♥r♦r ♦ ♥
A = 0,4 H
0,00,544
1,091,632,182,713,263,804,344,885,435,986,517,067,60
u/ue
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦ ♦♥rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba ♦♥çã♦ r♦♥â♠ ue = 3 m/s
β = 18 β = 18
β = 36 β = 36
β = 54 β = 54
β = 72 β = 72
β = 90 β = 90
0,000
0,069
0,138
0,207
0,276
0,345
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
1,000
T*
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦ ♦♥rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba ♦♥çã♦ r♦♥â♠ ue = 3 m/s
β = 18 β = 18
β = 36 β = 36
β = 54 β = 54
β = 72 β = 72
β = 90 β = 90
0,000
0,069
0,138
0,207
0,276
0,345
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
1,000
T*
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♥♥çã♦ t rr♥♦ ♥♦ ♦♥ sqr rr♥♦ s♥♦ ♦♥ rt ♣r♦♠trs ♦♠ b = 2H rba = 0,4 ♦ rrê♥ ue = 3 m/s
β = 18 β = 18
β = 36 β = 36
β = 54 β = 54
β = 72 β = 72
β = 90 β = 90
0,000
0,068
0,137
0,208
0,277
0,346
0,414
0,483
0,552
0,621
0,690
0,759
0,828
0,897
0,966
Ts*
1,000
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 18
ue = 1 m/s ue = 1 m/s
ue = 3 m/s ue = 3 m/s
ue = 9 m/s ue = 9 m/s
0,000
0,149
0,212
0,277
0,339
0,402
0,465
0,528
0,591
0,654
0,717
0,780
0,843
0,906
0,969
Ts*
1,000
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 54
ue = 1 m/s ue = 1 m/s
ue = 3 m/s ue = 3 m/s
ue = 9 m/s ue = 9 m/s
0,000
0,149
0,212
0,277
0,339
0,402
0,465
0,528
0,591
0,654
0,717
0,780
0,843
0,906
0,969
Ts*
1,000
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 90
ue = 1 m/s ue = 1 m/s
ue = 3 m/s ue = 3 m/s
ue = 9 m/s ue = 9 m/s
0,000
0,149
0,212
0,277
0,339
0,402
0,465
0,528
0,591
0,654
0,717
0,780
0,843
0,906
0,969
Ts*
1,000
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦ t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s ♦♠trs ♦♠s♣ç♠♥t♦ ♥tr ts b = 2H
0
100
200
300
0.08 0.10 0.12 0.14 0.16 0.18 0.20
18° 36° 54° 72° 90°
0
100
200
300
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
Nu
x
4 5 6 7 8 9 10
x/H#2
4 5 6 7 8 9 10
x/H
#3 #4
# posição das aletas para β=18°
#2 #3
Nu
x
(β)
Pico de Nux
rr♥♦ s♥♦
0
50
100
150
200
0.08 0.10 0.12 0.14 0.16 0.18 0.20
18° 36° 54° 72° 90°Parede superior
Nu
x
# posição das aletas para β=18°
(β)
4 5 6 7 8 9 10
x/H#2 #3 #4
Platô de Nux
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦ t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s ♦♠trs ♦♠s♣ç♠♥t♦ ♥tr ts b = 3H
0
50
100
150
200
250
300
350
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26
18° 36° 54° 72° 90°
0
50
100
150
200
250
300
350
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26
Parede superior
Parede inferior
Nu
x
#2 #3 #4
#2 #3
Nu
x
(β)
Pico de Nux
5 6 7 8 9 10 13
x/H
11 12
5 6 7 8 9 10 13
x/H
11 12
rr♥♦ s♥♦
0
50
100
150
200
0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26
18° 36° 54° 72° 90°Parede superior
Nu
x
# posição das aletas para β=18°
(β)
Platô de Nux
5 6 7 8 9 10 13
x/H
11 12
#2 #3 #4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H
0
50
100
150
200
250
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s
3 m/s
1 m/s
0
50
100
150
200
250
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
4 5 6 7 8 9 10
Nu
x
aleta n°2 aleta n°3
aleta n°2 aleta n°3
aleta n°4
rr♥♦ s♥♦
0
100
200
300
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s 3 m/s 1 m/sParede superior
4 5 6 7 8 9 10
Nu
x
aleta n°2 aleta n°3
x/H
aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s 3 m/s 1 m/s
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
Nu
x
aleta n°2 aleta n°3 aleta n°4
4 5 6 7 8 9 10
x/H
aleta n°2 aleta n°3
aleta
rr♥♦ s♥♦
0
100
200
300
400
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s 3 m/s 1 m/sParede superior
Nu
x
4 5 6 7 8 9 10
x/H
aleta n°2 aleta n°3 aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s 3 m/s 1 m/s
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
4 5 6 7 8 9 10
x/H
aleta n°2aleta n°3 aleta n°4
aleta n°2 aleta n°3 aleta n°4
rr♥♦ s♥♦
0
50
100
150
200
250
300
350
0.08 0.10 0.12 0.14 0.16 0.18 0.20
9 m/s 3 m/s 1 m/sParede superior
Nu
x
4 5 6 7 8 9 10
x/H
aleta n°2aleta n°3 aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s
0
100
200
300
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4 rba=0,6
0
100
200
300
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
Nu
x
4 5 6 7 8 9 10
x/H
4 5 6 7 8 9 10
x/H
Nu
x
aleta n°3aleta n°2
aleta n°2 aleta n°3
rba=0,4rba=0,2 rba=0,6
aleta n°4
rr♥♦ s♥♦
0
100
200
300
400
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4Parede superior
4 5 6 7 8 9 10
x/H
Nu
x
aleta n°2 aleta n°3
rba=0,4rba=0,2
aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4 rba=0,6
0
100
200
300
400
500
600
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
Nu
x
4 5 6 7 8 9 10
x/H
4 5 6 7 8 9 10
x/H
Nu
x
aleta n°3aleta n°2
aleta n°2 aleta n°3
rba=0,4rba=0,2 rba=0,6
aleta n°4
aleta
n°4
rr♥♦ s♥♦
0
100
200
300
400
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4Parede superior
4 5 6 7 8 9 10
x/H
Nu
x
aleta n°2 aleta n°3
rba=0,4rba=0,2
aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s
0
200
400
600
800
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4 rba=0,6
0
200
400
600
800
0.08 0.10 0.12 0.14 0.16 0.18 0.20
Parede superior
Parede inferior
Nu
x
4 5 6 7 8 9 10
x/H
4 5 6 7 8 9 10
x/H
Nu
x
aleta n°3aleta n°2
aleta n°2 aleta n°3
rba=0,4rba=0,2 rba=0,6
aleta n°4
aleta n°4
rr♥♦ s♥♦
0
100
200
300
400
0.08 0.10 0.12 0.14 0.16 0.18 0.20
rba=0,2 rba=0,4Parede superior
4 5 6 7 8 9 10
x/H
Nu
x aleta n°2aleta n°3
rba=0,4rba=0,2
aleta n°4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ú♠r♦ sst ♦ ♠♦s ♦s rr♥♦s t ♣r s ♦♠trs♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♦♥ sqr b = 3H ♦♥ rt
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
18 36 54 72 90
β ( ° )
Nu/N
u0
restrição da área de
escoamento
rba = 0,6
rba = 0,4
rba = 0,2
rr♥♦ s♥♦
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
18 36 54 72 90
β ( ° )
Nu
/Nu
0
restrição da área de
escoamento
rba = 0,6
rba = 0,4
rba = 0,2
rr♥♦ s♥♦
0.0
1.0
2.0
3.0
4.0
18 36 54 72 90
β ( ° )
Nu/N
u0
rba = 0,4
rba = 0,2
rr♥♦ ♥♦
0.0
1.0
2.0
3.0
4.0
18 36 54 72 90
β ( ° )
Nu/N
u0
rba = 0,4
rba = 0,2
rr♥♦ ♥♦
ue=1 m/s ue=3 m/s ue=9 m/s
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r r♥srê♥ ♦r ♥ ♥tr rçã♦ ♦ ①♦ ♦r t♦t ♠♥s♦♥ ♣r ♦ ♦r tr♦ trés s ts ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r ♦s r♥ts s♣ç♠♥t♦s t b = 2H ♦♥ sqr b = 3H♦♥ rt
rr♥♦ s♥♦ rr♥♦ s♥♦
rr♥♦ ♥♦ rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r ❱rçã♦ rçã♦ ♦ ♦r tr♦♦ trés ♥tr ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r ♦s s♦s ♦ s♣ç♠♥t♦ t b = 2H ♦ rrê♥ ue = 9 m/s
0
25
50
75
100
18 36 54 72 90
paredes
aletas
rba=0,2
rba=0,4
rba=0,6
rba=0,2
rba=0,4
rba=0,6
β (°)
Fra
ção
de
calo
r (%
)
rr♥♦ s♥♦
0
25
50
75
100
18 36 54 72 90
paredes
aletas
β (°)
Fra
ção
de
calo
r (%
)
rba=0,2
rba=0,4
rba=0,2
rba=0,4
rr♥♦ ♥♦
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r
♥
ê♥
♦
rrê♥
u
e♥
str
çã♦
tr♦
tér♠
tré
s
♥tr
♥♦
♦rtr♥
sr♦t♦t
♠
♥s♦♥
♣
r♦s
rr♥♦s
t
s♥
♦
s♣
r♦r
♥
♦♥r♦r
β=18
β=54
β=90
β=18
β=54
β=90
♦♥t
♣r♦
çã♦
♦♣r
ó♣r♦
t♦r
♥ê♥ r③ã♦ ♦q♦ t
r é ♣♦ssí ♦srr ♦ t♦ s r③õs ♦q♦ ♣s ♣r
t♣♦ rr♥♦ s♦r tr♦ tér♠ t♦t s strçã♦ ♥tr s♣rí
♣r s♣rí t srs q st r ♦ ♦♥strí ♦♠ ♦s rst♦s
♣r s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♣r ♦ rrê♥
ue = 9 m/s♦ rr♥♦ s♥♦ q ♣♦ss três rçõs rba ♦ ♠♦r ♥r♠♥t♦
♥♦ ♦r tr♥sr♦ ♣s ts ♦♦rr ♣r ♦ ♠♥♦r â♥♦ ♥♥çã♦ r
q♥♦ r③ã♦ ♦q♦ t é ♠♥t ♣r Pr st
rr♥♦ ♥ ♦ ♦r t♦t ♠♥s♦♥ r ♠ ♦ ♦r♦ q♥♦ s r
r③ã♦ ♦q♦ t ♣r β = 90 r
♥tr s s r③õs ♦q♦ t ♦♥rçã♦ ♥ ♦ ♠♥t♦
♣r ♦r tr♥sr trés s ts ♦ ♠♥♦r ♣♦ré♠ t♠é♠ ①♣rss♦ té
♣r β = 18 r ♠♦r ♠♥t♦ ♦ ♦r tr♦♦ ♣s ts ♦
♦sr♦ t♠é♠ ♣r ♦ s♦ ♠♥♦r â♥♦ ♥♥çã♦
P♦rt♥t♦ ♦♥stts q ♠♥r ♥♣♥♥t ♦ rr♥♦ ♦ ♠♥t♦
r③ã♦ ♦q♦ rst ♠ ♠♥t♦ tr♦ tér♠ t♦t ♣r t♦s s ♥♥çõs
t
r
t♦
r③ã
♦
♦q
♦
trb as♦r
♣
r
♦rtr♦
tré
s
sts
s♦r
♦
♦rtr♥
sr♦t♦t
♠
♥s♦♥
♣
r♠
♦s♦s
rr♥♦s
♦♠trs
♦♠b=2H
β=18
β=54
β=90
β=18
β=54
β=90
♦♥t
♣r♦
çã♦
♦♣r
ó♣r♦
t♦r
♦♠♣rt♦s s q♥ts ♦s
♦♠ ♦ ♦t♦ r♦♥r ♣r s♦ ♠♦r tr♥t ♥tr ♦s
s♦s ♣rs♥t♦s ♣r ♠ ♠s♠ r③ã♦ ♦q♦ t rba s r③õs ♥tr s
q♥ts ♦s ♦s r♥ts rr♥♦s sã♦ ♣rs♥ts ♥s s
s r③õs sã♦ ♥s ♦♠ q♥t ♦ ♦ rr♥♦ ♥♦ ♥♦ ♥♠r♦r
s ♦ ♥ú♠r♦ sst Nualinhado ♦ ♦ ♦♥t ♣rssã♦ Cpalinhado s
s ♣rs♥t♠ r③ã♦ ♣r ♦ ♦♥t ♣rssã♦ s s
♣r ♦ sst ♦ ♠s s r③õs ♦q♦ t rba = 0,2 rba = 0,4Prs q ♠♥r r s q♥ts ♦s sã♦ ♠♦rs ♣r ♦ rr♥♦
♥♦ ①t♦ ♣r ♦ ♥ú♠r♦ sst ♦s ♦s ♠♦rs â♥♦s ♥♥çã♦ t
♥♦ s♣ç♠♥t♦ b = 2H ♦♥♦r♠ st ♦r♠ ♣r st rr♥♦ ♥♦♥tr
s ♠♦r s♠♣♥♦ tér♠♦ ♥ ♠♦r ♣rt ♦s s♦s ♣♦ré♠ t♠é♠ ♠♦r ss♣çã♦
♥r ♠â♥ ♦♥sr♥♦ ♦ s♠♣♥♦ tér♠♦ ♣r ♦ s♣ç♠♥t♦ b = 2H t♥ê♥ ♦sr é q ♠♥♦rs â♥♦s ♥♥çã♦ ♦r♠ ♦
rr♥♦ ♥♦ té ♣♦r ♦t β = 54 ♦♠ ♦ ♠♥t♦ ♦ s♣ç♠♥t♦ ♥tr ts
r♥ç ♠é ♦♥sr♥♦ ♦ sst ♦ rr♥♦ ♥♦ é ♠♦r
♣r t♦s s ♥♥çõs t ♥t♦ ♦ s♠♣♥♦ rá♦ s
♦ rr♥♦ ♥♦ ♣rs♥t ♠♦r ♣r r ♣r t♦♦s ♦s s♦s
♥♦s ♠♥r ♣♦♥t ♦ ♠♦r s♠♣♥♦ tér♠♦ ♠é♦ ♣r ♦
rr♥♦ ♥♦ r♥t ♦ s♥♦ ♦rrs♣♦♥ rba = 0,4 β = 18 ♣r ♦ s♣ç
♠♥t♦ ts b = 3H st s♦ ♦ s♠♣♥♦ ♦ rr♥♦ ♥♦ é
r ♠♦r q ♦ s♥♦ P♦ré♠ ♦rrs♣♦♥♥t ♣r r é
♠♦r ♣r ♦ rr♥♦ ♥♦
Pr ♦ rr♥♦ s♥♦ ♦ ♠♦r s♠♣♥♦ tér♠♦ ♦sr♦ ♥♦♥trs
♥ ♣r rba = 0,4 β = 90 ♠s q r③ã♦ ♦ sst ♦ é
♠♦r ♣r ♦ rr♥♦ s♥♦ P♦r ♦tr♦ ♦ ♥♦ts q ♣r st s♦ ♦♠étr♦
ss♣çã♦ ♥r ♠â♥ ♠é é r ♠♥♦r ss♠
sts q t♥t♦ ♦ s♠♣♥♦ tér♠♦ q♥t♦ ♦ rá♦ sã♦ ♦rás ♣r
♠s♠ ♦♥rçã♦ ♦♠étr
③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H
β ❭ue ♠s ♠s ♠s r♥ç
rba = 0,2
rba = 0,4
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H
β ❭ue ♠s ♠s ♠s r♥ç
rba = 0,2
rba = 0,4
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H
β ❭ue ♠s ♠s ♠s r♥ç
rba = 0,2
rba = 0,4
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H
β ❭ue ♠s ♠s ♠s r♥ç
rba = 0,2
rba = 0,4
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
❯Õ PP❱ ❯❯
s♦♠♥t♦ tr♥t♦ ♣r♠♥♥t ♠é♦ ♠ ♦ ♥t♦♥♥♦ ♠ ♥s
♦r③♦♥ts ♠♥s♦♥s ♦♠ ts ♣♥s tr♥srs♠♥t ♥♥s s♣♦sts
♦r♠ ♥ ♦ s♥ ♦ st♦ trés s♠çã♦ ♥♠ér ♠
♣r ♥ t③♦s ♠ ♦♥♥t♦ ♦♠♣♦st♦ ♣♦r ♥♦ ts ❯♠ ③ q ♠s
s ♣rs ♦ ♥ ♠ ♦♠♦ s ts ♣rs♥t♠ s♣ssrs ♣rétr♠♥s sã♦
♦♥t♦rs tr♥srê♥ ♦r ♦♥ ♦ ♠ ♦♥srçã♦ s t♦s
♣rs♥ç s ts t♥t♦ ♥♦ s♣t♦ r♦♥â♠♦ ♦ s♦♠♥t♦ q♥t♦ ♥♦ tér♠♦
♦r♠ ♥st♦s ♦r♠ ♦ t♠é♠ ♥ ♦r♠ ♦rs ♠é♦s ♦ ♦s
P♦r ♠♦ ♠ çã♦ ♣ré à ♦♥strçã♦ ♦s s♦s ♦ ♣r♦♠ ♦ st
tr♦ ♦♥stt♦s ♣ ♦ ♣r♦r♠ ♦♠r CFX ♠ ♦♠♦ ♦ ♠♦♦
trê♥ ♣r s♦çã♦ ♦ ♣r♦♠ ♦s ♥s t♦s srt③çã♦ ♣♦r
♠♦ ♦ ♠ét♦♦ ♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ❱ ♦ r ♣r
s♦çõs ♦ ♦ ♥ú♠r♦ t♥t♦♥ ♥r ♥ét tr♥t ♣♦r ♠♦
♦ ♦♠♣rt♦ ♦♠ ♦trs ♣rsõs ♥♠érs ①♣r♠♥t♦s s♣♦♥ís ♥ trtr
♠♦♦ trê♥ ♠♦♥str♦ ♦ rá ♣r s♦çõs ♦
tr♥srê♥ ♦r ♠ s♦♠♥t♦s ♦♠ r♥t ♣rssã♦ rs♦ ♠ ♦♠♦ ♣r
♦ ♣r ♥r ♥ét tr♥t ♠ ♠ ♥ ♣♥♦
♠♥r r ♦♥stt♦s q ♥srçã♦ ts tr♥srss ♠ ♥s
♣rs♥t ♠ ♣♦t♥ ♦♥srá ♣r ♠♥tr tr♥srê♥ ♦r st♦ s
♠ ♦ ♣rt ♣ ♥t♥sçã♦ s q♥ts tr♥ts st♦ é s ♣r♦♣rs ♦
s♦♠♥t♦ ♦♠♦ s♦s tr♥t ♦♥sq♥t♠♥t ♦♥t tér♠
tr♥t P♦r ♦tr♦ ♦ ♦r♦ ♦♠ ♠♦♠ tçã♦ ♦s
♣rs♥t ♥♦s s♦♠♥t♦s tr♥t♦s ♣rs♥ç s ts ♦ ♠♥t♦ ♣rssã♦
t ♦ q ♠♣ ♠ ♠♦rs ①s ♣rssã♦ ♦♣rçã♦ ♦ q♣♠♥t♦
♥ê♥ ♠s s♥t ♦s ♣râ♠tr♦s ♦♠étr♦s ♦ r③ã♦ ♦
q♦ t s ♦ â♥♦ ♥♥çã♦ t ♣♦r ♠ ♦ s♣ç♠♥t♦ ♥tr
ts sqê♥ t♠s s ♦♥sõs ♣♦♥ts ♦s ♣r♥♣s rst♦s
❼ s q♥ts ♦s
♦ às rq♥ts ♠♥çs rçã♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦♠ ♦♦rrê♥
♦ r♦♠♥t♦ ♥♦ tr♦ ♥tr s ts s ♠♦rs rçõs ♥s q♥ts
♦s Cfx Nux ♦r♠ ♦srs ♣r ♦ rr♥♦ s♥♦ rã♦ ♦♥
♦♦rr ♦ r♦♠♥t♦ ♦ rtr③ tr♠♠♥t ♣♦r ♠ ♠♥t♦ r♣♥t♥♦
tr♥srê♥ ♦r ♦ ♣♦ Nux r♦♥♠♠♥t ♣♦r ♠ rçã♦
♥ ♦ ♥t♦ à ♣r ♣♦♥t♦ st♥çã♦ ♦♠ Cfx ♥♦
♦♠ ♦ s♦ ♦ ♦♥t trt♦ s♣r ♥t♦s ♦s ♠♥s♠♦s st♥
t♦s q rst♠ ♥s ♣rs ♥r ♠â♥ ♦s ♥♦ tr♦ ♥ t♦
s rõs rrçã♦ Cfx ♥t♦ ♥r ♠â♥ ♦ s♦♠♥t♦ ♣r♥
♣ é ♠♥í ♣ çã♦ ♦ s♠♥t♦ st ♦♠ ♦s órts ♦r♠♦s ♣♦r
♦sã♦ ♦ s s♦♠♥t♦ ♣♦ré♠ ①st♠ tr♦s ♣r ♥ ♦♥
♥r ♠â♥ é ♠♥í ♦ s♦♠♥t♦ ♣ çã♦ s♥t ♦r♠ rt
♦♠ s ♣rs Cfx ♣♦st♦ srs q ♠♦r ♥ã♦ t♥ s♦ ♦♠♥t
q♥t♦ st rrst♦ ♣♦r trt♦ s♣r ♦♦rr t♠é♠ ♥s s ♣♦♥ts
s ts
♦♠ s ♥ t♦♣♦♦ s♦♠♥t♦ ♣rs q ♦♦rr ♦ ♠♦ s♦
♠♥t♦ ♣rtr s ♣♦♥ts s ts sr♥♦ rõs ♦ rr♥t
s♥t s ♠s♠s sqê♥ ♦ s rs♦ ♦ s♦♠♥t♦ ♣r♥♣ té ♦
♣♦♥t♦ r♦♠♥t♦ ♦♥ rt♦♠ ♦ ♦♥tt♦ ♦♠ ♠ s♣rí ♦ ♥ t
♦ ♣r s rõs rrçã♦ r♦♠♥t♦ sã♦ s q ♣rs♥t♠ s
♠♦rs ♥trrê♥s ♥ tr♥srê♥ ♦r ♦ s ③♦♥s rrçã♦
♣♦rçã♦ ♦ rr♥t t♥ s ♦♠♦♥③r tr♠♠♥t ♦♠ ss♦
①♦s r♥ts t♠♣rtr sã♦ ♥♦♥tr♦s ♥sts ♦s P♦r ♦tr♦ ♦
♥ rã♦ ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦s r♥ts tér♠♦s sã♦ s
♥t♦s ♣♦s ♠s s ♠s ♠ts stã♦ ♠ r♦♥strçã♦ srs q
♠♦♥t♥t s ts ♥t♦ às ss ss t♠é♠ ♦♦rr ♦r♠çã♦ rrçã♦
♣♦ré♠ s ♥ê♥ s♦r ♦s rst♦s é ♠♥♦s s♥t
❼ s q♥ts ♦s
❯♠ ♦♥sã♦ ♥trss♥t rt ♣r s q♥ts ♦s Nu Cp é q
♦ rr♥♦ ♥♦ ♥ã♦ ♣rs♥t♦ s♥s ♦♥srá ♥tr ♦s r♥ts â♥
♦s ♥♥çã♦ ♥♣♥♥t r③ã♦ ♦q♦ t t③ P♦ré♠
♥♦ rr♥♦ s♥♦ q♥t♦ ♠♦r ♦ â♥♦ ♥♥çã♦ ♠♦r ♦ ♦♥t
♣rssã♦ t♠é♠ ♦ ♥ú♠r♦ sst ♠é♦ ♥♦♥tr♦ t♦ q é ♣♦t♥
③♦ ♣r ♠♦rs r③õs ♦q♦ ♦♥t♦ ♣r r③ã♦ ♦q♦ rba = 0,6①s ♣r ♦ rr♥♦ s♥♦ ♦ ♥♦♥tr ♠ ♥rsã♦ ♥st t♥ê♥
st♦ é ♦s ♠♥♦rs â♥♦s ♥♥çã♦ ♥ã♦ ♦r♠ ♦s q ♣rs♥tr♠ s ♠♥♦rs
q♥ts ♦s Nu Cp ♦♥stt♦s q st ♦♦rrê♥ s à ♦r♠
çã♦ t③ ♥ rçã♦ s ♦♠tr q ♣r♦③ ♠ rstrçã♦ ár ♠♦r
♦ q ♠♣♦st ♣ r③ã♦ ♦q♦ ts
♠♥r ♦ s ♣rs ♥r ♠â♥ ♦ s♦♠♥t♦ ♦♥srr♠
♦ t♦ ♦ rrst♦ s♦s♦ q ♦♦rr ♥s s♣rís sós ♣rs ts
♥tr♥♠♥t ♦ ♦ ♥s Pr t♥t♦ t③♦s ♦ ♦♥t ♣rssã♦
Cp q ♦ tr♠♥♦ ♣r ♦ tr♦ ♥ ♥tr sçã♦ ♥tr ♠
sçã♦ x = 30H ♦ ♦ ♥♠♥t♦ s ts ♦ ♦♥t ♣rssã♦ Cp
♣r ♦ rr♥♦ ♥♦ ♦ s♣r♦r ♦ ♦s s♦s rr♥♦ s♥♦ té r
③s ♣r rba = 0,4 b = 3H ♦♥t♦ ♦s ♠♦rs ♦rs Cp sã♦
♥♦♥tr♦s ♣r ♠♦r r③ã♦ ♦q♦ ♦♥rçã♦ s♥ Pr ♦
t♦ s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s á ♠ rçã♦ qrát ♥tr
rçã♦ ♦ ♥tr ♥♦ ♥ ♦ rs♣t♦ Cp ♦
♦r♠çã♦ ♦ ♥ú♠r♦ sst ♦ ♣r ♦ s♦♠♥t♦ ♦ ♦r ♣r
r ♠ ♦♥srçã♦ ♦ t♦ ár s♣r tr♦ tér♠ s ts ♦♥
sr♥♦ s r③õs ♦q♦ t ♦♠♥s ♦s ♦s rr♥♦s rba = 0,2
rba = 0,4 ♦♥rçã♦ ♥ ♣rs♥t♦ ♠ s♠♣♥♦ r s♣
r♦r P♦ré♠ sts q ♦s ♠♦rs ♦rs ♥♦♥tr♦s ♣r ♦ sst ♠é♦
♦r♠ ♣r ♦♥rçã♦ s♥ ♥ r③ã♦ ♦q♦ rba = 0,6 rçã♦
s ♦♥çõs r♦♥â♠s rst ♠ ♠♥t♦ té ♦ sst ♠é♦
❼ tr♥srê♥ ♦r ♦♥
çã♦ tr♦ tér♠ ♦r♠ ♦♥ ♣r♠t r ♦s r♥ts
t♦s s rçõs ♦♠étrs r♦♥â♠s s♦r strçã♦ t♠
♣rtrs ♥♦ ♦♠í♥♦ só♦ ♥s s rst♦s ♥ ♦r♠ ♦♥t♦r♥♦s
t♠♣rtr ♠♦strr♠ ♦ ♠s♠♦ ♦♠♣♦rt♠♥t♦ ♣r ♠♦s ♦s rr♥♦s ♠♦rs
rçõs tér♠s sã♦ ♦srs ♥s ts ♦♠ ♠♥çã♦ ♦ â♥♦ ♥
♥çã♦ β → 0 ♦♠ ss♦ ♦s r♥ts tér♠♦s q ♣r♠ ♥s ♣rs s
♦♥♥tr♠ ♥s ♣r♦①♠s s ss s ts Pr stçã♦ ♦♥trár ♥s
qs s ts ♣rs♥t♠ ♠♦rs â♥♦s ♥♥çã♦ ♦s r♥ts t♠♣
rtr sã♦ ♠s ♦♠♦ê♥♦s ♦ ♦♥♦ s ♣rs ♦ ♥
♦♠♦ ♠ ♦s ♣r♥♣s rst♦s ♣♦ssís ♥ç♦s s♦♠♥t trés ♥ás
tr♥srê♥ ♦r ♦♥ ♥♦♥tr♦s q tr♦ tér♠ trés s
ts é ♠ ♠é ♠♦r ♥♦s s♦s ♦ rr♥♦ ♥♦
t♥ê♥ srt ♠ ♦ r ♣r ♦s rst♦s q q♥tr♠
♣r ♦ ♦r t♦t tr♦♦ trés s s♣rís s ts trés ♦s qs
s ♦♥stt♦ q q♥t♦ ♠♥♦r ♦ â♥♦ ♥♥çã♦ β → 0 ♠♦r ♥ê♥
s ts ♥ tr♦ tér♠ ♦ st ♦rrçã♦ é t q ♣r ♦ ♠♥♦r â♥♦
♥♥çã♦ t β = 18 ♦ rr♥♦ s♥♦ ♠s ♠t ♦ ♦r
tr♦♦ ≈ 67% ♦♦rr trés s ts ♣r rba = 0,6♦♠ s ♥s q♥ts ♦s ♥ás ♣♦r ♠♦ s r③õs ♦ ♥ú♠r♦
sst ♦ ♦♥t ♣rssã♦ ♥tr ♦s rr♥♦s ♥ ♠ ♣rá rçã♦ ♥tr
s♠♣♥♦ tér♠♦ r♦♥â♠♦ ♣r ♦ rr♥♦ s♥♦ ♦♠ ♠♥♦r s♣ç♠♥t♦
♥tr ts ♠♦rs â♥♦s ♥♥çã♦ t ♥♠♥t ♥t ♦ ♣♦t♥
♦♥stt♦ ♦ s♦ ts ♣r ♦ ♥r♠♥t♦ ♥♦ ♣r♦ss♦ tr♥srê♥ ♦r
♠ ♥s ♦♠♥tár♦s s♦r ♣rs♣ts trs sr stã♦ ♦♠♥t♦s ♥s
s♣t♦s q ♣♦♠ sr ①♣♦r♦s
❼ s♣t♦s ♦♠étr♦s
é♠ s rtrísts ♥sts ♥st tr♦ srs ①♣♦rr ♦ t♦
r♥ts trçõs ♦♠étrs ts ♦♠♦ r♥ts s♣ç♠♥t♦s ♥tr ts
r♥ts trs t ♦r♠ ♥♣♥♥t r③ã♦ ♦q♦ t
♥s r♥ts ♦r♠t♦s t s ♥ã♦ ♣rs sts ♣râ♠tr♦s
♣♦♠ trr t♦♣♦♦ ♦ s♦♠♥t♦ ♦r♠ s♥t t♥♦ ♦r♠
çã♦ s ③♦♥s rrçã♦ ♦③çã♦ ♦s ♣♦♥t♦s r♦♠♥t♦ ♦♥♦r♠
♣rs♥t♦ ♥ sçã♦ ♦s rst♦s st♦ ♠♣ ♠ ♠♦çõs s♥ts ♥
strçã♦ t♠♣rtrs t♥t♦ ♦ só♦ q♥t♦ ♦ ♦ tr♥t♠♥t
sts ♠s ♦♠étrs ♣♦♠ sr rs ♥tr♦ ♠ ♠s♠♦ s♦ ♣♦r ①♠
♣♦ t③♥♦ t♠♥♦s t rás ♦ ♦♥♦ ♦ ♥ sts q ♥tr
♦tr♦s ♣♦ssís s♣t♦s ♦♠étr♦s rçã♦ s♣ssr t ♥ã♦ ♣rs♥t
♣♦t♥ ♥♦tá ♦r♦ ♦♠ ♦s rst♦s Prã♦ t
❼ s♣t♦s ♥s♦tró♣♦s
é♠ s rtrísts ♦♠étrs srs ♥stçã♦ r♥ts ♠trs
♦♥strçã♦ ♦ tr♦♦r ♦r r♥ts ♣çõs ♠ ♠♦s ♦s s♦s á
♣♦ss ♦♥srr ♣♥ê♥ s ♣r♦♣rs tér♠s ♦♠ ♦ ♠♣♦
t♠♣rtrs ♥s♦tr♦♣ t♥t♦ ♣r ♦ só♦ q♥t♦ ♣r ♦ ♦ ♠♣♥♦
r♥ç t♠♣rtrs s ♦♥çõs ♦♥t♦r♥♦ ♦♠ rçã♦ à ♥s♦tr♦♣
♥ t♠s ♣♦ss tr♠♥r ♦s t♦s ♦ tr♥s♣♦rt s q♥ts
tr♥ts ♦r♠ ♥s♦tró♣ ♣♦r ♠♦ ♦ ♦♦ ♥sõs ②♥♦s ♦
♦ ♥ês ②♥♦s trss ♦ ♣♦r ①♠♣♦ srs q ♣r ♦
s♦ ♦ s♦ ♦ ♠♦♦ rqr çã♦ st qçõs tr♥s♣♦rt
♠s♠ ♦r♠ q ♦♥srçã♦ ♦s t♦s ♦ à ♥s♦tr♦♣ ♦♥srçã♦
♣r♦tót♣♦s rts ♠ t♠é♠ ♥rq ♥ás rá ♦s rst♦s
❼ s♣t♦s tr♠♥s♦♥s
♦♠♦ ♦♥sê♥ ♣óts ♠♥s♦♥ ♦ s♦♠♥t♦ ♦ s♠♣♦ ♣r
çã♦ ♦ s♦♠♥t♦ ♣r♥♣ st♦ é s♣r③r♠s ♦s t♦s ♦s s♦♠♥t♦s
s♥ár♦s ♥trçã♦ ♦ ♦ ♦♠ s ♣rs trs ♦ ♥ rs♥tr
rtrísts ♠s r♣rs♥tts trê♥ q é ♥tr♠♥t ♠♦r
tr♠♥ trés ♦r♠çã♦ ♠t♠át tr♠♥s♦♥ ♠♥t♦ s
rás ♦ ♣r♦♠ t♦r♥ ♦ s♦ ♦t♠③çã♦ ♠ ♦♣çã♦ ♥ ♠s ♣r♦♠ss♦r
❼ s♣t♦s ót♠♦s
♦ ♦ r♥ ♥ú♠r♦ rás ♥♦s ♥♦ ♣r♦t♦ tr♦♦rs ♦r
♦ às rtrísts ♦♥ô♠s ♣çã♦ ♦ tr♠♥çã♦ ♦♠tr
♦♥çõs ♦♣rçã♦ ót♠ rqr t③çã♦ té♥s ♦t♠③çã♦ ét♦
♦s ♦t♠③çã♦ ♦♥sst♠ ♥ tr♠♥çã♦ ♣râ♠tr♦s ♦ ♣r♦♠ trés
♠♥♠③çã♦ ♠ ♥çã♦ st♦ ♥ ♣rtr ♠s tr♦
♦r ♣r r rçã♦ ♥tr♦♣ st♦ ♦♥ô♠♦ ♠ss t♦t ♦ tr♦♦r
♦r ♦ ♦tr♦ ♣râ♠tr♦ rtríst♦ ♣çã♦ s á ♠ r♥
r strtés ♦t♠③çã♦ ♥tr s ♠ét♦♦s s♦s ♠ r♥t
r ♥çã♦ st♦ ♠ rçã♦ às rás ♥trss ♠ét♦♦s ♥s♣r♦s
♥ ♥tr③ ts ♦♠♦ ♦s ♦rt♠♦s ♥ét♦s ♠ét♦♦s s rt st
♦r♠ srs ♦♠♦ tr♦ s♥♦♠♥t♦ ♦ st♦ ♣çã♦ strtés
♦t♠③çã♦ st ss ♣r♦♠s
srs q é♠ strté st♦ ♦t ♣r sr tr♦♦rs
♦r ♦♠ ♠♦r s♠♣♥♦ é r♦♠♥á ♦tr ♠ t♦r q ① ♥tr
♠♦r ♦♥rçã♦ ♠♦r ♣r♥♣ ♠♦tçã♦ s ♥♠ ♣r♠r♦ ♠♦♠♥t♦ ♦
♠♥t♦ tr♥srê♥ ♦r ♦r♠çã♦ ♠ t♦r q♦ ♥ çã♦
♥♦♦s tr♦♦rs ♦r ♣♦rá r ♠ ♦♥srçã♦ ♦tr♦s s♣t♦s ♦♠♦ ♦s
rçã♦ ♦♣rçã♦ ♠♥t♥çã♦ t
s♣t♦s ♥â♠ ♦s ♦♠♣t♦♥
Pr ♦tr s♦çã♦ ♣r♦♠s ♣rát♦s ♥♥r ♥♦♥♦ ♦ s♦♠♥t♦
♦s ♠ ♦r♠ ♥♠ér sr ♦t ♥ q s qçõs r♥s ♦
♣r♦♠ sã♦ ssttís ♣♦r ♣r♦①♠çõs érs rs♦s t③♥♦s ♠
♠ét♦♦ ♥♠ér♦ ❯♠ ③ q ♥st tr♦ t③♦s ♠ ♣r♦r♠ ♦♠r ♦s t♥s
s♥ts t♠ ♣r rtr③çã♦ s ♣r♥♣s ♥çõs ♣s à rr♠♥t
t③ ♥ s♦çã♦ ♦ ♣r♦♠ s♠♥t
rçã♦ ♠ ♥♠ér
t③çã♦ ♠ ♠ ♦♠ qs ♦♠étrs qs é ♣rt ♥
♠♥t ♥♦ ♦♥tr♦ ♦s rr♦s srt③çã♦ ♠♥t ♠♣♦rt♥t ♣r tr rr♦s
rr♦♥♠♥t♦ r♥t ♣♦r ①♠♣♦ s♦çã♦ s qçõs ♥rs q sã♦ ♦ts
♣♦ ♣r♦ss♦ srt③çã♦ ❩ P st tr♦ t③♦s ♦
r♦r ♠s ♥s②s s♥ ♣r t♦♦s ♦s s♦s
r stã♦ strs três ♦♥srçõs áss sttíst ♠
♣r ♦ CFX rs ♣♦ ó♦ ♥♠ér♦ ♣r♠♥t à ①çã♦ ♦ ♦rt♠♦
s♦çã♦ ♦ sst♠ ♥r ♦♥♦r♠ str♦ t♠s
❼ q ♦rt♦♦♥ ♥♦ s♦ r q ♦rt♦♦♥ ♣r ♠ ♠♥t♦ é ♦♠
♣t t③♥♦ ♦ t♦r ♥♦r♠ Ai ♦ t♦r q ♥ ♦s ♥trós
♠♥t♦s ♥ts ci ♦ t♦r q ♥ ♦ ♥tró ♦ ♠♥t♦ ♦ ♥tró
♠ ss s fi s q♥ts ♦♠♣ts ♣r sã♦ ♦
♦ss♥♦ ♦ â♥♦ ♥tr ♦ t♦r Ai ♦ t♦r ci ♦ ♦ss♥♦ ♦ â♥♦ ♥tr ♦ t♦r
Ai ♦ ♦ t♦r fi ♦r ♠í♥♠♦ ♦t♦ ♦ á♦ sts q♥ts ♣r t♦s
s s é ♥♦ ♦♠♦ q ♦rt♦♦♥ ♦ ♠♥t♦ s ♣♦rs ♠♥t♦s
♠ sã♦ ♦s q ♣rs♥t♠ st ♠étr ♣ró①♠ ③r♦ ♥q♥t♦ q ♣r ♦s
♠♦rs q ♦rt♦♥♦ é ♣ró①♠ ♠ P♦rt♥t♦ ♦ ♦♥t♦ ♦rt♦♦
♥ ♠ stá r♦♥♦ ♦ q♥t♦ ♦s â♥♦s ♥tr s s ♥ts
♠ ♠♥t♦ ♦ r♦♥trs ♥tr ♠♥t♦s ♥ts s ♣r♦①♠ ♦ â♥♦
ót♠♦ 90 ♣r ♠♥t♦s qrtrs ❨
❼ t♦r ①♣♥sã♦ ♦ ♦♥t♦ ①♣♥sã♦ ♠ stá r♦♥♦ ♦♠ t①
♠♥ç ♥ ♠♥t ♦s ♦♠s ♦ s árs ♠♥t♦s ♥ts
♠ ♠s r♥t ①♣♥sã♦ ♠ ♣r ♦ CFX♥♦ r③ã♦ ♥tr
stâ♥ ♠á①♠ stâ♥ ♠í♥♠ ♥tr ♦ ♥ó ♦ ♦♠ ♦♥tr♦ s ss
r♦♥trs ❯♠ ♦r♠çã♦ tr♥t é t③ ♥♦ s♦ ♦♠s ♦♥tr♦
r s ♦♠étrs r♥ts ♣r ♦ CFX rs ♥ts ①çã♦♦ ó♦ ♥♠ s♠çã♦ ♥♠ér
q ♦rt♦♦♥
A3
A1 A2
c2
c3
c1
f1
f2f3
t♦r ①♣♥sã♦
dmin
dmax
volume mín.
do setor
volume máx.
do setor
r③ã♦ s♣t♦
Amin
Amax
♦♥t ♣t♦ ❨
♦r♠s rtrárs q é r③ã♦ ♥tr ♦ ♠á①♠♦ ♦ ♠í♥♠♦ ♦♠s ♦s ss
st♦rs ❨
❼ r③ã♦ s♣t♦ ♦ str♠♥t♦ ♦ ♦♥t♦ r③ã♦ s♣t♦ ♠ stá
r♦♥♦ ♦♠ ♦ r q ♦s ♠♥t♦s ♠ sã♦ str♦s ♠ ♠s
r♥t q♥t♦ à r③ã♦ s♣t♦ ♠ ♣r ♦ CFX ♥♦ r③ã♦ ♥tr
♠á①♠ ♠í♥♠ árs s♣rs ♦♠ rçã♦ ♦s ♣♦♥t♦s ♥trçã♦ ❨
é♠ ♠♣♦rtâ♥ ♦ q ♠ é ♥ssár♦ ssrr ♥♣♥
ê♥ s♦çã♦ ♥♠ér ♦♠ rçã♦ à ♠ st♦ é r③♦ ♣♦r ①♠♣♦ trés
♦ st♦ r♥♦ ♠ Pr t♥t♦ r③s ♠ sqê♥ s♦s ♦♠ rçã♦
♥♦ ♥ú♠r♦ ♦s ♠♥t♦s ♠♥t♦ ♦ ♥í r♥♦ ♠
tr♦ s♣t♦ ♥♠♥t râ♥ ♣r rçã♦ s ♠s ♥♦s s♦s
♦♥â♠ ♦♠♣t♦♥ é ♦ ♥í ♦ r♥♠♥t♦ ♥s rõs ♥t♦ às s♣rís
st ♣r♦♠♥t♦ s ♦s rr♦s tr♥♠♥t♦ ①ê♥s ♦ ♠♦♦ trê♥
t③♦ ♦ s♦ ♣r ♦ ♠♦♦ trê♥ s♦♦ ♦ r♥♦ ♠
♦r à ♦♥çã♦ y+ < 1,0
ét♦♦ ♥♠ér♦ ♦r♠ ❱
st tr♦ s♦çã♦ ♣r s rás ♣♥♥ts s qçõs r♥s
♦♥srçã♦ ♦ tr♥s♣♦rt q r♣rs♥t♠ ♦ ♣r♦♠ ís♦ é ♦t ♣♦ ♠ét♦♦
♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês ♠♥ts ♥t ❱♦♠ t♦
❱
♣♦♥t♦ ♣rt ♦s ♠ét♦♦s ♦♠s ♥t♦s é ♥trçã♦ s qçõs
♦♥srçã♦ s♦r ♠ ♦♠ ♦♥tr♦❱ ♣ós ♣çã♦ ♦ ♦r♠ rê♥
♦ ♦r♠ ss q ♦♥rt ♥trs ♠ ♦♠ ♣r ♥trs ♠ s♣rí
s qçõs ♠ sr srt③s s ♥trs ♠ ♦♠ sã♦ srt③s ♣r
s♦♠ ♠s ♣r ♦ ❱ ♦ q ♦ st♦r ♣rt♥ s ♥trs ♠ s♣rí
sã♦ srt③s ♥♦s ♣♦♥t♦s ♥trçã♦ pi ♦③♦s ♥♦ ♥tr♦ s♠♥t♦
s♣rí ♠ ♠♥t♦ ♠ ♥tã♦ strís ♣r ♦s ❱s ♥ts
♦♠♦ s ♥trs s♣rí sã♦ s ♦♣♦sts ♣r ❱s ♥ts ♦s ♣♦♥t♦s
♥trçã♦ s ♦♥srçã♦ ♦ é ssr ❨
r str ♦♥strçã♦ ♠ ♦♠ ♦♥tr♦ ❱ ♥♦ q s
rás ♣♥♥ts s ♣r♦♣rs ♦ ♦só♦ sã♦ r♠③♥s ♥♦s érts
♦s ♠♥t♦s ♠ ♠ ♥ã♦strtr st rtríst sr ♥♦♠♥çã♦
s ♦r♠çã♦ ♥tr ♥♦s érts ♦ ♥ês rt① st é ♦r♠çã♦
t③ ♣♦ ♠ét♦♦ ❱ ♦ ♣♦í♦♥♦ q ♦r♠ ♦ ♦♠ ♦♥tr♦ t③ s
ssõs ♦s ♠♥t♦s q ♣♦ss♠ ♠ ♠s♠♦ ért ♠ ♦♠♠ P
s s♦♠s ♦♥tr♦ ♦ ♠ ♠♥t♦ ♠ ♦
♣♦♠ sr ♥♦s ♥♦s ♦ ♣♦♥t♦ ♠é♦ ♦s ss ♦s ♦♠ ♦ s r♥tr♦
st ♦r♠ ♠ ♠♥t♦ qrtr ♣♦ssrá s♠♣r qtr♦ s♦♠s ♦♥tr♦
♥ ♣♦ sr st♦ ♥ r ♦s ♠♦s ♣♦♥t♦s ♥trçã♦ ♣ t③♦s
♥♦ á♦ ♦s ①♦s ♥s s ♦ ♣♦í♦♥♦ q r♣rs♥t ♦ ♦♠ ♦♥tr♦ ❱
é♠ ss♦ ♣r srr rçã♦ ♠ rá qqr ♥tr♦ ♠ ♠♥t♦
♦ ♠ét♦♦ t③ s ♥çõs ♦r♠ ♦s ♠♥t♦s ♥t♦s
r ♦♥strçã♦ ♦ ♦♠ ♦♥tr♦ ❱ s♥♦ ♦r♠çã♦ ❱
A
B
C
D
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
♥çõs ♦r♠
♦ ♠ét♦♦ ❱ t♦♦s ♦s á♦s sã♦ t♦s ♠ ♥í ♦ ♥tã♦ ♠♦♥t♦s
♠ ♠ ♠tr③ ♦ ♣r♥í♣♦ tr♥s♦r♠çã♦ ♦♦r♥s ♦s ♣r ♦♦r
♥s ♦s é str ♥ r q ♠♦str ♠ ♠♥t♦ ♠ rtrár♦ ♥♦
sst♠ ♦♦r♥s ♦s x y ♥ r ♦ rs♣t♦ ♠♥t♦ ♣rã♦
♥♦ sst♠ ♦♦r♥s ♦s ξ η ♥ r ♦♠♥t t♦♦s ♦s ♥ós ♣r
q t♣♦ ♠♥t♦ qrtr srã♦ ♥♠r♦s té ♣♦r ♠♦ ♠
t ♦♥t r♦♥♦s ♦♠ ♦s ♥ós ♥♠rçã♦ ♦
r r♥s♦r♠çã♦ ♥tr s ♦♦r♥s ♦s ♦ sst♠ s ♦♦r♥s♦s t③s ♣s ♥çõs ♦r♠
3
2
1
1
4 43
2
2
2
3
3
4
4
1
1
x
y
(a) (b)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
s♦ s ♥çõs ♦r♠ Ni ♣r♠t ①♣rssr ♠ ♦♦r♥s ♦s q
qr ♣♦♥t♦ ♦③♦ ♥♦ ♥tr♦r ♠ ♦ ♠♥t♦ ♦r♦ ♦♠ s tr♥s♦r♠çõs
♥rs sr
x(ξ, η) = 4∑j=1
Nj(ξ, η)xj,y(ξ, η) = 4∑
j=1
Nj(ξ, η)yj
♥s qs Nj r♣rs♥t s ♥çõs ♦r♠ ξ η sã♦ s ♦♦r♥s ♦s xj yjsã♦ s ♦♦r♥s ♦s ♦s ♥ós ♥♦s érts ♦ ♠♥t♦ ♦r♦ ♦♠ ♥♠rçã♦
♦
Pr ♦ ♠♥t♦ qrtr r ♦ ♦♥♥t♦ qçõs ♥
s ss ♥çõs ♦r♠ st ♦♥♥t♦ qçõs ♦ ♥tr♦ rçã♦ s ♦♦r
♥s ♦s ♥♦ ♥tr♦r ♦ ♠♥t♦ ♣rã♦ r ♥♠r♠♥t ♣rsr♠
rá rr ♦ ♣♦♥t♦ ♠é♦ ss♠ s ♦♦r♥s ♥♦s ♣♦♥t♦s ♥trçã♦
♥st t♣♦ ♠♥t♦ srã♦ (12,0) (0, 1
2) (1
2,0) (0, 1
2)
N1(ξ, η) = 1
4(1 + ξ)(1 + η),
N2(ξ, η) = 1
4(1 − ξ)(1 + η),
N3(ξ, η) = 1
4(1 − ξ)(1 − η),
N4(ξ, η) = 1
4(1 + ξ)(1 − η)
r♠♦s s♦s
s rs s♣s ♣r t♦♦s ♦s tr♠♦s s♦s sã♦ s ♥♦s ♣♦♥t♦s
♥trçã♦ t③♥♦ s ♥çõs ♦r♠ s♥♦ ♦r♠ tr♦♥ ♠♥t♦s
♥t♦s
∂Λ
∂x∣ξ, η
= ∑j
∂Nj
∂x∣ξ, η
Λj
∂Λ
∂y∣ξ, η
= ∑j
∂Nj
∂y∣ξ, η
Λj
♥s qs Λ é ♠ rá ♥ér s♦♠tór♦ é ♦♠♣t♦ s♦r t♦s s ♥çõs
♦r♠ ♣r q ♠♥t♦ s rs rts♥s s ♥çõs ♦r♠ ♣♦♠
sr ①♣rsss ♠ tr♠♦s ss rs ♦s trés ♠tr③ tr♥s♦r♠çã♦
♦♥
⎡⎢⎢⎢⎢⎣∂N1
∂x⋯∂Nj
∂x∂N1
∂y⋯∂Nj
∂y
⎤⎥⎥⎥⎥⎦= ⎡⎢⎢⎢⎢⎣
∂x∂ξ
∂y
∂ξ
∂x∂η
∂y
∂η
⎤⎥⎥⎥⎥⎦
−1 ⎡⎢⎢⎢⎢⎣
∂N1
∂ξ⋯∂Nj
∂ξ∂N1
∂η⋯∂Nj
∂η
⎤⎥⎥⎥⎥⎦
♥ q ♠tr③ ♦♥ é ♣♦r
[J] = ⎡⎢⎢⎢⎢⎣∂x∂ξ
∂y
∂ξ
∂x∂η
∂y
∂η
⎤⎥⎥⎥⎥⎦
①♣rssã♦ ♠tr ♣r ♦ r♥t ♠ rá ♥ér Λ ♣♦rt♥t♦ é
♦t ♣rtr ♦♠♥çã♦ s qçõs
[Λ] = [J]−1[Θ][Λ]
s♥♦ [Θ] ♠tr③ s rs s ♥çõs ♦r♠ ♦♠ rçã♦ às rás ♦s
r♠♦s ♦♥t♦s
s tr♠♦s t♦s rqr♠ q ♦s ♦rs rá ♥♦s ♣♦♥t♦s
♥trçã♦ s♠ ♣r♦①♠♦s ♠ tr♠♦s ♦s ss ♦rs ♥♦s s sq♠s
çã♦ ♣♦ss♠ s♥t ♦r♠ ①♣rss ♣r rá ♥ér Λ
Λpi = Λup + ϑ∇Λ ⋅∆ri
♥ q Λup é ♦ ♦r ♥♦ ♥ó ♠♦♥t♥t ri é ♦ t♦r ♣rtr ♦ ♥ó ♠♦♥t♥t té ♦
♣♦♥t♦ ♥trçã♦ ♣
s♥♦ tr♠♦ ♦ ♦ rt♦ qçã♦ é ♠♦ ♦rrçã♦ ♥♠é
r t st tr♦ ♦rrçã♦ t③ é ♦ sq♠ t rs♦çã♦
rs♦t♦♥ s♠ q ♦♥sst ♠ ór♠ ♥ã♦♥r s♣ ♣r ϑ ♠ ♥ó
♦♠♣t♦ ♣r sr ♦ qã♦ ♣ró①♠♦ ♣♦ssí ①♦ t♦ é ♦ t③♥♦
♦rs ϑ Λ ♣rtr ♦ ♥ó ♠♦♥t♥t ór♠ ♣r ♦ ϑ é s♦ ♠ rtér♦s
♠tçã♦ P ♣ ❨
♦♣♠♥t♦ ♣rssã♦♦
❯♠ ①♦ ♠áss♦ srt♦ trés ♠ s♣rí ♦ ♦♠ ♦♥tr♦ é ♦
♣♦r
mpi = (ρfuj∆nj)pi
s♥♦ uj ♦♠♣♦♥♥t ♦ ∆nj ♦ t♦r srt♦ ♥♦r♠ s♣rí ♣♦♥
t♥♦ ♣r ♦r
♦r♠ srt③ s qçõs rt♦s ♣r s♦çã♦ ♦ ♠♦♠♥t♦
sr ♣♥ê♥ ♥r ♦ ♦♠ ♣rssã♦ rs st ♦r♠
♣rssã♦ sr ①trí s qçõs ♠♦♠♥t♦ ♣r q s ♦s stsç♠
♦♥srçã♦ ♠ss ♦♥t♦ é ♣♦ssí rs♦r sts qçõs
♠♥r ♦♣ trés ♠♦♥t♠ ♠ ♠tr③ s♦çã♦ q ♣r♠♥ ú♥
♦r♠çã♦ ♣rã♦ ♦ CFXé rst♥t ♦ tr♦ ❲ st
srt③çã♦ tr♥t ♦ ①♦ ♠ss t ♦ s♦♣♠♥t♦ ♣rssã♦♦ ♥
♠ ♦♦③ ♥r♥t ♦ ♣r♦r♠ ♦♠♣t♦♥
s♥t ①♣rssã♦ ♣r ♦ ♦♥t é t③ ♠ ♣♦♥t♦
♥trçã♦
ui,pi = ui,pi + fpi ⎛⎝ ∂p∂xi ∣pi −∂p
∂xi∣pi
⎞⎠ − cpifpi(uoi,pi − uoi,pi)
♥ q
fpi = dpi
1 − cpidpi , dpi = VA, cpi = ρf
∆t
s♥♦ A ♣r♦①♠çã♦ ♦ ♦♥t ♥tr qçã♦ q♥t ♠♦♠♥t♦
①♥♦ ♦ tr♠♦ tr♥s♥t srs q ♥st s♦ s rrs s♦r s rás
♥♠ ♠ ♠é s♦r ♦s ♦rs ♥♦s érts ♥ts ♦s ♣♦♥t♦s ♥trçã♦ á
♦ s♦rsrt♦ o ♥♦t ♦rs ♥♦ ♣ss♦ t♠♣♦ ♥tr♦r
sst♠ ♦♣♦ qçõs
♦♥♥t♦ qçõs ♥rs q é ♦r♥♦ ♣ ♣çã♦ ♦ ❱ é ♠
♦♥♥t♦ ♦♥♥t♦ qçõs srts ♦♥srçã♦ srt♦ ♥ ♦r♠
∑nbi
anbi φnbi = Bi
s♥♦ φ s♦çã♦ B ♦ ♠♦ ♦ rt♦ a ♦s ♦♥ts qçã♦ i ♦ ♥ú♠r♦
q ♥t ♦ ♦♠ ♦♥tr♦ ♦ ♥ó ♠ qstã♦ nb r♣rs♥t ♦s ③♥♦s ♠s
t♠é♠ ♥ ♦ ♦♥t ♥tr ♠t♣♥♦ s♦çã♦ ♥ és♠ ♣♦sçã♦ ❨
Pr ♦ sst♠ ♦♣♦ ♦ ♦♥♥t♦ qçõs ♠ss♠♦♠♥t♦ tr♠♥s♦♥
é ①♣rss♦ ♣♦r
anbi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
auu auv auw aup
avu avv avw avp
awu awv aww awp
apu apv apw app
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
nb
i
, φnbi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
u
v
w
p
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
nb
i
Bi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
Bu
Bv
Bw
Bp
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦i
♦♠♦ strté s♦çã♦ ♦ CFXt③ ♠ sq♠ ♦♣♦ q s♦♦♥
s qçõs r♦♥â♠s ♦s ♣rssã♦ ♥♠ ú♥♦ sst♠ st ♦r♠
t③ ♠ srt③çã♦ t♦t♠♥t ♠♣ít s qçõs ♥♦ t♠♣♦ Pr ♣r♦♠s
st♦st♦♥ár♦ ♦ ♣ss♦ t♠♣♦ s ♦♠♣♦rt ♦♠♦ ♠ ♣râ♠tr♦ rçã♦
q ♦♠ s ♠ ♦♥srçõs íss ♦♥③ s s♦çõs ♣r♦①♠s ♣r s s♦çõs
♦ st♦ st♦♥ár♦ st♦ r③ ♦ ♥ú♠r♦ trçõs ♥ssárs ♣r t♥r ♦♥
rê♥ Pr rs♦r ♦ sst♠ srt♦ s qçõs ♥r③s CFXt③ ♠
té♥ t♦rçã♦ ❯ ♥♦♠♣t ♦♠ r♦r ♠tr
rtér♦ ♣r ♦ rtér♦ ♦♥rê♥ ♦t♦ ♣r t♦s s s♠çõs
r③s ♥st tr♦ ♦ ♠é qrát ♦ rsí♦ ǫRMS ≤ 1 × 10−6é♠ ss♦ ♣ós s t♥r st rtér♦ t♦s s s♠çõs ♦r♠ rs q♥t♦ ♦
♠♥ q r♣rs♥t ♦♥srçã♦ q♥t tr♥s♣♦rt trés ♦ ♦♠í♥♦
s q♥ts ♠♦♥t♦rs q♥t♦ ♦ rtér♦ ♣r ♣♥♠ s qçõs q
stã♦ s♥♦ rs♦s ♥ s♠çã♦ ♥♠ér
♦♥çõs ♦♥t♦r♥♦
tr♦ ♠♣♦rt♥t s♣t♦ ♥â♠ ♦s ♦s ♦♠♣t♦♥ sã♦ s ♦♥
çõs ♦♥t♦r♥♦ s s♠çõs ♥♠érs s t♣♦s ♦♥çõs ♦♥t♦r♥♦ ♠s
rq♥t♠♥t t③s sã♦ ♦ rt ♦ ♠♥♥ ♦♥çã♦ ♦♥t♦r♥♦
♦ t♣♦ rt rtr③s ♣ s♣çã♦ ♦ ♦r s rás ♥♦s ♥ós ♦♠♣
t♦♥s s r♦♥trs ♥♦ s ♦♥çõs ♦♥t♦r♥♦ ♥♦♠ rs ♦♥çõs
♠♥♥ s ♠ sr srt③s ♦♥tr♥♦ ♦♠ ♠ qçã♦ ♦ ♦♥♥t♦
qçõs q sr rs♦♦ ♥ s♠çã♦ ❩ P
♦♥çã♦ s♠tr t♠é♠ ♦ t③ ♠ t♦♦s ♦s s♦s st é ♠
♦♥çã♦ ♦♥t♦r♥♦ ♦♥ t♦s s rás ①t♦ ♦ sã♦ ♠t♠t♠♥t
s♠étrs ♥ã♦ ♣♦ r sã♦ ♦ s♦♠♥t♦ trés r♦♥tr s ♦s
♣rs st r♦♥tr t♠é♠ sã♦ s♠étrs s ♦s ♥♦r♠s ♦ ♣♥♦ sã♦
♥s ❨
♦♦ trê♥
♠♦♦ trê♥ t♠ r♥ ♠♣t♦ ♥ ♥ás ♥♠ér ss♠ ♦♠♦
♠ s ♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs íss ♦ trt♠♥t♦ ♦♣♦ s♦çã♦
tér♠ t
♦♥♦r♠ ♦♥stt♦s ♥ rsã♦ ♦s tr♦s rrê♥ ♥♦ ♣ít♦
♠s ♠ ♠♦♦ trê♥ ♦ t③♦ ♥qs st♦s s♦ ♦ ♠♦♦
trê♥ ♦♥sr s♣t♦s té♥♦s ♦♥ô♠♦s ts ♦♠♦ ís ♣rs♥t ♥♦
♣r♦♠ sr rs♦♦ ♦ st♦ ♦♠♣t♦♥ ♣♦r ①♠♣♦
st tr♦ ss♠s ♣óts ♦ss♥sq ♣r ♠♦♠ s♦
s tr♥t ♦ ♠♦♦ ír♦ ♥tr ♦ s♦♥♦ ♣r rs♦ê
sr ♥ ♣óts ♦ss♥sq s♦s tr♥t é ♠ ♣r♦♣r ♦ s♦
♠♥t♦ ♣♦rt♥t♦ ♥sst ♠♦♠ ♠t♠át s s♣♠♥t ♠ q
♠ ♦♥srçã♦ ♦ stór♦ ♦ s♦♠♥t♦ ♠ s ♦♠♣r♠♥t♦ tr♥t
st♦ r ♦ t♦ q s♦s tr♥t é ♦♥sr ♠♥r ♥á♦ à
s♦s ♠ ás ♣rt♦ s♥♦ t♦r ♥ét ♦s ss P♦rt♥t♦ s♦s
tr♥t ss♠ ♠ ①♣rssã♦ ♥♦ s♥t ♦r♠t♦
µt = ρfvtlt
♥♦ q lt vt sã♦ q♥ts rtrísts s trê♥ ♦ ♣r♦♠
♦♠♣r♠♥t♦ ♦ rs♣t♠♥t
❯♠ ♦♥t♦ stór♦ ♥♠♥t ♥♦ s♥♦♠♥t♦ s qçõs trê♥
♦ ♦ ♦♠♣r♠♥t♦ ♠str ❲❳ t st ♣r♦♣♦sçã♦ Pr♥t
♦r♠ ♦ ♠♦♦ ér♦ trê♥ ♠s tr ♠ ♦ ♠s♠♦ Pr♥t ♦♥
♦ ♠♦♦ trê♥ ♠ qçã♦ ♥tr♦③♥♦ ♦ ♦♥t♦ ♥r ♥ét
s tçõs tr♥ts κ
♠ ♦♠♦♦r♦ s♥♦ ♦ ♣r♠r♦♠♦♦ trê♥ ♦♠♣t♦ ♦♥
sr♥♦ ♦ ♣râ♠tr♦ ♦♥ ω t① ss♣çã♦ ♥r ♣♦r ♥ t♠♣♦
♦♠ é♠ ♦ κ ❲❳ t ❯♠ ♠♦♦ trê♥ ♦♠♣t♦ é t♠é♠
♦♥♦ ♦♠♦ ♠♦♦ trê♥ s qçõs ♣♦s sã♦ ♥tr♦③s q♥ts
r♣rs♥tts s t♠♣♦ tr♥t t♠é♠ s ♦♠♣r♠♥t♦ r
tríst trê♥ ♥ã♦ ♥♦ ♥ss s♣r ♥♥♠ s ♣r♦r
sr ①st♠ ♥ ♦s ♠♦♦s três qçõs ♣r ♠♦♠ trê♥
❲
♠♦♦ ír♦ ♥tr ♦♥♦ ♦♠♦ ♦ ♥ês r trss
r♥s♣♦rt ♠ ♦♥srçã♦ ♦ tr♥s♣♦rt s t♥sõs s♠♥t♦ tr♥ts
rst♥♦ ♠ t rá ♥ ♣rsã♦ ♦ ♥í♦ q♥t s♣rçã♦ ♦ s♦
♠♥t♦ s♦ r♥ts ♣rssã♦ rs♦s ♠♦♦ s s ♥ ♦r♠çã♦ κ−ω♦r♥ ❲❳ ♣r rã♦ ♣ró①♠ às ♣rs ♥ ♦r♠çã♦ κ− ε ♣rã♦❯ P ♣r rõs str ♦ s♦♠♥t♦ r ♦♥t♦
♠ ♠♦çã♦ ♥ ♥çã♦ s♦s tr♥t é t ♣r ♦♥srr ♦ tr♥s
♣♦rt s t♥sõs ②♥♦s rst♥♦ ♥♦ ♠♦♦ r trss r♥s♣♦rt
♠♦♦ ♦r♦ ♦♠ ♥tr ♣rs♥t ♠♦r ♦♠ rçã♦ às ♦r♠çõs
κ − ω κ − ε ♦r♥s
♠♦♦ κ − ω é t♠é♠ t③♦ ♥ ♣rt ♦rít♠ ♠ ♠t ♣♦s
♣rs♥t ♦♠♣♦rt♠♥t♦ s♣r♦r ♦ ♠♦♦ κ − ε ♥st rã♦ ♣r s♦♠♥t♦s ♦♠
r♥t ♣rssã♦ rs♦s s♦♠♥t♦s ♥♦♠♣rssís ❯♠ ssã♦ áss
♣r ♠ ♠t sr♥ ①♣r♠♥t♠♥t ♣♦ sr st ♥ r á
♥ rã♦ str ♦ rõs sts ♣r ♦ ♠♦♦ κ − ω sr ♥♦♥♦
♠ ♦r ♦ s♦ ♦ ♠♦♦ κ − ε r③ã♦ ♣r st tr♥â♥ é q ♦ ♠♦♦ κ − ω♣rs♥t ♠ ♦rt s♥s ♣r ♦s ♦rs ♦rr♥t r s♣♦s ♣r ω
♦r ♠ ♠t Pr s♦♠♥t♦s rs s♠♥t♦ st♥ts s♣rís ♦
♠♦♦ κ−ε ♣rã♦ é t③♦ Pr ♥çr sts rtrísts ss ♠ r♥ts
rõs rsã♦ ♦♥ ♣♦r t♦②♥♦s ♦ ♠♦♦ κ − ε é tr♥s♦r♠ ♣r ♠
♦r♠çã♦ κ − ω ♦r♠çã♦ ③♦♥ é ♣♦rt♥t♦ s ♠ ♥çõs ♠str s qs r♥t♠
sçã♦ q κ − ω ♦ κ − ε ♣r♥♣ ♦♠♣① ♦♥ ♥ ♦r♠çã♦
♦ ♠♦♦ r s♦r ♥ss tr♠♥r stâ♥ ♣rtr ♣r q é
rqr ♣r s ♥çõs ♠str t
rt♠♥t♦ ♥t♦ à ♥tr só♦♦ ♥çõs ♣
r sás ① ♦r♠çã♦ ①♦ ②♥♦s
s♦çã♦ s qçõs ♦♥srçã♦ srts ♥s rõs ♣r é r♥
♠♣♦rtâ♥ ♣r ♠♦r s ♣çõs ♥strs q t③♠ ♥â♠ ♦s
♦♠♣t♦♥ P♦r ss♦ ♠ts ③s ♦s ♠♦♦s s♦s ♠ ω ♦♠♦ é ♦ s♦ ♦
sã♦ ♣rr♦s Pr sts ♠♦♦s ♦♥♦s ♣♦r ①♦②♥♦s ♦♥t♦ á
♥ss ♠ ♠ t♠♥t r♥ ♥t♦ às s♣rs sós ♦ q ♣♦
r Pr ♦ tí♣♦ ♠ ♠t tr♥t
Subcamada
viscosaCamada
logarítmica
Camada
turbulenta
U+
60
40
20
01 10 102
U+
y+
U+
103 104
= y+
1 ln y++ B
=
♦♥t ♣t♦ ❲❳ t
♥ã♦ sr ♥ç♦ ♦♠ sss♦ ♣r t♦t s ♣rs P♦r ♦tr♦ ♦ s♦ ♠
♠♦♦ t♦ ②♥♦s s t③♦ ♦♠ ♠s ♠t♦ r♥s rá s♦çã♦
♦♠♣r♦♠t ♠s♠ ♦r♠ Pr ♦♥t♦r♥r sts ♥♦♥♥♥ts ♦ CFXt③
♣♦r ♣rã♦ ♠ trt♠♥t♦ t♦♠át♦ ♥t♦ à ♣r ♣r ♠♦♦s s♦s ♠ ω
t♦♠t ♥r trt♠♥t ❨ st ♦r♠ ♦ ó♦ tr♥ ♥çã♦
♣r ♦ ♦ t ♣r ♠ ♦r♠çã♦ ①♦ ②♥♦s ♦♠ ♦ r♥♠♥t♦
♠
♦r♠ s ♥çõs ♣r ♥♦ CFXé ♠ ①t♥sã♦ ♦ ♠ét♦♦
❯ P ♠♦♦ q ♥ rã♦ ♦rít♠ ♦ t♥♥
é r♦♥ ♦♠ t♥sã♦ s♥t ♣r ♣♦r ♠♦ ♠ rçã♦ ♦rít♠
❨
s ♦r♥s ♥çõs ♣r rã♦ s♠ s♦s é ♥♦r
♣ ♣çã♦ ór♠s ♠♣írs sts ór♠s ♦♥t♠ s ♦♥çõs ♣r
♦♠ s rás ♣♥♥ts ♦s ♥ós ♣ró①♠♦s à ♣r ♦③çã♦ ss♠s str
♥ rã♦ ♦♠♣t♠♥t tr♥t rçã♦ ♦rít♠ ♣r ♦ ♣ró①♠
♣r é ♣♦r
u+ = Utan
uτ= 1K ln(y+) +C
♦♠
y+ = ρfuτ∆yµf
uτ =√
τint
ρf
♥ q u+ uτ Utan sã♦ s ♦s ♠♥s♦♥s ♣ró①♠ ♣r trt♦
t♥♥ à ♣r ♠ stâ♥ ∆y ♣rtr ♣r rs♣t♠♥t y+ é
stâ♥ ♠♥s♦♥ ♣rtr ♣r τint t♥sã♦ s♥t ♥ ♣r ♦ ♥trK ♦♥st♥t ♦♥ ár♠á♥ C é ♠ ♦♥st♥t ♣♥♥t r♦s ♣r
Pr strr ♦ trt♠♥t♦ ♣r ♦ à trê♥ sã♦ ♣rs♥ts s
♦r♥s ♣r ♦ ①♦ ♠♦♠♥t♦ ①♦ ♦r srs q ①st ♥ ♠
♦r♠çã♦ ss♠ ♣♦ trt♠♥t♦ t♦♠át♦ ♣r ♣r t① ss♣çã♦
s♣í ω
①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r
♦r♦ ♦♠ ♥s②s s ♥çõs ♣r sás s ♥t
♦♥s sã♦ ss ♠ ♣ótss q sã♦ ♣r♦♠áts s♣♠♥t ♣r s♦♠♥t♦s
①♦s ♥ú♠r♦s ②♥♦s Re < 105 ♣♦s ♣♦rçã♦ s♠ s♦s ♥ ♠
♠t é ♥♥ ♥♦ ♥ç♦ ♠ss ♠♦♠♥t♦ Pr s♦♠♥t♦s ①♦ ♥ú♠r♦
②♥♦s st♦ ♣♦ sr ♠ rr♦ té ♥ s♣ssr s♦♠♥t♦
trt♠♥t♦ t♦♠át♦ ♣r ♦ CFX♣♦ss s♥t ♦r♠çã♦ ♣r
♦ ①♦ ♠♦♠♥t♦ FU ❨
FU = ρfuτu∗
♥ q
u∗ = 4
¿ÁÁÁÀ(√µf
ρf∣∆U∆y∣)4 + (√a1κ)4 uτ = 4
√(uvisτ )4 + (ulogτ )4.
ss♠ u∗ r♣rs♥t ♠ s ♦ tr♥t a1 ♠ ♦♥st♥t ♦s s♦rs
rt♦s vis log ♥♥♦ ♠str ♥tr s rõs s♦s ♦rít♠
s tr♠♦s ♦ trt♦ sã♦ ①♣rss♦s ♣♦r
uvisτ = ⎛⎝√
µf
ρ∣∆U∆y∣⎞⎠ ulogτ = U
1/K ln(y+) +C
①♦ ♦r ♥ rã♦ ♣r
♣r t♠♣rtr ♠♥s♦♥ ♣ró①♠ ♥tr só♦♦ s ♠
♣r ♥rs trés s♠ s♦s rã♦ ♦rít♠ t♠♣rtr
♠♥s♦♥ T + é ♥ ♦♠♦ ❨
T + = ρfcfu∗(Tint − Tf)qint
♥ q Tint qint sã♦ t♠♣rtr ♦ ①♦ ♦r ♥ ♥tr
qçã♦ ♣♦ sr rrr♥ ♠♦♦ ♦r♥r ♠ ♦r♠ ♣r
tr♠♥çã♦ ♦ ①♦ ♦r trés ♥tr só♦♦
qint = ρfcfu∗(Tint − Tf)T +
Pr ♦ ♠♦ trt♠♥t♦ t♦♠át♦ ♣r t♦♠t trt♠♥t ♦
CFX ♠ ♠t tér♠ é ♠♦ t③♥♦ ♥çã♦ ♣r tér♠
r strçã♦ t♠♣rtr ♠♥s♦♥ T + é ♠♦ trés
♠str s♠ s♦s ♦♠ ♦rít♠ ♣r
T + = Pry∗e(−Γ) + [2,12ln(y∗) +ψ]e(−1/Γ) ,
s♥♦
ψ = (3,85Pr1/3 − 1,3)2 + 2,12ln(Pr) Γ = 0,01(Pry∗)41 + 5Pr3y∗ .
♥ú♠r♦ Pr♥t é ♥♦ ♦r♠ tr♦♥
Pr = µfcf
kf.
♥♠♥t q♥t y∗ é ♠ ♥çã♦ tr♥t ♦ y+
y∗ = ρfu∗∆yµf
.
rr♥♦ ♥♦
r ❱rçõs ♦♠étrs ♦♥rçã♦ ts ♥s ♣r ♠ s♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t rba ♦♥ ♦♥
90°
18°
36°
54°
72°
(a) (b)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
rr♥♦ s♥♦
r ❱rçõs ♦♠étrs ♦♥rçã♦ ts s♥s ♣r ♠ s♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t rba ♦♥ ♦♥ ♦♥
90°
18°
36°
54°
72°
(a) (b) (c)
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
r♦r s♦s
r ♦♠♥çã♦ s rçõs ♦♠étrs b rba ♦♠ s rçõs s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s ue ♦ Re ♣r ♦ ♠ ♥♥çã♦ t β
ts s♥s
b = 2Hrba = 0,2
Re1
Re2
Re3
rba = 0,4Re1
Re2
Re3
rba = 0,6Re1
Re2
Re3
b = 3Hrba = 0,2
Re1
Re2
Re3
rba = 0,4Re1
Re2
Re3
rba = 0,6Re1
Re2
Re3
ts ♥s
b = 2Hrba = 0,2
Re1
Re2
Re3
rba = 0,4Re1
Re2
Re3
b = 3Hrba = 0,2
Re1
Re2
Re3
rba = 0,4Re1
Re2
Re3
♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r
❨ ♥ ♦ ♦tr ♥s②s ❬❪ ❱t♦♥ t♦♦♦② ♥ ♦♠♣tt♦♥ ②♥♠s
P s♥ ♥ ♣♣t♦♥ ♦ ♣♥ s♠s ♦♥♥strtr ♠ss
❩ t ♠r s♠t♦♥ ♦ t ②♥♠ tr♥t ♦ tr♦ ♥♥ ♣r♦ t s ♦♠♣rt st② t♥ t♦ ♠♦s ♦ s r♥srs ♥ tr♣③♦ s ♥rs ♥♦s ♥ ♣
P P ❱ ♥♠♥ts ♦ t ♥ ♠sstr♥sr ❬❪ ♦♥ ❲② ♦♥s
❯ ♦ r♦♥ s ♦r♥ ♦ t tr♥sr♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣
❲❯ ♠r ♣rt♦♥ ♦r ♠♥r ♦r ♦♥t♦♥ ♥ ♣r♣t ♥♥s t tr♥srs ♥ rr②s ♥tr♥t♦♥ ♦r♥ ♦ t♥ ss r♥sr sr ♥ ♣
❱ P r♥ ♥ ♥tr♦t♦♥ ♦r s♥tsts ♥ ♥♥rs ❬❪ ①♦r❯♥rst② Prss ❯
❱❯ ①♣r♠♥t ♥stt♦♥ ♦ ♠① ♦♥t♦♥ ttr♥sr r♦♠ ♦♥t♥ ♥s ♥ ♦r③♦♥t rt♥r ♥♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣
❩ ❨ ❲ ♥ t ♥ ♠ss tr♥sr ❬❪♦ t Prss
❩ P ♦♠♣tt♦♥ ♠t♦s ♦r ②♥♠s ❬❪ ♣r♥r♥ s♥ss
❳ ❲ P P ♥tr♦çã♦ à ♠â♥ ♦s ♦s❬❪ r♣♦ ♥
t ①♣r♠♥t ♥stt♦♥ ♦ t tr♥sr ♥ ♦ ♦r s ♦r♥t ts ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣
❩ ❯ ♠r t tr♥sr ♥ ♣rssr r♦♣ ♥stt♦♥ ♦ r♥t t s ♠♦♥t s♠t♥♦s② ♥ ♥♥ ♥♦r♥ ♥ ♣
♠r ♦♠♣tt♦♥ ♦ ♥tr♥ ♥ ①tr♥ ♦s ♥♠♥ts ♦♦♠♣tt♦♥ ②♥♠s ❬❪ ttr♦rt♥♠♥♥
t ♦♥t t tr♥sr ♣rt♦♥s ♥ t♦♠♥s♦♥ r♣sss ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ♦ sr ♥ ♣
♠♣rtr ♥ ♦♥♥trt♦♥ ♣r♦s ♥ ② tr♥t ♦♥r② ②rs♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣
♥stt♦♥ ♦ rtt♥ tr♥t sr ②r♦ ♦r r♥ st♣ ♦r♥ ♦ s ♥♥r♥ ♠r♥ ♦t② ♦♥ ♥♥rs ♥ ♣
❩❯ ❯ ts ♦ r rr♥♠♥ts ♦♥ t tr♥sr♥ ♦ ♦r ♥ rt♥r rr♦♥ ♣ss ♣♣t♦♥ t♦ ♦♦♥ ♦ str♥ tr♥ ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥♥♥rs ♥ ♣
P t ♠r s♠t♦♥ ♦ t tr♥sr ② ♠① ♦♥t♦♥ ♥♦r③♦♥t ♥♥ ♥♥s ♥ ♥tr♥t♦♥ ♦♥rss ♦ ♥ ♥♥r♥ st t Pr♦♥s ♦ ♥r♦
❯ P ♥♠r ♦♠♣tt♦♥ ♦ tr♥t ♦s♦♠♣tr ♠t♦s ♥ ♣♣ ♠♥s ♥ ♥♥r♥ sr ♥ ♣
❩ ❨ ♠r st② ♦ tr♥t ♦ ♥ t tr♥sr ♥ r♦ss♦rrttr♥r ts t ts♣ s ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♣
P❩ t tr♥sr ♥ tr♠♥s♦♥ ♥♥t s ♠r t r♥sr Prt ♣♣t♦♥s ②♦r r♥s ♥ ♣
r♥srê♥ ♦r ♠â♥ ♦s ♦s ♦♠♣t♦♥ çã♦
❯ P ♥stt♦♥ ♦ tr♥t ♦s ♦r r ♥st♣ s ♥ ♠♦r♥♠ ♣
❯ P ②♥♦sstrss ♥ ss♣t♦♥rt ts ♥ tr♥t ♥♥ ♦ ♦r♥ ♦ ♥s ♠r ❯♥ Prss ♣
❨ t ♠r ♥②ss ♦ tr♥t ♦r♦♥t♦♥ ♦ ♥ ♥♥ tstr s♣ s ♦r♥ ♦ ♥♦♦② ♥ trs P ♥ ♣
❯❩ ❨ ♥ ②rs ♦ ♥str ①♣r♥ t tsst tr♥ ♠♦ r♥ t ♥ ♠ss tr♥sr tsr ♥ ♣
♦qt♦♥ ②s♦st② tr♥ ♠♦s ♦r ♥♥r♥ ♣♣t♦♥s ♦r♥ ♥ ♣
❯❱ t ♥ ♦ ♥ ♥tr♥ r♦♥ ♦ ♥♥t str s ♥r② ♦♥rs♦♥ ♥ ♥♠♥t sr ♥ ♣
P ❲ ❯ ❱t♦♥ ♠t♦♦♦② ♥ ♦♠♣tt♦♥ ②♥♠s ♣♣r ♣
P ❱❩ r ❩ P st♦ ♥♠ér♦ tr♥srê♥ ♦r ♦♥ ♠ ♥s ♦♠ ts ♥♥s ♣r ①♦ ♥ú♠r♦ r②♥♦s ♥ ❳♦♥rss♦ ♦♥ ♥♥r â♥ ♦rt③ ♦ ♥r♦
P ❱❩ r ❩ P ♠r ssss♠♥t ♦ ♠♥r ♦♥ ♦♥t t tr♥sr ♥ ♣r♣t ♥♥s t ♥♥ ♥s t ♦ r②♥♦s♥♠r ♥ r③♥ ♦♥rss ♦ r♠ ♥s ♥ ♥♥r♥ t ❱tór ♦ ♥r♦
P ❱❩ r ❩ P ♦♥srt♦♥s ♦♥ ♦♥t t tr♥sr ♥ ♣r♣t ♥♥s t ♥♥ ♥s ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥♦♠♣tt♦♥ ♥♥r♥ ♥ ①♣r♠♥t♥ t strt ♦♦ ❱♥♥ str ❱♥♥ ❳ ♦♥r♥
P ❲ ♦ t♥ t♦ s t ♥q ♥tst r♥t s♣♥ r♦r♥s ♥ ♣
❲ ❲ ♠r st② ♦ t tr♥t ♦ ♣st ♥ r♦ t tr♥ s♣rt♦♥ ♦r♥ ♥ ♣
♦ ♥ t tr♥sr ♥ ♣r♣t t s♦s♣♦r♦s ♥ s♦ s ♠r t r♥sr ②♦r r♥s ♥ ♣
❯ t t tr♥sr ♠♥tt♦♥ ♥ t ①♥r t s♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ♦ sr ♥ ♣
t tr♥sr ♥ ♦ tr♦ r ♣ss ♥ strrr♥♠♥t r♥♥ ♦r♥ ♦ ♥ ♥♦♦② r♥st♦♥ ♥♥r♥ ♥ ♣
PPP P❱ P ♠r ♥②ss ♦ ♠♥r t tr♥sr♥ ♥♥ t ♠♦♥s♣ s ♥tr♥t♦♥ ♦♠♠♥t♦♥s ♥ t ♥ss r♥sr sr ♥ ♣
❯❨ rst ♦rs ♥ tr♥ ❬❪ ♣rss
❱ ❲ t tr♥sr ♣rt♦♥s s♥ ♥ t♦qt♦♥ tr♥ ♠♦s ❳ ❱t♦♥ ♣♦rt ♣♦rt ♦ ❳❱ ♣
❱ ♦♠♥ t tr♥sr ♥ ②♥♠ ♠sr♠♥ts ♦♥str♠ ♦ r♥ st♣ ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥♥♥rs ♥ ♣
❲ trqt♦♥ ②s♦st② ♠♦ ♦r r②♥♦sr ♥rst♦s s♠t♦♥s ♦ tr♥st♦♥ ♦ ♦r♥ ♦ s ♥♥r♥♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣
❲❳ ssss♠♥t ♦ t str♠♥♥ qt♦♥ ♦r ♥ tr♥♠♦s ♦r♥ ♥ ♣
❲❳ t r♥ ♠♦♥ ♦r ❬❪ ❲ ♥strs ♥
❨ ❨ ❲ ♦r ♦♥t ♦♦♥ ♦ ♥ ♥ ♥♥♥r② ♦♥rs♦♥ ♥ ♠♥♠♥t sr ♥ ♣
❨ ❨ ❲ ❩ t♦♥ ♦ tr♥t ♦ ♥ t tr♥sr ♥ ♣♦r♦s ♥♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣
❨❯ ❩ ♠r st② ♦ ♣r♦② tr♥t ♦ ♥ t tr♥sr ♥ ♥♥t tr♥srs ♥ rr②s ♥tr♥t♦♥ ♦r♥ ♦ ♠r t♦s ♦r t ♦ ❯P t ♥ ♣
❨❯ ❩ ❩ ❩ ♥ ♥ t ♦♥ tr♥t t tr♥sr ♥ ♣r♣t ♥♥ t ♦♥♥♥ ♥s ♥tr♥t♦♥ ♦r♥ ♦ ♠r t♦s ♦rt ♦ ♠r r♦♣ Ps♥ ♠t ♥ ♣
❩ P t tr♥sr sts ♥ t ♦ ♦r s♦ts ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣
❩ P ❱❩ ♦♥t♦♥ t tr♥sr ♥♥♠♥t♦♥ rrt♥ ♦s ♥ r ♥ st♣ t ts ♦ s♠ sqr tr♥♣r♦♠♦tr t r♥sr ♥♥r♥ ②♦r r♥s ♥ ♣