Analisi fluidodinamica computazionale degli effetti del vento su elementi in aggetto da facciate continue di edifici elevati

(1)

"Scuola di Architettura, Urbanistica, Ingegneria delle Costruzioni”

Corso di Laurea Magistrale in Ingegneria dei Sistemi Edilizi

Analisi fluidodinamica computazionale degli

effetti del vento su elementi in aggetto da

facciate continue di edifici elevati

TESI DI LAUREA MAGISTRALE

Laureando:

ALESSANDRO CRISTANTIELLI

Matr. 927457

Anno Accademico

2019-20

Relatore

:

Prof. PAOLO RIGONE

Correlatore

:

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)



(12)

(13)



(14)

(15)



(16)



(17)

(18)



(19)

(20)

· (

𝑎𝑠

(21)

𝑘

𝑟2

∙ 𝑐

𝑟

∙ 𝑙𝑛 (

𝑧 𝑧0

) [7 + ∙ 𝑐

𝑟

∙ 𝑙𝑛 (

𝑧 𝑧0

) ]



(22)

(23)

(24)

(25)

(26)



(27)

𝜌𝑉

2

_𝑙

2

𝑙

𝜇 𝑉 𝑙

𝑅𝑒 =

𝜌𝑉

2

_𝑙

2

𝜇 𝑉 𝑙

=

𝜌 𝑉 𝑙

𝜇



𝜌



𝜇



𝑙

(28)

(29)

(30)

𝑐

𝑝

𝑐

𝑝



𝑝

𝐴



𝑝

𝐵



𝑣

𝐴



𝑣

𝐵

𝑝 + 𝜌

𝑣

2

2 = 𝑐𝑜𝑠𝑡

𝑝

𝐴

+ 𝜌

𝑣

𝐴2

2 = 𝑝

𝐵

+ 𝜌

𝑣

𝐵2

2 ; 𝑝

𝐵

− 𝑝

𝐴

= 𝜌

𝑣

𝐴2

2 (1 −

𝑣

𝐵2

𝑣

_𝐴2

)

= 𝐶

𝑃

(𝜌

𝑣

𝐴2

2 ) , 𝑐𝑜𝑛 𝐶

𝑃

= (1 −

𝑣

𝐵2

𝑣

_𝐴2

)

(31)

𝑝

𝐴

= 𝑝

0

𝑣

𝐴

= 𝑣

0

𝑑𝑎 𝑐𝑢𝑖: 𝑝

𝐵

− 𝑝

0

= 𝜌 𝐶

𝑃

(

𝑣

02

2 )

𝐶

𝑃

𝑣

𝐴

𝑐

𝑝

𝐶

𝑃

(

𝑡

)

=

𝑝

_𝐵

− 𝑝

₀

𝑞

_𝑎 

𝑞

_𝑎

= 0.5 · 𝜌 𝑉

2 .

𝐶

𝑃

𝐶

𝑃

(32)

(33)



(34)

(35)

(36)

(37)

(38)

(39)

(40)

(41)

∆𝑞

𝑞

⁄ = 𝜖 𝐶

𝐷

𝐴

(𝑀𝑂𝐷𝐸𝐿𝐿𝑂)

𝐴

(𝐺𝐴𝐿𝐿𝐸𝑅𝐼𝐴)

⁄

𝜖

1 (1 + ∆𝑞 𝑞

⁄

⁄ )

𝜖

(42)

(43)

𝑐

𝑝

(𝑡) =

𝑝 − 𝑝

_∞

1 2 ∙ 𝜌 ∙ 𝑉

2

𝐸𝑄. 1

𝑃

₀

(44)



(45)

(46)

(47)

(48)

(49)

(50)

(51)



(52)

𝑢 = 𝑢̅ + 𝑢′



𝑢 =

𝑢(𝑡)



𝑢̅



𝑢

′

=

𝑢

′

_𝑢

′

_{= 𝑢 − 𝑢̅}



𝑢



𝑣

(53)

τ = μ

𝑑𝑢

𝑑𝑦

𝜏

2

− 𝜏

1

∆𝑦

= 𝜇

𝜕

2

𝑢

𝜕 𝑦

2

𝜌𝑢

𝜕𝑢

𝜕𝑥

+ 𝜌𝑣

𝜕𝑣

𝜕𝑦

= −

𝑑𝑝

𝑑𝑥

+ 𝜇

𝜕

2

𝑢

𝜕 𝑦

2

𝐸𝑄. 2

𝑢 = 𝑢̅ + 𝑢′

𝑣 = 𝑣̅ + 𝑣

𝜌

𝑢

̅

𝜕

𝑢

̅

𝜕𝑥

+ 𝜌

𝑣

̅

𝜕

𝑣

̅

𝜕𝑦

= −

𝑑

𝑝

̅

𝑑𝑥

+ 𝜇

𝜕

2

𝑢

̅

𝜕 𝑦

2

− 𝜌

𝜕

𝑢

̅̅̅̅̅

′

_𝑣

′

𝜕𝑦

𝐸𝑄. 3

𝑢′ 𝑣′

𝜌 𝑢

_{̅̅̅̅̅̅̅̅}

′

_𝑣

′

𝜌

𝜕 𝑢̅̅̅̅̅̅′𝑣′ 𝜕𝑦

𝑓 = −

𝑑 𝑝̅

𝑑𝑥

+ 𝜇

𝜕

2

𝑢̅

𝜕 𝑦

2

− 𝜌

𝜕 𝑢

_̅̅̅̅̅̅

′

_𝑣

′

𝜕𝑦

𝐸𝑄. 3,1

𝜌 𝑢

′

_𝑣

′

̅̅̅̅̅̅̅̅

_τ

(54)

𝜇

𝑡

𝜌 𝑢

′

_𝑣

′

̅̅̅̅̅̅̅̅

𝜕 𝑢̅ 𝜕 𝛾

𝜌

𝑢

̅̅̅̅̅ = − 𝜇

′

_𝑣

′ 𝑡

𝜕 𝑢̅

𝜕𝑦

[

𝑘𝑔 𝑚3

] [

𝑚2 𝑠

]

(55)

[𝑚

2

_{⁄ ]}

_𝑠

2

[𝑚

2

_{⁄ ]}

_𝑠

3

𝜇

𝑡

= 𝑐

𝜇

𝜌

𝑘

2

ε

𝜇

𝑡

𝜇

_𝑡

= 𝜌

𝑘

ω

(56)

(

𝜕 𝑝̅ 𝜕𝑥

> 0)

−

𝑢

̅̅̅̅̅ = 𝑘

′

_𝑣

′

1 max(0.31 𝜔, 𝛺)

𝛺

𝜕 𝑢̅ 𝜕 𝛾

(57)

(58)

(59)

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(61)

(62)

(63)

(64)

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(66)

(67)

𝑐

𝑝

(𝑡) =

𝑝 −

𝑝

_𝑎

𝑞

_𝑎

(68)

(69)

(70)

(71)

(72)

(73)

(74)



(75)



(76)

(77)

(78)



(79)

(80)

(81)

(82)

(83)

(84)

(85)



(86)



(87)

𝑏1 5 ⁄

(

𝑏

1

5 ⁄ ) =

(88)



(89)



(90)

(91)

(92)

(93)

(94)

(95)



(96)



(97)

(98)

(99)



𝐾

𝑠

=

𝐶

𝑝,𝑛

𝐶

𝑝,𝑒𝑠𝑡_𝑓𝑎𝑐𝑎𝑑𝑒

𝐶

𝑝,𝑛

= 𝐶

𝑝,𝐴

− 𝐶

𝑝,𝐵

𝐶

𝑝,𝐴

𝐶

𝑝,𝐵

(100)

0.8

0.6

1.2

1.1

1.3

1.4

1.5

0.7

(101)

± 1.06 ± 0.76 𝟎. 𝟕𝟐 ± 0.84 ± 0.83 𝟎. 𝟗𝟗 ± 1.22 ± 0.83 𝟎. 𝟔𝟗 ± 0.81 ± 0.57 𝟎. 𝟕𝟎 ± 0.74 ± 0.93 𝟏. 𝟐𝟕 ± 0.57 ± 0.80 𝟏. 𝟒𝟎

𝐾

𝑠

=

𝐶𝑝,𝑛 𝐶𝑝,𝑒𝑠𝑡_𝑓𝑎𝑐𝑎𝑑𝑒 ± 0.92 ± 0.68 𝟎. 𝟕𝟒 ± 0.82 ± 0.79 𝟎. 𝟗𝟔 ± 1.05 ± 0.77 𝟎. 𝟕𝟑 ± 0.84 ± 0.63 𝟎. 𝟕𝟓 ± 0.77 ± 0.89 𝟏. 𝟏𝟔 ± 0.57 ± 0.76 𝟏. 𝟑𝟑

(102)

+0.73 + 0.56 𝟎. 𝟕𝟔 −0.86 −0.33 𝟎. 𝟑𝟗 +0.85 + 0.44 𝟎. 𝟓𝟏 −0.60 −0.35 𝟎. 𝟓𝟖 +0.9 + 0.55 𝟎. 𝟔𝟏 −0.87 −0.49 𝟎. 𝟓𝟕 +0.82 +0.49 𝟎. 𝟓𝟗 −0.75 −0.34 𝟎. 𝟒𝟔 +0.86 +0.39 𝟎. 𝟒𝟔 −0.59 −0.35 𝟎. 𝟓𝟗 +0.43 +0.46 𝟏. 𝟎𝟕 −0.62 −0.31 𝟎. 𝟓𝟎 +0.79 +0.49 𝟎. 𝟔𝟐 −0.71 −0.31 𝟎. 𝟒𝟒 +0.76 +0.33 𝟎. 𝟒𝟑 −0.54 −0.3 𝟎. 𝟓𝟔 +0.4 +0.44 𝟏. 𝟏𝟎 −0.62 −0.28 𝟎. 𝟒𝟔 +0.71 + 0.51 𝟎. 𝟕𝟐 −0.9 −0.36 𝟎. 𝟑𝟗 +0.79 + 0.43 𝟎. 𝟓𝟒 −0.63 −0.35 𝟎. 𝟓𝟔 +0.84 + 0.55 𝟎. 𝟔𝟓 −0.71 −0.34 𝟎. 𝟒𝟖 +0.83 +0.43 𝟎. 𝟓𝟏 −0.74 −0.36 𝟎. 𝟒𝟗 +0.84 +0.34 𝟎. 𝟒𝟎 −0.57 −0.31 𝟎. 𝟓𝟒 +0.50 +0.47 𝟎. 𝟗𝟒 −0.66 −0.34 𝟎. 𝟓𝟐 +0.81 +0.46 𝟎. 𝟓𝟔 −0.73 −0.36 𝟎. 𝟒𝟗 +0.80 +0.40 𝟎. 𝟓 −0.49 −0.23 𝟎. 𝟒𝟕 +0.51 +0.49 𝟎. 𝟗𝟔 −0.59 −0.26 𝟎. 𝟒𝟒

(103)

0.45 1.33 0.64 0.72 1.26 1.33 0.34 0.38 1.51 1.21 0.64 0.43 0.65 0.32 𝟎. 𝟒𝟗 0.72 0.95 𝟏. 𝟑𝟐 0.56 0.36 𝟎. 𝟔𝟒 0.62 0.46 𝟎. 𝟕𝟒 0.75 1.4 𝟏. 𝟐𝟗 0.71 0.95 𝟏. 𝟑𝟑 0.67 0.26 𝟎. 𝟑𝟖 0.61 0.23 𝟎. 𝟑𝟖 0.43 0.64 𝟏. 𝟒𝟗 0.46 0.59 𝟏. 𝟐𝟖 0.4 0.25 𝟎. 𝟔𝟒 0.38 0.18 𝟎. 𝟒𝟕

(104)



(105)



(106)

−1.33 1.08 −𝟎. 𝟖𝟏 −1.4 0.32 −𝟎. 𝟐𝟐

0.91 0.82 𝟎. 𝟗𝟎 0.39 0.89 𝟐. 𝟐𝟖

−1.8 1.13 −𝟎. 𝟔𝟑 −1.4 1 −𝟎. 𝟕𝟏

(107)



(108)

−0.82 1.16 −𝟏. 𝟒𝟏 −0.4 0.12 −𝟎. 𝟑 0.89 0.99 𝟏. 𝟏𝟏 −0.36 −0.08 𝟎. 𝟐𝟐 −0.84 1.3 −𝟏. 𝟓𝟒 −0.56 0.18 −𝟎. 𝟑𝟐 0.84 0.96 𝟏. 𝟏𝟒 −0.45 0.17 −𝟎. 𝟑𝟖 −0.91 1.11 −𝟏. 𝟐𝟐 −0.19 0.49 −𝟎. 𝟕𝟑 0.54 0.71 𝟏. 𝟑𝟏 −0.27 0.31 −𝟏. 𝟏𝟗

(109)



(110)

(111)

(112)

(113)

𝑅

2

= 1 −

𝐷𝑒𝑣𝐸

𝐷𝑒𝑣𝑇

𝑅

2

𝑅

2



𝑅

2

𝐷𝑒𝑣𝐸

𝐷𝑒𝑣𝑇



𝑅

2

𝐷𝑒𝑣𝐸 = 0



𝐷𝑒𝑣𝐸



𝐷𝑒𝑣𝑇

(114)

(115)

(116)

(117)

(118)

(119)

(120)

(121)

(122)

(123)



𝑐

̅

𝑝

(124)



(125)



(126)

−0.76 0.06 −𝟎. 𝟎𝟖 +0.93 + 0.19 𝟎. 𝟐 −0.62 0.34 −𝟎. 𝟒𝟒 +0.81 + 0.66 𝟎. 𝟖𝟏 −0.59 0.21 −𝟎. 𝟑𝟔 −0.56 0.44 −𝟎. 𝟕𝟗 +0.85 +0.11 𝟎. 𝟏𝟑 −0.78 0.4 −𝟎. 𝟓𝟏 +0.77 +0.33 𝟎. 𝟖𝟎 −0.4 0.21 −𝟎. 𝟓𝟑 −0.36 0.24. −𝟎. 𝟔𝟕 +0.67 +0.24 𝟎. 𝟑𝟔 −0.23 0.15 −𝟎. 𝟔𝟓 +0.77 +0.33 𝟎. 𝟖𝟎 −0.22 0.18 −𝟎. 𝟖𝟏

(127)

(128)

(129)

(130)

(131)

(132)