An accurate quantification of the flow structure along the acoustic signal
cycle in a forced two-phase jet
(VWHEDQ&DOYR%HUQDGD-XDQ$QWRQLR*DUFtD5RGUtJXH]-RVp/XLV6DQWROD\D6iHQ]/XLV$GULiQ$tVD0LJXHO-,JQDFLR *DUFtD3DODFtQ
/DERUDWRULRGH,QYHVWLJDFLyQHQ)OXLGRGLQiPLFD\7HFQRORJtDVGHOD&RPEXVWLyQ/,)7(&&6,&8QLYHUVLGDGGH =DUDJR]D0DUtDGH/XQD=DUDJR]D6SDLQ
Abstract.7KLVSDSHUSURYLGHVDQH[SHULPHQWDOVWXG\RIDQDFRXVWLFDOO\IRUFHGWZRSKDVHDLUMHWJHQHUDWHGE\ D FRQYHUJHQW QR]]OH 7KH XVHG SDUWLFOHV DUH WUDQVSDUHQW JODVV VSKHUHV ZLWK GLDPHWHUV EHWZHHQ DQG PP ZKLFK JLYHV 6WRNHV QXPEHU RI RUGHU DQG WKH VHOHFWHG IRUFLQJ IUHTXHQF\ f +] LQGXFHV D SRZHUIXO
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
1 Introduction
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
+HUHDQH[SHULPHQWDOVWXG\RIDIRUFHGWZRSKDVHDLU MHWLVGLVFXVVHG7KUHHFDVHVDUHVWXGLHGWKHXQIRUFHGMHW WKHVLQJOHSKDVHIRUFHGMHWDQGWKHWZRSKDVHIRUFHGFDVH 7KH FRPSDULVRQ RI WKHVH FDVHV SURYLGHV WKH HIIHFWV RI IRUFLQJDQGWKHSDUWLFOHORDGRQWKHIORZ
2 Experimental methodology
2.1 Flow generation and control
7KHSDUWLFOHODGHQIRUFHGMHWLVLQMHFWHGGRZQZDUGVE\D SLSH RI P LQ OHQJWK ILJ 7KH SLSH H[LW KDV D
FRQYHUJHQWQR]]OHZLWKDQH[LWGLDPHWHUD PPDQG DFRQWUDFWLRQUDWLRRIWRJLYHDWRSKDWH[LWYHORFLW\ SURILOH
Inlet air (4 bar)
Pressure regulator (2 bar)
Temperature and pressure transducers
Tracers seeder Injection pipe Particles feeder
Flow meter Control valve
Chamber
Figure 1.-HWJHQHUDWLRQVHWXS
7KHMHWGHYHORSVDWDPELHQWWHPSHUDWXUHDQGSUHVVXUH LQVLGH D WUDQVSDUHQW FKDPEHU î î PP DQGLWLVVXUURXQGHGE\DORZYHORFLW\FRIORZPV 7KH WUDQVSDUHQW FKDPEHU DOORZV WKH XVH RI RSWLFDO WHFKQLTXHV DV D 3KDVH 'RSSOHU 3DUWLFOH $QDO\]HU 3'3$
$QRULILFHSODWHDQGDGLIIHUHQWLDOSUHVVXUHWUDQVGXFHU PHDVXUHWKHMHWIORZDQGDFRPSXWHUFRQWUROVWKHDLUIORZ E\ PHDQV RI DQ HOHFWURSQHXPDWLF YDOYH 7KH FRQWURO DFFXUDF\LVEHWWHUWKDQ
$Q:VSHDNHUIRUFHVWKHMHW,WLVSODFHGDWWKHXSSHU HQG RI WKH MHW LQMHFWLRQ SLSH $Q DPSOLILHG VLQXVRLGDO
D&RUUHVSRQGLQJDXWKRUFDOYREHU#XQL]DUHV
C
Owned by the authors, published by EDP Sciences, 2014
VLJQDOJHQHUDWRUGULYHVWKHVSHDNHUDQGLWDOVRVXSSOLHVD SHULRGLFDO WULJJHU VLJQDO V\QFKURQL]HG ZLWK WKH IRUFLQJ VLQXVRLGDOVLJQDO7KLVWULJJHULVXVHIXOWRPHDVXUHRIWKH DUULYDOSKDVHRIHDFKSDUWLFOHGHWHFWHGE\WKH3'$
7KH SDUWLFOHV DUH WUDQVSDUHQW JODVV VSKHUHV ZLWK D PHDQGLDPHWHUD PPDUPVGLDPHWHUVD
PP DQG D GHQVLW\UP NJP $ URWDWLQJ VFUHZ
FRQWUROV WKH LQMHFWHG PDVV UDWH RI SDUWLFOHV $ F\FORQLF GHYLFH VHHG WKH MHW ZLWK WUDFHUV RI $O2 aPP WR PHDVXUHWKHJDVYHORFLW\
7KHMHWH[LWYHORFLW\LVDGMXVWHGWRU PVDQGWKH IRUFLQJ IUHTXHQF\ LV f +] 6R WKLV MHW KDV D
5H\QROGVQXPEHU5H DQGDQH[LWGLDPHWHUEDVHG 6WURXKDOQXPEHU6W fDU 7KLVIUHTXHQF\ZDV VHOHFWHGEHFDXVHWKH\FDXVHWKHSRZHUIXOSHUWXUEDWLRQRI WKH MHW &URZ &KDPSDJQH 7KH JODVV VSKHUHV DUH VHOHFWHGWRREWDLQPHGLXP6WRNHVQXPEHU6WNa7KH SDUWLFOHDLUPDVVUDWLRLVKM
2.2 Measurement and post-processing
$ WZRFRORXU 3'3$ RI $HURPHWULFV PHDVXUHV WKH GLDPHWHU WKH UDGLDO DQG WKH D[LDO YHORFLW\ RI SDUWLFOHV FURVVLQJWKHSUREHYROXPH%HVLGHVWKHWULJJHUVXSSOLHG E\WKHVLJQDOJHQHUDWRUUHVHWVDFORFNRIWKH3'3$DWWKH EHJLQQLQJ RI HDFK IRUFLQJ VLJQDO F\FOH 7KLV FORFN PHDVXUHVWKHDUULYDOSKDVHRIHDFKGHWHFWHGSDUWLFOH:LWK WKLV PHDVXUHPHQWV DORQJ WKH HQWLUH IRUFLQJ VLJQDO F\FOH DUHGRQH
7UDFHUV DQG SDUWLFOHV DUH GLVFULPLQDWHG XVLQJ WKH 'RSSOHUVLJQDO LQWHQVLW\ DQG PHDVXUHG GLDPHWHU 7KH VPDOO $O2 WUDFHUV JLYH D ORZ LQWHQVLW\ VLJQDO DQG XVXDOO\VPDOOGLDPHWHUV
7KH IORZ IRUFLQJ FDXVHV DQ LQKRPRJHQHRXV WUDFHU VHHGLQJWLOOWKHVHFWLRQz DDQGWKHFDOFXODWHGPHDQV RIWKHJDVSKDVHFRXOGEHELDVHG7RDYRLGWKLVPRPHQWV RI WKH RYHUDOO WHPSRUDO VWDWLVWLFV DUH REWDLQHG IURP FRQGLWLRQDOYHORFLW\PRPHQWVIRUJLYHQVLJQDOSKDVHVI
II I I
I I
I
V
V V
ZLWK
U u U
U
U U U
u U
U
u
u u
,QHT!ILVDSKDVHDYHUDJHDQG!LVDQRYHUDOO
DYHUDJH &RQGLWLRQDO PHDQV DUH QRW ELDVHG VLQFH WKH IRUFHGMHWLVQHDUO\SHULRGLFDQGWUDFHUFRQFHQWUDWLRQGRHV QRWFKDQJHDORWIRUDIL[HGVLJQDOSKDVH
7KHVKRZQPRPHQWVRIWKHSDUWLFOHYHORFLW\DUHPDVV DYHUDJHG8VHGSRVWSURFHVVLQJUHPRYHVWKHELDVFDXVHG E\ WKH SDUWLFOH YHORFLW\ DQG WKH SUREH YROXPH VL]H 'HWDLOVFDQEHIRXQGLQ>@9HORFLW\PHDQVDUHVKRZQIRU VHYHUDOSDUWLFOHVL]HFODVVHV(DFKFODVVKDVDZLGWKRI PPDQGFHQWUDOYDOXHVPP
3 Unforced two-phase jet
,Q WKLV VHFWLRQ WKH EHKDYLRXU RI WKH XQIRUFHG MHW LV GLVFXVVHG0HDVXUHPHQWVRIWKHVLQJOHSKDVHJDVMHW63 MHW DQG RI WKH GLVSHUVHG SKDVH DUH SURYLGHG 6LQFH WKH SDUWLFOHJDVPDVVUDWLRLVVPDOOJUHDWFKDQJHVRIWKHJDV G\QDPLFVDUHQRWH[SHFWHG
)LJDQGVKRZWKHMHWH[LWFRQGLWLRQV7KHJDVKDVD WRSKDWPHDQYHORFLW\SURILOHILJZLWKORZWXUEXOHQFH LQWHQVLW\ DERXW DQGIRU WKH D[LDO DQG WKHUDGLDO FRPSRQHQWLQWKDWRUGHU3DUWLFOHVKDYHDVPDOOHUD[LDO YHORFLW\ EHFDXVH WKH UHVLGHQFH WLPH RI WKH JODVV EHDGV LQVLGHWKHFRQYHUJHQWQR]]OHLVVPDOOHUWKDQLWVUHVSRQVH WLPHDQGWKH\GRQRWDFFHOHUDWHDVPXFKDVWKHJDV
6 8 10 12 14 16
0.3 0.6 0.9 1.2 1.5 1.8
-8 -6 -4 -2 0 2 4 6 8
U single-phase U
P
Vu single-phase
Vu P
U (
m
/s
) u V (m/s
)
r (mm)
Figure 2.([LWFRQGLWLRQVRIWKHJDVDQGSDUWLFOHVIRUWKH
XQIRUFHGFDVHz D
0 100 2 10-5 4 10-5 6 10-5 8 10-5 1 10-4
1.2 10-4
0 1 2 3 4 5 6 7
Total 15Pm
25Pm 35Pm
C V
r (mm)
Figure 3.3DUWLFOHYROXPHFRQFHQWUDWLRQ8QIRUFHGMHWz
D
7KH GLVSHUVHG SKDVH IRFXVHV DURXQG WKH MHW D[LV ILJ EHFDXVHSDUWLFOHVERXQFHRQWKHQR]]OHZDOO7KHVPDOOHU SDUWLFOHVGRQRWIRFXVEHFDXVHWKH\DUHGUDJJHGE\WKHDLU ZHOODIWHUWKHUHERXQG
7KHVLQJOHSKDVHJDVMHWKDVWKHXVXDOSRWHQWLDOFRQH DQGWKHK\SHUEROLFYHORFLW\GHFD\DWWKHMHWD[LVILJ 7KHOLQHDUDGMXVWRIWKHLQYHUVHJDVYHORFLW\LQWKHUHJLRQ
z!DJLYHV
U z D
7KH GLVSHUVHG SKDVH ILUVW DFFHOHUDWHV EHFDXVH LWV YHORFLW\ LV VPDOOHU WKDQ WKH DLU YHORFLW\ DQG JDV GUDJ WKHP $IWHU UHDFK LWV PD[LPXP YDOXH z a D WKH
PRPHQWXP H[FKDQJH UHYHUVH DQG SDUWLFOHV VXIIHU GHFHOHUDWLRQ ,Q WKH ODVW PHDVXUHG VHFWLRQV WKH SDUWLFOH YHORFLW\ LV FORVH WR WKH JDV YHORFLW\ 7KH PD[LPXP YHORFLW\ LV SUHVHQW DW HDUOLHU ORFDWLRQV IRU WKH VPDOOHVW SDUWLFOHV GXH WR LWV KLJKHU H[LW YHORFLW\ DQG LWV VPDOOHU UHVSRQVHWLPH7KLVOHWVFODVVLI\WKHIORZLQWZRUHJLRQV
WKH]RQHQHDUWKHH[LWQHDUILHOGzDZKHUHERWK
WKHJDVIORZDQGGLVSHUVHGIOLHGDUHHYROYLQJDQGWKHIDU ILHOGz!DZKHUHWKHJDVDOPRVWUHDFKDVHOIVLPLODU
IORZDQGWKHGLVSHUVHGSKDVHYHORFLW\ILWVWRWKHHYROXWLRQ RIWKHJDVYHORFLW\
2 4 6 8 10 12 14 16
0 10 20 30 40
SP jet total
5Pm 25Pm
45Pm
U (
m
/s
)
z/D
0
Figure 4.0HDQD[LDOYHORFLW\RIWKHJDVDQGWKHSDUWLFOHVDORQJ WKHD[LV8QIRUFHGFDVH
0 0.5 1 1.5 2 2.5
0 10 20 30 40
SP jet total
5Pm 25Pm
45Pm
V u
(m/s
)
z/D
0
Figure 5.5PVD[LDOYHORFLW\RIWKHJDVMHWDQGWKHSDUWLFOHV DORQJWKHD[LV8QIRUFHGFDVH
7KHUPVYHORFLW\RIWKHSDUWLFOHVILJKDUGO\UHDFWV WRWKHYHORFLW\IOXFWXDWLRQVRIWKHJDVLQWKHQHDUILHOGDQG WKH\ DUH FRQWUROOHG PDLQO\ E\ WKH LQLWLDO FRQGLWLRQV DQG WKHLQHUWLD%XWGRZQVWUHDPSDUWLFOHVUHVSRQGWRWKHJDV
WXUEXOHQFHSURJUHVVLYHO\$JDLQVPDOOVL]HVDGDSWEHIRUH WRWKHJDVIOXFWXDWLRQVGXHWRLWVVPDOOHULQHUWLD
0 2 4 6 8 10 12 14
-30 -20 -10 0 10 20 30
exit
2.5D
0
5D
0
7.5D
0
10D
0
SP jet 10D
0
U (
m
/s
)
r (mm)
Figure 6.0HDQD[LDOYHORFLW\SURILOHVRIWKHGLVSHUVHGSKDVH IRUVHYHUDOVHFWLRQVRIWKHQHDUILHOG8QIRUFHGFDVH
-1.2 -0.8 -0.4 0 0.4 0.8 1.2
-20 -15 -10 -5 0 5 10 15 20 exit
2.5D
0
5D
0
7.5D
0
10D
0
V P
(m/
s
)
r (mm)
Figure 7.0HDQUDGLDOYHORFLW\SURILOHVRIWKHGLVSHUVHGSKDVH IRUVHYHUDOVHFWLRQVRIWKHQHDUILHOG8QIRUFHGFDVH
7KH SURILOHV RI PHDQ D[LDO YHORFLW\ ILJ HYROYHV IURP D QHDUO\ IODW SURILOH DW WKH QR]]OH H[LW WKHUH LV D ZHDNPLQLPXPDWWKHD[LVWRDEHOOVKDSHGSURILOHDWWKH HQG RI WKH QHDU ILHOG z D ,Q WKLV VHFWLRQ WKH
SDUWLFOHV ORFDWHG LQ WKH RXWHU OD\HUV DUH VORZHU LQ PHDQ WKDWWKHDLU7KHSURILOHVRIPHDQUDGLDOYHORFLW\VILJ VKRZV WKH SDUWLFOH IRFXVLQJ FRQWLQXHV GRZQVWUHDP IRUP WKHQR]]OHH[LW7KHUDGLDOYHORFLW\SURILOHVVKRZQHJDWLYH YDOXHVXQWLOz DVRWKHWRWDOPDVVIOX[SRLQWLQZDUGV
7KHUDGLDO]RQHZLWKVEHFRPHVQDUURZHUZKHQWKH
D[LDO ORFDWLRQ LQFUHDVHV 'RZQVWUHDP VHFWLRQz D
10 15 20 25 30 35
-20 -15 -10 -5 0 5 10 15 20 exit
2.5D
0
5D
0
7.5D
0
10D
0
D 30
(
P
m)
r (mm)
Figure 8.DSURILOHVIRUVHYHUDOVHFWLRQVEDVHGRQQXPEHU GLVWULEXWLRQ8QIRUFHGFDVH
7KHPHDQGLDPHWHUDGHFUHDVHVZLWKWKHUDGLXVILJ
6R WKH VPDOOHVW VL]HV H[SHULHQFH DQ HQKDQFHG GLVSHUVLRQVLQFHWKH\UHVSRQGEHWWHUWRWKHJDVIORZ
4 Forced jet
1RZ WKH PDLQ IHDWXUHV RI WKH IRUFHG MHW DUH GLVFXVVHG )LUVWUHVXOWVDERXWWKHVLQJOHSKDVHIRUFHGMHWDUHVKRZQ $IWHUWKDWWKHWZRSKDVHMHWLVH[SORUHG
4.1 Single-phase forced flow
9LVXDOL]DWLRQV RI WKH XQIRUFHG DQG IRUFHG VLQJOHSKDVH IORZ ILJ VKRZ WKH QRWLFHDEOH FKDQJHV RI WKH IORZ ILHOGLQWKHQHDUILHOG
D E
Figure 9.9LVXDOL]DWLRQVRIWKHXQIRUFHGDDQGIRUFHGEMHW 7KHXQIRUFHGMHWGHYHORSVDQD[LV\PPHWULFPL[LQJOD\HU DW WKH QR]]OH H[LW VXUURXQGLQJ WKH SRWHQWLDO FRUH RI FRQVWDQWYHORFLW\9RUWLFHVFDQEHVHHQLQVLGHWKLVPL[LQJ OD\HU 7KH GLVWDQFH EHWZHHQ WZR FRQVHFXWLYH YRUWLFHV URXJKO\ VFDOHV ZLWK WKH H[LW GLDPHWHU EXW WKH\ FKDQJH RYHU WLPH DQG LQ JHQHUDO LW LQFUHDVHV ZLWK WKH D[LDO FRRUGLQDWH
11.5 12 12.5 13 13.5 14 14.5 15
0 1 2 3 4 5 6 7
-6 -4 -2 0 2 4 6
U
SP Vu SP Vv SP
U SP
(
m
/s
) X V,
V
Y (
m
/s
)
r (mm)
Figure 10.0HDQD[LDOYHORFLW\DQGUPVRID[LDODQGUDGLDO YHORFLW\IRUWKHIRUFHGVLQJOHSKDVHIORZz D
8 10 12 14 16 18 20 22
0 45 90 135 180 225 270 315 360
U
I SP
(m/s
)
Signal phase I (º)
Figure 11.3KDVHDYHUDJHGD[LDOYHORFLW\)RUFHGVLQJOHSKDVH
FDVHz Dr
7KHDFRXVWLFIRUFLQJDUUDQJHVWKHQHDUILHOGDQGIORZ EHFRPHV QHDUO\ SHULRGLF DQG FRKHUHQW ZLWK WKH IRUFLQJ VLJQDO 7KH YRUWLFHV LQVLGH WKH PL[LQJ OD\HU LQFUHDVH LWV LQWHQVLW\ HPHUJH SHULRGLFDOO\ IURP WKH H[LW DQG WKH GLVWDQFHEHWZHHQWKHPVHHPVWREHQHDUO\FRQVWDQWDERXW
DZKLOHWKH\PRYHVGRZQVWUHDP%HVLGHWKLVRWKHU
PLQRUVHFRQGDU\YRUWLFHVDUHSUHVHQWDQGVRPHWLPHVWKLV ZHDNYRUWLFHVSDLUZLWKWKHPDLQVWUXFWXUHV7KHFRKHUHQW IORZVWUXFWXUHVXUYLYHVXQWLOz D
r (mm)
S
igna
l
p
ha
se
(º)
-10 -5 0 5 10
0 45 90 135 180 225 270 315 360
Figure 12.3KDVHDYHUDJHGYHORFLW\YVSKDVHDQGUDGLXVz
D5HIHUHQFHYHFWRU PV
r (mm)
S
ign
a
l
ph
a
s
e
(º)
-20 -10 0 10 20
0 45 90 135 180 225 270 315 360
Figure 13.3KDVHDYHUDJHGYHORFLW\YVSKDVHDQGUDGLXVz
D5HIHUHQFHYHFWRUV PV
)LJDQGSORWWKHSKDVHDYHUDJHGDLUYHORFLW\IRU
zD0 DQGLQWKDWRUGHU,QWKHVHSORWVVLJQDO
SKDVHFDQEHWKRXJKWDVDSVHXGRVSDWLDOD[LDOFRRUGLQDWH DQGWKHYRUWH[HPHUJHVFOHDUO\7KHYRUWH[FRUHLVORFDWHG DERXWraPPRXWVLGHRIWKHH[LWQR]]OHHGJH
7KLV SHULRGLF IORZ VWUXFWXUH FKDQJHV WKH MHW GHYHORSPHQW DORQJ LWV D[LV 7KH SRWHQWLDO FRUH RI WKH XQIRUFHGMHWzDZLWKFRQVWDQWYHORFLW\DWWKHD[LVLV
UHSODFHG E\ D ]RQH ZLWK GHFUHDVLQJ D[LDO YHORFLW\ ILJ $W WKH HQG RI WKH QHDU ILHOG WKH IRUFHG FDVH KDV D VPDOOHUYHORFLW\WKDQWKHXQIRUFHGMHW)RUWKHIRUFHGMHW WKHOLQHDUDGMXVWRIWKHLQYHUVHJDVYHORFLW\DORQJWKHD[LV IRUz!DJLYHV
U z D
U &RPSDULQJ ZLWK HT WKH YLUWXDO RULJLQ RI WKH IRUFHG MHW PRYHV XSVWUHDP DQG KDV D VOLJKWO\ GHFD\LQJ VORSH
5PVYHORFLW\RIWKHIRUFHGFDVHLVKLJKHULQWKHQHDU ILHOG z D EHFDXVH KHUH WKH IORZ KDV SRZHUIXO
FRKHUHQW YHORFLW\ IOXFWXDWLRQV ILJ DQG $V YLVXDOL]DWLRQV VXJJHVW FRKHUHQW VWUXFWXUHV ZHDNHQ
GRZQVWUHDPDQGWKHIRUFHGIORZUHFRYHUWKHUPVYHORFLW\ OHYHO RI WKH XQIRUFHG FDVH &RPSDULQJ WKH QRQ GLPHQVLRQDOUPVYHORFLW\ILJWKHIRUFHGFDVHUHDFK WKH VHOIVLPLODULW\ IRU WKH VHFRQG YHORFLW\ PRPHQWV DW HDUO\VHFWLRQVzaDZKLOHWKHQRQGLPHQVLRQDOUPV
YHORFLW\RIWKHXQIRUFHGMHWLVVWLOOJURZLQJ
0 2 4 6 8 10 12 14 16
0 1 2 3 4 5 6 7 8
0 10 20 30 40
U unforced U forced
Vu unforced
Vu forced
U SP
(
m
/s
) u S V
P (
m
/s
)
z/D
0
Figure 14.0HDQDQGUPVRID[LDOYHORFLW\DORQJWKHMHWD[LV )RUFHGDQGXQIRUFHGVLQJOHSKDVHIORZ
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 10 20 30 40
unforced forced
V u SP
/U
SP
z/D
0
Figure 15.1RQGLPHQVLRQDOUPVD[LDOYHORFLW\DWWKHMHWD[LV )RUFHGDQGXQIRUFHGDLUMHW
4.2 Two-phase forced flow
)LJVKRZVWKHH[LWFRQGLWLRQVRIWKHIRUFHGWZRSKDVH MHW IRU WKH YHORFLW\ RI ERWK SKDVHV 7KH PHDQ YHORFLW\ SURILOHV DUH VLPLODU WR WKH RQHV RI WKH XQIRUFHG MHW +RZHYHUWKHUPVYHORFLW\PDUNHGO\LQFUHDVHVGXHWRWKH IRUFLQJ
6 8 10 12 14 16
0 1 2 3 4 5
-6 -4 -2 0 2 4 6
U
C
U
P
Vu C
Vu P
U (
m
/s
) u V (m/
s
)
r (mm)
Figure 16.([LWFRQGLWLRQVRIWKHFRQWLQXRXVCDQGWKH
GLVSHUVHGPSKDVH)RUFHGFDVHz D
0 500 1000 1500 2000 2500 3000 3500
0 1 2 3 4 5 6
total 15Pm
25Pm 35Pm
C N
(1
/c
m
3 )
r (mm)
Figure 17.3DUWLFOHFRQFHQWUDWLRQSURILOHV)RUFHGFDVHz
D
:KHQJODVVEHDGVDUHDGGHGWRWKHIORZFKDQJHVDUH REVHUYHG :KLOH WKH FKDQJH RI WKH PHDQ YHORFLW\ LV QRW UHOHYDQWWKHUPVYDOXHVDUHVPDOOHUDWWKHQHDUILHOGVHH WKHGHYHORSPHQWRIWKHJDVPRYHPHQWDORQJWKHD[LVILJ 'RZQVWUHDP ERWK WKH VLQJOHSKDVH DQG WKH FRQWLQXRXVSKDVHKDYHVLPLODUWXUEXOHQFHOHYHOV
,QIDFWSDUWLFOHVZHDNHQWKHFRKHUHQWVWUXFWXUHRIWKH JDV IORZ ,W FDQ EH PHDVXUHG E\ WZR DGKRF GHILQHG YDULDEOHVWKH0RGXODWLRQMDQGWKH&RKHUHQFHCRI WKHD[LDOYHORFLW\7KH\DUHGHILQHGDV
u/
M C U
U
M I V
0RGXODWLRQ LV WKH UPV YDOXH RI WKH SKDVHDYHUDJHG PHDQYHORFLW\DQGLWPHDVXUHVWKHSRZHURIWKHYHORFLW\ ZDYHFRKHUHQWZLWKWKHIRUFLQJVLJQDO(TJLYHVVHQVH WR WKH FRKHUHQFH 7KH WRWDO YHORFLW\ YDULDQFHVu LV WKH
VXPRIWKHVTXDUHRIPRGXODWLRQMDQGWKHPHDQYDOXH
RI WKH SKDVHDYHUDJHG YDULDQFH VuI 3KDVHDYHUDJHG
YDULDQFHLVFDXVHGE\WKHWXUEXOHQFHLQFRKHUHQWZLWKWKH IRUFLQJ6RFRKHUHQFHLVZKHQWKHUHLVQRWXUEXOHQFH DQGLWLVZKHQWKHUHLVQRFRKHUHQWIORZVWUXFWXUH
0 2 4 6 8 10 12 14 16
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0 10 20 30 40
U
C
U
SP
Vu C/U
C
Vu SP/U
SP
U (
m
/s
) V
u /U
z/D
0
Figure 18.0HDQDQGQRQGLPHQVLRQDOUPVD[LDOYHORFLW\DWWKH MHWD[LV)RUFHGFDVHVLQJOHSKDVHMHW63DQGFRQWLQXRXVSKDVH &RIWKHWZRSKDVHIORZ
0 1 2 3 4 5
0 0.2 0.4 0.6 0.8 1
0 2 4 6 8 10
M
C
M
SP
C
C
C
SP
M (
m
/s
)
C
z/D
0
Figure 19.0RGXODWLRQDQG&RKHUHQFHDORQJWKHD[LV6LQJOH SKDVHMHW63DQGFRQWLQXRXVSKDVH&
7KH FRKHUHQW VWUXFWXUHV RI ERWK IORZV KDYH VLPLODU
HYROXWLRQVILJ0RGXODWLRQVDWXUDWHVDWzaDDQG
WKH SRWHQWLDO FRUH UHJLRQ RI WKH XQIRUFHG MHW z D
UHWDLQLWVPDLQIHDWXUHLWLVDUHJLRQZLWKORZWXUEXOHQFH LQWHQVLW\%XWWKHFRQWLQXRXVSKDVHKDVZHDNHUFRKHUHQW YRUWLFHVDQGWKH\GLVVROYHHDUOLHUVLQFHWKHFRKHUHQFHRI WKH WZRSKDVH FDVH JRHV WR IDVWHU 6R WKH GLVSHUVHG SKDVH LQKLELWV WKH SUHVHQFH DQG JURZWK RI WKH FRKHUHQW YRUWLFHV
PRPHQWXP WR WKH JDV XQWLO ERWK SKDVHV KDYH VLPLODU YHORFLWLHV7KHVPDOOHVWVL]HVUHDFWTXLFNHUWRWKHJDVIORZ GXHWRLWVVPDOOHUUHVSRQVHWLPH
2 4 6 8 10 12 14 16
0 10 20 30 40
air total
5 Pm 25 Pm
45 Pm
U
(m/
s
)
z/D
0
Figure 20.0HDQD[LDOYHORFLW\RIERWKSKDVHVDORQJWKHD[LV )RUFHGMHW
r (mm)
S
ign
a
l
ph
a
s
e
(º)
-15 -10 -5 0 5 10 15
0 45 90 135 180 225 270 315 360
12000 10800 9600 8400 7200 6000 4800 3600 2400 1200 650
Figure 21.7RWDOSDUWLFOHQXPEHUFRQFHQWUDWLRQYVUDGLXVDQG
SKDVHz D
7KH GLVSHUVHG SKDVH DOVR KDV D FRKHUHQW VWUXFWXUH DORQJ WKH IRUFLQJ VLJQDO F\FOH VLQFH SDUWLFOHV DUH GULYHQ E\ WKH VWUXFWXUHGJDVIORZ 7KH ILUVW FRQVHTXHQFH LV WKH IRUPDWLRQ RI KLJKFRQFHQWUDWLRQ SDUWLFOH FOXVWHUV LQ WKH QHDU ILHOG 7KHVH FOXVWHUV DUH FRKHUHQW ZLWK WKH IRUFLQJ VLJQDODQGWKHFRKHUHQWDLUYRUWLFHV
0HDVXUHGSDUWLFOHFRQFHQWUDWLRQYVUDGLXVDQGSKDVH
LQz DWKHHQGRIWKHKLJKFRKHUHQFH]RQHILJ
VKRZV KRZ YRUWLFHV FRQFHQWUDWH HIIHFWLYHO\ SDUWLFOHV LQ VRPHSKDVHVRIWKHIRUFLQJVLJQDO3KDVHVZLWKPD[LPXP FRQFHQWUDWLRQ PDWFK ZLWK WKH SKDVHV RI VPDOOHVW D[LDO YHORFLW\ $Q D[LV\PPHWULF VWUHDN RU ³WRQJXH´ RI SDUWLFOHVGUDJJHGE\WKHDLUHPHUJHVIURPWKLVPD[LPXP 7ZR VXFFHVVLYH FOXVWHUV DUH FRQQHFWHG E\ D VWUHWFKHG FROXPQ RI SDUWLFOHV ,QVLGH WKLV FROXPQ DLU PRYHPHQW FRQFHQWUDWHVWKHSDUWLFOHV
Figure 22.9LVXDOL]DWLRQRIWKHGLVSHUVHGSKDVH)RUFHGFDVH 'RZQVWUHDPz D WKH FRQWLQXRXV SKDVH ORVV LWV
FRKHUHQW SHULRGLF PRYHPHQW EXW SDUWLFOHV UHWDLQ FRKHUHQF\ ZLWK WKH IRUFLQJ VLJQDO GXH WR LWV LQHUWLD ,Q SDUWLFXODU FOXVWHUV VXUYLYH XQWLO DGYDQFHG VHFWLRQV VHH
WKHYLVXDOL]DWLRQLQILJ$WDERXWzaDFOXVWHUV
EHJLQWRUHFRQQHFWWRILQDOO\GLVVROYH
5 Effect of forcing on particle dispersion
$FRXVWLFIRUFLQJJUHDWO\HQKDQFHVWKHSDUWLFOHGLVSHUVLRQ DW WKH HQG RI WKH QHDU IORZ ILHOG )LJ SORWV WKH SHUFHQWDJHRIWKHSDUWLFOHPDVVUDWHZKLFKSDVVHVLQVLGH WKH UDGLXVr LQ WKH VHFWLRQz D :KLOH PRVW RI WKH
SDUWLFOHPDVVSDVVLQVLGHr PPIRUWKHXQIRUFHGFDVH
LWVSUHDGVEH\RQGr PPZKHQIRUFLQJLVHQDEOHG6R
GLVSHUVLRQLVHQKDQFHGE\DIDFWRUWKUHH
0 0.2 0.4 0.6 0.8 1 1.2
0 5 10 15 20 25 30
unforced forced
C
u
m
m
ul
ated
p
a
rti
cl
e m
a
s
s
r
a
te
r (mm)
Figure 23.3DUWLFOHPDVVIORZLQVLGHDFLUFOHRIUDGLXVrz
D
6 Conclusions
LQVWUXPHQWKDVEHHQGRQHWRDYRLGELDVHVDQGREWDLQULJKW VWDWLVWLFDO PRPHQWV RI WKH GLVSHUVHG SKDVH DV FRQFHQWUDWLRQ YHORFLW\ PRPHQWV HWF 0HDVXUHPHQWV FRYHUWKHHQWLUHIRUFLQJVLJQDOF\FOH
7KUHHFDVHVDUHFRPSDUHGWKHXQIRUFHGWZRSKDVHMHW WKHIRUFHGVLQJOHSKDVHJDVMHWDQGWKHIRUFHGWZRSKDVH MHW7KLVOHWVHYDOXDWHWKHHIIHFWRISDUWLFOHVDQGIRUFLQJLQ WKHIORZ
)RUFLQJ LQGXFHV D QHDUO\ SHULRGLF VWUXFWXUH FRKHUHQW ZLWK WKH H[FLWDWLRQV VLJQDO &RKHUHQW YRUWLFHV HPHUJH IURP WKH QR]]OH HGJH 7KH FRKHUHQW IORZ VWUXFWXUH LV QRWDEOH LQVLGH WKH ROGHU SRWHQWLDO FRUH RI XQIRUFHG FDVH DQGLWGLVDSSHDUVSURJUHVVLYHO\LQzaD$IWHUWKDWD
VHOIVLPLODUMHWGHYHORSVTXLFNO\ZKLOHWKHXQIRUFHGMHWLV VWLOOHYROYLQJWRZDUGVWKLVVWDWH
3DUWLFOHV ZHDNHQ WKH SHULRGLFDO IORZ VWUXFWXUHV DQG SURPRWH WKHLU HDUOLHU GLVVROXWLRQ 7KH GLVSHUVHG IORZ LV DOVR DIIHFWHG E\ WKH JDV FRKHUHQW VWUXFWXUH 7KH JDV PRWLRQ DQG SDUWLFOH LQHUWLD SURPRWH WKH SDUWLFOH FOXVWHULQJ 7KH FOXVWHUV DUH IXOO\ GHYHORSHG MXVW GRZQVWUHDP RI WKH IXOO\ FRKHUHQW JDV IORZ DQG UHWDLQV VRPHGHJUHHRIFRKHUHQWVWUXFWXUHWLOOzaDGXHWRLWV
LQHUWLD
)LQDOO\ DFRXVWLF IRUFLQJ SURPRWHV WKH HQKDQFHG SDUWLFOHGLVSHUVLRQ7KHRXWHUPRVWUDGLXVZLWKSUHVHQFHRI SDUWLFOHVLQFUHDVHVE\DIDFWRU
References
5$*RUH&7&URZH
Int. J. Multiphase Flow15,3*XDOWLHUL)3LFDQR*6DUGLQD&0&DVFLRODJ. Fluid Mech.715
6& &URZ )+ &KDPSDJQHJ. Fluid Mech.48
5$ 3HWHUVHQ 00 6DPHWJ. Fluid Mech.194
(./RQJPLUH-.(DWRQJ. Fluid Mech.236
%-/i]DUR-&/DVKHUDVJ. Fluid Mech.235