Progetto girante centrifuga

8/18/2019 Progetto girante centrifuga

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ISTITUTO TECNICO STATALE COMMERCIALE

“PIERO GOBETTI”

anno scolastico 2011-2012

classe ! C ITIS "e#iti in$%st#iali

STU&IO CALCOLO E &ISEGNO &I UNA

GIRANTE &I UNA POMPA CENTRI'UGA

prof. BONI STEFANO

prof. VASIRANI FABIOPag.1


2/22

INDICE

ASPETTI FONDAMENTALI RIGUARDANTI IL FUNZIONAMENTO DELLE MACCHINE

IDRAULICHE OPERATRICI ..........................................................................................pag. 3

CONDIZIONI DI IMPIEGO .............................................................................................pag. 8

STUDIO DEL MOTORE ELETTRICO.............................................................................pag.

STUDIO DELLA GIRANTE..............................................................................................pag.

DISEGNO DELLE PALE INTERNE ALLA GIRANTE.................................................pag. !"

Pag.!


3/22

ASPETTI FONDAMENTALI RIGUARDANTI IL

FUNZIONAMENTO DELLE MACCHINE

IDRAULICHE OPERATRICI

U#a $a%%&'#a '(ra)*'%a op+ra,r'%+ - )# ('po','/o a,,o a ,raf+r'r+ a* *'0)'(o %&+ *a a,,ra/+ra )#a

+#+rg'a o,,o *a for$a (' pr+'o#+ + (' /+*o%',. La $a%%&'#a r'%+/+ )#a +#+rg'a $+%%a#'%a (a )#

$o,or+ %&+ (' o*',o - +*+,,r'%o o +#(o,+r$'%o +2 a,,ra/+ro ' )o' %o$po#+#,'2 *a ,ra$+,,+ a* *'0)'(o

'# $o(o (a %o#f+r'rg*' )#a pr+'o#+ + )#a /+*o%', #+%+ar'+ p+r o(('far+ *+ +'g+#+

(+**4),+#a. L+ $a%%&'#+ op+ra,r'%' %&+ $',a#o *'0)'(' ' )(('/'(o#o '# ()+ gra#(' %a,+gor'+.

Macc(ine $ina)ic(e* %o#f+r'%o#o a* f*)'(o )#a )# /a*or+ (' pr+'o#+ '# %orr'po#(+#a a( )#

/a*or+ (+**a por,a,a *+ga,' a**+ p+r(',+ (' %ar'%o + a**a pr+/a*+#a g+o(+,'%a %)' '* *'0)'(o /'+#+

'#/'a,o.

Macc(ine +ol%)et#ic(e* g+#+ra#o )#a por,a,a %+r,a (' *'0)'(o %&+ p)5 ragg')#g+r+ /ar' /a*or' ('

pr+'o#+ *+ga,' a**+ p+r(',+ (' %ar'%o2 a**a pr+/a*+#a g+o(+,'%a + a**a pr+'o#+ (' f)#'o#a$+#,o

(+**4),+#a.

C' o%%)p+r+$o (' )#a $a%%&'#a op+ra,r'%+ ('#a$'%a a(a,,a a**a +*a6ora'o#+ (' )# *'0)'(o 7#+*

#o,ro %ao a%0)a + '# par,'%o*ar+ (+* )o %o$po#+#,+ pr'#%'pa*+ %'o- *a g'ra#,+.

Da**a $+%%a#'%a ,+or'%a app'a$o %&+ p+r )# p)#,o (' )# %orpo %&+ ' $)o/+ #+**o pa'o /a*+ *a

+g)+#,+ *+gg+9

/a : /; < /r

(o/+

/a : /+*o%', (+* p)#,o (+* %orpo '# $o/'$+#,o r'p+,,o a( )# r'f+r'$+#,o ao*),o 7#+* #o,ro %ao)# o+r/a,or+ '# %o#(''o#' ,a'o#ar'+ =$>?@

/; : /+*o%', (' )# r'f+r'$+#,o r+*a,'/o %o**+ga,o r'g'(a$+#,+ a* %orpo '# $o/'$+#,o 7#+* #o,ro

%ao )# o+r/a,or+ $o6'*+ o*'(a*+ a* %orpo r'p+,,o a* r'f+r'$+#,o ao*),o 7#+* #o,ro %ao )#

o+r/a,or+ '# %o#(''o#' ,a'o#ar'+ =$>?@

/r :/+*o%', r+*a,'/a (+* p)#,o (+* %orpo r'p+,,o a* r'f+r'$+#,o r+*a,'/o 7#+* #o,ro %ao )#

o+r/a,or+ $o6'*+ o*'(a*+ a* %orpo.

Trapor,a#(o '* %o#%+,,o pr+%+(+#,+ a* %ao (+**a g'ra#,+ %+#,r'f)ga a66'a$o9

Pag.3

o+r/a,or+ '# %o#(''o#' ,a'o#ar'+

/;

/r

/a

o..+r/a,or+ $o6'*+

p)#,o


4/22

Ora %o#'(+r'a$o *+ %o#(''o#' (' f)#'o#a$+#,o a**a 6o%%a (' ap'ra'o#+.

)1 : /+*o%', ,a#g+#'a*+ (' )# p)#,o

po,o )**a 6o%%a (' ap'ra'o#+ r'p+,,o

a* r'f+r'$+#,o ao*),o =$>?@

%1 : /+*o%',a a'a*+ (' '#gr+o (+*

*'0)'(o )**a 6o%%a (' ap'ra'o#+

r'p+,,o a* r'f+r'$+#,o ao*),o =$>?

1 : /+*o%', (+* *'0)'(o '# '#gr+o

r+*a,'/a a**a g'ra#,+ '# $o/'$+#,o =$>?

(a**a r+*a'o#+ opra a66'a$o

o$$a#(o ' /+,,or'9

%1 : )1


5/22

Ora %o#'(+ro *+ %o#(''o#' (' f)#'o#a$+#,o )**a 6o%%a (' %ar'%o

)! : /+*o%', ,a#g+#'a*+ (' )# p)#,o

po,o )**a 6o%%a (' %ar'%o r'p+,,o

a* r'f+r'$+#,o ao*),o =$>?

%! : /+*o%', (' )%',a (+* *'0)'(o

)**a 6o%%a (' %ar'%o r'p+,,o

a* r'f+r'$+#,o ao*),o =$>?

! : /+*o%', (+* *'0)'(o )**a 6o%%a

%ar'%o r+*a,'/a a**a g'ra#,+ '#

$o/'$+#,o =$>?

(a**a r+*a'o#+ opra a66'a$o

o$$a#(o ' /+,,or'9%! : )!?@ #+* %ao (' )#a g'ra#,+

%+#,r'f)ga f)#'o#a#,+ %o# *'0)'(' ,+or'%a$+#,+ '#%o$pr'$'6'*' 0)+,a por,a,a $a'%a %o'#%'(+r

%o# 0)+**a a**4)%',a (+**a g'ra#,+.

S+ /og*'o %o#f+r'r+ +#+rg'a a* *'0)'(o (+66o2 a,,ra/+ro *4'$p'+go (' )#a g'ra#,+2 ,ra$+,,+rg*' )#

*a/oro2 0)+,o a//'+#+ app*'%a#(o '* ,+or+$a (+**a /ar'a'o#+ (+**4 +#+rg'a %'#+,'%a.

L=T2−T1=1 /!∗m∗v2!−1 /!∗m∗v1![ j ]

I* *a/oro %o$p'),o )**a $aa $ (' *'0)'(o - )g)a*+ a**a /ar'a'o#+ (' +#+rg'a %'#+,'%a %&+ )6'%+

'# *'0)'(o ,ra *4)%',a (a**a 6o%%a (' %ar'%o + *4'#gr+o (a**a 6o%%a (' ap'ra'o#+.

I# 0)+o %ao '* *a/oro - LAVORO IDRAULICO %'o- )#a 0)a#,', (' +#+rg'a %&+ *a g'ra#,+

,ra$+,,+ a* *'0)'(o.

N+* %ao (+**a g'ra#,+ *+ /+*o%', /1 + /! o#o +#,ra$6+ %o$po,+ (a ,r+ ,+r$'#'9

)12 )! : ,+r$'#' %&+ ,+#go#o pr++#,+ *4+ff+,,o (+* %a$po %+#,r'f)go + (+**+ a%%+*+ra'o#'

%+#,r'f)g&+ %&+ )6'%+ '* *'0)'(o ,ra '#gr+o + )%',a (+**a g'ra#,+ r'p+,,o a* r'f+r'$+#,oao*),o=$>? @

%12 %! : ,+r$'#' %&+ ,+#go#o pr++#,+ *a /ar'a'o#+ (' +#+rg'a %'#+,'%a %&+ )6'%+ '* *'0)'(o ,ra

'#gr+o + )%',a (+**a g'ra#,+ r'p+,,o a )# r'f+r'$+#,o ao*),o 7*a/oro p+r a'o#+ =$>?@

12! : ,+r$'#' %&+ ,+#go#o pr++#,+ *a /ar'a'o#+ (' +#+rg'a %'#+,'%a %&+ )6'%+ '* *'0)'(o ,ra

'#gr+o + )%',a (+**a g'ra#,+ r'p+,,o a )# r'f+r'$+#,o r+*a,'/o po,o )**a ,+a g'ra#,+ 7*a/oro p+r

r+a'o#+ =$>?@

N+**o ,)('o (+**a g'ra#,+ - %&'aro %&+ r'%o#,r+r+$o )# '#%r+$+#,o (' +#+rg'a (+* *'0)'(o %&+ /+rr

,rafor$a,a '# pr+'o#+ p+r%'5 ,)('+r+$o %o$+ *+ /ar'a'o#' (+**+ ,r+ /+*o%',2 ,ra '#gr+o + )%',a

Pag.

%!

A! )!


6/22

g'ra#,+2 '#f*)'%o#o #+* (+f'#'r+ *+ %o#(''o#' (+* *'0)'(o (opo %&+ +o &a a,,ra/+ra,o *a g'ra#,+.

N+**a #o,ra ,ra,,a'o#+ 'po,'+r+$o p+r +$p*'%', %&+ '* *'0)'(o a66'a )#a /'%o', %'#+$a,'%a +

0)'#(' a#%&+ )#a /'%o', ('#a$'%a #)**+. I# 0)+,a o,,'%a )pporr+$o %&+ #+* %o#,a,,o ,ra *'0)'(o

+ g'ra#,+ #o# ' for$' # *o ,ra,o *'$',+ *a$'#ar+ # *o ,ra,o *'$',+ ,)r6o*+#,o.

Pa'a$o a %o#'(+rar+ *4+ff+,,o (+**+ '#go*+ /+*o%',.

Do/r ++r+ u2u1 %o$+ - fa%'*+ /+(+r+ ++#(o *a /+*o%', p+r'f+r'%a (+**a g'ra#,+ $agg'or+(o/+ '* ragg'o (+**a g'ra#,+ - $agg'or+@

Do/r ++r+ w2≈w1 '# 0)a#,o ' - /',o %&+ p+r '$p+('r+ *o ,a**o (+**a po$pa2 f+#o$+#' ('%a/',a'o#+ + f+#o$+#' (' (',a%%o (' /+#a - #+%+ar'o %&+ '* %a#a*+ '#,+rpa*ar+ 'a a +'o#+

%o,a#,+ o (+6o*$+#,+ %o#/+rg+#,+@

Do/r ++r+ c2c1 '# 0)a#,o *4+#+rg'a %'#+,'%a %&+ po'+(+ '* *'0)'(o a**4)%',a (+**a g'ra#,+ (o/r++r+ $agg'or+ (' 0)+**a a**4'#gr+o2 0)+,o - (o/),o a* fa,,o %&+ w2≈w1 + u2u1 .

P+r%'5 '* *a/oro '(ra)*'%o for#',o a**4)#', (' $aa (+* *'0)'(o ar9

L= c2!−c1!/!u2 !−u1 !/! [ j ]

poo +pr'$+r*o a#%&+ #+**a for$a +g)+#,+

L= c2!u2!/!−c1 !u1 !/! [ j ]

App*'%a#(o '* ,+or+$a (' Car#o, )' ,r'a#go*' 0)a*'a'

w!= c!u!−!∗c∗u∗%o α

(a %)'

L=w2!!∗c2∗u2∗%o α2/!−w1!!∗c1∗u1∗%o α1 /! [ j ]

++#(o

w2≈w1

a/r+$o

Pag.

G

%

)

A

A


7/22

L=c2∗u2∗%o α2 −c1∗u1∗%o α1 [ j ]

#+* #o,ro %ao p+r far+ '# $o(o %&+ *a g'ra#,+ ,raf+r'%a '* $a'$o *a/oro '(ra)*'%o a* *'0)'(o

po#'a$o 1 : >! %o'%%&

L=c2∗u2∗%o α2 [ j ]

P+r '##a*ar+ a#%ora (' p' '* *a/oro '(ra)*'%o ,raf+r',o a* *'0)'(o 6'og#+r+66+ %&+ fo+ ! : "

p+r5 '# 0)+,a +/+#,)a*', *a +#+rg'a ,raf+r',a a* *'0)'(o ar+66+ ,),,a (' ,'po %'#+,'%o2 a/r+$o *a %!

a*,a p+rf+,,a$+#,+ ra('a*+ 2 *+ pa*+ a**4)%',a (a**a g'ra#,+ ar+66+ro r'/o*,+ '# a/a#,'. Ma #o' a**a

)%',a (a**a g'ra#,+ #o# /og*'a$o )#a /+*o%', 6+#J )#a pr+'o#+ + 0)+,o *o ' p)5 o,,+#+r+ %o#

)#a /o*),a ('/+rg+#,+ %&+ ra**+#,a#(o '* *'0)'(o #+ '##a*a *a pr+'o#+ 7/+(' +0)a'o#+ ('

B+r#o)**'@ 0)+,o a%%org'$+#,o pro/o%a (+**+ p+r(',+ %&+ ' a%%+#,)a#o $a# $a#o %&+ *a %! '

+*+/a.

P+r%'5 #+**a ,ragra#(+ $agg'ora#a (+' %a' *+ g'ra#,' (+**+ po$p+ %+#,r'f)g&+ &a##o *+ pa*+ r'/o*,+

a**4'#('+,ro r'p+,,o a**a ('r+'o#+ (' )1 + )!.

Pag.K


8/22

CONDIZIONI DI IMPIEGO

D'a$o (' +g)',o ' (a,' (' '$p'+go + (' prog+,,o (+**a po$pa9

por,a,a : !""=$>&? : "2" =$>?@

pr+/a*+#a $a#o$+,r'%a

H : "=$?@

*'0)'(o

H!O@

(+#', o $aa /o*)$'%a *'0)'(o

Q : 1"""=g>$?@

'po,+'9 /'%o', %'#+$a,'%a

: " =$>?@

'po,+'9 /'%o', ('#a$'%a

: " =PaW?@

X a'o#a$+#,o g'ra#,+ %o# $o,or+ +*+,,r'%o a'#%ro#o %o# 1 %opp'a po*ar+@

Y fr+0)+#a (' r+,+

f : "=H?@

Pag.8


9/22

STUDIO DEL MOTORE ELETTRICO

D+,+r$'#o '* #)$+ro (' g'r'>$'#),o (' f)#'o#a$+#,o (+* $o,or+ +*+,,r'%o9

# : g'r'>$'#),o ,+or'%' $o,or+ =g'r'>$'#),o?2

f : fr+0)+#a (+**a %orr+#,+ +*+,,r'%a (' r+,+ : "=H?2 p : #)$+ro %opp'+ po*ar' pr++#,' )**o ,a,or+ (+* $o,or+ : 12

n=F"∗ f / p=F"∗" /1=3""" [ giri /minuto] @

#+ff : #)$+ro (' g'r'>$'#),o r+a*' (+* $o,or+ =g'r'>$'#?2

: %orr'$+#,o (+* $o,or+ a* r+g'$+ (' f)#'o#a$+#,o ,+or'%o : 32

s=n−neff / n ;da cui 9 neff =n∗1− s=3"""∗1−"2"3 =!1" [ giri /min ]

STUDIO DELLA GIRANTE

P+r (+f'#'r+ ' para$+,r' g+o$+,r'%' + %'#+$a,'%' (' 6a+2 *a ,'po*og'a + '* r+#('$+#,o (+**a po$pa

fa%%'o )o (' ()+ '#('%' %ara,,+r','%' %&+ o#o #)$+r' a,,ra/+ro ' 0)a*' %*a'f'%o *a g+o$+,r'a (+**a

$a%%&'#a.

: pr'$o '#('%+ %ara,,+r','%o (a %)' (+,+r$'#o '* r+#('$+#,o ,o,a*+ X, + *a ,'po*og'a (+**a g+o$+,r'a

(+**a $a%%&'#a2

#0 : +%o#(o '#('%+ %ara,,+r','%o (a %)' (+,+r$'#o *+ /+*o%', a'a*+ + ra('a*+ (+* *'0)'(o pr++#,'

r'p+,,'/a$+#,+ #+* %a#a*+ '#,+rpa*ar+ $+r'('a#o a**a 6o%%a (' ap'ra'o#+ + a**a $a#(a,a (+**ag'ra#,+2

[ : /+*o%', a#go*ar+ (' f)#'o#a$+#,o g'ra#,+ =ra(>?2

g : /a*or+ (+**a a%%+*+ra'o#+ (' gra/', : 281=$>?2

: por,a,a po$pa : "2"=$>?

ω=!∗∗neff /F"=!∗∗!1" /F"=3"B [ rad / s ]

k =∗ Q / B g ∗ H 3=3"B∗ "2"F /B

281∗" 3="2F

nsq= neff ∗ Q / B H 3= !1"∗ "2"F /B

"3=3F2F!

Pag.


10/22

(a* ('agra$$a a**+ga,o #+**a f'g.! pr+%+(+#,+ o,,+#go '* r+#('$+#,o '(ra)*'%o (+**a $a%%&'#a

op+ra,r'%+ %&+ %o$+ ' /+(+ - a* $a'$o *'/+**o p+r *a por,a,a '# 0)+,'o#+2 %'5 /)o* ('r+ %&+ '

para$+,r' (' f)#'o#a$+#,o (+**a $a%%&'#a o#o ,a,' '#('/'()a,' %o# )#a 6)o#a %+*,a9

Pag.1"


11/22

X' : r+#('$+#,o '(ra)*'%o po$pa : "2K.

A/r+$o po' %&+ '* r+#('$+#,o ,o,a*+ (+**a $a%%&'#a ar (a,o (a

X, : X'WX/WXo.

Ipo,''a$o9

X/ : r+#('$+#,o /o*)$+,r'%o %&+ ,'+#+ %o#,o (+**a r'%'r%o*a'o#+ (' *'0)'(o ,ra $a#(a,a +

ap'ra'o#+ : "2@

Xo : r+#('$+#,o orga#'%o o $+%%a#'%o %&+ ,'+#+ %o#,o (+**+ r+',+#+ $+%%a#'%&+ pa'/+ : "2K@

a**ora

X, : "2KW"2W"2K : "2.

La po,+#a aor6',a (a**a po$pa ar9

N =∗ g ∗ H ∗Q / t =1"""∗281∗"∗"2"F /"2FB=B!18 [W ] @

*a %opp'a aor6',a (a**a po$pa ar9

= N /= B!18/3"B=1B1 [ N ∗m ]

Ora ('$+#'o#'a$o *4a*6+ro %&+ $)o/+ *a g'ra#,+ p+r po' ,a6'*'r#+ '* ('a$+,ro (' '$6o%%o.

Co,r)'a$o *4a*6+ro '# a%%'a'o ,'p'a,o (a 6o#'f'%a 3CrN'Mo UNI EN 1""83\1 %o# %ar'%o

$a'$o R$ : 3" =N>$$? + %ar'%o (' #+r/a$+#,o R+H : K=N>$$?.

L4a*6+ro - ogg+,,o a ,or'o#+ p+r%'5 op+ra#(o #+* +,,or+ propor'o#a*+ (+* ('agra$$a (' ,ra'o#+9

amm= !e" /3=KFD /3=!DD [ N /mm!]

am m= am m / 3=!DD / 3=1BK [ N /mm!]

p+r '%)r+a %o#,ro +/+#,)a*' f+#o$+#' /'6ra,or' pr+#(o ;a$$ : 1"" =N>$$?.

Co#'(+ro po' )# %o+ff'%'+#,+ %orr+,,'/o (+**a %opp'a %&+ ,'+#+ %o#,o (+**+ ',)a'o#' (' ,ra#',or'o

%o$+ a**4a//'a$+#,o (+**a po$pa '# %)' *a %opp'a #+%+ar'a p)5 r')*,ar+ $agg'or+ (' 0)+**a ('

f)#'o#a$+#,o a r+g'$+9

% : 12!

M+ff : MW% : 11W12! : 1 =NW$? : 1"""=NW$$?.

A**a f'#+ (o/r ++r+9

amm≥ eff /Wt = eff /∗d 3/1F

(a %)'

d ≥ 3 1F∗ eff /∗ am m= 3 1F∗1F""" / 321B∗1"" ≈ !"2 [mm ]

Pag.11


12/22

pr+#(o ( : ! p+r ,+#+r pr++#,+ *a pr++#a (+**4a**ogg'a$+#,o (+**a *'#g)+,,a (' %o**+ga$+#,o ,ra

a*6+ro + g'ra#,+@

'* ('a$+,ro +,+r#o (+* $oo (+**a g'ra#,+ ar (' ($oo : =$$? '# 0)a#,o (+/+ op',ar+ *a

%a/a 6ro%%'a,a %&+ por,a *a *'#g)+,,a. P+r 0)+,o a*6+ro *a *'#g)+,,a &a )#a *arg&+a 6 : 8=$$? +

)#a a*,+a & : K=$$?. La *)#g+a (+**a *'#g)+,,a *a %a*%o*o %o# *+ +g)+#,' r+*a'o#'

,)('o (+* ,ag*'o9

am m=D" [ N /mm!]

am m≥3∗ eff /!∗ d /! ∗#∗$

(a %)'

$ ≥3∗ eff /!∗d / ! ∗#∗ am m =3∗1F"""/ !∗! /! ∗8∗" ≈! [m m ]

A(o,,o ()+ *'#g)+,,+ + ,+#+#(o pr++#,+ *+ 6o$6a,)r+ (' +,r+$', (+**a *'#g)+,,a +a ar

8]K]3 UNI "\A.

Da 0)' (+)$'a$o a#%&+ '* ('a$+,ro (+* $oo ($ : "2"=$?

Da* +%o#(o ('agra$$a '# f'g. 1 %o# '* /a*or+ #0 pr+%+(+#,+ o,,+#go (+' %o+ff'%'+#,' %&+ $'

+r/o#o p+r (+,+r$'#ar+ *+ /+*o%', a'a*+2 pr++#,+ a**a 6o%%a (4ap'ra'o#+ + *a /+*o%', ra('a*+

)**a $a#(a,a.

^%1 : "21K@

^%! : "213.

L+ /+*o%', )**a 6o%%a (' ap'ra'o#+ + ) 0)+**a (' $a#(a,a o#o (a,+ (a9

ca1= %c1∗ !∗ g ∗ H ="21KD∗ !∗281∗D"=D2B8 [m / s ]ve$ocit& assia$e a$$a #occa d ' aspira(ione

cr2= %c2∗ !∗ g ∗ H ="213D∗ !∗281∗D"=B2!! [m / s] v e$ocit& radia$e a $$o scarico de$$a girante

*a %r! p)5 ++r+ o,,+#),a a#%&+ (+,+r$'#a#(o )* ('agra$$a (' f'g. '* /a*or+ (+* #)$+ro (' pr+'o#+ _ + '* #)$+ro (' f*)o ` %a*%o*a,' %o# '* /a*or+ (' pr+%+(+#,+9

="2D= g ∗ H /u2!

(a %)'

u2= g ∗ H /= 281∗" /"2=3123! [m / s ]

="21B=cr2 /u2

(a %)'

Pag.1!


13/22

cr2=∗u2= B238 [m / s]

%&+ - /'%'#a a**a pr+%+(+#,+

I* /a*or+ (+**4ar+a (+**a 6o%%a (4ap'ra'o#+ *o %a*%o*o ,+#+#(o %o#,o (+* r+#('$+#,o /o*)$+,r'%o

(+**a $a%%&'#a %&+ %o#'(+ra '* r'%'r%o*o )**+ ,+#),+ a#,+r'or' + po,+r'or'.

A1: ar+a +'o#+ (' '$6o%%o (+**a g'ra#,+ =$?

)1∗ca1=Q / v="2"DF /"2D="2"D8 [m3/ s]

)1=Q / ca1∗ v ="2"F /2B8∗"2 = "2"1"8 [m! ]=1"8"" [mm!]

T),,a 0)+,a ar+a (+/+ ++r+ %o#'(+ra,a +%*)(+#(o *a pr++#a (+**+ pa*+2 p+r%'5 (o/r ++r+

$agg'ora,a (' )#a %+r,a 0)a#,', p+r ,+#+r pr++#,+ *a +'o#+ (4'#go$6ro (+**+ pa*+.

Ora ,)('a$o *+ %o#(''o#' g+o$+,r'%&+ (+**a g'ra#,+ a**4'$6o%%o a* *4a*,+a (+* ('a$+,ro (+*

$oo %&+ - '* ('a$+,ro '#,+r#o (+**a +'o#+ (' ap'ra'o#+.

)1' : /+*o%', ,a#g+#'a*+ (+**a g'ra#,+ #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro (+* $oo =$>?@

)1+ : /+*o%', ,a#g+#'a*+ (+**a g'ra#,+ #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $a'$o =$>?@

)1 : /+*o%', ,a#g+#'a*+ (+**a g'ra#,+ #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $+('o=$>?@

1' : /+*o%', r+*a,'/a (+* *'0)'(o #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro (+* $oo =$>?@

1+ : /+*o%', r+*a,'/a (+* *'0)'(o #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $a'$o =$>?@

1: /+*o%', r+*a,'/a (+* *'0)'(o #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $+('o =$>?@%a1 : /+*o%', a'a*+ a**4ap'ra'o#+ =$>?@

1' : a#go*o (+**a pa*a #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro (+* $oo r'p+,,o a* p'a#o

p+rp+#('%o*ar+ a**4a+ (+**a g'ra#,+ =b?@

1+ : a#go*o (+**a pa*a #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $a'$o r'p+,,o a* p'a#o

p+rp+#('%o*ar+ a**4a+ (+**a g'ra#,+ =b?@

1 : a#go*o (+**a pa*a #+**a +'o#+ (' ap'ra'o#+ a* ('a$+,ro $+('o r'p+,,o a* p'a#o

p+rp+#('%o*ar+ a**4a+ (+**a g'ra#,+ =b?@

(' : ('a$+,ro $oo o ('a$+,ro '#,+r#o (+**a 6o%%a (4ap'ra'o#+ =$$?@

(+ : ('a$+,ro +,+r#o (+**a 6o%%a (4ap'ra'o#+ =$$?@

( : ('a$+,ro $+('o (+**a +'o#+ a( a#+**o a**a 6o%%a (' ap'ra'o#+ =$$?@

D : ('a$+,ro (+**a 6o%%a (' %ar'%o =$$?@

Pag.13

N

A

%a

)


14/22

!: a#go*o (+**a pa*a a**a +'o#+ (' %ar'%o /a*),a,a r'p+,,o a**a ,a#g+#,+ a D =b?.

u1i=!∗∗neff ∗di /!∗F" =!∗321B∗!1"∗"2"B /!∗F" =F28 [m / s ]

ca1=u1i∗,a# (β1')da cuiβ1'=ar%,a# (ca1/u1i)=ar%,a# (2B8/F28)=382F[* ]

,+#+#(o %o#,ro (+**a pr+ro,a'o#+ (+* *'0)'(o pr++#,+ a**4ap'ra'o#+

1' : 38b

ca1=w1i∗'# 1'da cui w1i=ca1 /'# 1 '=2B8 / '# B" * =82! [m / s ]

a**4a)$+#,ar+ (+* ('a$+,ro (' '$6o%%o a)$+#,a *a ) f'#o a )1+ c )1' p+r%'5 ar a#%&+ 1+ d 1'

+ *a +'o#+ (' '#go$6ro (+**a pa*a ,+#(+ a ('$'#)'r+ (a* ('a$+,ro (+* $oo a* ('a$+,ro $a'$o

(' ap'ra'o#+.

Co#'(+r'a$o *a '#go*a pa*a + ,a6'*'%o *4'#go$6ro %&+ +a offr+ a**4 ap'ra'o#+

p : p+or+ pa*a : =$$?@

+ : '#go$6ro pro/o%a,o (a**a pa*a a**4ap'ra'o#+ =$$?@

Pag.1

pa*a

6o%%a (4a.p'ra3'o#+

N1'

.p

.+1

D

(+

('

6!


15/22

se(1= sp / '# 1'∗! sp /!=F / '# 38 * ∗! 3≈8 [m m ]

Co#'(+r'a$o )# #)$+ro : K pa*+ p+r (+,+r$'#ar+ '* /a*or+ (+* ('a$+,ro +,+r#o (+ (' ap'ra'o#+2

a/r+$o9

)1=∗ de!

−di!

/ B−de−di ∗ ( ∗ se( /!

1"8""=321B∗de !−B!/B−de−B ∗∗8 /!

r'o*/o p+r ,+#,a,'/' 0)+,a +0)a'o#+ #+**a '#%og#',a (+ + *o $agg'oro p+r ,+#+r %o#,o (+**a

/ar'a'o#+ (' 1 (+ e 1! =$$?.

N+**4a#+**o %o$pr+o ,ra (' + (+ *a ) a)$+#,a 0)'#(' 1+d 1' p+r%'5 ora ,)('a$o *a pa*a

a**4a*,+a (' (+

u1e=!∗∗neff ∗de /!∗F" =!∗321B∗!1"∗"21! / !∗F" = !321B [m / s]

ca1=u1e∗,a#(β1e )dacuiβ1e=ar%,a# (ca1/u1e)=ar%,a# (28/!321)=13231[* ]

,+#+#(o %o#,o (+**a pr+ro,a'o#+ (+* *'0)'(o pr+#(o

1+ : 13b

ca1=w1e∗'# 1 e dacui w1e= c1 / '# 1 e= 2B8 /'# 13 * =!B23F [ m/ s ]

Ora %o#'(+ro 0)+**o %&+ a//'+#+ a**4a*,+a (+* ('a$+,ro $+('o (+**a +'o#+ a( a#+**o pr++#,+

)**a 6o%%a (' ap'ra'o#+

d = dedi /!="21!"2"B /!="2"8 [m ]=82 [m m ]

u1=!∗∗neff ∗d / !∗F" = !∗321B∗!1"∗"2"8/ !∗F" =12"" [m / s]

ca1=u1∗,a# 1 da cui 1=ar%,a# ca1 /u1 =ar%,a# 2B8 /12""=!"2"F [* ]

,+#+#(o %o#,o (+**a pr+ro,a'o#+ (+* *'0)'(o pr+#(o

1 : !"b

ca1=w1∗'# 1 da cui w1= ca1 / '# 1 =2B8 / '# !" * =1F2"! [m / s]

R',)('o *a +'o#+ (' '#gr+o %o# *4a#go*o pr++#,+ #+* ('a$+,ro $+('o (+**4a#+**o (4ap'ra'o#+

se(1= sp / '# 1 ∗! sp /!=F / '# !" * ∗! 3≈1128 [m m ]

)=∗ de !−di ! / B−de−di ∗ ( ∗ se( /!

1"8""=321B∗de !−B!/B− de−B ∗K∗1128 /!

%&+ /a*+ p+r (+ : 1=$$? /a*or+ $o*,o /'%'#o a 0)+**o %+*,o

Pag.1


16/22

p+r%'5 ,+#+#(o %o#,o (+**+ p+r(',+ (' %ar'%o + (+**+ for$a'o#' (' o,a#+ '$6ra,,a#,' )**+ par+,'

'#,+r#+ (+**a g'ra#,+ (o/),+ a**a pr++#a (' *'0)'(' #o# a%%)ra,a$+#,+ f'*,ra,' (+ : 1!=$$?.

Ora ,)('o *a g+o$+,r'a (+**a g'ra#,+ a**a 6o%%a (' %ar'%o (+,+r$'#a#(o '* ('a$+,ro (+**a g'ra#,+

a**a $a#(a,a + *4a#go*a'o#+ (+**+ pa*+.

D : ('a$+,ro (+**a g'ra#,+ a**a $a#(a,a =$$?@

u2=!∗∗neff / F" ∗ + /! ; dacui

+=!∗u2 /!∗neff /F" =!∗3123! / !∗321B∗!1" /F" ="2!" [m ] ;

po#go

D : "2!1"=$? : !1"=$$?@

+ r'%a*%o*a#(o

u2=!∗∗neff /F" ∗ + /!=3128 [m / s ] ;

%o$+ /+('a$o - )# /a*or+ a%%+,,a6'*+ p+r )#a g'ra#,+ '# g&'a p+r '* 0)a*+ &o9

=ϱ∗u2!="""∗3128 !=!"BB83 [ N /m!]=2! [ N / mm!] amm g"isa,

Co$+ app'a$o (a**a +'o#+ '#''a*+9

L=c2∗u2∗%o α2 [ j / k g ]

/a*+ a#%&+ L : gWHr a**ora

g ∗ Hr =c2∗u2∗%o ![ j /k g ]

Hr : pr+/a*+#a g'ra#,+ =$?@

%! : /+*o%', ao*),a (+* *'0)'(o a**4)%',a (+**a g'ra#,+ =$>?@

,),,o - '**),ra,o #+**a f'g)ra o,,o,a#,+

%!, : /+*o%', ao*),a a**a $a#(a,a +#a %orr+'o#+ =$>?@

!, : /+*o%', r+*a,'/a a**a 6o%%a (' %ar'%o +#a %orr+'o#+=$>?@!, : a#go*o ,ra %!, + )! =b?@

!, : a#go*o ,ra !, + )! =b?@

%!: /+*o%', ao*),a a**a $a#(a,a %o# %orr+'o#+ =$>?@

! : /+*o%', r+*a,'/a a**a 6o%%a (' %ar'%o %o# %orr+'o#+=$>?@

! : a#go*o ,ra %! + )! =b?@

! : a#go*o ,ra ! + )! =b?@

Pag.1


17/22

Pag.1K

%!

G!

%r!

N!

A!

)!

A!,

G!

%!

N!

%!W%o.7G!8

%!,W%o.7G!,8

%!,

%r!

A!

G!,

N!,


18/22

N+**o ,)('o (+' ,r'a#go*' (+**+ /+*o%', (+66o ,+#+r %o#,o (+**o %o,a$+#,o (+**a ('r+'o#+ r+a*+

(+* *'0)'(o (a 0)+**a (+**a pa*a2 0)'#(' *a ('r+'o#+ (' ! + '* /a*or+ (' ! ' o,,+rra##o %o# )#a

oppor,)#a %orr+'o#+ (+**a ('r+'o#+ (+* prof'*o pa*ar+ a**a $a#(a,a@ '#,ro()%o )# %o+ff'%'+#,+

%orr+,,'/o (+**a pr+/a*+#a %H : "2K8 %&+ %o**+ga *a pr+/a*+#a #o$'#a*+ (+**a g'ra#,+ Hr a 0)+**a

%orr+,,a HrW

Hr =cH ∗ Hr -

Hr = H / i

Hr -= Hr /cH = H / i∗cH

H = Hr -∗ i∗cH = c2∗u2∗%o ! ∗ i∗cH / g

c2∗%o ! = H ∗ g / u2∗ i∗cH ="∗28 /3128∗"2K∗"2K8=!82"F [m / s ]

/a*+ a#%&+ *a

cr2=u2−c2∗%o ! ∗,a# ! [m / s ]

(a %)'

!=ar%,a# cr2 / u2−c2∗%o ! =ar%,a# B2!! / 3128−!82"F = BK211≈B8 [* ]

%&+ - *4a#go*o (' '#%*'#a'o#+ (+**a pa*a a**a $a#(a,a.

D+#,ro *a g'ra#,+ *a /+*o%', r+*a,'/a a**4)%',a ar ,a*+ %&+9

w2∗%o ! =u2−c2∗%o ! da cui

w2=u2−c2∗%o !/%o ! =3128−!82"F /"2FF=.K3 [m / s ]

)+,o /a*or+ ('ff+r'%+ ,roppo (a 12 '# par,'%o*ar+ *a /+*o%', r+*a,'/a ,ra *4ap'ra'o#+ + *a

$a#(a,a ('$'#)'%+ ,roppo + %'5 %o$por,+r+66+ )# %o#(o,,o '#,+rpa*ar+ +%%+'/a$+#,+ ('/+rg+#,+

%&+ p)5 (ar+ *)ogo a (',a%%o (' /+#a2 %a/',a'o#+ + ,a**o (+**a po$pa %o# %a,,'/' f)#'o#a$+#,'

%&+ por,a#o a**a (',r)'o#+ (+**a g'ra#,+ + a %a,,'/+ pr+,a'o#'. B'og#a por,ar+ *a '* /a*or+ (' !

/'%'#o a 0)+**o (' 1. P+r far+ 0)+,o $a#,+#+#(o '#a*,+ra,+ *+ pr+,a'o#' (+**a g'ra#,+ o%%orr+a)$+#,ar+ *a /+*o%', p+r'f+r'%a )!. No# po,+#(o ag'r+ )* #)$+ro (' g'r' #+ff '#,+r/+#'a$o )*

('a$+,ro +,+r#o (+**a g'ra#,+ D.

Pr+#(o

D : "2! =$? : !" =$$?

/o*go ' %a*%o*' pr+%+(+#,' + o,,+#go

)! : 382"K=$?@

%r! : 233=$>?@

: 13 =N>$$?@

%!W%o7! : !32 =$>?@

Pag.18


19/22

! : !"2!1 =b? %&+ arro,o#(o a !1 =b?

! : 121=$>?

o,,+#go !e1 %&+ - 0)+**o %&+ /o*+/a$o.

Ora ,)('o '* /a*or+ (+ #)$+ro (' pa*+ %o# )#a for$)*a +$p'r'%a9

( =F2∗ +de / +−de ∗'# 1 ! /! =F2∗!"1! /!"−1! ∗'# !"!1 /!

: 23

Da**4+p+r'+#a r')*,a %&+ '* #)$+ro (' pa*+ %o# '* 0)a*+ &o r+#('$+#,o $a'$o - '#f+r'or+ a*

/a*or+ o,,+#),o %o# *a for$)*a pr+%+(+#,+. P+r%'5 ('$'#)'%o f'#o a :K.

Co$+ /+('a$o %4- %orr'po#(+#a ,ra '* r')*,a,o o,,+#),o + *a %+*,a '#''a*+.

D+,+r$'#o ora *4'#go$6ro (o/),o a**a pr++#a (+**+ pa*+ )**o %ar'%o (+**a g'ra#,+9

se(2= sp / '# ! ∗! sp /!=F / '# !1 * ∗!3≈112 [m m]

L4ar+a (+**a +'o#+ #+,,a a**o %ar'%o ar9

)2∗cr2=Q / v="2"DF /"2D="2"D8 [m3/ s]

)2=Q / cr2∗ v ="2"F/ 233∗"2 ="2"111 [m!]=111"" [mm!]

6! : p+or+ (+* %a#a*+ '#,+rpa*ar+ a**o %ar'%o =$$?@

(a**a +g)+#,+ +0)a'o#+ o,,+#go '* /a*or+ (' 6!9

Pag.1

.p

.+3!

N!

6!

6o%%a ('.%ar'%o


20/22

)2=∗ +∗#2− ( ∗#2∗ se(2

#2= )2 /∗ +− ( ∗ se(2 =111"" /321B∗!"−K∗112 =12K[m m ]

pr+#(o 6! :12=$$? p+r g*' ,+' $o,'/' %o# %)' &o %+*,o (+.

Pag.!"


21/22

DISEGNO DELLE PALE INTERNE ALLA

GIRANTE

Co#'(+ro '* %a#a*+ '#,+rpa*ar+ %o$pr+o ,ra '* ('%o a#,+r'or+

+ 0)+**o po,+r'or+.

Co#'(+ro *a o#a '#,+r#a a* ('%o a#,+r'or+ (' %o#g')#'o#+

%o# *a pa*a + %o,r)'%o ) +a )# +r'+ (' p)#,' +0)'(',a#,' a par,'r+

(a* ('a$+,ro D f'#o a**4ap'ra'o#+ (' ('a$+,ro (+.

Co#'(+ro *a o#a '#,+r#a a* ('%o po,+r'or+ (' %o#g')#'o#+

%o# *a pa*a + %o,r)'%o ) +a )#a +r'+ (' p)#,' (',a#,' ,ra *oro

%o$+ ' pr+%+(+#,' a par,'r+ (a* ('a$+,ro D f'#o a**4ap'ra'o#+

(' ('a$+,ro ('.

Co#'(+ro *4a+ $+('a#o (+* %a#a*+ '#,+rpa*ar+ + %o,r)'%o

) +o )#a +r'+ (' p)#,' (',a#,' ,ra *oro %o$+ ' pr+%+(+#,'

a par,'r+ (a* ('a$+,ro D f'#o a**4ap'ra'o#+ %o# ('a$+,ro (.

Tra%%'o )# #)$+ro (' *'#++ para**+*+2 (',a#,' ,ra *oro %o$+ ' p)#,' %+*,' #+* %a#a*+ '#,+rpa*ar+2 par'a* #)$+ro (' p)#,' pr++#,' #+**a o#a '#,+r#a a* ('%o po,+r'or+.

Par,+#(o (a**a pr'$a r'ga %o# )#a '#%*'#a'o#+ par' a ! %+#(o )**+ r'g&+ %a$6'a#(o '#%*'#a'o#+

f'#o a( arr'/ar+ a 1'2 po' (a ! a 1 + '#f'#+ (a ! a 1+.

Co#'(+ro *a *)#g&+a (+* +,,or+ (+**a pa*a %o$pr+o ,ra ()+ *'#++ para**+*+ (+**a f'g)ra

pr+%+(+#,+ + *+ r'por,o '# )#a pro'+'o#+ (+**a g'ra#,+ '# )# p'a#o p+rp+#('%o*ar+ a**4a+ '# %)' &o

ragg'o par' a* ragg'o (+* p)#,o (o/+ &o /a*),a,o *a pr+%+(+#,+ *)#g&+a (+**a pa*a. D'+g#o '*

prof'*o (a ! a 1'2 (a ! a 12 (a ! a 1+.

Pag.!1

D

(+(

('

&


22/22

Da**a pa*a '# (' a**a pa*a '# D ('+g#o ,a#,' a' ra('a*' +0)'(',a#,' a#go*ar$+#,+ %&+ $' +r/o#o

p+r ap+r+ *+ %oor('#a,+ (+**4+,ra(oo pa*ar+ + (+**4'#,ra(oo pa*ar+.

A**a f'#+ o,,+#go '* ('+g#o (+**a pa*a.

Pag.!!

('

D

&

'#,ra(o..o

+.,ra(o..o

Progetto girante centrifuga

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