Experimental Study of a Single Droplet Impinging on Dry Surface with and without a Crossflow: Jet Fuel and Biofuel Mixtures

81,9(56,'$'( '$ %(,5$ ,17(5,25

(QJHQKDULD

([SHULPHQWDO 6WXG\ RI D 6LQJOH 'URSOHW ,PSLQJLQJ

RQ 'U\ 6XUIDFH ZLWK DQG ZLWKRXW D &URVVIORZ -HW

)XHO DQG %LRIXHO 0L[WXUHV

9HUVmR FRUULJLGD DSyV GHIHVD

1XQR )LOLSH &RVWD &XQKD

'LVVHUWDomR SDUD REWHQomR GR *UDX GH 0HVWUH HP

(QJHQKDULD $HURQiXWLFD

&LFOR GH HVWXGRV LQWHJUDGR

2ULHQWDGRU 3URI 'RXWRU $QGUp 5HVHQGH 5RGULJXHV GD 6LOYD

$FNQRZOHGJPHQWV

, ZRXOG OLNH WR H[SUHVV P\ JUDWLWXGH WR P\ VXSHUYLVRU 'U $QGUp 5HVHQGH 5RGULJXHV GD 6LOYD IRU WKH VXJJHVWLRQV GHGLFDWLRQ HQFRXUDJHPHQW DQG JXLGDQFH LQ DOO VWDJHV RI WKLV ZRUN 0\ WKDQNV DOVR JR WR 3URIHVVRU -RUJH 0DQXHO 0DUWLQV %DUDWD IRU JLYLQJ PH WKH RSSRUWXQLW\ WR EHORQJ DQG FROODERUDWHG LQ WKH $HUR* ² $HURQDXWLFV DQG $VWURQDXWLFV 5HVHDUFK &HQWHU

0\ WKDQNV WR 'U $GULDQD 6RXVD 'U ,OtGLR &RUUHLD 'U 6yQLD 6RXVD DQG 6yQLD 0LJXHO IRU WKHLU KHOS LQ PHDVXULQJ WKH WKHUPRSK\VLFDO SURSHUWLHV RI WKH VXEVWDQFHV DQG DOVR WR WKH /DERUDWRU\ 7HFKQLFLDQ 5XL 0DQXHO 7RPp 3DXOR IRU DOO WKH KHOS DQG FRQWULEXWLRQ JLYHQ LQ WKH FRQVWUXFWLRQ RI WKH H[SHULPHQWDO IDFLOLW\

0DQ\ WKDQNV WR 'DQLHOD DQG (GXDUGR IRU WKHLU KHOS DQG VXJJHVWLRQV GXULQJ WKLV ZRUN

/DVW EXW QRW OHDVW , DP WUXO\ JUDWHIXO WR P\ IDPLO\ HVSHFLDOO\ WR P\ SDUHQWV DQG WR )LOLSD IRU DOO WKHLU HQFRXUDJHPHQW GHGLFDWLRQ DQG VXSSRUW JDYH WR PH

5HVXPR

2 LPSDFWR GH JRWDV HP GLIHUHQWHV VXSHUItFLHV p XP IHQyPHQR PXLWR FRPSOH[R H LPSRUWDQWH H SRVVXL XPD YDULHGDGH GH DSOLFDo}HV FRPR VLVWHPDV GH H[WLQomR GH IRJR SLQWXUD SRU SXOYHU L]DomR SXOYHUL]DomR GH FXOWXUDV H SUHSDUDomR GH PLVWXUD HP PRWRUHV GH FRPEXVWmR LQWHUQD (PERUD HVWHV IHQyPHQRV VHMDP DPSODPHQWH HVWXGDGRV R SUHVHQWH WUDEDOKR WHP FRPR REMHWLYR HVWXGDU D LQIOXrQFLD HP PLVWXUDU XP ELRFRPEXVWtYHO QXP FRPEXVWtYHO GH DYLmR FRQYHQFLRQDO H FDUDFWHUL]DU R UHVXOWDGR GR LPSDFWR GH XPD JRWD QXPD VXSHUILFLH VHFD FRP H VHP HVFRDPHQWR FUX]DGR (VWH HVWXGR SHUPLWH R GHVHQYROYLPHQWR GH PRGHORV QXPpULFRV SDUD GHWHUPLQDU R OLPLWH GRV GLIHUHQWHV IHQyPHQRV GH LPSDFWR

1HVWH HVWXGR XPD LQVWDODomR H[SHULPHQWDO IRL SURMHWDGD SDUD HVWXGDU R FRPSRUWDPHQWR GR LP SDFWR GH JRWDV QXPD VXSHUItFLH GH DOXPtQLR SROLGD H VHFD )RUDP DQDOLVDGDV TXDWUR VXEVWkQFLDV GXDV PLVWXUDV75% JF  25% HV O H 50% JF  50% HV O H RXWUDV GXDV VXEVWkQFLDV 100% JF H H2O 2 FRPEXVWtYHO GH DYLmR IRL XVDGR SDUD FRPSDUDU R HIHLWR GR ELRFRPEXVWtYHO QR UHVXO

WDGR GH LPSDFWR H R H2O IRL XVDGR FRPR VXEVWkQFLD GH FRQWUROH 2EVHUYRXVH TXH DV PLVWXUDV

H[LEHP XP OLPLWH VSODVKQmRVSODVK GLIHUHQWH SDUD D PHVPD FRQGLomR LQLFLDO VXJHULQGR TXH DV SURSULHGDGHV GR ELRFRPEXVWtYHO LQIOXHQFLDP R UHVXOWDGR GR LPSDFWR 3DUD HVWXGDU R HIHLWR GH XP HVFRDPHQWR FUX]DGR QR LPSDFWR GH JRWDV XP W~QHO GH YHQWR WDPEpP IRL SURMHWDGR 2EVHUYRXVH TXH FRP D DSOLFDomR GH XP HVFRDPHQWR FUX]DGR D JRWD VREUH XPD GHIRUPQDomR TXH SDUHFH ID]HU YDULDU D FRQGLomR GR LPSDFWR )RL UHDOL]DGD XPD FRPSDUDomR HQWUH R LPSDFWR QRUPDO H R LPSDFWR FRP XP HVFRDPHQWR FUX]DGR )RUDP XWLOL]DGDV WUrV YHORFLGDGHV SDUD R HVFRDPHQWR FUX]DGR 7m/s 10m/s H 15m/s

)RUDP REVHUYDGRV GLIHUHQWHV UHVXOWDGRV FRPSDUDQGR XP LPSDFWR FRP XP HVFRPHQWR FUX]DGR FRP XP LPSDFWR QRUPDO H RV FRPSRQHQWHV GD YHORFLGDGH SDUHFHP WHU DOJXP VLJQLILFDGR QD WUDQVLomR GRV IHQyPHQRV GH LPSDFWR 2V UHVXOWDGRV IRUDP FRPSDUDGRV FRP DOJXQV FULWpULRV GH WUDQVLomR SURSRVWRV QD OLWHUDWXUD H RV UHVXOWDGRV GR SUHVHQWH HVWXGR LQGLFDP TXH DOJXQV GHVWHV SRGHP VHU XWLOL]DGR SDUD RXWURV HVWXGRV 9HULILFRXVH WDPEpP TXH XP HVWXGR GD UXJRVLGDGH VXSHUILFLDO GD VXSHUILFLH GH LPSDFWR SHUPLWLULD WLUDU PDLV FRQFOXV}HV

3DODYUDVFKDYH

%LRFRPEXVWtYHO 0RWRUHV GH $YLmR (VFRDPHQWR FUX]DGR *RWDV /LPLWH 6SODVKQmRVSODVK

$EVWUDFW

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 DQG WZR RWKHU VXEVWDQFHV 100% JF DQG H2O -HW IXHO ZDV

XVHG WR FRPSDUH WKH HIIHFW RI ELRIXHO RQ WKH LPSDFW UHVXOW DQG H2O ZDV XVHG DV WKH FRQWURO

VXEVWDQFH ,W ZDV REVHUYHG WKDW WKH EOHQGV H[KLELW D GLIIHUHQW VSODVKQRQ VSODVK WKUHVKROG VXJJHVWLQJ WKDW WKH ELRIXHO SURSHUWLHV LQIOXHQFH WKH LPSDFW UHVXOW 7R VWXG\ WKH HIIHFW RI D FURVVIORZ LQ WKLV SKHQRPHQRQ D ZLQG WXQQHO ZDV DOVR GHVLJQHG DQG D FRPSDULVRQ EHWZHHQ QRUPDO LPSDFW DQG LPSDFW ZLWK D FURVVIORZ ZDV PDGH 7KUHH FURVVIORZ YHORFLWLHV ZHUH XVHG DQG WKH YHORFLW\ RI WKH LPSDFW ZDV GLYLGHG LQWR WZR YHORFLW\ YHFWRUV

'LIIHUHQW UHVXOWV ZHUH REVHUYHG FRPSDULQJ FURVVIORZ LPSDFW ZLWK QRUPDO LPSDFW DQG WKH YHORFLW\ FRPSRQHQWV VHHP WR KDYH VRPH VLJQLILFDQFH LQ WKH WUDQVLWLRQ RI WKH LPSDFW SKHQRPHQD 7KH UHVXOWV ZHUH FRPSDUHG ZLWK VRPH WUDQVLWLRQ FULWHULD SURSRVHG LQ WKH OLWHUDWXUH DQG WKH GDWD LQGLFDWH WKDW QRQH RI WKHP SUHVHQWV D JRRG FRUUHODWLRQ IRU WKH GDWD ,W ZDV DOVR YHULILHG WKDW D VWXG\ RI WKH VXUIDFH URXJKQHVV RI WKH XVHG SODWH ZRXOG DOORZ GUDZLQJ PRUH FRQFOXVLRQV

.H\ZRUGV

%LRIXHO $HUR (QJLQHV &URVVIORZ 'URSOHWV 6SODVKQRQ6SODVK 7KUHVKROG

&RQWHQWV

 ,QWURGXFWLRQ 

 0RWLYDWLRQ                                        /LWHUDWXUH 5HYLHZ                                    'URSOHW:DOO ,QWHUDFWLRQV                            'HSRVLWLRQ6SODVK 7UDQVLWLRQ &ULWHULD                      2EMHFWLYHV                                        ([SHULPHQWDO 6WXG\   ([SHULPHQWDO )DFLOLW\                                  :LQG 7XQQHO 'HVLJQ                               &DOLEUDWLRQ                                    ,QMHFWLRQ 6\VWHP                                 ,PDJH $FTXLVLWLRQ 6\VWHP                            :RUN )OXLGV 3URSHUWLHV                                  'HQVLW\                                      6XUIDFH 7HQVLRQ                                 9LVFRVLW\                                     6XPPDU\ RI :RUN )OXLGV 3URSHUWLHV                       ,PDJH 'DWD 3URFHVVLQJ                                

 5HVXOWV DQG 'LVFXWLRQ 

 3KHQRPHQD 9LVXDOL]DWLRQ                                6SODVK1RQ 6SODVK 7KUHVKROG $QDOLVH                          1RUPDO ,PSDFW                                  ,PSDFW ZLWK &URVVIORZ                              6XPPDU\                                        &RQFOXVLRQV  %LEOLRJUDSK\  L[

/LVW RI )LJXUHV

 0RUSKRORJ\ RI GURS LPSDFW RQ D GU\ VXUIDFH >@                    9HORFLW\ YHFWRUV DQG LPSDFW DQJOH UHSUHVHQWDWLRQ                   &RQWDFW DQJOH UHSUHVHQWDWLRQ DGDSWHG IURP >@                    ([SHULPHQWDO IDFLOLW\                                  6FKHPDWLF RI WKH VFUHHQV SODFLQJ                            6HWWOLQJ &KDPEHU                                    :LQG WXQQHO FRQWUDFWLRQ CR = 2                           *XLOORWLQHV UHSUHVHQWDWLRQ                               &DOLEUDWLRQ FKDUW                                    9HORFLW\ REWDLQHG E\ YDU\LQJ G2                          

 6FKHPDWLF IRU YHORFLW\ SURILOHV PHDVXUHPHQWV YHUWLFDOO\ WR WKH OHIW DQG KRUL]RQ WDOO\ WR WKH ULJKW                                    +RUL]RQWDO YHORFLW\ PHDVXUHV                              9HUWLFDO YHORFLW\ PHDVXUHV                               1( 6LQJOH 6\ULQJH 3XPS                              ,PDJH ZLWK [ UHVROXWLRQ DQG 1/5120 V VKXWWHU                 ,PDJH ZLWK [ UHVROXWLRQ DQG 1/10240 V VKXWWHU                 3\FQRPHWHUV XVHG                                   'DWD 3K\VLFV ² 2&$+                                 %URRNILHOG '97 59&3 5KHRPHWHU RQ WKH OHIW                     &RQH DQG SODWH JHRPHWU\                                ,PDJH RI DQ 75% JF  25% HV O LPSDFW D DQG LWV EDFNJURXQG E          5HVXOW IURP LPDJH VXEWUDFWLRQ ZLWK FRQWUDVW DOWHUDWLRQ IRU YLVXDOL]DWLRQ SXUSRVHV   5HVXOWLQJ ELQDU\ LPDJH                                 5HVXOWLQJ LPDJH RI FKDQJLQJ YDOXHV RI 0 VXUURXQGHG E\ YDOXHV RI 1           5HVXOWLQJ LPDJH RI FKDQJLQJ YDOXHV RI 1 WR 0                      5HDO LPDJH RI WKH UHIHUHQFH WR WKH OHIW D SURFHVVHG LPDJH RI WKH UHIHUHQFH WR

WKH ULJKW                                        3URFHVVHG LPDJH RI D GURSOHW IDOO                            3URFHVVHG LPDJH RI D GURSOHW EHIRUH LPSDFW                      $ GURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH IRU D 75% JF  25% HV O PL[WXUH

D0= 3.06mmRe = 4967W e = 825La = 29912                 

 $ GURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH IRU D 50% JF  50% HV O PL[WXUH D0= 3.07mmRe = 3863W e = 798La = 18708                 

 $Q H2OGURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH D0= 4.06mmRe = 15588W e =

828La = 293454                                    $Q H2OGURSOHW ZLWK 4.06 mm RULJLQDO GLDPHWHU LPSLQJLQJ RQWR DQ DOXPLQXP SODWH

LQ D FURVVIORZ RI 7 m/s Rea= 18618W ea= 1181La = 293454            $Q 100 % JF GURSOHW ZLWK 3.02 mm RULJLQDO GLDPHWHU VXIHULQJ DHURGLQDPLF EUHDNXS

LQ D 10m/s FURVVIORZ                                  'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR %DL DQG *RVPDQ·V >@ FULWHULRQ

ZLWK WZR GLIIHUHQW A FRHIILFLHQW YDOXHV                       [L

 'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR 0XQGR HW DO >@ FULWHULRQ     'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR 5DQG\ HW DO >@ FULWHULRQ      'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV YHUWLFDO LPSDFW YHORFLW\

FRPSDUHG WR %DL DQG *RVPDQ·V >@ FULWHULRQ                      'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV DEVROXWH LPSDFW YHORFLW\

FRPSDUHG WR %DL DQG *RVPDQ·V >@ FULWHULRQ                      'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV YHUWLFDO LPSDFW YHORFLW\

FRPSDUHG WR 0XQGR HW DO >@ FULWHULRQ                         'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV DEVROXWH LPSDFW YHORFLW\

FRPSDUHG WR 0XQGR HW DO >@ FULWHULRQ                         'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV YHUWLFDO LPSDFW YHORFLW\

FRPSDUHG WR 5DQG\ HW DO >@ FULWHULRQ                         'URSOHWV EHKDYLRU IRU LPSDFW ZLWK FURVVIORZ UHODWLQJ WR LWV DEVROXWH LPSDFW YHORFLW\

FRPSDUHG WR 5DQG\ HW DO >@ FULWHULRQ                       

/LVW RI 7DEOHV

 ,QIOXHQFH RI GLIIHUHQW SDUDPHWHUV RQ WKH LPSDFW RXWFRPH DGDSWHG IURP >@     7\SLFDO YDOXHV RI $ GHSHQGLQJ RQ WKH VXUIDFH URXJKQHVV DGDSWHG IURP >@      'HVLJQ SDUDPHWHUV RI WKH VHWWOLQJ FKDPEHU                       3DUDPHWHUV RI WKH FRQWUDFWLRQ GHVLJQ                         &DOLEUDWLRQ WHVWV                                    9HORFLWLHV XVHG LQ WKLV VWXG\                              5DQJH RI YDOXHV IURP WKH H[SHULPHQWDO ZRUN                      5HVXOWV RI WKH WHVWV SHUIRUPHG WR GHWHUPLQH WKH GHQVLW\ RI WKH VXEVWDQFHV      6XUIDFH WHQVLRQ WHVWV UHVXOWV                              9LVFRVLW\ WHVWV UHVXOWV                                  :RUN )OXLGV 3URSHUWLHV                                 5HVXOWV REWDLQHG IRU QRUPDO LPSDFW                          5HVXOWV REWDLQHG IRU WKH GURSOHWV LPSDFW ZLWK D 7 m/s FURVVIORZ            5HVXOWV REWDLQHG IRU WKH GURSOHWV LPSDFW ZLWK D 10 m/s FURVVIORZ           &RPSDULVRQ EHWZHHQ 1RUPDO ,PSDFW 1, ZKHUH VSODVK RFFXUV DQG &URVVIORZ ,P

SDFW &, ZKHUH GHSRVLWLRQ RFFXUV                          &RPSDULVRQ EHWZHHQ 1RUPDO ,PSDFW 1, DQG &URVVIORZ ,PSDFW &, ZKHUH VSODVK

RFFXUV IRU ERWK FDVHV                                

1RPHQFODWXUH

a, b 'HSHQGHQW FRQVWDQWV

A, B 6XUIDFH URXJKQHVV FRHILFLHQW C_p &RQWUDFWLRQ YHORFLW\ SUHVVXUH

d 6FUHHQ ZLUH GLDPHWHU

D₀ 'URSOHW GLDPHWHU EHIRUH LPSDFW D_eq ,QOHW HTXLYDOHQW GLDPHWHU

F 'LPHQVLRQOHVV SDUDPHWHU IRU ZDOO YHORFLW\

G1, G2 *XLOORWLQHV WKDW DOORZ FRQWUROOLQJ WKH FURVVIORZ YHORF LW\  DQG  UHVSHFWLYHO\

H +HLJKW

K 3UHVVXUH GURS FRHIILFLHQW

K_c 'LPHQVLRQOHVV VSODVKLQJ SDUDPHWHU

l 0HVK OHQJWK L 1R]]OH OHQJWK La /DSODFH QXPEHU m 0DVV Oh 2KQHVRUJH QXPEHU Re 5H\QROGV QXPEHU s 'LVWDQFH EHWZHHQ  C_pi DQG  C_pi U 9HORFLW\ U_x +RUL]RQWDO YHORFLW\ FRPSRQHQW U_y 9HUWLFDO YHORFLW\ FRPSRQHQW ˜ u₂ ([LW YHORFLW\ QRQXQLIRUPLW\ V 9ROXPH W e :HEHU QXPEHU

W e_c &ULWLFDO :HEHU QXPEHU

x &RQWUDFWLRQ QR]]OH D[LDO OHQJWK FRRUGLQDWH

X 1R]]OH VKDSH SDUDPHWHU

*UHHN 6\PEROV

β 2SHQ DUHD UDWLR

h +HLJKW GLIIHUHQFH UHJLVWHUHG LQ WKH PDQRPHWHU href +HLJKW GLIIHUHQFH UHIHUHQFH

θ ,PSDFW DQJOH θ_c &RQWDFW DQJOH μ '\QDPLF YLVFRVLW\ ν .LQHPDWLF YLVFRVLW\ ρ 'HQVLW\ ρ_air $LU 'HQVLW\ ρ_H2O :DWHU 'HQVLW\ σ 6XUIDFH WHQVLRQ

τ_s 6XUIDFH URXJKQHVV DYHUDJH KHLJKW

6XEVFULSWV

a $EVROXWH YHORFLW\

e 0D[LPXP

i 0LQLPXP

x +RUL]RQWDO FRRUGLQDWH YHORFLW\ y 9HUWLFDO FRRUGLQDWH YHORFLW\

0 %HIRUH ,PSDFW

1 ,QOHW

2 ([LW

/LVW RI $FURQ\PV

$670 $PHULFDQ 6RFLHW\ IRU 7HVWLQJ DQG 0DWHULDOV &, &URVVIORZ ,PSDFW

&5 &RQWUDFWLRQ 5DWLR ISV )UDPHV SHU VHFRQG

+()$ +\GURSURFHVVHG (VWHUV DQG )DWW\ $FLGV +92 +\GURSURFHVVHG 9HJHWDEOH 2LO

-) -HW )XHO

1(;7%/ 1H[W *HQHUDWLRQ %LRPDVVWR/LTXLG

1, 1RUPDO ,PSDFW

&KDSWHU 

,QWURGXFWLRQ

7KLV ILUVW FKDSWHU SUHVHQWV WKH PRWLYDWLRQ DQG WKH REMHFWLYHV RI WKH SUHVHQW H[SHULPHQWDO VWXG\ $ UHYLHZ RI WKH FXUUHQW OLWHUDWXUH ZDV PDGH WR LQWURGXFH VRPH FRQFHSWV VXFK DV WKH HIIHFW RI WKH LQFLGHQW DQJOH ZDOO URXJKQHVV DQG WKH HIIHFW RI D FURVVIORZ LQ D GURSOHW LPSLQJHPHQW RQ D GU\ VXUIDFH 6RPH GHSRVLWLRQVSODVK WUDQVLWLRQ FULWHULD SURSRVHG LQ WKH OLWHUDWXUH ZKLFK DUH DOVR SUHVHQWHG LQ WKLV VHFWLRQ

 0RWLYDWLRQ

7KH FRQVWDQW LQFUHDVH LQ RLO SULFHV DQG WKH DSSOLFDWLRQ RI HQYLURQPHQWDO WDUJHWV LQ YDULRXV FRXQ WULHV HVFDODWHG WKH SXUVXLW WR FUHDWH FOHDQHU DQG PRUH HIILFLHQW HQHUJ\ SURGXFWLRQ 1RUPDOO\ LW WDNHV \HDUV RI LQWHQVH WHVWLQJ DQG KLJK IXQGLQJ XQWLO WKH DSSOLDQFH RI WKH QHZ V\VWHPV IRU FOHDQHU HQHUJ\ SURGXFWLRQ LV ILQLVKHG

7R E\SDVV WKLV SUREOHP WKH SUHVHQW VWXG\ DLPV WR VXFFHVVIXOO\ DSSOLHG ELRIXHOV WR ORZ HPLVVLRQ DHUR HQJLQHV FRPEXVWRUV $W WKH VDPH WLPH WKLV ZRXOG GHFUHDVH FRVWV DQG UHGXFH JUHHQKRXVH JDVHV HPLVVLRQV $OVR FXUUHQW OHJLVODWLRQ DOORZV WKH XVH RI ELRIXHOV LQ WKH DHURQDXWLFDO LQGXVWU\ $V LW ZDV PHQWLRQHG LQ 3L]]LRO >@ WKH VWDQGHU VSHFLILFDWLRQ $670 ' GHILQHV WKDW WKH PD[L PXP EOHQGLQJ UDWLR DOORZHG IRU +()$ +\GURSURFHVVHG (VWHUV DQG )DWW\ $FLGV W\SH DOWHUQDWLYH IXHOV LV 50 % LQ YROXPH 7KH ELRIXHO XVHG LQ WKLV VWXG\ LV D +()$ W\SH DOWHUQDWLYH IXHO ZKLFK LV NQRZQ XQGHU WKH FRPPHUFLDO QDPH RI 1(;7%/ 1H[W *HQHUDWLRQ %LRPDVVWR/LTXLG ,Q WKH SUHVHQW ZRUN WKH ELRIXHO XVHG LV FDOOHG +92 +\GURSURFHVVHG 9HJHWDEOH 2LO ZKLFK LV DOVR WKH QDPH JLYHQ WR +()$ W\SH IXHOV ZKHUH DQLPDO ELRPDVV LV QRW LQYROYHG >@

7R EH DEOH WR DSSO\ WKLV VXEVWDQFH LQ DHUR HQJLQHV FRPEXVWRUV WKH WKHUPRSK\VLFDO SURSHUWLHV RQ GURSOHW DWRPL]DWLRQ DQG WKH FKDUDFWHUL]DWLRQ RI GURSOHWVSUD\ LPSLQJHPHQW SURFHVVHV QHHGHG WR EH VWXGLHG )RU WKLV WKH GHVLJQ DQG FRQVWUXFWLRQ RI DQ H[SHULPHQWDO IDFLOLW\ ZDV UHTXLUHG

 /LWHUDWXUH 5HYLHZ

 'URSOHW:DOO ,QWHUDFWLRQV

7KH EHKDYLRU RI GURSOHWV LPSDFWLQJ RQ GU\ VXUIDFHV LV QRW IXOO\ XQGHUVWRRG ,W LQYROYHV D QXPEHU RI LQIOXHQFLQJ SDUDPHWHUV DQG WKH RXWFRPHV DUH QRUPDOO\ FODVVLILHG E\ REVHUYLQJ WKH PRUSKRORJ LFDO FKDUDFWHULVWLFV RI WKH LPSLQJLQJ GURS ,Q KLV H[SHULPHQWDO ZRUN 5LREER HW DO >@ LGHQWLI\ VL[ SRVVLEOH RXWFRPHV IRU GURSOHW LPSDFW RQ GU\ VXUIDFHV GHSRVLWLRQ SURPSW VSODVK FRURQD VSODVK UHFHGLQJ EUHDNXS SDUWLDO UHERXQG DQG UHERXQG VKRZQ LQ ILJXUH 

'HSRVLWLRQ RFFXUV ZKHQ WKH GURS LPSDFWV RQ WKH VXUIDFH DQG RQO\ VXIIHUV GHIRUPDWLRQ ,PSDFWLQJ ZLWK WKH VXUIDFH WKH GURSOHW ZLOO VSUHDG RXW DQG IRUPHG ZKDW LV FDOOHG D ODPHOOD ZLWK D YLVLEOH RXWHU ULP :KHQ WKLV ODPHOOD UHDFKHV WKH PD[LPXP VSUHDGLQJ GLDPHWHU LW UHFRLOV DQG IRUPV D OLTXLG ILOP RYHU WKH VXUIDFH )RU KLJK :HEHU DQG 5H\QROGV QXPEHUV SURPSW VSODVK PD\ RFFXU DQG 

)LJXUH  0RUSKRORJ\ RI GURS LPSDFW RQ D GU\ VXUIDFH >@

WKLV LPSDFW KDSSHQV ZKHQ VPDOOHU GURSOHWV DUH HMHFWHG IURP WKH LPSDFW UHJLRQ &RURQD VSODVK LV REVHUYHG ZKHQ D GURS LPSDFWV ZLWK VXIILFLHQW YHORFLW\ VR WKH RXWHU ULP IRUPHG E\ WKH ODPHOOD KDV VXIILFLHQW HQHUJ\ WKDW HOHYDWHV DQG FUHDWHV D FURZQOLNH VKDSH :KHQ LW UHDFKHV WKH PD[LPXP FURZQ KHLJKW VPDOOHU GURSOHWV VHSDUDWH IURP WKLV VKDSH 7KLV SKHQRPHQRQ LV DOVR UHIHUUHG DV FURZQ VSODVK >@ $OWKRXJK ERWK SKHQRPHQD GHVFULEHG WKH RFFXUUHQFH RI VSODVK WKH SURPSW VSODVK GRHV QRW SUHVHQW D FURZQOLNH VKDSH )XUWKHUPRUH WKH VHFRQGDU\ DWRPL]DWLRQ RFFXUV LQ GLIIHUHQW VWDJHV IRU ERWK SKHQRPHQD 7KH UHFHGLQJ EUHDNXS RFFXUV DIWHU WKH VSUHDGLQJ RI WKH GURSOHW ,W KDSSHQV LI ZKHQ WKH ODPHOOD VWDUWV WR UHFHGH DIWHU WKH PD[LPXP VSUHDGLQJ GLDPHWHU LV UHDFKHG WKH G\QDPLF FRQWDFW DQJOH UHDFKHV ]HUR 7KHQ VRPH GURSOHWV DUH OHIW EHKLQG 7KH SDUWLDO UHERXQG DQG FRPSOHWH UHERXQG GHSHQG RQ WKH FRQWDFW DQJOH DQG WKH PD[LPXP GLDPHWHU UHDFKHG ,W RQO\ KDSSHQV LI D UHFHGLQJ SKDVH LV REVHUYHG )RU KLJK HQHUJ\ LPSDFWV GXULQJ WKH UHFHGLQJ SKDVH QRW DOO HQHUJ\ LV GLVVLSDWHG DQG LI WKDW HQHUJ\ UHDFKHV WKH LPSDFW SRLQW WKH IOXLG LV HOHYDWHG 'XULQJ WKH UHFHGLQJ SKDVH WKH FRQWDFW DQJOH ZLOO GHILQH LI D SDUWLDO UHERXQG ORZ FRQWDFW DQJOHV RU D FRPSOHWH UHERXQG KLJK FRQWDFW DQJOHV KDSSHQV  0RLWD DQG 0RUHLUD >@ DOVR UHSRUWHG WKH RFFXUUHQFH RI ILQJHU EUHDNXS WKLV SKHQRPHQRQ ZDV HQFRXQWHUHG DW PRGHUDWH LPSDFW YHORFLWLHV DQG LV DQ HDUO\ FRQVHTXHQFH RI VRPH LQVWDELOLWLHV GXULQJ WKH VSUHDGLQJ SKDVH :KHQ WKH ODPHOOD LV VSUHDGLQJ VRPH ILQJHUVOLNH VKDSH VWUXFWXUHV DUH FUHDWHG DQG EUHDN XS LQ WKH ILQDO VWDJH RI VSUHDGLQJ 7KLV ILQJHULQJ SKHQRPHQRQ LV DOVR GHVFULEHG E\ <DULQ >@

7KH RXWFRPH RI D GURSOHW LPSDFW RQ D VROLG VXUIDFH LV JRYHUQHG E\ D QXPEHU RI SDUDPHWHUV VXFK DV GURSOHW YHORFLW\ VL]H LPSDFW DQJOH IOXLG SURSHUWLHVYLVFRVLW\ VXUIDFH WHQVLRQ VXUIDFH URXJKQHVV DQG HYHQ LI D JDV ERXQGDU\ OD\HU LV DSSOLHG LQ WKH QHDUZDOO UHJLRQ >@

7KH UHODWLYH PDJQLWXGH RI WKH GLIIHUHQW W\SHV RI IRUFHV LQYROYHG LQ WKH LPSDFW LV QRUPDOO\ SUH VHQWHG DV GLPHQVLRQOHVV QXPEHUV 7KLV QXPEHUV FDQ EH XVHG WR SUHGLFW WKH RXWFRPH RI D GURS 

LPSDFW 7KH GLPHQVLRQOHVV QXPEHUV HPSOR\HG LQ WKLV ZRUN DUH

 7KH :HEHU QXPEHU W e UHODWHV WKH LQHUWLDO IRUFHV ZLWK WKH VXUIDFH WHQVLRQ IRUFHV W e= ρU

2 0D0

σ 

 7KH 5H\QROGV QXPEHU Re UHODWHV WKH LQHUWLDO IRUFHV ZLWK WKH YLVFRXV IRUFHV Re= ρU0D0

μ 

 7KH 2KQHVRUJH QXPEHU Oh UHODWHV YLVFRXV IRUFHV WR LQHUWLDO DQG VXUIDFH WHQVLRQ IRUFHV Oh= √ W e Re = μ √ ρσD₀ 

 7KH /DSODFH QXPEHU La PHDVXUHV WKH UHODWLYH LPSRUWDQFH RI VXUIDFH WHQVLRQ DQG YLVFRXV IRUFHV DFWLQJ RQ WKH OLTXLG

La=ρσD0 μ2 

:KHUH D0DQG U0UHSUHVHQW WKH GLDPHWHU DQG WKH YHORFLW\ RI WKH GURSOHW EHIRUH LPSDFW $QG ρ

σDQG μ DUH WKH OLTXLG GHQVLW\ VXUIDFH WHQVLRQ DQG YLVFRVLW\ UHVSHFWLYHO\

7KH LPSDFW DQJOH θ LV IRUPHG E\ WKH DQJOH IRUPHG EHWZHHQ WKH DEVROXWH YHORFLW\ YHFWRU RI WKH LQFLGHQW GURSOHW DQG WKH LPSDFW VXUIDFH ILJXUH 

)LJXUH  9HORFLW\ YHFWRUV DQG LPSDFW DQJOH UHSUHVHQWDWLRQ

-D\DUDWQH DQG 0DVRQ >@ ILQG WKDW WKH GURSOHWV RXWFRPHV GHSHQG RQ WKH LPSDFW DQJOH 7KLV DQJOH DOVR LQIOXHQFHV WKH GLUHFWLRQ RI WKH VHFRQGDU\ GURSOHWV IRU VPRRWK VXUIDFHV $ VPDOO LQFL GHQW DQJOH RI WKH GURSOHW OHDGV WR D VPDOO UHIOHFWLRQ DQJOH ZKLOH D ODUJH LQFLGHQW DQJOH OHDGV WR D ODUJH GHIOHFWLRQ DQJOH >@ $FFRUGLQJ WR <DR DQG &DL >@ LI WKH LPSDFW DQJOH LV QRW 90 ž WKH WDQJHQWLDO YHORFLW\ RI WKH GURSOHW GHVWDELOL]HV WKH OLTXLG ILOP DQG HQKDQFHV WKH IUDJPHQWDWLRQ RI WKH GURSOHW IROORZLQJ WKH LPSLQJHPHQW

,W LV ZRUWK PHQWLRQ WKDW LPSDFW DQJOH GLIIHUV IURP FRQWDFW DQJOH θc 7KH FRQWDFW DQJOH LV LQIOXHQFHG E\ WKH OLTXLG SURSHUWLHV DQG WKH VXUIDFH WRSRJUDSK\ :KHQ D GURSOHW LPSDFWV RQ D VROLG VXUIDFH D OLTXLG ILOP LV IRUPHG DQG GXH WR WKH LQIOXHQFH RI WKH VXUIDFH WHQVLRQ DQG VXUIDFH IRUFHV WKLV ILOP UHDFKHV D PD[LPXP GLDPHWHU DQG WKHQ UHFRLOV :KHQ WKLV SURFHVV UHDFKHV HTXLOLEULXP WKH FRQWDFW DQJOH FDQ EH PHDVXUHG 7KLV DQJOH LV DOVR NQRZQ DV ZHWWDELOLW\ 

RI WKH VXUIDFH >@ ,I D ZHWWHG VXUIDFH LV SUHVHQWHG WKH FRQWDFW DQJOH ZLOO YDU\ EHWZHHQ 90ž DQG 180ž DQG LI D QRQZHWWHG VXUIDFH LV SUHVHQWHG EHWZHHQ 0 žDQG 90 ž ILJXUH  >@

)LJXUH  &RQWDFW DQJOH UHSUHVHQWDWLRQ DGDSWHG IURP >@

7KH VXUIDFH URXJKQHVV LV DOVR DQ LPSRUWDQW SDUDPHWHU LQ WKH GURSOHWV LPSLQJHPHQW G\QDPLFV >@ >@ >@ >@ DQG LW LV QRUPDOO\ FKDUDFWHUL]HG E\ LWV DYHUDJH KHLJKW τs 0XQGR HW DO >@ REVHUYHG WKDW WKH VXUIDFH URXJKQHVV DOWHUV WKH LPSDFW DQJOH RI LPSLQJLQJ GURSOHWV )RU VPDOO GURSOHWV WKLV HIIHFW EHFRPHV PRUH HYLGHQW 7KLV DOVR DIIHFWV WKH YROXPH QXPEHU DQG WKH VL]H GLVWULEXWLRQ RI VHFRQGDU\ GURSOHWV )RU URXJK VXUIDFHV WKH FULWLFDO WKUHVKROG IRU VSODVK LV ORZHUHG LQ UHODWLRQ WR VPRRWK VXUIDFHV >@ $OVR WKH PDVV RI WKH VSODVK GHFUHDVHV ZLWK WKH LQFUHDVH RI VXUIDFH URXJKQHVV >@

0XQGR HW DO >@ DOVR VKRZHG WKDW WKH GURSOHWV ZLWK KLJK NLQHWLF HQHUJ\ SUHVHQWHG D PRUH LUUHJXODU EHKDYLRU IRU URXJK VXUIDFHV FRPSDUHG WR VPRRWK VXUIDFHV )RU URXJK VXUIDFHV WKH KLJK WDQJHQWLDO PRPHQWXP OHDGV WR GLVLQWHJUDWLRQ LQWR VHFRQGDU\ GURSOHWV DQG WKH QRUPDO SKHQRPHQD DUH QR ORQJHU REVHUYHG 'URSOHWV ZLWK ORZ NLQHWLF HQHUJ\ LPSDFWLQJ LQ URXJK VXUIDFHV GLG QRW SUHVHQW GLIIHUHQW UHVXOWV IRU WKRVH LPSDFWHG RQ VPRRWK VXUIDFHV 7KH GURSOHW GHSRVLWV DQG VSUHDG RXW IRUPLQJ D OLTXLG ILOP GHSRVLWLRQ DQG LQ WKLV FDVH WKH VXUIDFH URXJKQHVV GRHV QRW SURPRWH VSODVKLQJ RI WKH SULPDU\ GURSOHW

)RU VPRRWK VXUIDFHV WKH GLDPHWHU GLVWULEXWLRQV RI VHFRQGDU\ GURSOHWV GHSHQG RQ WKH IOXLG SURS HUWLHV DQG NLQHPDWLF SDUDPHWHUV )RU URXJK VXUIDFHV WKH VHFRQGDU\ GURSOHWV KDYH VPDOOHU PHDQ GLDPHWHUV DQG VPDOOHU GLDPHWHU GLVWULEXWLRQ >@

7DEOH  ,QIOXHQFH RI GLIIHUHQW SDUDPHWHUV RQ WKH LPSDFW RXWFRPH DGDSWHG IURP >@

$Q LQFUHDVH RI 'HSRVLWLRQ 3URPSW 6SODVK 5HFHGLQJ %UHDNXS &RPSOHWH 5HERXQG &URZQ 6SODVK 3DUWLDO 5HERXQG

U₀ ↓ ↑ ↑ ↑ ↑ D₀ ↓ ↑ σ ↓ ↑ ↑ ↓ ↑ μ ↑ ↓ ↓ ↓ τs ↓ ↑ ↓ θc ↑ ↑ ↑

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

7KH WHPSHUDWXUH WKH SUHVHQFH RI D OLTXLG ILOP LQ WKH VXUIDFH FDQ DOVR DOWHU WKH RXWFRPH RI GURSOHW LPSDFW KRZHYHU WKH\ DUH QRW YDULDEOHV LQ WKH SUHVHQW VWXG\

5LREER HW DO >@ SUHVHQWHG D FRUUHODWLRQ EHWZHHQ WKH SDUDPHWHUV DQG WKH RXWFRPHV RI WKH LPSLQJHPHQW SKHQRPHQD 7DEOH  SUHVHQWV WKLV FRUUHODWLRQ ZKHUH WKH XSZDUG DUURZ DQG WKH 

GRZQZDUG DUURZ UHSUHVHQW DQ LQFUHDVH DQG D GHFUHDVH UHVSHFWLYHO\ LQ WKH LPSRUWDQFH RI WKH YDULDEOH LQ WKH LPSDFW RXWFRPH

 'HSRVLWLRQ6SODVK 7UDQVLWLRQ &ULWHULD

7KH RXWFRPH RI D GURSOHW LPSLQJLQJ RQ D ZDOO GHSHQGV RQ D QXPEHU RI FRQGLWLRQV 7R EH DEOH WR HVWDEOLVK WKH WUDQVLWLRQ FULWHULD EHWZHHQ LPSLQJHPHQW UHJLPHV D QXPEHU RI HPSLULFDO FRUUH ODWLRQV KDV EHHQ SURSRVHG 7KHVH FRUUHODWLRQV GHWHUPLQH WKH OLPLW EHWZHHQ GLIIHUHQW LPSDFW SKHQRPHQD DQG DUH XVHG WR GHVFULEH KRZ D GURSOHW ZLOO EHKDYH RQ WKH VXUIDFH

,Q WKH OLWHUDWXUH WKH 5H\QROGV QXPEHU :HEHU QXPEHU 2KQHVRUJH QXPEHU DQG /DSODFH QXPEHU DUH XVHG LQ WKHVH PRGHOV 6WRZ DQG +DGILHOG >@ SUHVHQWHG WKH VSODVKLQJ SDUDPHWHU Kc ZKLFK LV XVHG WR GHWHUPLQH ZKHQ VSODVK RFFXUV ,W LV GHILQHG DV

K_c = B.Oha.W eb 

:KHUH D DQG E GHSHQG RQ WKH H[SHULPHQWDO FRQGLWLRQV 7KLV UHODWLRQ GLFWDWHV WKDW WKH WUDQVLWLRQ EHWZHHQ WKH GLIIHUHQW UHJLPHV RFFXUV ZKHQ WKH GLPHQVLRQOHVV SDUDPHWHUV EHFRPH FULWLFDO 7KH QXPHULFDO YDOXH IRU WKLV WKUHVKROG GHSHQGV RQ VL]H YHORFLW\ WHPSHUDWXUH LQFLGHQW DQJOH DQG IOXLG SURSHUWLHV DV ZHOO DV GLIIHUHQW ZDOO FRQGLWLRQV ZDOO WHPSHUDWXUH UHODWLYH ILOP WKLFNQHVV VXUIDFH URXJKQHVV >@ 7KHUH LV D YDULHW\ RI PRGHOV LQ WKH OLWHUDWXUH KRZHYHU LQ WKH SUHVHQW ZRUN RQO\ WKUHH FRXOG EH DSSOLHG

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ec LV UHDFKHG VSODVK RFFXUV

W e_c= A.La−0.18 

7DEOH  7\SLFDO YDOXHV RI $ GHSHQGLQJ RQ WKH VXUIDFH URXJKQHVV DGDSWHG IURP >@

τs>õP@ $          

7KH PRGHO SUHVHQWHG E\ 0XQGR HW DO >@ XVHV WKH VSODVKLQJ SDUDPHWHU Kc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 SUHVHQWV WKH ERXQGDU\ OLPLW IRU WKLV FULWHULD

Oh.Re1.25= 57.7 

7KH ODVW FRUUHODWLRQ XVHG LQ WKH SUHVHQW ZRUN ZDV SURSRVHG E\ 5DQG\ HW DO >@ ZKR XVHG D ODUJH QXPEHU RI K\GURFDUERQ IXHOV DQG DOFRKROV WR GHYHORS WKHLU FULWHULD $OWKRXJK 5DQG\ HW DO >@ REVHUYHG GLIIHUHQW GLVLQWHJUDWLRQ PHFKDQLVPV D VLQJOH WKUHVKROG ZDV GHYHORSHG WR ILW DOO WKHLU GDWD 7KLV FRUUHODWLRQ ILWWHG ZHOO ZLWK WKHLU H[SHULPHQWDO UHVXOWV IRU KLJK 5H\QROGV QXPEHUV KRZHYHU ZKHQ YLVFRXV IRUFHV DQG ZHWWDELOLW\ HIIHFWV EHFDPH PRUH VLJQLILFDQW ORZHU 5H\QROGV QXPEHUV WKH GDWD GLG QRW ILW ZHOO ZLWK WKLV FRUUHODWLRQ 7KLV H[SHULPHQW ZDV FRQGXFWHG ZLWK DQ DOXPLQXP GLVN ZLWK YHU\ ORZ VXUIDFH URXJKQHVV (TXDWLRQ  SUHVHWV WKH WUDQVLWLRQ FULWHULD SURSRVHG

Oh.Re0.609= 0.85 

 2EMHFWLYHV

7KLV VWXG\ DLPV WR DQDO\VH WKH LPSDFW SKHQRPHQD RI PL[WXUHV RI ELRIXHO DQG FRQYHQWLRQDO MHW IXHO 7R DFFRPSOLVK WKLV JRDO LW ZDV GHVLJQ DQG FRQVWUXFWHG DQ H[SHULPHQWDO IDFLOLW\ WR VWXG\ WKH EHKDYLRU RI D VLQJOH GURSOHW LPSLQJLQJ RQ D GU\ VXUIDFH ZLWK DQG ZLWKRXW D FURVVIORZ $ ZLQG WXQQHO ZDV GHVLJQHG WR VWXG\ WKH GLIIHUHQFH EHWZHHQ QRUPDO LPSDFW DQG WKH LPSDFW ZLWK D FURVVIORZ 7KH GURSOHW ZDV H[SRVHG WR WKH LQIOXHQFH RI WKUHH GLIIHUHQW FURVVIORZ YHORFLWLHV 7 10 DQG 15 m/s 7KLV IDFLOLW\ DOORZHG WR YLVXDOL]H WKH GLIIHUHQW LPSDFW SKHQRPHQD RI WKH GURSOHWV DQG LGHQWLI\ WKH GLIIHUHQW LPSDFW UHJLPHV

)RXU VXEVWDQFHV ZHUH XVHG 100% JF  75% JF DQG 25% HV O 50% JF DQG 50% HV O DQG H2O

:DWHU H2O LV DQ H[WHQVLYHO\ VWXGLHG IOXLG DQG LV XVHG DV D UHIHUHQFH VXEVWDQFH &RPSDULQJ WKH

UHVXOWV RI WKH WZR PL[WXUHV ZLWK 100% JF  WKH LQIOXHQFH RI DGGLQJ WKH ELRIXHO ZLOO EH DQDO\]HG /DVWO\ WKH UHVXOWV ZHUH FRPSDUHG WR WKH WUDQVLWLRQ FULWHULD

&KDSWHU 

([SHULPHQWDO 6WXG\

,Q WKLV FKDSWHU LV GHVFULEHG WKH H[SHULPHQWDO IDFLOLW\ DQG WKH SURFHGXUH RI WKH H[SHULPHQWDO VWXG\ )LUVW LW·V SUHVHQWHG WKH ZLQG WXQQHO FRQVWUXFWLRQ DQG FDOLEUDWLRQ 7KHQ LW·V VKRZHG WKH LQMHFWLRQ V\VWHP DQG WKH LPDJH DFTXLVLWLRQ V\VWHP XVHG LQ WKLV ZRUN DQG DOVR VRPH FKDUDFWHULV WLFV RI WKH ZRUNLQJ IOXLGV DUH SUHVHQWHG WR EHWWHU XQGHUVWDQG VRPH UHVXOWV )LQDOO\ D GHVFULSWLRQ RI KRZ WKH LPDJH DQDO\VLV LV PDGH DQG VRPH UHVXOWV DUH SUHVHQWHG

 ([SHULPHQWDO )DFLOLW\

)LJXUH  ([SHULPHQWDO IDFLOLW\

$ VFKHPDWLF LPDJH RI WKH H[SHULPHQWDO IDFLOLW\ LV SUHVHQWHG LQ ILJXUH  $ YHQWLODWRU ZLWK 15 kW ZDV XVHG WR SURYLGH D FURVVIORZ ZLWK 3000 m3/h WKURXJK D ORZVSHHG ZLQG WXQQHO 7KH ZLQG WXQQHO KDV D UHFWDQJXODU H[LW QR]]OH ZLWK 200×40 mm2_{DQG WKH LPSDFW VXUIDFH LV D VPRRWK}

DOXPLQXP SODWH ZLWK 700×80 mm2_{ 7KLV SODWH LV SODFHG DFURVV WKH H[LW QR]]OH DQG LV HTXLGLVWDQW}

WR WZR JODVVHV RQH RI ZKLFK LV D GLIIXVLRQ JODVV XVHG WR VSUHDG WKH OLJKW HYHQO\ 7KH OLJKW LV SURYLGHG E\ D 20W /HG OLJKW DQG LV DOLJQHG ZLWK WKH LPSDFW VXUIDFH DQG GLUHFWO\ DFURVV IURP WKH KLJKVSHHG FDPHUD

 :LQG 7XQQHO 'HVLJQ

 'LIIXVHU

7KH GLIIXVHU LV XVHG WR GHFHOHUDWH WKH FURVVIORZ DQG W\SLFDOO\ WKH\ KDYH DQJOHV EHORZ 7, 5 ž KRZHYHU WKDW ZRXOG UHTXLUH D ORQJ GLIIXVHU >@ 'XH WR D ODFN RI VSDFH D VPDOO RQH ZDV XVHG DQG LQ WKLV FDVH VHSDUDWLRQ PD\ RFFXU 7R DYRLG WKLV D VFUHHQ ZDV SODFHG ZKHUH WKH 

GLIIXVHU·V DQJOH VXIIHUV D VXGGHQ FKDQJH UHPRYLQJ WKH GLUHFW HIIHFWV RI OD\HU JURZWK DQG LQFLGHQW VHSDUDWLRQ >@ 7KH GLIIXVHU XVHG KDV D OHQJWK RI 335 mm DQG LWV DQJOH LV DERXW 48.24 ž ,W KDV 100 mm VTXDUH LQOHW DQG D 40×400 mm H[LW QR]]OH ,Q WKH SUHVHQW ZRUN WKLV GLIIXVHU ZDV DOUHDG\ EXLOW DQG WKH IROORZLQJ SDUWV RI WKH ZLQG WXQQHO ZHUH EXLOW FRQVLGHULQJ LWV FKDUDFWHULVWLFV

 6HWWOLQJ &KDPEHU

$FFRUGLQJ WR 0HKWD DQG %UDGVKDZ >@ WKH VHWWOLQJ FKDPEHU FRQVLVWV RI WZR FRPSRQHQWV KRQ H\FRPE DQG VFUHHQV 7KH KRQH\FRPEV DUH HIIHFWLYH WR UHPRYH VZLUO DQG ODWHUDO PHDQ YHORFLW\ YDULDWLRQV SURYLGLQJ WKDW WKH IORZ \DZ DQJOHV DUH ORZHU WKDQ 10 ž 7KLV VHFWLRQ RI WKH VHWWOLQJ FKDPEHU ZDV DOUHDG\ FRQVWUXFWHG DQG ZDV RQO\ YHULI\ WKDW WKH FHOO OHQJWK RI WKH KRQH\FRPEV ZDV 6 WR 8 WLPHV LWV GLDPHWHU LQ RUGHU WR PD[LPL]H WKH RYHUDOO EHQHILW

7KH QH[W VWHS ZDV WR SODFH WKH VFUHHQV LPSRVLQJ D VWDWLF SUHVVXUH GURS SURSRUWLRQDO WR U2_{ 7KLV}

DOORZV D PRUH XQLIRUP YHORFLW\ SURILOH RI WKH IORZ DQG UHGXFHV WKH ERXQGDU\ OD\HU WKLFNQHVV JLYLQJ WKH IORZ DQ LQFUHDVHG DELOLW\ WR ZLWKVWDQG D SUHVVXUH JUDGLHQW 9DULDWLRQV LQ WKH ORQJL WXGLQDO PHDQ YHORFLW\ DUH QHDUO\ DOO UHPRYHG E\ D VFUHHQ ZLWK D SUHVVXUH GURS FRHIILFLHQW RI 

7KHUH DUH VRPH SDUDPHWHUV WR WDNH LQWR DFFRXQW LQ RUGHU WR EXLOG D VHWWOLQJ FKDPEHU WKH SUHVVXUH GURS FRHIILFLHQW K WKDW QHHGV WR KDYH D YDOXH RI 1.5 LQ RUGHU WR UHGXFH WKH \DZ DQG VZLUO DQJOHV RI DERXW 40ž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β=  1 −d l 2  K= 6.51 − β β2  U d βν −1 3  ZKHUH d LV WKH VFUHHQ ZLUH GLDPHWHU DQG l WKH PHVK OHQJWK

7KH QH[W VWHS ZDV WR FDOFXODWH WKH VSDFLQJ EHWZHHQ VFUHHQV DQG IRU WKLV WZR SURSULHWLHV VKRXOG EH FRQVLGHUHG >@

 7KH VSDFLQJ EHWZHHQ VFUHHQV PXVW EH HQRXJK IRU WKH VWDWLF SUHVVXUH IXOO\ UHFRYHU IURP D SHUWXUEDWLRQ EHIRUH UHDFKLQJ WKH QH[W VFUHHQ

 7KH PLQLPXP VSDFLQJ IRU WKH WXUEXOHQWUHGXFWLRQ SRLQW RI YLHZ VKRXOG EH WKH PDJQLWXGH RI WKH HGG\ FRQWDLQLQJ WKH PD[LPXP HQHUJ\

,W ZDV DOVR IRXQG WKDW   RI WKH VHWWOLQJ FKDPEHU GLDPHWHU SHUIRUPV VXFFHVVIXOO\ >@ $OVR WKH GLVWDQFH EHWZHHQ WKH ODVW VFUHHQ DQG WKH FRQWUDFWLRQ HQWU\ VKRXOG EH WKH VDPH EHLQJ WKDW LI LW LV D VKRUWHU GLVWDQFH VLJQLILFDQW GLVWRUWLRQ RI WKH IORZ VKRXOG EH H[SHFWHG7DEOH  VXPPDUL]HV WKH FKDUDFWHULVWLFV RI WKH VHWWOLQJ FKDPEHU ILJXUH  VKRZV WKH VFKHPDWLF RI WKH ZLQG WXQQHO 

WR YLVXDOL]H WKH ORFDWLRQ RI WKH VFUHHQV DQG ILJXUH  VKRZV WKH VHWWOLQJ FKDPEHU XVHG LQ WKH SUHVHQW ZRUN

7DEOH  'HVLJQ SDUDPHWHUV RI WKH VHWWOLQJ FKDPEHU 6HFWLRQ $UHD KHLJKW [ ZLGWK >mm@  [  $UHD >m2_{@ } (TXLYDOHQW 'LDPHWHU >mm@  +RQH\FRPEV &HOO $UHD >mm2_{@ } &HOO 'LDPHWHU >mm@  &HOO /HQJKW >mm@  6FUHHQV d>mm@  l>mm@  β  K ≈  6SDFLQJ EHWZHHQ VFUHHQV >mm@ 

)LJXUH  6FKHPDWLF RI WKH VFUHHQV SODFLQJ

)LJXUH  6HWWOLQJ &KDPEHU

 &RQWUDFWLRQ

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 WKHUH DUH WZR LPSRUWDQW FRHIILFLHQWV WR EH DVVXPHG LQ RUGHU WR DYRLG VHSDUDWLRQ &SL DQG &SH GHILQHG DV

Cpi= 1 −  V_i U₁,_∞ 2  Cpe= 1 −  U₂,_∞ V_e ₂ 

:KHUH L DQG H UHSUHVHQW WKH SRLQW RI PLQLPXP DQG PD[LPXP ZDOO YHORFLW\ DQG  DQG  FRUUH VSRQG WR WKH LQOHW DQG H[LW IORZ YHORFLWLHV UHVSHFWLYHO\ 7KH QH[W VWHS ZDV WR GHWHUPLQDWH WKH WZR GLPHQVLRQOHVV SDUDPHWHU )L DQG )H DQG FDOFXODWH WKH QR]]OH VKDSH SDUDPHWHU GHILQHG DV

X =  1 + 1 CR  F i F e 1 2−1 

ZKLFK UHSUHVHQWV WKH PDWFK SRLQW RI WKH WZR FXELF DUFV 7R FDOFXODWH WKH QR]]OH OHQJWK RQH RI WKH IROORZLQJ HTXDWLRQ ZDV XVHG F i= CR− 1 CR X −2 L H₁ −3  F e= CR− 1 CR3 (1 − X) −2 L H₁ −3  $QG WKH FRQWRXU RI WKH FRQWUDFWLRQ ZDV GHILQHG E\

H− H₂ H₁− H₂ = 1 − 1 X2 x3 L3, x L ≤ X  H− H₂ H₁− H₂ = 1 (1 − X)2  1 − x L 3 , x L > X 

:KHUH H1DQG H2 UHSUHVHQW WKH LQOHW KHLJKW DQG WKH H[LW KHLJKW UHVSHFWLYHO\ DQG x WKH OHQJWK

FRRUGLQDWH $FFRUGLQJ WR WKH 6WUDWIRUG VHSDUDWLRQ FULWHULD IRU WXUEXOHQW IORZ >@ WKH &SL YDOXH 

ZDV REWDLQHG XVLQJ Cpi= 0.7 _x 0 H1 + 0.9 xi H1 s H1 ₋1 3 10−6_Re x 1 15 _ Re_x=U1,∞ H₁ x0 H1 + 0.9 xi H1 ν = O 106 _

$Q LWHUDWLYH PHWKRG ZDV XVHG ZKHUH s LV WKH GLVWDQFH EHWZHHQ 0.8 DQG 0.4 RI &SL DQG x0 LV WKH

GLVWDQFH IURP WKH YLUWXDO RULJLQ RI D ERXQGDU\ OD\HU WR WKH QR]]OH EHJLQQLQJ DQG xi UHSUHVHQWV WKH D[LDO FRRUGLQDWH IRU WKH PLQLPXP ZDOOYHORFLW\ 7 0RUHO >@ VXJJHVWHG 0.3 DV D W\SLFDO YDOXH RI WKH UDWLR EHWZHHQ x0DQG H DQG WKH UHPDLQLQJ UDWLRV ZHUH WDNHQ IURP KLV JUDSKLFV 7KH H[LW

YHORFLW\ QRQXQLIRUPLW\ LV JLYHQ E\ ˜

u₂= (0.19 ± 0.01) Cpe 

,W LV SURSRUWLRQDO WR &SH ZKHQ LV OHVV WKDQ 0.1 DQG LW ZLOO HQVXUH WKDW WKH QRQXQLIRUPLW\ RI WKH YHORFLW\ GLVWULEXWLRQ DW WKH H[LW ZLOO QRW EH PRUH WKDQ 2 ,W LV DOVR VXJJHVWHG WKDW WKH ODVW VFUHHQ VKRXOG EH SODFHG DW D GLVWDQFH RI 0.2 RI WKH LQOHW HTXLYDOHQW GLDPHWHU Deqi VR WKH ´WRWDOµ

QR]]OH OHQJWK LV WKH VXP RI 0, 2 Deqi DQG L

7DEOH  VXPPDUL]HV WKH FKDUDFWHULVWLFV RI WKH FRQWUDFWLRQ VKRZQ LQ ILJXUH 

7DEOH  3DUDPHWHUV RI WKH FRQWUDFWLRQ GHVLJQ &RQWUDFWLRQ 5DWLR CR  Cpi  Cpe  H₁,QOHW KHLJKW >mm@  H₂2XWOHW KHLJKW >mm@  X  L/HQJKW >mm@ 

µ7RWDOµ QR]]OH OHQJKW >mm@ 

:LGWK >mm@ 

)LJXUH  :LQG WXQQHO FRQWUDFWLRQ CR = 2

 &DOLEUDWLRQ

7KH FDOLEUDWLRQ RI WKH FURVVIORZ ZDV PDGH E\ DGMXVWLQJ WZR JXLOORWLQHV G1G2 VKRZQ LQ ILJXUH

 WKDW DOORZHG DLU WR SDVV WKURXJK WKH ZLQG WXQQHO 7KH PHDVXUHPHQWV RI WKH YHORFLW\ YDOXHV ZHUH PDGH WKURXJK D SLWRW WXEH WKDW ZDV SODFHG DW 1 cm RI WKH QR]]OH H[LW 7KLV ZDV FRQQHFWHG WR D 8VKDSHG PDQRPHWHU DQG UHJLVWHUHG WKH GLIIHUHQFH EHWZHHQ WKH WRWDO SUHVVXUH DQG WKH VWDWLF SUHVVXUH ∝ h ZLWK DQ HUURU RI ±0.5 mm 7KH YHORFLW\ U ZDV FDOFXODWHG XVLQJ HTXDWLRQ  1 2 × ρair× U2= ρH2O× g × h ⇐⇒ U =  2 × ρH2O× g × (h) ρ_air 

)LJXUH  *XLOORWLQHV UHSUHVHQWDWLRQ

7KH SRVLWLRQ RI WKH JXLOORWLQHV IRU WKH GHVLUHG YHORFLWLHV ZDV QRW NQRZQ VR ILYH WHVWV ZHUH SHUIRUPHG LQ RUGHU WR YHULI\ WKH SRVLWLRQ LQ ZKLFK ZRXOG REWDLQ D JUHDWHU YHORFLW\ UDQJH 7DEOH  VKRZV WKH SRVLWLRQV WDNHQ E\ WKH JXLOORWLQHV DQG ILJXUH  LOOXVWUDWHV WKH UHVXOWV

7DEOH  &DOLEUDWLRQ WHVWV 7HVW $ 7HVW % 7HVW & 7HVW ' 7HVW ( G₁>mm@ G₂>mm@ G₁>mm@ G₂>mm@ G₁>mm@ G₂>mm@ G₁>mm@ G₂>mm@ G₁>mm@ G₂>mm@                                         

)LJXUH  &DOLEUDWLRQ FKDUW

$V LW LV SRVVLEOH WR REVHUYH WKURXJK ILJXUH  WHVW E LV WKH RQH WKDW KDV D JUHDWHU YHORFLW\ UDQJH ,Q WKLV ZD\ WKH YDULDWLRQ RI WKH FURVVIORZ ZLOO EH PDGH RQO\ ZLWK WKH G2 KDYLQJ G1

DOZD\V RSHQ ,Q SODQQLQJ WKH H[SHULPHQWDO VWXG\ LW ZDV GHILQHG WKDW WKUHH YHORFLWLHV ZRXOG EH VWXGLHG 7m/s 10m/s 15m/s 7R REWDLQ WKHVH YHORFLWLHV LW ZDV QHFHVVDU\ WR GUDZ D FKDUW WKDW UHODWHV WKH YHORFLW\ RI WKH ZLQG WXQQHO ZLWK WKH SRVLWLRQ RI G2ILJXUH  DQG DQ HTXDWLRQ ZDV

REWDLQHG ,Q RUGHU WR JXDUDQWHH WKH YHORFLWLHV IRU WKH H[SHULPHQWDO VWXG\ D WXEH ZDV SODFHG LQ WKH LQOHW RI WKH FURVVIORZ EHIRUH WKH GLIIXVHU DQG WKH VWDWLF SUHVVXUH ZDV PHDVXUHG ZKLW D PDQRPHWHU VR D UHODWLRQ FRXOG EH DFKLHYHG EHWZHHQ WKH YHORFLWLHV LQ WKH ZRUNLQJ VHFWLRQ DQG LQ WKLV UHIHUHQFH 7DEOH  VKRZV WKH ZDWHU FROXPQ PLOOLPHWHUV REWDLQHG IRU WKH YHORFLWLHV LQ WKHVH WZR SRVLWLRQV

)LJXUH  9HORFLW\ REWDLQHG E\ YDU\LQJ G2

7DEOH  9HORFLWLHV XVHG LQ WKLV VWXG\ 8 >m/s@ href >mm@ h >mm@

  

  

  

6LQFH WKH FRQWUDFWLRQ ZDV PDGH LQ WKH ZRUNVKRS LW ZDV QHFHVVDU\ WR GUDZ WKH YHORFLW\ SURILOH DW WKH QR]]OH H[LW )LYH SRLQWV ZHUH FKRVHQ YHUWLFDOO\ DQG D 5mm VSDFLQJ ZDV XVHG KRUL]RQWDOO\ DQG WKH YHORFLW\ SURILOHV ZHUH PHDVXUHG )LJXUH  VKRZV D VFKHPDWLF RI WKH SRLQWV DW EOXH ZKHUH WKH YHORFLWLHV ZHUH PHDVXUHG 7KH UHG OLQH LV D UHSUHVHQWDWLRQ RI WKH SRVLWLRQ RI WKH YHORFLW\ SURILOHV )LJXUHV  DQG  SUHVHQW WKH KRUL]RQWDO DQG YHUWLFDO YHORFLW\ SURILOHV UHVSHFWLYHO\ 7R JXDUDQWHH D VWDEOH FURVVIORZ LQIOXHQFH WKH DOXPLQXP SODWH ZDV SODFHG 70 mm DERYH WKH EDVH RI WKH H[LW QR]]OH

)LJXUH  6FKHPDWLF IRU YHORFLW\ SURILOHV PHDVXUHPHQWV YHUWLFDOO\ WR WKH OHIW DQG KRUL]RQWDOO\ WR WKH ULJKW

)LJXUH  +RUL]RQWDO YHORFLW\ PHDVXUHV

)LJXUH  9HUWLFDO YHORFLW\ PHDVXUHV

 ,QMHFWLRQ 6\VWHP

7KH LQMHFWLRQ V\VWHP LV FRQVWLWXWHG E\ DQ 1( 6LQJOH 6\ULQJH 3XPS ILJXUH  ZLWK D SXPSLQJ UDWH RI 1.459 õl/hr IRU D 1 ml V\ULQJH RU 127.2 ml/min IRU D 60 ml V\ULQJH )RU WKLV ZRUN ZDV XVHG D 50 ml V\ULQJH ZLWK D GLDPHWHU RI 28.0 mm 7KH SXPSLQJ UDWH ZDV HVWDEOLVKHG DW 0.5 ml/min DQG WKH V\ULQJH ZDV FRQQHFWHG WR D QHHGOH ZLWK DQ LQQHU GLDPHWHU RI 1.50 mm 7KHVH FKDUDFWHULVWLFV DOORZ WKDW WKHUH LV SUDFWLFDOO\ QR DFFHOHUDWLRQ JLYHQ WR WKH GURSOHW E\ WKH LQMHFWLRQ V\VWHP DOORZLQJ WKH GURSOHW WR GURS E\ WKH IRUFH RI JUDYLW\

7DEOH  VKRZV WKH ZRUNLQJ FRQGLWLRQV XVHG LQ WKLV H[SHULPHQWDO ZRUN EHLQJ D0WKH GURSOHW·V

GLDPHWHU DQG U0WKH GURSOHW YHORFLW\ EHIRUH LPSDFW 7KH RWKHU IRXU UHSUHVHQW WKH GLPHQVLRQOHVV

QXPEHUV 5H\QROGV :HEHU 2KQHVRUJH DQG /DSODFH

)LJXUH  1( 6LQJOH 6\ULQJH 3XPS

7DEOH  5DQJH RI YDOXHV IURP WKH H[SHULPHQWDO ZRUN D₀>mm@   U₀>m/s@   5H   :H   2K×103 _{ } /D  

 ,PDJH $FTXLVLWLRQ 6\VWHP

$ KLJKVSHHG FDPHUD )$67&$0 PLQL 8; ZDV XVHG WR FDSWXUH WKH PRWLRQ RI WKH GURSOHWV ,W KDV D  PHJDSL[HO LPDJH UHVROXWLRQ DW IUDPH UDWHV XS WR 2000 fps IUDPHV SHU VHFRQG DQG LW FDQ JR XS WR 160000 fps ZLWK D UHVROXWLRQ UHGXFWLRQ $OVR D 0DFUR /HQV 7RNLQD $7; 0 $) 352 ' ZLWK D PLQLPXP IRFXV GLVWDQFH RI 300 mm D IRFDO OHQJWK RI 100 mm D  PDFUR UDWLR DQG D ILOWHU VL]H RI 55 mm ,Q RUGHU WR EH DEOH WR REVHUYH VRPH RI WKH SKHQRPHQD VRPH FKDUDFWHULVWLFV ZHUH FKDQJHG WKH UHVROXWLRQ ZDV UHGXFHG WR LQFUHDVH WKH QXPEHU RI LPDJHV FDSWXUHG  KLJKHU ISV DQG WKH VKXWWHU ZDV DOVR LQFUHDVH JLYHQ WKDW VRPH RI WKH GURSOHWV UHDFKHG YHORFLWLHV WKDW EOXUUHG WKH LPDJHV %\ GHFUHDVLQJ WKH VKXWWHU WR 1/10240 V WKH H[SRVHU WLPH ZDV GHFUHDVHG DQG WKH EOXUUHG LPDJH SUREOHP ZDV VROYHG 7KHUHIRUH LQ WKLV VWXG\ LPDJHV ZHUH WDNHQ ZLWK D IUDPH UDWH RI 10000 fps DQG D VKXWWHU RI 1/10240 V +RZHYHU E\ GHFUHDVLQJ WKH VKXWWHU WKH LPDJH EHFRPHV GDUNHU EHFDXVH WKH H[SRVHU WLPH LV VPDOOHU 7KLV LV VKRZQ LQ ILJXUH  DQG ILJXUH 

)LJXUH  ,PDJH ZLWK [ UHVROXWLRQ DQG 1/5120 V VKXWWHU

)LJXUH  ,PDJH ZLWK [ UHVROXWLRQ DQG 1/10240 V VKXWWHU

7KH FDPHUD ZDV FRQQHFWHG WR D FRPSXWHU DQG WKH LPDJHV ZHUH PDQXDOO\ WDNHQ ZKLW WKH KHOS RI D WULJJHU

 :RUN )OXLGV 3URSHUWLHV

7KH H[SHULPHQWDO ZRUN DLPV WR VWXG\ WKH FKDUDFWHULVWLFV RI ELRIXHO GURSOHWV DQG IRU WKDW SXU SRVH WKH ILUVW VWHS ZDV WR VWXG\ WKH SK\VLFDO SURSULHWLHV RI WKHVH VXEVWDQFHV 7KH SDUDPHWHUV RI WKH H[SHULPHQWDO VWXG\ RQO\ DOORZ IRU WKH VWXG\ RI 100% JF  75% JF DQG 25% HV O 50% J F DQG 50% HV O DQG H₂O DV D FRQWURO VXEVWDQFH KRZHYHU IRU WKH VWXG\ RI WKH SK\VLFDO SURSULHWLHV LW ZDV RI LQWHUHVW DOVR H[DPLQH 75% HV O DQG 25% JF DQG 100% HV O

 'HQVLW\

7KH GHQVLW\ ρ RI D IOXLG LV GHILQHG DV WKH PDVV RI WKH IOXLG SHU XQLW YROXPH >@ 7R GHWHUPLQH WKH GHQVLW\ WKH S\FQRPHWHU PHWKRG ZDV XVHG 7KLV PHWKRG XVHV D S\FQRPHWHU ILJXUH  ZLWK D NQRZQ YROXPH RI 25 ml DQG WKH PDVV RI WKH VDPH ZDV PHDVXUHG ZLWK DQG ZLWKRXW WKH VXEVWDQFH 7KHVH WZR DUH VXEWUDFWHG DQG WKH VXEVWDQFH·V PDVV LV FDOFXODWHG 7KH SUHFLVLRQ VFDOH XVHG ZDV D 0HWWOHU 7ROHGR 3% 'HOWD5DQJH ZLWK DQ HUURU RI ±0.01 g DQG WKH GHQVLW\ ZDV FDOFXODWHG E\ WKH HTXDWLRQ 

ρ= m

V 

)LJXUH  3\FQRPHWHUV XVHG

)RU HDFK VXEVWDQFH WZR WHVWV ZHUH PDGH DQG WKH PHDQ YDOXH ZDV FDOFXODWHG 7KLV ZRUN ZDV SHUIRUPHG DW D WHPSHUDWXUH RI 20ž C DQG DW D 50% KXPLGLW\ 7DEOH  LOOXVWUDWHV WKH UHVXOWV

7DEOH  5HVXOWV RI WKH WHVWV SHUIRUPHG WR GHWHUPLQH WKH GHQVLW\ RI WKH VXEVWDQFHV 6XEVWDQFH 7HVW QXPEHU P >g@ ρ>g/ml@ ρ>kg/m3@ ¯ρ >kg/m3@   -) _ _ _ _    -)    +92 _ _ _ _    -)    +92 _ _ _ _    -)    +92 _ _ _ _    +92 _ _ _ _ 

 6XUIDFH 7HQVLRQ

7KH SHQGDQW GURSOHW PHWKRG ZDV XVHG WR GHWHUPLQH WKH VXUIDFH WHQVLRQ σ RI WKH VXEVWDQFHV DQG D 'DWD 3K\VLFV ² 2&$+ ILJXUH  UHFHQWO\ FDOLEUDWHG ZLWK D 0.6% DFFXUDF\ ZDV XVH 7KLV VWXG\ FRQVLVWV LQ FDSWXULQJ DQ LPDJH RI D GURSOHW WKDW KDQJV RQ D QHHGOH DQG DQDO\]LQJ LW ZLWK WKH 'DWD 3K\VLFV 6&$ VRIWZDUH 7KLV VRIWZDUH DQDO\VHV WKH GURSOHW VKDSH EDVH RQ WKH <RXQJ/DSODFH·V HTXDWLRQ WKDW GHVFULEHV WKH SUHVVXUH GLIIHUHQFH EHWZHHQ WKH DUHDV LQVLGH DQG RXWVLGH RI D FXUYHG OLTXLG VXUIDFH >@ 7KLV ZRUN ZDV SHUIRUPHG DW D WHPSHUDWXUH RI 20ž C DQG DW D 50% KXPLGLW\ DQG WKH UHVXOWV DUH SUHVHQWHG LQ WDEOH 

)LJXUH  'DWD 3K\VLFV ² 2&$+

7DEOH  6XUIDFH WHQVLRQ WHVWV UHVXOWV

6XEVWDQFH 7HVW  >mN/m@ 7HVW  >mN/m@ 7HVW  >mN/m@ ¯σ>mN/m@   -)       -)    +92       -)    +92       -)    +92       +92     

 9LVFRVLW\

7R PHDVXUH WKH YLVFRVLW\ D %URRNILHOG '97 59&3 5KHRPHWHU ILJXUH  ZLWK D FRQH DQG SODWH JHRPHWU\ ILJXUH  IRU VPDOO VDPSOHV ZDV XVHG 7KLV LQVWUXPHQW ZDV XVHG WR PHDVXUH WKH G\QDPLF YLVFRVLW\ μ DQG KDV DQ DFFXUDF\ RI ±1.0 % RI WKH UDQJH 5KHRFDOF7 VRIWZDUH ZDV XVHG WR FRQWURO WKH UKHRPHWHU IURP D FRPSXWHU 7KH LQVWUXPHQW RQO\ PHDVXUHG WKH G\QDPLF YLVFRVLW\ KRZHYHU WKH NLQHPDWLF YLVFRVLW\ ν ZDV REWDLQHG GLYLGLQJ WKH G\QDPLF YLVFRVLW\ E\ WKH GHQVLW\ RI WKH VXEVWDQFHV 7KLV ZRUN ZDV SHUIRUPHG DW D WHPSHUDWXUH RI 23ž C DQG WDEOH  VKRZ WKH UHVXOWV RI WKHVH WHVWV

)LJXUH  %URRNILHOG '97 59&3 5KHRPHWHU RQ WKH OHIW

)LJXUH  &RQH DQG SODWH JHRPHWU\

7DEOH  9LVFRVLW\ WHVWV UHVXOWV 6XEVWDQFH μ>P a.s@ ρ>kg/m3@ ν>mm2/s@   -)      -)    +92      -)    +92      -)    +92      +92    

 6XPPDU\ RI :RUN )OXLGV 3URSHUWLHV

7DEOH  SUHVHQWV LQ WKH IRUP RI D VXPPDU\ WKH SURSHUWLHV RI WKH VXEVWDQFHV WKDW DUH XVHG LQ WKH H[SHULPHQWDO VWXG\ 7KH FRQWURO VXEVWDQFH H2O LV LQFOXGHG LQ WKLV WDEOH EHFDXVH LW LV RQH

RI WKH VXEVWDQFHV XVHG LQ WKH H[SHULPHQWDO VWXG\ KRZHYHU LWV SURSHUWLHV DUH UHSRUWHG LQ WKH OLWHUDWXUH

7DEOH  :RUN )OXLGV 3URSHUWLHV

6XEVWDQFH ρ>kg/m3@ σ>N/m@ μ>P a.s@   -)      -)    +92      -)    +92    H₂O   

 ,PDJH 'DWD 3URFHVVLQJ

7KH TXDQWLWDWLYH FKDUDFWHUL]DWLRQ RI VRPH FKDUDFWHULVWLFV RI WKH GURSOHWV DV WKH GLDPHWHU DQG WKH LPSDFW YHORFLW\ ZHUH PDGH WKURXJK LPDJH GDWD SURFHVVLQJ $V LW ZDV PHQWLRQHG EHIRUH WKH LPDJHV ZHUH FDSWXUHG E\ D KLJKVSHHG FDPHUD DQG LW ZDV QHFHVVDU\ WR HQVXUH D JRRG LPDJH TXDOLW\ WR EH DEOH WR REWDLQ DFFXUDWH PHDVXUHPHQWV )RU SURFHVVLQJ WKH FDSWXUHG LPDJHV DQ DOJRULWKP ZDV GHYHORSHG XVLQJ 0DWODE 6RIWZDUH

)LJXUH  LV DQ H[DPSOH RI D W\SLFDO LPDJH RI 75% JF  25% HV O LPSDFW DQG LWV EDFNJURXQG 8VLQJ WKLV WZR LPDJHV ZH DUH DOORZHG WR FDOFXODWH WKH GURSOHWV FKDUDFWHULVWLFV

)LJXUH  ,PDJH RI DQ 75% JF  25% HV O LPSDFW D DQG LWV EDFNJURXQG E

,Q 0DWODE LPDJHV DUH HVVHQWLDOO\ D PDWUL[ RI SL[HOV [colums, rows] KDYLQJ HDFK SL[HO D YDOXH ZKLFK LQ WKLV FDVH YDULHV EHWZHHQ 0 H 3533 +DYLQJ WKHVH WZR LPDJHV WKH ILUVW VWHS ZDV WR VXEWUDFW WKH LPDJH LQ VWXG\ ZLWK WKH EDFNJURXQG 7KLV ZLOO OHDYH LQ WKH ILQDO LPDJH RQO\ WKH SL[HO YDOXHV WKDW DUH GLIIHUHQW LQ WKH WZR LPDJHV WKDW LV WKH GURSOHW·V SL[HOV )LJXUH 

)LJXUH  5HVXOW IURP LPDJH VXEWUDFWLRQ ZLWK FRQWUDVW DOWHUDWLRQ IRU YLVXDOL]DWLRQ SXUSRVHV

$IWHU VXEWUDFWLQJ WKH WZR LPDJHV D IXQFWLRQ ZDV XVHG WR FRQYHUW WKH SL[HO YDOXHV WR ELQDU\ YDOXHV 

EHLQJ HYHU\ YDOXH 1 VKRZQ LQ ZKLWH DQG 0 VKRZQ LQ EODFN )LJXUH  VKRZV WKH ELQDU\ LPDJH FUHDWHG ZKHUH WKH ZKLWH SL[HOV UHSUHVHQW WKH GURSOHW DQG WKH EODFN RQHV WKH EDFNJURXQG

)LJXUH  5HVXOWLQJ ELQDU\ LPDJH

+RZ LW LV SRVVLEOH WR REVHUYH LQ ILJXUH  WKH LPDJH SRVVHVVHV EODFN SL[HOV LQVLGH WKH GURSOHW·V VHFWLRQ VR D IXQFWLRQ ZDV XVHG WKDW FKDQJHV IURP 0 WR 1 HYHU\ EODFN SL[HO RU D VHW RI EODFN SL[HOV WKDW ZDV FRPSOHWHO\ VXUURXQGHG E\ ZKLWH SL[HOV ILJXUH 

)LJXUH  5HVXOWLQJ LPDJH RI FKDQJLQJ YDOXHV RI 0 VXUURXQGHG E\ YDOXHV RI 1

'HVSLWH DOO WKLV WKH LPDJH ZDV QRW UHDG\ WR EH DQDO\]HG LW ZDV VWLOO SRVVLEOH WR REVHUYH VRPH ZKLWH SL[HOV VFDWWHU DURXQG 7KHQ DQRWKHU IXQFWLRQ ZDV XVHG WR UHPRYH WKRVH ZKLWH SL[HOV ZLWKRXW UHPRYLQJ WKH RQHV IURP WKH GURSOHW·V VHFWLRQ 7KLV IXQFWLRQ XQOLNH WKH RQH SUHYLRXVO\ PHQWLRQHG FKDQJHG WKH SL[HO YDOXH IURP 1 WR 0 RI DOO SL[HOV LVRODWHG RU JURXSHG LQWR VHWV VPDOOHU WKDQ 50 SL[HOVILJXUH 

)LJXUH  5HVXOWLQJ LPDJH RI FKDQJLQJ YDOXHV RI 1 WR 0

7R GHWHUPLQH WKH GURSOHW GLDPHWHU D IXQFWLRQ ZDV XVHG WR FDOFXODWH WKH ELJJHVW QXPEHU RI ZKLWH SL[HOV 1 IRU WKH URZV DQG DOVR IRU WKH FROXPQV 7KH ELJJHVW YDOXH REWDLQHG UHSUHVHQWV WKH GURSOHW GLDPHWHU LQ SL[HOV

+DYLQJ WKH GURSOHWV GLDPHWHU LQ SL[HOV LW ZDV QHHGHG WR NQRZQ WKH YDOXH RI RQH SL[HO LQ PLO OLPHWHUV 7KXV LQ WKH EHJLQQLQJ RI HYHU\ WHVW DQ LPDJH RI DQ REMHFW ZDV WDNHQ WKDW ZRXOG EH XVHG DV D UHIHUHQFH IRU WKH FRQYHUVLRQ IURP SL[HO WR PLOOLPHWHU ,Q WKLV VWXG\ D QHHGOH ILJXUH  ZDV XVHG DV WKLV UHIHUHQFH DQG WKH VDPH LPDJH SURFHVVLQJ ZDV DSSOLHG WKXV REWDLQLQJ WKH GLDPHWHU LQ SL[HOV RI WKH QHHGOH 0HDVXULQJ WKH QHHGOH·V GLDPHWHU ZLWK D GLJLWDO FDOLSHU WKH GLDPHWHU ZDV REWDLQHG LQ PLOOLPHWHUV 2EWDLQLQJ WKH YDOXH RI RQH SL[HO LQ PLOOLPHWHUV DOORZHG WR FDOFXODWH WKH GURSOHWV GLDPHWHU LQ WKLV VFDOH

)LJXUH  5HDO LPDJH RI WKH UHIHUHQFH WR WKH OHIW D SURFHVVHG LPDJH RI WKH UHIHUHQFH WR WKH ULJKW

7R FDOFXODWHG WKH LPSDFW YHORFLW\ D IXQFWLRQ ZDV DGGHG WR WKH DOJRULWKP WKDW IRXQG WKH FHQWURLG RI WKH REMHFW 7KLV IXQFWLRQ DOORZHG WR NQRZ WKH SRVLWLRQ RI WKH REMHFW LQ WKH LPDJH PDWUL[ )RU WKLV FDOFXODWLRQ WZR LPDJHV ZHUH QHFHVVDU\ JLYHQ WKDW WZR SRVLWLRQV ZHUH QHHGHG DQG WKH GLIIHUHQFH EHWZHHQ WKHVH SRVLWLRQV DOORZHG WR FDOFXODWH WKH WUDYHOHG GLVWDQFH RI WKH GURSOHWV

)LJXUH  3URFHVVHG LPDJH RI D GURSOHW IDOO

)LJXUH  3URFHVVHG LPDJH RI D GURSOHW EHIRUH LPSDFW

7KURXJK WKH FHQWURLG SRVLWLRQ RI ILJXUH  DQG ILJXUH  WKH GLVWDQFH EHWZHHQ WKH GURSOHWV SRVLWLRQ LV FDOFXODWHG .QRZLQJ WKH GLVWDQFH D WLPH SHULRG ZDV QHHGHG WR FDOFXODWH WKH LPSDFW YHORFLW\ 7KH WLPH SHULRG ZDV FDOFXODWHG WKURXJK WKH FDPHUD·V IUDPH UDWH *LYHQ WKDW WKH IUDPH UDWH ZDV 10000fps WKHQ 100 õs SDVV EHWZHHQ HDFK IUDPH ,Q WKH FDVH RI WKLV VWXG\ 5 IUDPHV DUH XVHG EHWZHHQ WKH WZR LPDJHV VR WKH WLPH SHULRG LV 500 õs +DYLQJ WKH WLPH SHULRG DQG WKH WUDYHOHG GLVWDQFH LW ZDV SRVVLEOH WR FDOFXODWH WKH LPSDFW YHORFLW\ RI WKH GURSOHW

)RU WKLV ZRUN WKH PD[LPXP HUURU IRU WKH GURSOHWV GLDPHWHU FDOFXODWLRQ ZDV FRQVLGHUHG WR EH KDOI RI WKH SL[HO YDOXH >@ 6R WKH PD[LPXP HUURU REWDLQHG IRU WKH GURSOHWV GLDPHWHU LV 20.3 õP )RU WKH LPSDFW YHORFLW\ WKH HUURU YDOXH ZDV REWDLQHG E\ GLYLGLQJ KDOI RI WKH KLJKHVW SL[HO YDOXH IRU WKH WLPH SHULRG VR WKH PD[LPXP HUURU REWDLQHG IRU WKH LPSDFW YHORFLW\ FDOFXODWLRQ LV 0.0406 m/s

:LWK D FURVVIORZ WKH VDPH LPDJH SURFHVVLQJ ZDV XVHG DOWKRXJK LQ WKLV FDVH WZR FRRUGLQDWHV RI WKH FHQWURLG ZHUH REWDLQHG ,W ZDV LPSRUWDQW WR ILQG RXW KRZ PDQ\ SL[HOV WKH GURSOHW PRYHG KRUL]RQWDOO\ DQG YHUWLFDOO\ 7KLV DOORZHG WKH VHSDUDWLRQ RI WKH WZR FRPSRQHQWV RI YHORFLW\ WKDW ZHUH QHHGHG IRU WKH VWXG\ +DYLQJ WKH KRUL]RQWDO Ux DQG YHUWLFDO YHORFLW\ Uy WKH GURSOHWV DEVROXWH YHORFLW\ RI LPSDFW Ua ZDV REWDLQHG FDOFXODWLQJ WKH UHVXOWLQJ YHFWRU PRGXOH DQG ILJXUH  UHSUHVHQW WKH FRRUGLQDWH V\VWHP DQG WKH YHORFLW\ FRPSRQHQWV PHQWLRQHG 7KH LPSDFW DQJOH θ ZDV DOVR FDOFXODWHG DQG LW LV DOVR UHSUHVHQWHG LQ WKH ILJXUH

&KDSWHU 

5HVXOWV DQG 'LVFXWLRQ

7KLV VHFWLRQ GHWDLOV WKH UHVXOWV REWDLQHG LQ WKH H[SHULPHQWDO VWXG\ )LUVW LW LV SUHVHQWHG WKH SKHQRPHQD REVHUYHG LQ WKLV ZRUN 7KHQ VRPH UHVXOWV RI WKH GURSOHW FKDUDFWHULVWLFV DUH SUH VHQWHG 7KH LPSDFW FRQGLWLRQV GLIIHU VR WKH UHVXOWV DQG GLVFXVVLRQ DUH SUHVHQWHG ILUVW IRU WKH QRUPDO LPSDFW DQG WKHQ IRU WKH LPSDFW ZLWK D FURVVIORZ $ FRPSDULVRQ ZLWK WKH WUDQVLWLRQ FUL WHULD VKRZQ LQ WKH OLWHUDWXUH UHYLHZ LV DOVR PDGH DQG LQ WKH HQG D VXPPDU\ FRPSDULQJ DOO WKH YDULDEOHV LV PDGH

 3KHQRPHQD 9LVXDOL]DWLRQ

7KHUH DUH D YDULHW\ RI SKHQRPHQD WKDW FDQ EH HQFRXQWHU E\ VWXG\LQJ GURSOHW LPSDFW )LUVW ZHUH LGHQWLILHG WKH YDULRXV LPSLQJHPHQW UHJLPHV RI WKH GURSOHW IRU WKH VWXG\ FRQGLWLRQV

)LJXUH  $ GURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH IRU D 75% JF  25% HV O PL[WXUH D0= 3.06mmRe = 4967W e = 825La = 29912

)LJXUH  VKRZV D VHTXHQFH RI LPDJHV WKDW UHSUHVHQW WKH LPSDFW RQ D GU\ VXUIDFH )UDPH 12 VKRZV WKH PRPHQW RI WKH GURSOHW·V LPSDFW DQG QR VHFRQGDU\ DWRPL]DWLRQ RFFXUV 7KURXJK WKH REVHUYDWLRQ RI WKH IROORZLQJ IUDPHV WKH ERXQGDU\ FRQGLWLRQ VHHQ LV VSUHDG DQG RFFXUV ZKHQ WKH GURSOHW LPSDFWV RQ D VXUIDFH ZLWK PRGHUDWHG YHORFLW\ DQG VSUHDGV RXW WR IRUP D ZDOO ILOP $IWHU UHDFKLQJ WKH PD[LPXP VSUHDG GLDPHWHU WKH ZDOO ILOP UHFRLOV WRZDUGV WKH FHQWHU RI WKH GURSOHW UHFHGLQJ VWDJH

)LJXUH  $ GURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH IRU D 50% JF  50% HV O PL[WXUH D0= 3.07mmRe = 3863W e = 798La = 18708

7KH ERXQGDU\ FRQGLWLRQ FDOOHG SURPSW VSODVK LV GLVSOD\HG LQ ILJXUH  7KLV SKHQRPHQRQ RFFXUV IRU KLJK 5H\QROGV QXPEHUV DQG LV FKDUDFWHUL]HG E\ WKH IRUPDWLRQ RI VPDOOHU GURSOHWV ZKHQ WKH GURSOHW LPSLQJHV ZLWK WKH VXUIDFH DW WKH EHJLQQLQJ RI WKH VSUHDGLQJ SKDVH )UDPH 8 ,Q WKH QH[W IUDPHV DUH VKRZQ WKH VSUHDGLQJ RI WKH GURSOHW DQG LQ IUDPHV 1017 DQG 24 WKH VHFRQGDU\ GURSOHWV IRUPHG E\ WKH LPSLQJHPHQW DUH REVHUYHG

,Q ILJXUH  LV SUHVHQWHG WKH ILQJHULQJ SKHQRPHQRQ )UDPH  VKRZV WKDW VSODVK GRHV QRW RFFXU ZKHQ WKH GURSOHW LPSDFWV RQ WKH VXUIDFH LQVWHDG WKH VSUHDGLQJ SKDVH EHJLQV 7KH ILQJHULQJ SKHQRPHQRQ RFFXUV ZKHQ WKH ODPHOOD IRUPHG KDV VXUIDFH SHUWXUEDWLRQV WKDW H[WHQGHG UDGLDOO\ FUHDWLQJ ZKDW LV FDOOHG ¶ILQJHUV· >@ ,Q IUDPHV  WR  LW LV SRVVLEOH WR REVHUYH WKH RFFXUUHQFH RI WKLV SKHQRPHQRQ ,Q WKH VSUHDGLQJ SKDVH DQ RXWHU ULP ZDV IRUPHG DQG WKHVH ILQJHUV ZHUH IRUPHG LQ WKLV ULP ,Q VRPH FDVHV ZKHQ WKH ODPHOOD UHDFKHV WKH PD[LPXP GLDPHWHU WKHVH ·ILQJHUV· VHSDUDWH IURP WKH ODPHOOD FUHDWLQJ ZKDW LV FDOOHG VDWHOOLWH GURSOHWV >@ $IWHU WKH ODPHOOD UHDFKHG WKH PD[LPXP GLDPHWHU WKH UHFHGLQJ VWDJH EHJDQ DQG WKH GURSOHW UHFRLOHG IUDPH 

)LJXUH  $Q H2OGURSOHW LPSLQJLQJ RQWR DQ DOXPLQXP SODWH

D0= 4.06mmRe = 15588W e = 828La = 293454

$Q H2O GURSOHW LPSDFW ZLWK D FURVVIORZ LV GLVSOD\ LQ ILJXUH  ,Q WKLV VHTXHQFH D YDULHW\

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 7KURXJK IUDPH    DQG  ZDV QRWLFHDEOH WKDW WKH FURVVIORZ FUHDWHG DQ XSZDUGV PRYHPHQW WKDW HOHYDWHG WKH VHFRQGDU\ GURSOHWV WKLV LV VKRZQ FRPSDULQJ WKH OHIW VLGH DQG WKH ULJKW VLGH RI WKH ILJXUH

)LJXUH  VKRZV D GURSOHW EUHDNXS SKHQRPHQRQ )UDPHV  DQG  VKRZV WKDW WKH GURSOHW EHJDQ WR VXIIHU GHIRUPDWLRQ E\ LQWHUDFWLQJ ZLWK WKH FURVVIORZ $IWHU WKLV GHIRUPDWLRQ WKH GURSOHW ZDV IODWWHQHG IUDPH  DQG EHJDQ WR IRUP D EDJ IUDPHV  WR  ,Q WKLV EDJ ZDV DOVR VHHQ WKH IRUPDWLRQ RI D SOXPH VR WKLV SKHQRPHQRQ LV D PXOWLPRGH EDJSOXPH EUHDNXS >@ 7KLV SKHQRPHQRQ LV FRQVWLWXWHG E\ WKUHH PDLQ FRPSRQHQWV WKH GURSOHWV· EDJ ULQJ DQG SOXPH 7KH ULQJ LV WKH WKLFNHU SDUW RI WKH SHULPHWHU RI WKH EDJ DQG WKH SOXPH LV WKH VPDOO GURSOHW LQVLGH WKH EDJ ,Q IUDPH  WKH EDJ EUHDNXS VWDJH RFFXUV OHDYLQJ WKH ULQJ DQG WKH SOXPH VWLOO LQWDFW IUDPH  2QO\ LQ IUDPH  WKH EUHDNXS SKHQRPHQD ZDV FRPSOHWHG ZKHQ WKH ULQJ DQG WKH SOXPH DOVR EUHDN XS 7KLV SKHQRPHQRQ ZDV QRW VWXGLHG LQ WKH SUHVHQW ZRUN

)LJXUH  $Q H2OGURSOHW ZLWK 4.06 mm RULJLQDO GLDPHWHU LPSLQJLQJ RQWR DQ DOXPLQXP SODWH LQ D

FURVVIORZ RI 7 m/s Rea= 18618W ea= 1181La = 293454

)LJXUH  $Q 100 % JF GURSOHW ZLWK 3 .02 mm RULJLQDO GLDPHWHU VXIHULQJ DHURGLQDPLF EUHDNXS LQ D 10 m/s FURVVIORZ  

 6SODVK1RQ 6SODVK 7KUHVKROG $QDOLVH

 1RUPDO ,PSDFW

7KH GLIIHUHQFH EHWZHHQ GHSRVLWLRQ DQG VSODVK LWV FRQVLGHUHG KHUH WR EH WKH PLQLPXP LQWHUYDO REWDLQDEOH ZLWK WKH H[SHULPHQWDO IDFLOLW\ 7KH LPSDFW YHORFLW\ GURSOHW VL]H DQG GLPHQVLRQOHVV QXPEHUV ZLOO EH SUHVHQWHG LQ WKLV VHFWLRQ 7DEOH  SUHVHQWV WKH UHVXOWV REWDLQHG IRU D GURSOHW LPSDFW ZLWKRXW WKH LQIOXHQFH RI D FURVVIORZ QRUPDO LPSDFW

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

RI DOO YDULDEOHV VWXG\ ,W VHHPV WKDW DOO WKHUPRSK\VLFDO SURSHUWLHV LQIOXHQFH WKH LPSDFW RXWFRPH 7R EH DEOH WR FRPSDUH WKHVH SURSHUWLHV EHWZHHQ WKH PL[WXUHV DQG H2O LW ZRXOG EH RI LQWHUHVW

WR VWXG\ WKH LPSDFW SKHQRPHQD ZLWK WKH VDPH GURSOHW GLDPHWHU

7DEOH  5HVXOWV REWDLQHG IRU QRUPDO LPSDFW

 -) -)  +92 -)  +92 H₂O

'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK

U₀>m/s@         5H         :H         2K×103 _{   } /D     D0 >mm@     ρ>kg/m3@     σ>N/m@     μ>P a.s@    

$V LW ZDV PHQWLRQHG LQ FKDSWHU  VRPH DXWKRUV KDYH SURSRVHG VRPH FULWHULD WR SUHGLFW WKH RFFXU UHQFH RI VHFRQGDU\ DWRPL]DWLRQ LQ GU\ VXUIDFHV 7KHVH FULWHULD SURSRVH DQ HPSLULFDO FRUUHODWLRQ EHWZHHQ VRPH GLPHQVLRQOHVV QXPEHUV WKDW GHVFULEH WKH VSODVKQRQVSODVK ERXQGDU\

7KH ERXQGDU\ OLQH SURSRVHG E\ %DL DQG *RVPDQ >@ LV SUHVHQWHG LQ HTXDWLRQ  7KH FRHIILFLHQW $ VKRZQ LQ WDEOH  GHSHQGV RQ WKH VXUIDFH URXJKQHVV ,Q WKH SUHVHQW ZRUN WKH VXUIDFH URXJKQHVV ZDV QRW PHDVXUHG VR LW LV RQO\ NQRZQ WKDW WKH LPSDFW VXUIDFH LV DQ DOXPLQXP SODWH WKDW ZDV SROLVKHG IRU WKLV H[SHULPHQWDO VWXG\ 7KLV SODWH ZDV FRQVLGHUHG WR EH ¶VPRRWK· EXW WKHUH ZDV QRW D VSHFLILF YDOXH NQRZQ IRU WKH VXUIDFH URXJKQHVV $FFRUGLQJ WR 5DQJH >@ WKH VXUIDFH URXJKQHVV RI SROLVK DOXPLQXP LV 0.1470 õm DQG FRQVLGHULQJ WDEOH  A = +RZHYHU 6LOYD >@ DQG 5RGULJXHV >@ VXJJHVW WKDW WKH FRHIILFLHQW A IRU D ¶VPRRWK· DOXPLQXP SODWH LV  6R ERWK YDOXHV RI A ZHUH DSSOLHG WR WKH FULWHULRQ DQG FRPSDUHG ZLWK WKH H[SHULPHQWDO UHVXOWV (TXDWLRQV  DQG  UHSUHVHQW WKH GLIIHUHQW HPSLULFDO FRUUHODWLRQV XVHG

W e_c= 4534 × La−0.183  

)LJXUH  'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR %DL DQG *RVPDQ·V >@ FULWHULRQ ZLWK WZR GLIIHUHQW A FRHIILFLHQW YDOXHV

W e_c= 2630 × La−0.183 

7KH UHVXOWV IRU WKH VSODVKQRQVSODVK ERXQGDU\ DUH SUHVHQWHG LQ ILJXUH  7KH GDVKHG OLQHV UHSUHVHQW HTXDWLRQV  DQG  ZKLW WKH WZR GLIIHUHQW A FRHIILFLHQWV 7KH EOXH GDWD SRLQWV UHSUHVHQW WKH FDVHV ZKHUH VSODVK RFFXUUHG DQG WKH UHG RQHV ZKHUH VSODVK ZDV QRW REVHUYHG 7KLV ILJXUH VXJJHVWV D GLIIHUHQFH LQ WKH EHKDYLRUV RI WKH 100% JF DQG H2O WR WKDW RI WKH PL[WXUHV

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

)LJXUH  'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR 0XQGR HW DO >@ FULWHULRQ

)LJXUH  'URSOHWV EHKDYLRU IRU QRUPDO LPSDFW FRPSDUHG WR 5DQG\ HW DO >@ FULWHULRQ

5DQG\ HW DO >@ FULWHULRQ ILJXUH  VHHPV WR JLYH WKH EHWWHU FRUUHODWLRQ LI DOO VXEVWDQFHV DUH FRQVLGHUHG 'HVSLWH WKH IDFW WKDW WKH UHVXOWV IURP 100% JF DQG H2ODUH IRXQG LQ WKH GHSRVLWLRQ

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nm ZKLFK FRXOG H[SODLQ WKH SUR[LPLW\ RI 

WKH H[SHULPHQWDO GDWD ZLWK WKLV FRUUHODWLRQ +RZHYHU WR EH DEOH WR FRQFOXGH WKLV LW ZRXOG EH QHFHVVDU\ WR PHDVXUH WKH VXUIDFH URXJKQHVV RI WKH DOXPLQXP SODWH RI WKH SUHVHQW ZRUN 7KLV LV DOVR VXSSRUWHG E\ ZKDW ZDV SURSRVHG E\ %DL DQG *RVPDQ >@ EHFDXVH WZR YDOXHV RI WKH VXUIDFH URXJKQHVV ZHUH XVHG DQG E\ REVHUYLQJ ILJXUH  LV SRVVLEOH WR VHH WKDW %DL DQG *RVPDQ·V FRUUHODWLRQ FRXOG SRWHQWLDOO\ SUHGLFW WKH EHKDYLRU IRU WKH PL[WXUHV

 ,PSDFW ZLWK &URVVIORZ

,Q WKLV VHFWLRQ WKH VDPH FKDUDFWHULVWLFV RI WKH GURSOHWV ZLOO EH SUHVHQWHG +RZHYHU WKH GURSOHWV LPSDFW ZDV VWXGLHG ZLWK WKH LQIOXHQFH RI D FURVVIORZ 6RPH DXWKRUV EHOLHYH WKDW WKH GURSOHW LPSDFW EHKDYLRU ZLOO EH DIIHFWHG E\ WKH LPSDFW DQJOH ,Q WKLV FDVH WKH LPSDFW DQJOH θ ZDV GHILQHG DV WKH DQJOH IRUPHG EHWZHHQ WKH LPSDFW VXUIDFH DQG WKH UHVXOWLQJ YHORFLW\ YHFWRU DE VROXWH YHORFLW\ RI WKH GURSOHWV YHORFLW\ FRPSRQHQWV ILJXUH  7KH IROORZLQJ UHVXOWV VKRZ WKDW WKH LPSDFW DQJOH DQG WKH LPSDFW YHORFLW\ ZHUH DIIHFWHG E\ WKH FURVVIORZ 7KHUHIRUH WKH IROORZLQJ GDWD ZLOO SUHVHQW WZR W\SHV RI YHORFLW\ QDPHO\ WKH DEVROXWH YHFWRU RI YHORFLW\ RU DE VROXWH YHORFLW\ Ua DQG WKH YHUWLFDO LPSDFW YHORFLW\ Uy 7KH DEVROXWH YHORFLW\ ZDV FDOFXODWHG IURP WKH WZR YHORFLW\ FRPSRQHQWV REWDLQHG LQ WKH LPDJH DQDO\VLV 7KHVH UHVXOWV ZLOO EH GLYLGHG LQWR VHFWLRQV GHSHQGLQJ RQ WKH FURVVIORZ YHORFLW\

  PV

7DEOH  5HVXOWV REWDLQHG IRU WKH GURSOHWV LPSDFW ZLWK D 7 m/s FURVVIORZ

 -) -)  +92 -)  +92 H₂O

'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK 'HSRVLWLRQ 6SODVK

U_y>m/s@         U_a>m/s@         Re_y         Re_a         W e_y         W e_a         θ>ž@         2K×103 _{   } /D     D₀>mm@    

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

5HVXOWV VKRZ WKDW WKH LPSDFW DQJOH LQFUHDVHV ZLWK WKH LQFUHDVH RI WKH GURSOHWV LPSDFW YHORFLW\ KRZHYHU WKH YHUWLFDO YHORFLW\ DOVR LQFUHDVHV ZKLFK PLJKW VXJJHVW WKDW ZKHQ WKH GURSOHW LP SDFW YHORFLW\ ZDV KLJKHU WKH HIIHFW RI WKH FURVVIORZ LQ WKH GURSOHW ZDV GLPLQLVKHG 7KH VSODVK SKHQRPHQRQ VHHPV WR UHTXLUH KLJKHU LPSDFW YHORFLWLHV IRU WKH H2ODQG WKH 75% JF 25% HV O

PL[WXUH IRU VSODVK WR RFFXU $V EHIRUH PRUH WKHQ RQH WKHUPRSK\VLFDO SURSHUW\ VHHPV WR GHILQH WKH FDXVH IRU VSODVK RFFXUV 7KH VDPH FULWHULD ZHUH DSSOLHG LQ WKLV FDVH DQG ILJXUHV  DQG