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~r � ~V n+1 = 0 (12)

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~r � [ 1�n~rpn+1] =

~r � ~~V� t

(13)

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%CU= pwrU Qy |tHL C@Uv R= |a@=D Q=OQ@

~ni;j = ~rfi;j (14)

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$z = 12h(~r~V ) + (~r~V )T

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f(x; t) =

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0 in gas

(6)

p=kDv= |xrO=at QO 'OwW|t QWDvt u=} QH \UwD f |Sv=Qo q Q}eDt xm u}= x@ xHwD =@%Ovm|t jOY

dfdt

= @f@t

+ ~V � ~rf = S (7)

|xrO=at xm =Hv; R= "CU= R=i wO sQH pO=@D xtWJ |xrtH |xOvyOu=Wv S QDt=Q=Bu; (�) |m}t=v}O CHRr w (�) |r=oJ 'xOW xDWwv |R=iwO \wrNt |=Q@ u=} QH

[19]%OwW|t x@U=Lt 8 |x]@=Q j@=]t

� = f�l + (1� f)�v

� = f�l + (1� f)�v (8)

"CU= `}=t R=i Qou=Wv l T} wvQ} R w Q=N@ R=i Qou=Wv v T} wvQ} R x]@=Q u}= QO

|OOa pOt "3wQW}B Qr} w= VwQ =@ w xOW =Hx@=H xm@W |wQ CmQL xR=Ov= |xrO=at |R=UxDUUo

%OwW|t u=}@ 9 |x]@=Q j@] u=tR QO~V n+1 � ~V n

�t=� ~r � (~V ~V )n � 1

�n~rpn+1 + 1

�n~r �$� n

+ ~g n + 1�n

~Fnb (9)

CQwYx@ 9 |x]@=Q QO xm |}xrtH =yvD "CU= pw= x@DQt R= jwi |R=UxDUUo CkOR= K} QY CQwYx@ C=Q=@a |x}k@ w CU= Q=Wi CQ=@a OwW|t x@U=Lt |vt[CQ=@a 9 |xrO=at pL |=Q@ |}xrLQtwO |x} RHD "OvwW|t ?=UL xDWPo u=tR

%R= CU=|Wv=Qo '|HRr '|}=Hx@=H CqtH T=U=Q@ (~~V ) x]U=w CaQU l} %pw= |xrLQt%OwW|t x@U=Lt �p@k u=tR R= swrat� CaQU u=O}t R= xO=iDU= =@ w |tHL |wQ}v w~~V � ~V n

� t= �~r � (~V ~V )n + 1

�n~r � $� n + ~g n + 1

�n~Fnb (10)

81

"""uQ=kDt

|=yxUO

vy|wQu

w}U=D}w=

m|xO}O

B|OOa

pL

|D}w=m |=UB ?} Q[ w Q]k 'pw] |OOa |x@U=Lt |@Uv |=]N OYQO "2 pmW?ULQ@ �21�19\@=wQ� COQ=J} Q|r}rLD\@=wQ =@ xU}=kt QOlU}O xDi=} xaUwD

"CPDR QDt=Q=B

lU}O l} CWB xDi=} xaUwD |D}w=m |=UB ?} Q[ w Q]k 'pw] Q}}eD "3 pmW"CPDR QDt=Q=B ?ULQ@ 38mm Q]k =@

|mU}O QwD=D} w=m CWB xDi=} xaUwD uw}U=D}w=m "2"4"OQ}o|t Q=Qk|UQQ@ OQwt|mU}O QwD=D} w=mCWB xDi=} xaUwD uw}U=D} w=mVN@u}= QO'1000kg/m3 %(�) |r=oJ %CU= xOW xDiQo Q_v QO KQW u}= x@ ?; X=wN"0 072N/m %( )|L]UVWm w '1 0�10�6 m2/s %(�)|m}D=tv}UCHRr'0 5542kg/m3 %(�) |r=oJ %CU= xOW ZQi KQW u}= x@ R}v Q=N@ X=wN'|OOa sD} Qwor= OwW|t x_Lqt "24 18�10�6 m2/s %(�)|m}D=tv}UCHRr|v=tR |xaUwD "OQ=O =Q 1800 OwOL |r=oJ C@Uv =@ u=} QH u=O}t pL C}r@=kOOa s} SQ QO 54mm Q]k =@ lU}O l} CWB xDi=} xaUwD uw}U=D} w=m |x}L=v"CU= xOW xO=O u=Wv 4 pmW QO 1 7�106 ROrwv} Q OOa w 0 20 uw}U=D} w=m(�) uw}U=D} w=m OOa 'Oa@ uwO@ OOa u} QDsyt 'uw}U=D} w=m =@ x=Qty |=yu=} QH QO

%R= CU= CQ=@a xm CU=� = p1 � pv

0 5�V 21(17)

(t = 13ms) OQ}o|t pmW x@=OQo w OyO|t |wQ u=} QHV}=OH 'lU}OCWB QOpN=O QO x}rw= uw}U=D} w=m =Pr w OwW|t xv}tm Q=Wi '|QwLt uQ=kDt |x@=OQo u}= QO|x}L=v 'u=tR |] QO x@=OQo Q=Wism |x}L=v |H} QOD VQDUo =@ "OQ}o|t pmW u;x}L=v u}= QO Q=Wi Q=Okt '|D} w=m |x}L=v |Q}opmW =@ "O@=}|t xaUwD uw}U=D} w=m"OwW|t |Q}owrH Q=Wi QDW}@ Vy=m R= w Ov=t|t |k=@ Q=N@ Q=Wi C@=F Q=Okt =@ Q@=Q@'u=tR CWPo =@ w OQ}o|t pmW t = 49ms u=tR QO |t�=O |xDi=} xaUwD |D} w=m

xOW |R=UR=@ w |ak=w O=R; K]U xU}=kt "1 pmW

uw}U=D}w=m sQH p=kDv= |OOa pOt "2"3Q_v QO =@ =} '|OOa� |r}rLD \@=wQ T=U=Q@ uw}U=D} w=m sQH p=kDv= j}kO |=ypOt|UQQ@ =@ u}kkLt "CU= xOW G=QNDU= R=i wO lQDWt RQt QO pO=aD |x]@=Q uDiQo'|r}rLD hrDNt |=ypOt w |r} Q pOt� uw}U=D} w=m sQH p=kDv= hrDNt |=ypOtxS} wx@ ��|D} w=m |R=UpOt QO [3]Rv=m\UwD xOW x�=Q= pOt xm [20]OvO=O u=Wv �|OOaQO "OQ=O =Q CkO u} QDW}@ �� Q=N@ |=yQ=DN=U V}=OH w |DWoR=@ CH |x}L=v QO

%OwW|t xDWwv u}vJ p=kDv= |xrO=at 'pOt u}=@f@ t

+ ~V :~rf = Cdest�vMin(Pl � Pv; 0)f�l(0 5�lV 21)t1

+ Cprod(1� f)f 2

�lt1Cdest = 9� 105; Cprod = 3 0� 104 (15)

x@ xYNWt pw] C@Uv CQwYx@ xm CU= O=R; u=} QH |xYNWt u=tR hQat t1"OwW|t h} QaD (D=V1) O=R; u=} QH CaQU

G}=Dv |x�=Q= "4=yxQo O=OaD x@ pL CkO |oDU@=w |UQQ@ "1"4

xaUwD uw}U=D} w=m pL |=Q@ |OOa sD} Qwor= '?U=vt |OOa |xm@W ?=NDv= |=Q@OvJ R= xO=iDU= =@ 0 30 uw}U=D} w=m OOa QO 38mm Q]kx@ |mU}O CWB xDi=}O=a@= =@ pL u=O}t |=Q@ "OW xU}=kt j}kO Q}O=kt =@ G}=Dv w '=QH= Cw=iDt |xm@W1 27mm w 1 58mm '2 38mm xQo O=a@= =@ xm@W xU R= 115�282mm

xaUwD |D} w=m |=UB ?} Q[ w Q]k 'pw] |x@U=Lt |OOa pL G}=Dv xm OW xO=iDU=QO [21]|r}rLD \@=wQ =@ xU}=kt QO x]w@ Qt |@Uv |=]N OYQO w 2 pmW QO xDi=}�8�CPDR� lU}O `=aW OL=w QO pwrU� |UOvy QDt=Q=B ?ULQ@ w 3 pmW

%R= CU= CQ=@a h} QaD ?ULQ@ QDt=Q=B u}= "CU= xOW xO=O u=WvCPDR = Number of cells

Disk Radius(16)

`=aW =Hv}= QO� |OOa |xm@W QO XNWt pw] |=Q@ xm OyO|t u=Wv CPDR

%x@ Ov=\w@ Qt xOW xO=iDU= |xm@W xU "CU= xOW xO=iDU= pwrU OvJ R= '�lU}O|oDU@=w xm OwW|t xOy=Wt "CPDR= 15 w CPDR= 12 'CPDR= 8sm ,=D@Uv �CPDR= 8� xm@W u} QDCWQO |=Q@ |DL xm@W |=yxQo x@ =y?=wHxHwD =@ "�xDi=} xaUwD |D} w=m pw] u}tND QO =]N OYQO 12 88 QFm =OL� CU=CU=UB ?} Q[ |=]N Vy=m '|Ov@xm@W CkO V}=Ri= Q}F-=D u} QDsyt '2 pmW x@R= xO=iDU= Qo}O C} Rt "�CU= OYQO 0 2 =@ Q@=Q@ =]N u}= CPDR= 15 QO�"CU= |DWoR=@ CH w |D} w=m |}=yDv= |x}L=v QDj}kO |R=UR=@ 'h} Q_ |xm@WQO CPDR Q}O=kt =@ ?U=vt |=yxm@W R= xO=iDU= =@ xr=kt u}= QO xOW x�=Q= G}=Dv

"CU= xOt; CUO x@ 15 =D 12 xR=@

82

OQixO}Ov

UBOtLt

w|LwQ

u=UL=

"(� = 0 20; V1 = �31 20m=s; Re = 1 7� 106; ddisk = 54mm) lU}O CWB xOQDUo |R=UxQiL |x}L=v |xaUwD "4 pmW

(� = 0 15; V1 =lU}OCWB xOQDUo |R=UxQiL |x}L=v |xaUwD "5 pmW"�36 m=s; Re = 8 6� 106; ddisk = 240 mm)

uw}U=D} w=m s} SQu}= QO �CP � Q=Wi?} Q[w|OwtaCaQU|D} w=m 6pmW QOw OQ}o|t pmW x@=OQo |D} w=m pN=O QO OW xQ=W= xm u=vJ "CU= xOW xO=O u=Wv=Hv; R= "(Vmax = 30 m/s) OyO|t |wQ x}L=v u}= QO |Owta CaQU xv}W}@|Q=Okt |D} w=m |x}L=v QO |@Uv Q=Wi 'CU= QiY Q@=Q@ O=R; u=} QH |@Uv Q=Wi xmu=} QH "(Pv � P1 = 2763� 100000 = �97237 Pa) OwW|t |ivtpmW uwmU |x]kv w OUQ|t Q=Wi Q=Okt u} QDq=@ x@ lU}O x@ OQwNQ@ R= Oa@u}= "OOQo|tQ@ O=R; u=} QH Q=Wi x@ G} QODx@ Q=Wi '|D} w=m |x}L=v R= GQ=N "OQ}o|t

'|D} w=m |x}L=v x@ `}=t CH CWoR=@ QF= QO "O@=}|t xaUwD |DWoR=@ CH |x}L=v|oS} w wO u}=Q@=v@ (t = 51ms) OwW|t =OH |D} w=m R= Q=N@ lJwm |=yQ=DN=UCH |xaUwD "1 %CU= x_Lqt p@=k |t�=O |xDi=} xaUwD |D} w=m |=yDv= QO |Q=DiQ|DWoR=@ CH CmQL QF= Q@ |rY= u=} QH x@ Q=N@ |=y?=@L V}=OH "2 &|DWoR=@Q=N@ Q=Wi =@ Q@=Q@ w 'C@=F Q=Wi Q=Okt uw}U=D} w=m |x}L=v QO [21]"|D} w=m pN=O x@|x]kv l} |DWoR=@ CH R=e; C}akwt QO xm OyO|t u=Wv |@ QHD G}=Dv "CU=|x]kv u}= C}akwt "�51ms w 49ms QO 4 pmW� OQ}o|t pmW �S� uwmU?} Q[ Q=Okt OwW|t Ea=@ Qt= u}= "CU= Q=O}=B=v w Ovm|t Q}}eD u=tR =@ uwmU

"�Cp = 0 42 %uw}U=D} w=m s} SQ u}= QO� OW=@ 1 R= QDsm ?D=Qtx@ u; Q=Wi|D} w=m |x}L=v '�O=R; u=} QH CaQU V}=Ri= =}� uw}U=D} w=m OOa Vy=m =@� = 0 15 s} SQ QO xDi=} xaUwD |D} w=m '5 pmW QO "OwW|t QDnQR@ xDi=} xaUwD|v=tR C}akwt wO QO '�240mm Q]k x@ |mU}O |=Q@� Re = 5 83� 106 w|t�=O Cr=L x@ xDi=} xaUwD |D} w=m x}v=F|r}t 30 u=tR QO "CU= xOW xO=O u=WvV}=Ri= COWx@ xDi=} xaUwD |D} w=m pw] 'uw}U=D} w=m |xaUwD R=i |] QO "OUQ|t|D} w=m pmW |xU}=kt ,qFt [1]"CU= sm Q=}U@ |D} w=m Q]k C=Q}}eD |rw O@=}|t|r=L QO xm OyO|t u=Wv s} SQ u}= QO x}v=F|r}t 30 w 21 u=tR wO QO xDi=} xaUwDu; Q]k 'O@=}|t V}=Ri= 1450mm x@ 965mm Q=Okt R= |D} w=m |x}L=v pw] xmpmW |rm Cw=iD OwW|t Ea=@ |oS} w u}ty "OUQ|t 208mm x@ 204mm R=uOw@ QDxO}Wm 'uDi=} xaUwD R=i QO u; pmW w |}=yv Cr=L QO xDi=} xaUwD |D} w=m|=yQ=DN=UV}=OH '|DWoR=@CH OWQ QF= Q@ "OW=@ |}=yv xDi=} xaUwD |D} w=m pmWC}akwt "�30ms QO 5 pmW� CU= x_Lqt p@=k |D} w=m |=yDv= QO Q=N@ lJwm

"CU= xOW xO=O u=Wv pmW u}= QO R}v Q=O}=B=v uwmU |x]kv

83

"""uQ=kDt

|=yxUO

vy|wQu

w}U=D}w=

m|xO}O

B|OOa

pL

"Q=Wi ?} Q[ w |Owta CaQU |=yQwDv=m "6 pmW

|@ QHD G}=Dv "OQ=O |ovy=ty [21]|@ QHD G}=Dv w �COQ=J} Q |x]@=Q� 20 |x]@=QpvwD |xQ=w}O C}OwOLt Q}F-=D w CU= Iv}= 0 5 Q]k =@ lU}O x@ \w@ Qt ?; pvwD|mOv= |Q_v |x]@=Q w |@ QHD G}=Dv u}=Q@=v@ "CU= xOWv KqY= |@ QHD G}=Dv Q@OOa ?ULQ@ |D} w=m Q]k u} QDW}@ |x]@=Q 8 pmW QO "OvQ=O Cw=iD Qo}Om} =@|=UB ?} Q[ "CU= xOW sUQ |D} w=m |=UB ?} Q[ 9 pmW QO w 'uw}U=D} w=m|xYNWt QDt=Q=B '10 pmW QO "CU= xOW x@U=Lt 21 |x]@=Q T=U=Q@ |Q_v'xv}W}@ Q]k 'xv}W}@ pw]� |D} w=m |xYNWt xU Qy xm ( Lmax

(Dmax�C0 5D )

) QwD=D} w=m|tD} Q=or |xLiY QO uw}U=D} w=m OOa ?ULQ@ OwW|t pt=W =Q �=UB ?} Q[pmW l} QO QwD=D} w=m C=aq]= s=tD 'xYNWt QDt=Q=B s}UQD =@ "CU= xOW sUQ?ULQ@ xYNWt QDt=Q=B C=Q}}eD 'xOW xO=O u=Wv |xOwOLt QO "OwW|t x�=Q= OL=w

"CU= |]N ,=@} QkD �

\wQNt CWB xDi=} xaUwD uw}U=D}w=m "3"4Q=Wi QwDv=m 11 pmW QO "CU= \wQNt '=yQwD=D} w=m pw=ODt |=yxUOvy R= |m}|=Q@ 0 20 uw}U=D} w=m OOa s} SQ QO xDi=} xaUwD |D} w=m |xaUwD 12 pmW QO wxOy=Wt "CU= xOW xO=O u=Wv 900 T-=Q |x} w=R w 7 34mm Q]k =@ \wQNt l}OWQ =@ w CU= \wQNt CWB |=yx@=OQo C}akwt R= uw}U=D} w=m R=e; xm OwW|t|D} w=m R= \wQNt CWB |D} w=m Q]k w pw] "O@=}|t xaUwD |D} w=m |x}L=v '=yx@=OQoQDsm w u=} QH V}=OH |x}L=v Vy=m 'xr�Ut u}= p}rO "CU= QDsm lU}O CWBQO "CU= lU}O =@ xU}=kt QO \wQNt CWB QO Q=Wism |=yx@=OQo xOwOLt uOW"CU= xOW xO=O u=Wv \wQNt CWB |ki= w |Owta CaQU |=y|D} w=m 13 pmW|mU}O =yQwD=D} w=m CWB u=} QH Q=DiQ x@=Wt pmW wO u}= QO xOW xOy=Wt Q=DiQ

"CU=QwD=D} w=m OQwtQO '|mU}O QwD=D} w=m |UOvy |=yQDt=Q=B |=Q@ xOWx�=Q= \@=wQQO \wQNt CWB |D} w=m O=a@= Q}}eD Q@ Q=PoQ}F-=D pt=a "CU= jO=Y R}v |]wQNtT-=Q |x} w=R R= |a@=D u; Q=Okt xm CU= CD0 ?} Q[ '|mU}O QwD=D} w=m =@ xU}=ktQO xDi=} xaUwD |D} w=m pw] |=Q@ xOt; CUOx@ G}=Dv 14 pmW QO "CU= \wQNt

u=} QH |x}L=v w |D} w=m pN=O Q=Wism |x}L=v u}@ pO=aD O=H}= |=Q@ Q=Wi V}=Ri=QO "OyO|t |wQ |O}OW Q=Wi V}=Ri= 'uw}U=D} w=m |x}L=v |=yDv= QO "CU= O=R;

%s} Q=O x}L=v u}= QO &CU= ?; Q=N@ Q=Wi Q@=Q@ Q=Wi '|D} w=m |x}L=v pN=O8><>:1) Cp = P�P10 5�V 21 ;

2) � = P1�Pv0 5�V 21

P = Pv(|D} w=m pN=O);) Cp = Pv � P10 5�V 21

;) Cp = �� (18)

|ivt =@ Q@=Q@ Q=Wi ?} Q[ |D} w=m pN=O QO xm OwQ|t Q=_Dv= |Q_v ^=Lrx@ u}=Q@=v@Q=Wi ?} Q[ "CU= xOW O}}-=D xr�Ut u}= '?6 pmW QO "OW=@ uw}U=D} w=m OOau}= 'lU}O x@ O=R; u=} QH OQwNQ@ |x]kv QO "CU= �0 15 Q@=Q@ |D} w=m pN=O QOS |=}=B=v uwmU |x]kv QO ?} Q[ u}= Q=Okt .(CP = 1) CU= xv}W}@ ?} Q[

"CU= 0 17 Q@=Q@lU}O CWB xDi=} xaUwD |D} w=m |OOa G}=Dv |@=} RQ= "1"2"4

xaUwD |=y|D} w=m |=UB ?} Q[ w pw] 'Q]k |=Q@ |]@=wQ |Q_v p}rLD =@ u}kkLt[21]%OvOQm u=}@ u}vJ =Q |QwLt uQ=kDt xDi=}

dcavitymax

Dcavitator=�

CD�(1� 0 132�0 5)

�0 5(19)

lcavitymax

Dcavitatormax=

�+0 008�(1 7�+0 066)h

CD�(1�0 132�0 5)

i0 5 (20)

CD = CD0(1 + �); CD0 = 0 79 (21)

%R= Ov=CQ=@a =UB ?} Q[ |=Q@ Qi=W � CUrB w QW}i \@=wQCD = CD0(1 + �); CD0 = 0 84 (22)

CD = CD0(1 + � + 0 028 �2); CD0 = 0 8053 (23)

?ULQ@|D} w=m pw] u} QDW}@ |=Q@ |Q_v |x]@=Q w|@ QHD '|OOa G}=Dv '7 pmW QO=@ |@ wN Q=}U@ CkO =@ xrY=L |OOa G}=Dv "CU= xOW s}UQD uw}U=D} w=m OOa

84

OQixO}Ov

UBOtLt

w|LwQ

u=UL=

?ULQ@lU}OCWB xDi=} xaUwD|D} w=m |=Q@ L(D�C0 5

D )QDt=Q=B Q}}eD "10 pmW

"COQ=J} Q |Q_v \@=wQ =@ |OOa G}=Dv |xU}=kt 'uw}U=D} w=m OOa

(� = '|]wQNt R=UxQiL h=Q]= QO Q=Wi |xQiL "11 pmW0 20; V1 = �31 20 m=s; Re = 1 87 � 105; dcone =

"7 34 mm; Cone angle = 900)

lU}O w \wQNt |wQ xDi=} xaUwD |D}w=m |OOa pL G}=Dv |xU}=kt "1 pwOH"�� = 0 25�

lcavitymaxDcavitator

dcavitymaxDcavitator

lcavitymaxdcavitymax

QwD=D} w=m pmW2 57 1 69 4 34 Cone (900)

2 55 2 07 5 28 Disk (1800)

"CU= G=QNDU= p@=k 20 w 19 \@=wQ T=U=Q@ xUOvy R= |D} w=m Q]k x@ pw] C@Uv%O};|t CUO x@ |D} w=m Q]k x@ pw] C@Uv 19 Q@ 20 |xrO=at s}UkD =@

lcavitymax

dcavitymax= � + 0 008�(1 7� + 0 066)

(24)

|YNWt Q=Okt |r}rLD pOt Qy w xUOvy Qy |=Q@ xm 'CD0 C@=F R= CQ=@a u}=|D} w=m Q]k x@ pw] Q=Okt C@=F uw}U=D} w=m OOa QO u}=Q@=v@ "CU= pkDUt 'CU=

"CU= xUOvy R= pkDUt

G}=Dv u}@ xU}=kt 'uw}U=D} w=m OOa ?ULQ@ xDi=} xaUwD |D}w=m pw] "7 pmWQwD=D} w=m |=Q@ Q[=L j}kLD |OOa G}=Dv w �20 |x]@=Q� |Q_v \@=wQ [21]|@ QHD

"|mU}O

|OOa G}=Dv xU}=kt 'uw}U=D}w=m OOa ?ULQ@ xDi=} xaUwD |D}w=m Q]k "8 pmW|=Q@ [21]|@ QHD |=yxO=O w �19 |x]@=Q� COQ=J} Q |Q_v |x]@=Q =@ Q[=L j}kLD

"|mU}O QwD=D}w=m

G}=Dv =@ Q[=L |OOa G}=Dv |xU}=kt 'xDi=} xaUwD |D} w=m |=UB ?} Q[ "9 pmW"|mU}O QwD=D}w=m |=Q@ �21 |x]@=Q� |Q_v w [21]|@ QHD

|OOa G}=Dv "CU= xOW xU}=kt [21]|@ QHD |=yxO=O w |Q_v \@=wQ =@ \wQNt CWBuw}U=D} w=m Q=DiQ "OvQ=O |ovy=ty |Q_v \@=wQ w |@ QHD |=yxO=O =@ |@ wN CkO =@CU= lU}O CWB xDi=} xaUwD uw}U=D} w=m Q=DiQ x@=Wt \wQNt CWB xDi=} xaUwDu}= =@ &CU= QDlR=v w QDx=Dwm lU}O =@ xU}=kt QO \wQNt |xDi=} xaUwD |D} w=m |rwpqkDU= "�1 pwOH� CU= QwD=D} w=m |xUOvy R= pkDUt lcavitymax

dcavitymaxQDt=Q=B 'OwHw

85

"""uQ=kDt

|=yxUO

vy|wQu

w}U=D}w=

m|xO}O

B|OOa

pL

|]wQNt QwD=D}w=m CWB xDi=} xaUwD |D} w=m |x}L=v |xaUwD "12 pmW

"|Owta w |ki= CaQU |=yQwDv=m "13 pmW

|Q=Wi |=UB u=R}t xm CU= QmP p@=k "OwW|t |rwtat \}=QW R= QDsm Q=}U@ xDi=}xDi=} xaUwD uw}U=D} w=m s=ovy QO =Q} R &CU= sm Q=}U@ xDi=} xaUwD |D} w=m \}=QW QOQ=Wi '|t�=O uw}U=D} w=m wkw "CU= OwOLt ,=D@Uv sUH CWB QO Q=Wi Vy=m|=UB xm u}= x@ xHwD =@ "OQ=O|t x=ov C@=F Q=N@ Q=Wi Q=Okt QO =Q sUH CWBxDi=} xaUwD |D} w=m \}=QW QO 'CU= sUH h=Q]= QO Q=Wi p[=iD =@ pO=at |Q=WiQO 'p=Ft |=Q@ "O@=}|t Vy=m |Q=Wi |=UB =Pr w xOW QDOwOLt Q=Wi Ci= u}=

=UB |wQ}v Vy=m QO xDi=} xaUwD uw}U=D}w=m C}ty= "1"3"4Q=N@ |=yx}q u}@ l =m]Y= R= |W=v xDi=} xaUwD |D} w=m K]U |wQ |WQ@ VvD|D} w=m pN=O |=yR=o |r=oJ xm u}= x@ xHwD =@ "CU= |vwQ}@ u=} QH w |D} w=m pN=O,qwtat |}xDUwB |=UB =} |WQ@ VvD R= |W=v |wQ}v CU= sm Q=}U@ xDi=} xaUwD'xDi=} xaUwD |D} w=m p}mWD \}=QW QO u}=Q@=v@ [21]"CU= |WwBsWJ p@=k w 'lJwmxaUwD |D} w=m |=UB |wQ}v xH}DvQO w CU= |Q=Wi |=UB '=UB |wQ}v |rY= VN@

86

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"CU= |QwQ[� = 0 15 s} SQ QO |v=UwvQ}e Q=DiQ "2"4"4

s} SQ QO 18mm Q]k =@ |}xv=wDU= |xvO@ |wQ |D} w=m |v=tR |xaUwD 17 pmW QOp}mWD pLt R= '|D} w=m |x}L=v R=e; "CU= xOW xO=O u=Wv � = 0 15 uw}U=D} w=m"CU= xv=wDU= |xQ=w}O |wQ xOW =OH u=} QH |x}L=v QO Q=Wism w x}rw= |=yx@=OQo|Q}owrH =yx@=OQo uwQO Q=Wi QDW}@ Vy=m R= 'uw}U=D} w=m |=y?=@L |Q}opmW =@`} RwD 18 pmW QO "Ovm|t =O}B xaUwD G} QODx@ C@=F Q=Wi |x}L=v u}= w OwW|t|D} w=m pN=O QO "CU= xOW xO=O u=Wv xv=wDU= |wQ Q@ |r=oJ w Q=Wi ?} Q[|r=oJ� 0 554kg/m3 Q@=Q@ |r=oJ w (Cp = �� = �0 15) Q=Wi ?} Q[u=} QH Q=Okt x@ |r=oJ w Q=Wi ?} Q[ '|D} w=m |x}L=v s=tD= R= TB "CU= �Q=N@

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"CU= XNWt 31 2p1 + 0 20 = 34 17)

|}xv=wDU= |xvO@ |wQ uw}U=D}w=m "4"4� = 0 30 s} SQ QO |D}w=m |v=Uwv Q=DiQ "1"4"4

xvO@ wrH QO QwD=D} w=m |x}@aD "CU= |}xv=wDU= ,qwtat |}=} QOQ} R |=yx@=DQB |xvO@CQwY QO "OwW|t sUH |wQ |t�=O uw}U=D} w=m |x}L=v l} |Q}opmW Ea=@R= |NQ@ QO |D} w=m |x}L=v |=QPo Q=DiQ wkw p=tDL= 'QwD=D} w=m R= xO=iDU= sOa|wQ uw}U=D} w=m |=QPo Q=DiQ '15 pmW QO [21]"OQ=O OwHw uw}U=D} w=m OOa |=ys} SQ"CU= xOW xO=O u=Wv � = 0 30 \}=QW QO 240mm Q]k =@ |}xv=wDU= |xvO@|Q}opmW R= TB "CU= Q=O}=B=v ,qt=m |D} w=m |x}L=v 'OwW|t xOy=Wt xm u=vJ'|D} w=m |=OD@= x@ |DWoR=@ CH CmQL QF= Q@ '(t = 55ms) |D} w=m |xaUwD wR} Q |=y?=@L x@ p}O@D xOW =OH VN@ "OwW|t =OH u; R= |D} w=m R= |WN@

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'|}xv=wDU= |xvO@ |wQ |�RH uw}U=D} w=m |xaUwD "17 pmW"(� = 0 15; V1 = �36 m=s; d = 18 mm; Re = 6 50� 105)

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"|D} w=m pN=O x@ |DWoR=@ CH CmQL QF= QO |rY= u=} QH x@ Q=N@xaUwD uw}U=D} w=m |UOvy |=yQDt=Q=B xOW xO=iDU= |OOa sD} Qwor= '|rm Qw]x@ "6xaUwD xR=@ QO =Q |D} w=m pmW w uOW xDU@ |xwLv 'O=a@= Ovv=t =yQwD=D} w=m xDi=}

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=UB |wQ}v %DQwD=D} w=m Q]k %Dcavitator

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"6 50� 105)

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%R= CU= CQ=@a uw}U=D} w=m |OOa p}rLD |rm"CU= QDnQR@ lU}O CWB xDi=} xaUwD |D} w=m 'hrDNt |=yQwD=D} w=m u}@ QO "1|xk]vt R= uw}U=D} w=m |x}L=v %O=O KQW u}vJ u=wD|t =Q xr�Ut u}= p}rOu=} QHV}=OH |x}L=v "OwW|t R=e; QwD=D} w=mCWB |=yx@=OQo w u=} QHV}=OHw CU= QDW}@ QwD=D} w=m `=wv= Qo}O =@ xU}=kt QO lU}O CWB x@=OQo p}mWD w

"CU= xv}W}@ lU}O |xDi=} xaUwD uw}U=D} w=m |x}L=v xH}DvQOpkDUt 'uw}U=D} w=m |=ys} SQ s=tD QO xDi=} xaUwD |D} w=m Q]k x@ pw] C@Uv "2

"CU= Qw=D} w=m |xUOvy R=R= |W=v |wQ}v 'xDi=} xaUwD |D} w=m pN=O Q=N@ |r=oJ uOw@sm x@ xHwD =@ "3u}=Q@=v@ &CU= R}J=v |vwQ}@ u=} QH w |D} w=m pN=O Q=N@ |=yx}q u}@ l =m]Y=CQwY QO "CU= |Q=Wi |=UB 'xDi=} xaUwD |D} w=m |=UB |wQ}v |rY= VN@|=Q@ |QDsm u=wD '|}=} QOQ} R x@=DQB |wQ xDi=} xaUwD |D} w=m |Q=Oxov w O=H}=

"Ow@ Oy=wN R=}v OQwt x@=DQB Qwv=t w CmQL

=yCWwv=B1. surface tracking methods2. hoemgenous equilibrium ow models

3. transport based equation model4. Rayleigh5. donor-acceptor6. simple line interface construction (SLIC)7. piecewise linear interface construction (PLIC)

89

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�References� `@=vt1. Wang, G., Senocak, I., Shyy, W., Ikohagi, T. and Cao,

S. \Dynamics of attached turbulent cavitating ows",Progress in Aerospace Sciences, 37, pp. 551-581 (2001).

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13. Frobenius, M. and Schilling, R. \Three-dimensional un-steady cavitating e�ects on a single hydrofoil and in aradial pump- measurement and numerical simulation",Cav03-GS-9-005, Proceedings of the 5th InternationalSymposium on Cavitation, Osaka (2003).

14. Li, D., Grekula, M. and Lindell, P. \A modi�ed SSTk-! turbulence model to predict the steady and un-steady sheet cavitation on 2D and 3D hydrofoils", Pro-ceedings of the 7th International Symposium on Cavita-tion CAV2009 (2009).

15. Liu, D., Hong, F. and Lu, F. \The numerical and ex-perimental research on unsteady cloud cavitating ow of3D elliptical hydrofoil", J. of Hydrodynamics, 22(5), pp.759-763 (2010).

16. Huang, B. and Wang, G. \Partially averaged navier-stokes method for time-dependent turbulent cavitating ows", J. of Hydrodynamics, 23(1), pp. 26-33 (2011).

17. Phoemsapthawee, S., Leroux, J., Kerampran, S. andLaurens, J. \Implementation of a transpiration velocitybased cavitation model within a RANS solver", EuropeanJournal of Mechanics B/Fluids, 32, pp. 45-51 (2012).

18. Bakir, F., Rey, R., Gerber, A., Belmari, T. and Hutchin-son, B. \Numerical and experimental investigations ofthe cavitating behaviour of an inducer", Int. Jour. OfRotating Machinery, 10, pp. 15-25 (2004).

19. Tang, H., Wrobel, L.C. and Fan, Z. \Tracking of im-miscible interfaces in multiple-material mixing process",Comput. Materials Science, 29, pp. 103-118 (2004).

20. Passandideh-Fard, M. and Roohi, E. \A computationalmodel for cavitation using volume-of- uid method", Ac-cepted to be Presented in the 13th Conference of CFDSociety of Canada, CFD (2006).

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90