Indagine sperimentale del flusso bifase acqua-aria in regime intermittente entro condotti orizzontali

&DSLWROR
,QWURGX]LRQH
 *HQHUDOLWj
,OWHUPLQHIDVHLQGLFDXQDSDUWHRPRJHQHDGLXQVLVWHPDHWHURJHQHR
GHOLPLWDWDG XQDVXSHUILFLHFRQQHVVDRPHQRDWWUDYHUVRFXLXQDRSL
JUDQGH]]HVRQRGLVFRQWLQXH6LSDUODGLIOXVVRPXOWLIDVHTXDQGRXQVLVWHPD
FRVWLWXLWRGDSLIDVLPXRYHLQXQDFHUWDUHJLRQHGHOORVSD]LRSHUHVHPSLRLQXQ
FRQGRWWR
)HQRPHQLGLTXHVWRJHQHUHVLLQFRQWUDQRLQVYDULDWLF PSLGHOO
LQJHJQHULD
SHUHVHPSLRTXDQGRVLHVWUDHLOJUHJJLRGDLJLDFLPHQWLFLzFKHJHQHUDOPHQWHVL
RWWLHQH qXQDPLVFHODGLSHWUROLRDFTXDJ VHVDEELDPDQFKHXQFRPXQH
VFDPELDWRUHGLFDORUHFKHVIUXWWLXQIOXLGRLQHEROOL]LRQHRQFRQGHQVD]LRQHqVHGH
GLXQIOXVVRELIDVHOLTXLGRYDSRUH
,QSDUWLFRODUHLI XVVLOLTXLGRJDVKDQQRXQDJUDQGHLPSRUWDQ]DLQVYDULDWH
DSSOLFD]LRQLQRQRVWDQWHFLzODORURQDWXUDHVWUHPDPHQWHFRPSOHVVDKDIDWWRVuFKH
OHULFHUFKHLQTXHVWRFDPSRDEELDQRFRQGRWWRDULVXOWDWLGLQDWXUDVRVWDQ]LDOPHQWH
HPSLULFDHGL OLPLWDWD DSSOLFDELOLWj,PDJJLRULSUREOHPLFKHV LQFRQWUDQR
QHOO
DIIURQWDUHO VWXGLRLWDOLVLVWHPLVRQROHJDWLFRPHVLSXzIDFLOPHQWHLQWXLUH
DOODFRPSOHVVDJ RPHWULDGHOO
LQWHUIDFFLDI DLO OLTXLGRHLOJDV
4XHVWRODYRURSUHVHQWDLULVXOWDWLGLXQ
LQGDJLQHVSHULPHQWDOHVX XQD
PLVFHODDUL  FTXDLQPRWRHQWURF QGRWWLUL]]RQWDOLYROWDDGDSSURIRQGLUHOD
FRQRVFHQ]DGHOODVWUXWWXUDORF OHG OIOXVVR*OLHVSHULPHQWLVRQRVWDWLHVHJXLWL
VXOO
LPSLDQWRHVLVWHQWHSUHVVRLO'LSDUWLPHQWRGL( HUJHWLFDGHO3ROLWHFQLFRGL
0LODQRHOO
DPELWRGLXQSURJUDPPDGLULFHUFDILQDQ]LDWRFRQIRQGL08567




H




 2SHUDWRULGLPHGLD
/DQDWXUDQRQVWD]LRQDULDGHLIOXVVLELIDVHUHQGHLIILFROWRVRVHJXLUHWXWWHO
IOXWWXD]LRQLGHOOHJUDQGH]]HFKHOLGHVFULYRQRHGLPSRQHLOULFRUVRDLOURYDORUL
PHGL6LFRQVLGHULLQXQGDWRSXQWRXQDJUDQGH]]D)FKHVLDIXQ]LRQHGHOWHPSRLO
VXRYDORUHP GLRq
   
³

 
7W
W



GWW)
7

7W)
LQFXL O
LQWHUYDOORGL LQWHJUD]LRQH7GHY
HVVHUHVXIILFLHQWHPHQWHOXQJR
SDUDJRQDWRDOOHFRVWDQWLGLWHPSRGHOOHIOXWWXD]LRQL,OYDORUHGL W) GLSHQGHVLD
GDOO·LVWDQWHLQL]LDOHWVLDGDOO·LQWHUYDOOR7QHOFDVRLQFXL)VLDXQDJUDQGH]]D
VWD]LRQDULDODPHGLDQRQGLSHQGHGDWHVLVFULYH
   
³
 
7
GWW)
7

7)
4XDORUD)VLUHODWLYDDGXQ VRODGHOOHGXHIDVLVL LQGLFDRQ)NGRYHN O
SHULO OLTXLGRHN JSHULOJDVLQTXHVWRFDVRqSRVVLELOHHIIHWWXDUHO
LQWHJUD]LRQH
VRORTXDQGRqSUHVHQWHODIDVHLQTXHVWLRQHRWWHQHQGRODIRUPD
 
 
³
 
N
7
N
N
N
N
GWW)
7

)
GRYH7NUDSSUHVHQWDLOW PSRFXPXODWRGLSHUPDQHQ]DG OODI VHN
6LSXzDQFKHFDOFRODUHO PHGLDDUHLFDVXGLXQDVH]LRQHWUDVYHUVDOHGHO
FRQGRWWRLQXQFHUWRLVWDQWHDGVHPSLRSHUF VWUXLUHPRGHOOLPRQRGLPHQVLRQDOL
FKHVL LQGLFDFRQ
 
³
 
$
NN
G$)
$

) [
$QDORJDPHQWHVLFDOFRODODPHGLDVXXQGRPLQLRWULGLPHQVLRQDOH9
 
 
³
 
9
N
9
N
G9)
9

) [
&RPHQ OFDVRGHOOHPHGLHWHPSRUDOLVLSXzIDUHULIHULPHQWRVRORDO
GRPLQLR$NRFFXSDWRG OODIDVHN
 
³
 
N
$
N
N
N
N
G$)
$

) [






,QEDVHDOOHSURSULHWjG JOLLQWHJUDOLTXHVWLRSHUDWRULGLPHGLDVSD]LDOHH
WHPSRUDOHFRPPXWDQRIUDORU 
    GWG$W)
$

7

G$GWW)
7

$

7 $
N
$ 7
N
³ ³³ ³
¿
¾
½
¯
®
­
 
¿
¾
½
¯
®
­
[[
,QJHQHUDOHO PHGLDGHOSURGRWWRGLGXHJUDQGH]]HQRQqXJXDOH
SURGRWWRGHLORURYDORULPHGL
       
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
z
³³³
$$$
G$*
$

G$)
$

G$*)
$

[[[[
%LVRJQDRVVHUYDUHFKHV )H*IRVVHURFRVWDQWLVLSRWUHEEHURHVW DUUH
GDOO
LQWHJUDOHODGLYHQWHUHEEHXQ
XJXDJOLDQ]DD ORUDVL LQWURGXFHXQ
FRHIILFLHQWHUDSSUHVHQWDWLYRGHOODQRQXQLIRUPLWjGHOOHGLVWULEX]LRQLGL)H*
   
   [[
[[
*)
*)
& 
 'HILQL]LRQHGHOOHJUDQGH]]HIRQGDPHQWDOL
 )UD]LRQHGLYXRWR
/DIUD]LRQHGLYXRWRHJqXQDJUDQGH]]DDGLPHQVLRQDOHFKHLQGLFDTXDOH
SRU]LRQHGLXQGRPLQLRVSD]LDOHRWHPSRUDOHVL RFFXSDWDG OODI VHJDVVRVDLQ
EDVHDTXHVWDGHILQL]LRQHVLSRVVRQRFDOFRODUHTXDWWURGLYHUVLYDORULGHOODIUD]LRQH
GLYXRWR
x /DIUD]LRQHGLYXRWRORFDOHUDSSUHVHQWDLOUDSSRUWRIUDLOWHPSRGLSHUPDQHQ]D
GHOODI VHJDVVRVDHODGXUDWDFRPSOHVVLYDGHOO
RVVHUYD]LRQHLQXQFHUWR
SXQWRGHOORVSD]LR/DSUHVHQ]DGHOODI VHNLQXQSXQWR[DOO
LVWDQWHWq
FRQWUDGGLVWLQWDDOYDORUHXQLWDULRGHOODVXDIXQ]LRQHFDUDWWHULVWLFDIXQ]LRQH
GHQVLWjGLIDVH
 
¯
®
­
 
WLVWDQWHDOO
NIDVHQHOOqQRVH
WLVWDQWHDOO
NIDVHQHOOqVH
W3
N
[
[
[
SHUWDQWRODIUD]LRQHGLYXRWRORFDOHqDPHGLDQHOWHPSRGL3J[W
     W3GWW3
7

J
7
JJ
[[[   H
³





x /DIUD]LRQHGLYXRWROXQJRXQDFRUGDqGHILQLWDFRPH
   
JO
J
/
JJ
//
/
G/W3
/

W

  H
³
[
x /DIUD]LRQHGLYXRWRPHGLDDUHLFDqLOUDSSRUWRIUDO
DUHDRFFXSDWDG OJ VH
O
DUHDGHOODVH]LRQHQRUPDOHGH FRQGRWWR
   
JO
J
$
JJJ
$$
$
G$W3
$

3W

   H
³
[
x /DIUD]LRQHGLYXRWRPHGLDLYROXPHLQILQHqG ILQLWDFRPH
 
 
 
JO
J
9
J
9
JJ
99
9
G9W3
9

3W

   H
³
[
/DIUD]LRQHGLYXRWRSXzHVVHUHFDOFRODWDDQFKHLWHUDQGROHRSHUD]LRQLG
PHGLDVSD]LDOHHWHPSRUDOHS UWLFRODUHLPSRUWDQ]DDVVXPHO IUD]LRQHGLYXRWR
VXOODVH]LRQHGHOFRQGRWWR
   [
JJ
W H H H
 7LWROR
,OWLWRORGHOODPLVFHODqLOU SSRUWRIUDODSRUWDWDLQPDVVDGHOJDVHODSRUWDWD
FRPSOHVVLYD
JO
J
00
0
[



 
6LGHILQLVFHDQFKHXQWLWRORLQYROXPHRYYHURLODSSRUWRIUDODSRUWDWDLQ
YROXPHGHOJDVHTXHOODWRWDOH
JO
J

99
9



 H
 9HORFLWj
6L LQGLFDRQXN[WODFRPSRQHQWHSDUDOOHOD DO
DVVHG OFRQGRWWRGHOOD
YHORFLWjORFDOHHGLVWDQWDQHDGHOOIDVHN






/HYHORFLWjVXSHUILFLDOLVRQRLQYHFHOHYHORFLWjGLFLDVFXQDIDVHPROWLSOLFDWH
SHUODIUD]LRQHGLYXRWRRGLOLTXLGR
 
OJOOO
JJJ
XXM
XM
H H 
H 
,OVLJQLILFDWRILVLF GHOOHY ORFLWjRVuGHILQLWHY HQHFKLDULWRGDLOURYDORUL
PHGL
   
$
9
G$X
$

M
N
$
NNN

 H 
³
[[
3HUWDQWRODYHORFLWjVXSHUILFLDOHGLXQDIDVHUDSSUHVHQWDODYHORFLWjKH
TXHOODIDVHDYUHEEHVHIOXLVVHGDVRODQHOFRQGRWWRFRQODVWHVVDSRUWDWDLQYROXPH
1HOVHJXLWRODYHORFLWjVXSHUILFLDOHPHGLD
N
M YHUUjLQGLFDWDVHPSOLFHPHQWHFRQ
-N6LGHILQLVFRQRDQFKH OHYH RFLWjVXSHUILFLDOLWRW OL
OJ
OJ
---
MMM
 
 
,OUDSSRUWRGHOOHY ORFLWjGHWWRDQFKHUDSSRUWRGLVF UULPHQWRqGD GD
H
H
   

9
9
$
9
$
9
X
X
6
O
J
O
O
J
J
O
O
J
J




5LFRUGDQGROHUHOD]LRQLHVLRWWLHQH
H
H
H
H
 
H
H
U
U
 
H
H
U
U



[
[
0
0


J
O
OJ
JO


/HYHORFLWjGLVFRUULPHQWRVR RLQILQHOHYHORFLWjGHOOHGXHIDVLLQXQVLVWHPD
GLULIHULPHQWRFKHWUDVODFRQYHORFLWjSDULDMSDUDOOHODPHQWHOO
DVV GHOFRQGRWWR
MXX
MXX
OOM
JJM
 
 






 3DUDPHWURGL0DUWLQHOOL
/HFRUUHOD]LRQLHV VWHQWLLQOHWWHUDWXUDVSHVVRH SULPRQROHYDULHJUDQGH]]H
LQIXQ]LRQHGLXQSDUDPHWURG ILQLWRGD0DUWLQHOOLQHJDQQL4XDUDQWD
JR
)
OR
)
G]
GS
G]
GS
;
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
 
GRYH 
OR
)
G]GS H 
JR
)
G]GS VRQRLJUDGLHQWLGLSUHVVLRQHG YXWLDOO
DWWULWRFKH
FLDVFXQDGHOOHGXHIDVLDYUHEEHVHIOXLVVHGDVRODQHOFRQGRWWRFRQODVWHVVDSRUWDWD
LQDOWUHSDUROHVRQRLJUDGLHQWLGLSUHVVLRQHSHUDWWULWRFDOFRODWLFRQOHYHORFLWj
VXSHUILFLDOL
4XHVWRSDUDPHWURIRUQLVFHXQ
LQGLFD]LRQHGLTXDQWRODPLVFHODELIDVHVLD
SLVLPLOHD OLTXLGR;!!RDOJDV;
 5HJLPLGL RWRHPDSSHGLIOXVVR
/DSULQFLSDOHGLIILFROWjQHOORVWXGLRHLIOXVVLELIDVHFRQVLVWHQHOORVWDELOLUH
TXDOHVLDODJHRPHWULDGHOI XVVRRYYHURODI UPDGHOO
LQWHUIDFFLDW DOHIDVL,QIDWWL
QRQqSRVVLELOHFRQRVFHUHDSULRULFRPHLGXHIOXLGLVLGLVSRQJDQRUHFLSURFDPHQWH
WXWWDYLDTXHVW
LQIRUPD]LRQHqLQGLVSHQVDELOHSHULOFD FRORGLJUDQGH]]HFRPHO
FDGXWHGLSUHVVLRQHHLFR IILFLHQWLGLVFDPELRWHUPLFR
6SHULPHQWDOPHQWHVLRVV UYDQRGLYHUVLUHJLPLGLPRWRDVHFRQGDGHOOD
JLDFLWXUDGHOFRQGRWWRGHOODSRUWDWDHGHOOHSURSULHWjWHUPRILVLFKHGLFLDVFXQD
GHOOHGXHIDVL/DILJXUDUDSSUHVHQWDLSLFRPXQLUHJLPLGLPRWRSHUOHPLVFHOH
OLTXLGRJDVLQFRQGRWWLRUL]]RQWDOL
x 0RWRVWUDWLILFDWROHGXHIDVLVRQRVHSDUDWHGDXQ
LQWHUIDFFLDSLDQDRQLO
OLTXLGRQHOODS UWHLQIHULRUHGHOWXERDFDXVDGHOODIRU]DGLJUDYLWjTXHVWR
UHJLPHKDOXRJRSHUEDVVHY ORFLWjGHOOLTXLGRHGHOJDV$OO
DXPHQWDUHGHOOD
YHORFLWjGHOJDVO
LQWHUIDFFLDVLLQ UHVSDIRUPDQGRRHFKHVLSURSDJDQR
QHOODGLUH]LRQHGHOIOXVVRODORURDPSLH]]DGLSHQGHROWUHFKHGDOOH
SURSULHWjI VLFKHGHLIOXLGLGDOODYHORFLWjUHODWLYDUDOHGXHIDVL
x 0RWRDQXODUHLOOLTXLGRVLGLVSRQHFRQWURODSDUHWHGHOFRQGRWWRIRUPDQGR
XQDQHOORGLVSHVVRUHYDULDELOHSLHOHYDWRQHOODSDUWHLQIHULRUHO
DQHOOR
SXzHVVHUHFRQWLQXRRPHQRHGqSRVVLELOHFKHODVXDVXSHUILFLHVLSU VHQWL
LQFUHVSDWDGDSLFFROHQGHLOJDVIOXLVFHDOO
LQWHUQRWUDVFLQDQGRPLQXVFROH
JRFFLROLQHGLOLTXLGR

)LJXUDUHJLPLGLPRWRDPRWRVWUDWLILFDWREP WRD QGHFPRWRDWDSSLG
PRWRDILRWWLHPRWRDQXODUHIPRWRDEROOH

x 0RWRDEROOHLOIOXVVRVLSUHVHQWDIRUPDWRGDXQDPDWULFHFRQWLQXDGLOLTXLGR
LQFXLLOJDVqGLVSHUVRVRWWRIRUPDGLEROOHFKHVLFRQFHQWUDQRQHOODSDUWH
VXSHULRUHGHOFRQGRWWRSHUTXHVWRPRWLYRLHQHGHWWRDOYROWDPRWR
GLVSHUVR
x 0RWR DWDSSL ODSDUWHLQIHULRUHGHOFRQGRWWRqRFFXSDWDG XQRVWUDWRGL
OLTXLGRDYHQWHDOWH]]DYDULDELOHVRSUDGLHVVRLOJDVVLPXRYHVRWWRIRUPDGL
JURVVHEROOHDOOXQJDWHVHSDUDWHIUDORURGDWDSSLGLOLTXLGRFKHRFFOXGRQR
O
LQWHUDVH]LRQHGHOFRQGRWWR
x 0RWRDILRWWLTXDQGRDSDUWLUHGDXQUHJLPHGLPRWRDWDSSLVLDXPHQWDOD
YHORFLWjGHOJDVLWDSSL LQJOREDQRX DIUD]LRQHGHOODI VHJDVVRVD
VRWWRIRUPDGL LQXVFROHERO LFLQH6S VVRPRWRDWDSSLHPRWRDILRWWL
YHQJRQRLQGLFDWLLQG VWLQWDPHQWHFRPHRWRLQWHUPLWWHQWH
3HUGHWHUPLQDUHDJHYROPHQWHLOUHJLPHGLPRWRFKHVL LQVWDXUDLQ
FRUULVSRQGHQ]DGLGHWHUPLQDWHFRQGL]LRQLGLIOXVVRVLULFRUUHDPDSSH
ELGLPHQVLRQDOLVXOOHTXDOL LFDPSLGLHVLVWHQ]DGHLGLYHUVLUHJLPLVRQRGHILQLWLL
IXQ]LRQHGLSDUDPHWULFDUDWWHULVWLFLGHOI XVVR4XHVWHPDSSHQRQVRQRSHUDOWURGL
YDOLGLWjJHQHUDOHLQTXDQWRq HVWUHPDPHQWHGLIILFLOHQHUHFRQWRGLWXWWHO
YDULDELOL LQJ RFRYHORFLWjVXSHUILFLDOLP VVHYROXPLFKHYLVFRVLWjWHQVLRQH
VXSHUILFLDOHGHOOLTXLGRGLDPHWURVFDEUH]]DHGLQFOLQD]LRQHG OFRQGRWWR
)LJXUDPDSSDGL0DQGKDQHHWDO

)LJXUDPDSSDGL7 LWHOH'XNOHU
)LJXUDFRQIURQWRIUDOHPDSSHGL7DLWHOH'XNOHUHGL0DQGKDQH

/DFRVWUX]LRQHGHOODSULPDDSSDGLIOXVVRVLGHYHD%DNHUFKH
LGHQWLILFzUHJLPLGLPRWRLQIXQ]LRQHGLGXHJUXSSLXQRDGLPHQVLRQDOHHXQR
QRFKH HVSULPRQRO
HIIHWWRGHOOHSRUWDWHLQPDVVDVSHFLILFKHGHOOHPDVVH
YROXPLFKHGHOOHYLVFRVLWjGHOOHWHQVLRQLVXSHUILFLDOLGH GXHIOXLGL
8QDPDSSDGLXVRPROWRIUHTXHQWHqTXHOODGRYXWDD0DQGKDQHHW O
UDSSUHVHQWDWDLQILJXUDVLWUDWWDGLXQDPDSSDEDVDWDVXULOLHYL
VSHULPHQWDOLU ODWLYLP VFHOHDFTXDDULDRPLVFHOHGLIOXLGLFRQSURSULHWjV PLOL
DTXHOOHGLDFTXDHGULDLQFRQGRWWLDYHQWLGLDPHWURLQIHULRUHD PQHO
GHLFDVLLOVXRXVRqPROWRVHPSOLFHULVSHWWRDOODPDSSDGL%DNHULQTXDQWROHVXH
FRRUGLQDWHQRQVRQRDOWURFKHO YHORFLWjVXSHUILFLDOLGH GXHIOXLGL
/DSULPDSSDEDVDWDVXPRGHOOLV PLWHRULFLGHOOHWUDQVL]LRQLG UHJ PHIX
SURSRVWDGD7 LWHOH'XNOHUHVVLSUHVHURLQF QVLGHUD]LRQHLPHFFDQLVPLG
WUDQVL]LRQHIUDFL TXHUHJLPLGLPRWRVWUDWLILFDWRDRQGHLQWHUPLWWHQWHDEROOHHG
DQXODUHLQGLYLGXDQGRLVHJXHQWLJUXSSLDG PHQVLRQDOL
 
O
O
J
JO
J
JO
HUIVXS
O
'-
).
FRVJ'
-
)
FRVJ
G]
GS
7
Q
 
D
UU
U
 
DUU
¸
¸
¹
·
¨
¨
©
§
 
7HVSULPHOUDSSRUWRWUDOHIRU]HGRYXWHDOODWXUEROHQ]DTXHOOHGRYXWHDO
JDOOHJJLDPHQWRHFDUDWWHUL]]DODWUDQVL]LRQHIUDPRWRLQWHUPLWWHQWHHPRWRDEROOH
)qXQQXPHURGL)URXGHPRGLILFDWRG FXLGLSHQGRQROHWUDQVL]LRQLIUDPRWR
VWUDWLILFDWRHLQ HUPLWWHQWHHIUDPRWRVWUDWLILFDWRHGQXODUH.qLOSURGRWWRGL)
SHUODUDGLFHTXDGUDWDGHOQXPHURGL5H\QROGVVXSHUILFLDOHGHOOLTXLGRHGqOHJDWR
DOODWUDQVL]LRQHIUDPRWRVWUDWLILFDWRHPRWRD QGH4XHVWLSDUDPHWULUDIILJXUDWLLQ
IXQ]LRQHGHOSDUDPHWURGL0DUWLQHOOLG ILQLVFRQRJOLD GDPHQWLUDSSUHVHQWDWLLQ
ILJXUDODILJXUDLQYHFHULSRUWDODPDSSDGL7DLWHOH'XNOHUVXOORVWHVVR
SLDQRFRRUGLQDWRGHOODPDSSDGL0DQGKDQH
/RVWXGLRHLPHFFDQLVPLG WUDQVL]LRQHqVWDWRDSSURIRQGLWRQHOFRUVRGHJOL
DQQLSRUWDQGRDULVXOWDWLGLFDUDWWHUHV PSUHLJHQHUDOH7DLWHOVXJJHUu
XQDSURFHGXUDSHUGHWHUPLQDUHLOUHJLPHGLPRWRGLXQDTXDOVLDVLPL FHODJDV
OLTXLGRQF QGRWWLYHUWLFDOLRUL]]RQWDOLRLQF QDWL1HOFDVRGLXQDPLVFHODDFTX 
DULDLQXQFRQGRWWRUL]]RQWDOHLULVXOWDWLGLWDOHSURFHGXUDWURYDQRULVFRQWURLQ
TXDQWRRVVHUYDWRGD0DQGKDQHHWDO




&DSLWROR
0RGHOOL
 (TXD]LRQLGLFRQVHUYD]LRQH
,OPRWRGLXQJHQHULFRIOXLGRPRQRIDVHqGHVFULWWRGDHTXD]LRQLLQWHJUDOLFKH
HVSULPRQRODFRQVHUYD]LRQHGHOODPDVVDGHOODTXDQWLWjG PRWRHGHOO·HQHUJLD6HOH
YDULDELOLVRQRF QWLQXHFRQODORURGHULYDWDQHOGRPLQLRGLLQWHJUD]LRQHHGLQROWUH
HVLVWHORMDFRELDQRGHOODWUDVIRUPD]LRQHIUDF RUGLQDWH HXOHULDQHVSD]LDOLH
ODJUDQJLDQHPDW ULDOLDOORUDY OHLOWHRUHPDGHOWUDVSRUWRGL5H\QROGVHVL
RWWHQJRQROH HTXD]LRQLGLFRQVHUYD]LRQHLQIRUPDGLIIHUHQ]LDOH8QDJ QHULFD
HTXD]LRQHGLFRQVHUYD]LRQHVLSXzVFULYHUHQHOODIRUPD
  )U’ <U’
w
<Uw
-X $$
W
GRYHU<qODJUDQGH]]DFKHVLFRQVHUYD-LOIOXVVRLQXVFLWDHU)LOWHUPLQHGL
VRUJHQWHOHTXD]LRQLVSHFLILFKHVLRWWHQJRQRV VWLWXHQGR<-)VHFRQGRTXDQWR
LQGLFDWRQHOODW EHOOD
(TXD]LRQHGLFRQVHUYD]LRQH< - )
0DVVD   
4XDQWLWjGLPRWR X W,S )
(QHUJLD H
L
 W ,SXT $ X)$
7DEHOODYDORULDVVXQWLGDLSDUDPHWULQ OO
HTXD]LRQH


6HLOIOXLGRQ QqFRVWLWXLWRGDXQDVLQJRODIDVHORVFDPELRIUDRSHUDWRUL
GLIIHUHQ]LDOLHGLQWHJUDOLQRQqSLSRVVLELOHLQIDWWLVHEEHQHO TXD]LRQLGLELODQFLR
LQIRUPDGLIIHUHQ]LDOHYDOJDQRSHUFLDVFXQDIDVHVHSDUDWDPHQWHQRQSRVVRQRHVVHUH
DSSOLFDWHDOO·LQWHURGRPLQLRGLLQWHJUD]LRQHVHQ]DFKHVLDYLRODWDODFRQWLQXLWj'·DOWUD
SDUWHqLPSRVVLELOHXGGLYLGHUHWDO GRPLQLRSDUWLFRVWLWXLWHGDXQDVRODI VHLQ
TXDQWRODJHRPHWULDGHOO·LQWHUIDFFLDqVFRQRVFLXWD DSULRULHVVHQGRDVXDYROWD
IXQ]LRQHGHOORVSD]LRHGHOWHPSR3HUTXHVWRP WLYRVLUHQGHQ FHVVDULRGHVFULYHUH
LOIOXVVRDWWUDYHUVRLYDORULPHGLHOOHJUDQGH]]HLQJLRFROHLQIRUPD]LRQLSHUVH
GXUDQWHLOSURFHVVRGLPHGLDY QQRUHLQWURGRWWHQHOPRGHOORVXFFHVVLYDPHQWH
DWWUDYHUVRO FRVLGGHWWHUHOD]LRQLGLFK XVXUD
 0RGHOORRP JHQHR
,OPRGRSLVHPSOLFHSHUDIIURQWDUHORVWXGLRLXQIOXVVRELIDVHqTXHOORGL
VFKHPDWL]]DUORFRQXQDPLVFHODRPRJHQHDDY QWHODGHQVLWjHODYLVFRVLWjG XQ
IOXLGRPRQRIDVHILWWL]LR'LFRQVHJXHQ]DOHGXHIDVLKDQQRODVWHVVDYHORFLWjX+LQ
PRGRFKHLOUDSSRUWRGLVF UULPHQWR6VLDXQLWDULRULV OYHQGRODULVSHWWRDOOD
IUD]LRQHGLYXRWRSHU6 VLRWWLHQH
[
[


O
J


U
U

 H H
/·HTXD]LRQHHYLGHQ]LDO·LQFRQJUXHQ]DLQWULQVHFDGLTXHVWRPRGHOOR
LQIDWWLQRQKDVHQVRSDUODUHGLIUD]LRQHGLYXRWRLQXQFRQWLQXRRPRJHQHR
/DPDVVDYROXPLFDGHOODPLVFHODSHUGHILQL]LRQHqGDWDGDOUDSSRUWRIUD
SRUWDWDLQPDVVDHSRUWDWDLQYROXPH
 
JO
OJ
JOOJ
OJ
O
O
J
J
OJ
OJ
OJ
+
[[
0
0
0
000
00
99
00
UU
UU
 
U

U
UU
 
U

U

 


 U









6LRWWLHQHFRVuO·HVSUHVVLRQHGHOODPDVVDYROXPLFDRPRJHQHDJ QHUDOPHQWHVFULWWDHOOD
IRUPD
OJ+
[[
U


U
 
U
,QWURGXFHQGRQHOODO·HVSUHVVLRQHGHOODIUD]LRQHGLYXRWRVLULFDYDDQFKH
 
OJ+
 UHHU U
/·HVSUHVVLRQHDOHFRQGRPHPEURGHOODUDSSUHVHQWDODPDVVDYROXPLFD
PHGLDGHOODPLVFHODLQXQFHUWRLVWDQWHHYLHQHFKLDPDWDPDVVDYROXPLFDPHGLD





IRWRJUDILFDRYYLDPHQWHFRLQFLGHFRQODPDVVDYROXPLFDRPRJHQHDVRORQHOFDVRLQFXL
LOUDSSRUWRGLVF UULPHQWRVLDXQLWDULR8Q·HVSUHVVLRQHDQDO JDDOODYLHQHXVDWD
SHULOFDOFRORGHOODYLVFRVLWj
OJ+
[[
P


P
 
P
7DORUDSHUVHPSOLFLWjV SRQH
O
P P
+

/HHTXD]LRQLGLFRQVHUYD]LRQHSHULOPRGHOORRP JHQHRVLRWWHQJRQRGDOOD
DYHQGRFXUDGLSRUUH
+
U 6HEEHQHVLWUDWWLGXQPRGHOORDWWUDHQWHSHUODVXD
VHPSOLFLWjOHLSRWHVLVXFXLqEDVDWRVRQRPROWRUHVWULWWLYHHGLPSHGLVFRQROD
GHVFUL]LRQHG JUDQSDUWHG LIHQRPHQLRVVHUYDELOLVSHULPHQWDOPHQWHQRQRVWDQWHFLz
DQFKHTXDQGRWDOLLSRWHVLQRQVRQRYHULILFDWHLOPRGHOORRP JHQHRSXzVVHUHXWLOH
SHUIRUQLUHLQGLFD]LRQLG PDVVLPDFLUFDLOFRPSRUWDPHQWRGLXQIOXVVRELIDVH
 0RGHOORDGXHIOXLGL
 (TXD]LRQLGLFRQVHUYD]LRQHPHGLDWHHOORVSD]LRHQHO
WHPSR
6LFRQVLGHULXQJHQHULFRYROXPHDOO·LQWHUQRGLX FRQGRWWRVHGHGLXQIOXVVR
ELIDVHFRPHTXHOORUDSSUHVHQWDWRLQILJXUD VL LQGLFKLFRQD
L
O·HVWHQVLRQH
GHOO·LQWHUIDFFLDW DOHIDV FRQDNZODVXSHUILFLHG FRQWDWWRWUDODIDVHNODSDUHWHGHO
FRQGRWWRFRQ9N[WLOYROXPHRFFXSDWRGDOODI VHNFRQNHQNZOHQRUPDOL
DOO·LQWHUIDFFLDHGOODSDUHWHXVFHQWLGD9NHFRQXLODYHORFLWjGHOO·LQWHUIDFFLD
)LJXUDPRGHOORDGXHIOXLGL


/HHTXD]LRQLGLFRQVHUYD]LRQHORFDOLHGVWDQWDQHHSHUFLDVFXQDGHOOHGXHIDVL
VLRWWHQJRQRDQF UDGDOO·HTXD]LRQHDJJLXQJHQGRXQSHGLFHFKHVSHFLILFKLD
TXDOHIDVHVLIDFFLDU IHULPHQWR
 
NNNNNN
NN
W
<U’ <U’
w
<Uw
-X $$
4XHVWHHTXD]LRQLFKHYDOJRQRDOO·LQWHUQRGL9NYHQJRQRPHGLDWHSULPDVXO
YROXPH9HVXFFHVVLYDPHQWHULVS WWRDOHPSR
  ^ `
³³
<U’ 
¿
¾
½
¯
®
­
<U’
w
<Uw
NN
9
NNN
9
NNN
NN
G9
9

G9
W9

-X $$
*UD]LHDOODUHJRODGL/HLEQLW]

HDOWHRUHPDGL* XVV

VLRWWLHQH
 > @  G$
9

G$
9

W
NZLL
NNN
N
D
NN
D
NNNLNN
9
NNN
9
NN
9
NNNN
9
NNN
³³
<U
<UH H’<UH’
w
<UHw
-Q-XXQ
-X
$$
$$
(VHJXHQGRRUDODPHGLDWHPSRUDOHVLJLXQJHDGXQ·HVSUHVVLRQHIRUPDOPHQWH
LGHQWLFDDOODFKHSHUzqLQGLSHQGHQWHGDOYROXPH9HFKHFRUULVSRQGHDOOH
HTXD]LRQLGL,VKLL,OPHGHVLPRU VXOWDWRVLSXzUDJJLXQJHUHDQFKLQYHUWHQGR
O·RUGLQHFRQFXLVLHVHJXRQROHRSHUD]LRQLG PHGLDFRPHLOOXVWUDWRG 'HOKD\HH
$FKDUG
 &RQGL]LRQLDOO·L WHUIDFFLD
$OODIURQWLHUDWUDXQDIDVH HO·DOWUDQRQqSLVRGGLVIDWWDODFRQWLQXLWjH
SHUWDQWRVLUHQGHQ FHVVDULRLPSRUUHODFRQVHUYD]LRQHGHLIOXVVLDWWUDYHUVR
O·LQWHUIDFFLD
 > @ G$
9

L
D
NNNLNN
JON
 <U
³
¦
 
-XXQ $
&RPHVL LQWXLVFHLOFDOFRORGLWDOLIOXVVLQRQqEDQDOHS UTXHVWRP WLYR
WDOYROWDVLSUHIHULVFH HYLWDUORDGGL]LRQDQGRPHPEURDPHPEUROH HTXD]LRQLGL
FRQVHUYD]LRQHSHULO OLTXLGRHSHULOJDVRWWHQHQGRLOFRVL GHWWRPRGHOORPLVWR

5HJRODGL/HLEQLW]
   
 
 
³³³
w

w
w
 
w
w
W9W9W9
G$)G9
W
)
)G9
W
[[[
QX$
qO·HTXLYDOHQWHGH WHRU PDGHOWUDVSRUWRGL5H\QROGV

7HRUHPDGL* XVV
 
   
 
 
G$G9G9
W9W9W9
³³³
w
’ ’
[[[
Q))) $$$
1HOFDVRLQFXL9QRQGLSHQGDHVSOLFLWDPHQWHGD[LOSULPRDGGHQGRDOVHFRQGRPHPEURVFRPSDUH