�1395

Q=y@�'h

}QWl}

v=mt|U

Ovyt12

8�119

"X'1|

xQ=tW'

32�3

|xQwO

Ori

gina

lArt

icleu=} QH |OOa |R=Ux}@W QO QF-wt |=yQDt=Q=B j}kLD

|xv=wQB pwL |vw}U=D}w=m w |vw}U=D} w=m Q}eDTMB4119 OQ=Ov=DU=

�OWQ= T=vWQ� � �|@w}= =[QOtL=�Q=}O=DU=� OvtOQN O}aU

QDW= lr=t |DavY x=oWv=O 'l}v�t |UOvyt |xOmWv=O

|}=} QO |xv=wQB pwL |vw}U=D} w=m w |vw}U=D} w=m Q}e |=yu=} QH Q=DWwv u}= QOw Qw=DWo 'CU=QD ?}=Q[ "CU= xOW pL |Oa@xU RANS VwQ =@ DTMB4119"OW xU}=kt |@ QHD G}=Dv =@ w G=QNDU= |R=Ux}@W CWy QO xv=wQB u}= |=Q@ R}v |yOR=@"Ot; CUO x@ R}v xQiL |xaUwD |xk]vt w C}akwt w OW XNWt uw}U=D} w=m |wor=

|Q@ R w xv=wQB |Q=m jta '|wQW}B ?} Q[ %syt QDt=Q=B xU |=Q@ |OOa C=k}kLD 'xwqax@Kw]U |wQ |wQW}B ?} Q[ QF= |xar=]t "OW s=Hv= |vw}U=D} w=m u=} QH QO xv=wQB K]U=@ "OwW|t xOy=Wt |QDW}@ Q=N@ R=i Q=Okt 'QDsm |wQW}B ?} Q[ =@ xm O=O u=Wv xv=wQB|}=Hx@=H '�l}D=DUwQO}y Q=Wi V}=Ri=� O=R; ?; \}=QW QO xv=wQB |Q=m jta uOQ@ u}}=BQUm |vLvt |xrk Vy=m w 'xrtL |x@r |m}ORv QO xQiL sHL C=Q}}eD 'xQiL |xOwOLt'|v}at Q=Okt =D |Q@ R `=iDQ= V}=Ri= 'u}vJty "CiQo Q=Qk |UQQ@ OQwt Q=N@ R=i |tHL

"OQm OWQ u; R= TB w OW Q=N@ R=i |tHL QUm Q=Okt Vy=m Ea=@

ahmadreza.ayoobi@gmail.comkheradmand@mut-es.ac.ir

RQt 'K]U |Q@ R `=iDQ= 'xv=wQB |Q=m jta '|vw}U=D} w=m u=} QH %|O}rm u=oS=w"xQiL

xtOkt "1|=y|DNU w Ovm|t KQ]t =yxv=QW}B u}= h=Q]= =Q |QDxO}J}B |=yu=} QH 'O}OH"OQw;|t OwHwx@ =yu; p}rLD w =yQw=vW |xv=QW}B |L=Q] w |UQQ@ |=Q@ =Q |O=} R|@=} RQ= Qw_vtx@ |v=QL@ w |rwtat \}=QW QO xOW |L=Q] |xv=wQB |UQQ@ w p}rLD

"CU= |QwQ[ |L=Q] C=twRrt jkLD QO xv=wQB ptar=Tma w =y|oO}J}B u}=uw}U=D} w=m |R=Ux}@W w u=} QH |R=UpOt w |UQQ@ |=Q@ Q}N= |=yp=U QO|=yOm w [12�9]|RQt u=tr= [8w7]'pvB p}@k R= |Dw=iDt |=yVwQ R= xv=wQB |wQs=Q; u=} QH |wQ xm |y=oW}=tR; j}kLD l} QO "CU= xOW xO=iDU= [13] RANS

s=Hv= 1|QDt}Uwrw QrB=O QR}r R= xO=iDU= =@ w xv=wQB |xQB l} |m}ORv QO VwWet w|x} Q_v x@C@UvCHRr C=}YwYN u}}aD |=Q@ u=} QH C=}�RH |Q}oxR=Ov= [14]'OW|x@r QO |t=Q;x@ |RQt |=yx}q V=WDe= x@ QPo xm O=O u=Wv 'p}Uv=DB l}Uqm=@ 2xOwOLt \Uw u=} QH |RQt |x}q R}v w OyO|t MQ xQB QDw \Uw QO xrtLVvmtyQ@ XwYNQO j}kLD Qo}O |wU R= "OQ=O Cy=@W |rwtat |Oa@ wO Q=DiQ|vw}U=D} w=mQ}e |=yxv=QW}B OQmrta |wQ CHRr QF= |v}@V}B |=Q@ 3GRrQ}e � GRrVwQ Q@|vD@t |Oa@xU |x@DQtsm p}Uv=DB Ovw}B R= xO=iDU= =@ [15]|vw}U=D} w=m w|x} Q_v ZQi Q@ |vD@t |Oa@ wO |r=QoDv= |RQt |x}q |r}rLD VwQ w |RQt u=tr=uDUw}B |=Q@ xQ=w}O Pwiv pOt R= Qw_vt u}O@ "OW s=Hv= |R=Ux}@W |=Q@ |Q=wv|=yu=} QH w OW xO=iDU= |rN=O |RQt |x}q |=yu=} QH =@ GRr Q}e |HQ=N u=} QH

Cw=iDt |=yxv}tR QO u; RwQ@ R}v w Ov}=WwN=v Q=DiQ ^=Lrx@ uw}U=D} w=m |xO}OBu=L=Q]|=Q@ �� [3]u=Uv= uO@ QO |DL w [2]|}=[i |=yCm =Q =D [1]=} QOQ} R R= ��OWQ pt=W uw}U=D} w=m Ca}@] ,=twta "CU= xOw@ xOvvmu=Qov xW}ty 'u=kkLt w|wQ |WRQr |=ywQ}v w xvO@ |wQ Q=Wi u=Uwv [4]R} wv O=H}= '=yxQiL uO}mQD w |}xQwOw |Qwx]we jta 'Qw=vW CaQU Q}_v �� |Q=m \}=QW x@ xDU@ "CU= [5]xv=wQB CiW'uw}U=D} w=m R= |Dw=iDt `=wv= xv=wQB �� xQ}e w Qw=vW Qwv=t\}=QW 'xv=wQB |v=QwOCaQUx@ QHD =Q ?=y |WJ}B w xQB lwv |WJ}B '|Q@= '|@=@L '|}x}q uw}U=D} w=m p}@k R=w xv=wQB |xQB |m}ORv QO O}OW Q=Wi O=H}= Ea=@ |}xQiL |W=B wQi RwQ@ "Ovm|t"OwW|t u; CUOu}}=B QO �u=mU pFt� Qo}O |m}t=v}OwQO}y p}=Uw |wQ u}vJty[6]u=mU w xv=wQB |xQB |wQ |OH V}=U w |vmxr=J x@ QHvt ?re= =yQ=Wi u}=|DL w R} wv ?Hwt Ov=wD|t xvO@ |wQ xR=Ov= R= V}@ Q=Wi C=v=Uwv 'xwqax@ "OwW|t

"OwW xvO@ C=a]k CUmWQ=Okt� |DL=Q '�q=@ |};Q=m � ?wN OQmrta %uwJ |}=y|OvtR=}v uOQw;Q@ |=Q@|}=} QO |=yxv=QW}B �QDsm V}=U� |O=YDk= |Q=OQ@xQy@ w C}vt= '�sm VRQr w R} wv|=yxv=QW}B |UOvy C=YNWt |oO}J}B "OvwW|t |L=Q] QDxO}J}B |=yxUOvy =@

pw�Ut xOvU} wv �"1394 1 15 VQ}PB '1393 12 18 x}LqY= '1393 7 9 Ci=} QO %M} Q=D

"""u=}QH

|OOa

|R=Ux}

@WQOQF

-wt|=yQD

t=Q=Bj}k

LDl} R= [8]xv=wQB uw}U=D} w=m |=kr= Q=Wi C=v=Uwv |x@U=Lt |=Q@ u=QoVywSB|x@U=Lt "2 'xv=wQB |}x}q uw}U=D} w=m |x@U=Lt "1 %|}xrLQt wO |D=@U=Lt VwQ|xO=U VwQ Q@ |vD@t =yv; j}kLD &OvOQm xO=iDU= |DWm |xvW=B |wQ Q=Wi C=v=Uwvu}rw= QO "OW <=[Q= |DL=Qx@ =D=m \QW u; QO xm CU= SQCM |}xLiY pvBO=R; u=} QH \N |x} Q_v T=U=Q@ w |RQt \QW |xr}Uwx@ xQiL pmW 'xrLQt|xir-wt 'xv=wQB |xQB lwv l}ORv |xQiL j}kO pmW x@ |@=}CUO |=Q@ "OW u}}aDuw}U=D} w=m R= '|Oa@ |xrLQt QO "OW xDiQo Q_v QO |RQt \QW |wQ |[Qa u=} QHpt=W Q=Wi C=v=Uwv |x@U=Lt |=Q@ u=tRty Qw]x@ xvO@ |}xLiY u=} QH w xv=wQBuw}U=D} w=m l}t=v}OwQO}y |x�=Q= QO u}kkLt "OW xO=iDU= 'xvO@ w xv=wQB p@=kDt QF=w O=} R |w}mU= =@ |}xQBCiy xv=wQB xU uw}U=D} w=m x=Dwm Tv=mQi R} wv h}] ww xv=wQB uw}U=D} w=m R=e; G}=Dv |Q=PoT=}kt [21]'CN=wvm} Q}e |OwQw u=} QH =@C=QF= ?=DR=@ w xv=wQB pt=m T=}kt x@ pOt |=yuwtR; R= uw}U=D} w=m l}DUwm =wQO}y|OOa \=@DQ=l} =yv; "OvDiQo hOy =Q |OOa |=yVwQ QO uw}U=D} w=m |wQ =yxDUyl}DUwm =wQO}y =@ xv=wQB uw}U=D} w=m l}t=v}OwQO}y |R=iOvJ GRr |R=Ux}@W u}@Q[=L |Q=PoT=}kt uwv=k C}r@=k w OQmrta |wQ =Q =yT=}kt QF= w OvOQm Q=QkQ@ u;

"OvOQm |UQQ@Q=}U |xv=wQB wO h=Q]= |vw}U=D} w=m u=} QH |OOa |R=Ux}@W |UQQ@ R= hOyVwQ |}=v=wD V}=tR; "1 %R= CU= CQ=@a [22]hQLvt CiW l} |wQ Q=Ow}mU=Cw=iDt |=y|L=Q] ?@Ux@ u=} QH |=y|oS} w C=Q}}eD X}NWD QO =yv; |OOax@ w Ovm|t pQDvm =Q uw}U=D} w=m uO}mQD w OWQ xm |m} R}i Vv=O Ow@y@ "2 &=yxQB|R=Ux}@W R= =yv; "OR=OQB|t =yxv=wQB wv u}= |wQ uw}U=D} w=m V}=U w R} wv O}rwDOvO=O u=Wv w OvOQm xO=iDU= j}kLD u}= QO 6p=}U sHL |=QH= =@ x=Qty 5nQR@ ?=OQo,=D@Uv ?w=vD ?@Ux@ u=} QH |=y|oS} w QO |rY= Cw=iD p}rLD Q}N= VwQ QO xm|R=Ux}@W '?U=vt |xm@W R= |Q=OQwNQ@ =@ 'xwqax@ "CU= Q}PBu=mt= |L=Q] sm&OQ=O =Q uw}U=D} w=m |xaUwD QO syt |=yQ=mwR=U uO=O u=Wv |}=v=wD nQR@ ?=OQo"CU= xv=wQB |xDiQW}B |L=Q] C=W}=tR; |=Q@ |ak=w ptmt l} |OOa |R=Ux}@Wuw}U=D} w=m 'OvQ}o|t Q=Qk u}ovU |Q=PoQ=@ \}=QW QO xm |}=} QO |=yxv=wQB QOOwHw =@ xQB lwv QO "OwW|t O}rwD uw}U=D} w=m `=wv= Qo}O R= QDOwR =yxQB lwv |@=OQouwO@ 'OwW xrtL |x@r QO |rLt Vmt Gw= Vy=m Ea=@ Ov=wD|t xm x} wv=F u=} QH"OR=Ov=|t Q}N-=D x@ =Q xrtL x@r uw}U=D} w=m 'xv=wQB Qw=DWo w CU=QD u=R}t uOQm QF-=Dt"CU= �|}x}q uw}U=D} w=m� [23]R} wv |rY= `@vt w uw}U=D} w=m wv u} QDG}=Q 'u; R= Oa@

"s}=xDN=OQB |}x}q uw}U=D} w=m |UQQ@ x@ Q[=L j}kLD QO|xQiL w Q=N@ R=i |=ypmW R= xO=iDU= =@ xv=wQB Q@ uw}U=D} w=m u}= R= V}B =DxQiL j}kO C}akwt =t= "CU= xDiQo Q=Qk |UQQ@ OQwt xv=wQB Kw]U |wQ xOW p}mWDxO=iDU= =@ u; CiQW}B Q=Okt w CyH w xQiL p}mWD `]kt R}v w 'u; CL=Ut w|UQQ@ Kw]U |Q@ R w |Q=m jta 'Q=Wi ?} Q[ p}@k R= syt |=yQDt=Q=B Q}}eD R=w O@=}|t xaUwD p�=Ut pL |=y|OvtR=}v 'swra CiQW}B w xaUwD =@ "CU= xOWv=Q =yQDt=Q=B w C=}�RH QFm =OL |UQQ@ 'u}= w O}=Ri=|t R}v p�=Ut |=y|oO}J}B Q@Q=Wi ?} Q[ QDt=Q=B R= xO=iDU= =@ Q[=L j}kLD 'Cra u}tyx@ "Ovm|t |QwQ[w OR=U Tmavt =Q xv=wQB Kw]U |wQ Q=Wi C=Q}}eD Ov=wD|t =Q} R CU= xOW s=Hv=CyH w `]kt Qy |wQ xOW p}mWD |xQiL CL=Ut w C}akwt w u=mt CkO =@

"OyO u=Wv =Q Qo}O |=yQDt=Q=B Q}F-=D =@ xQiL CiQW}Bu=} QH 'GRr TmwDU= � Q} w=v CqO=at VwQ R= xO=iDU= =@ Q[=L |xar=]t QO|R=Ux}@W DTMB4119 OQ=Ov=DU= |xv=wQB pwL |vw}U=D} w=m w |vw}U=D} w=mQ}ew Qw=DWo 'CU=QD |wQ}v ?}=Q[� |r=QoDv= |=yQDt=Q=B "CU= xOW |Oa@xU |OOa

�|HQ=N u=} QH p�=Ut� |�RHOvJ =}l} |=yxv=QW}B |vw}U=D} w=m w |vw}U=D} w=mQ}e=yCHQD=w w xv=QW}B =@ x=Qty w =yvD Cm =O '|Oa@xU w |Oa@ wO p} wiwQO}y p}@k R=u}@ u=} QH pL QO VwQ u}= xm O=O u=Wv QwmPt |xar=]t "CiQo Q=Qk |UQQ@ OQwtxDUUo |=[i =@ G}=Dv w OQ=O |a} QU |=Qoty ?;CH 4u=NQJ w C@=F |=yCtUkl} h=Q]= Q=O}=B=v |vw}U=D} w=m s]qDt u=} QH |UQQ@ QO "OvQ=O |tm |oDU@=w xOWQw_vtx@ [16]'|DWm CN=wvm} Q}e |xr=@vO QO xv=wQB pt=m |xR=Ov= =@ |}=} QO |xv=wQBpOt w K� ! SST |W=WDe= pOt 'GRr TmwDU= � Q} w=v CqO=at R= |R=Ux}@Wu=} QH |Q=O}=B=v |=y|oS} w w xv=wQB OQmrta w 'OW xO=iDU= sQH p=kDv= |vw}U=D} w=mCra j}kLD u}= G}=Dv "OW xO=O j}@]D |y=oW}=tR; G}=Dv =@ |vw}U=D} w=m |W=WDe=|xQB lwv l}ORv Z=@kv= 'OWQ 'uw}U=D} w=m R=e; pt=W xQiL |xaUwD uOw@ |@ w=vD

"OQm x�=Q= Vv=Qo QF= w xr=@vO 'CN=wvm} Q}e |OwQw u=} QH =Q xv=wQB|xm@W =@ |R=iOvJ RwmU} w u=} QH |x} Q_v T=U=Q@ w Qo}O |}xar=]t QO|tHL QUm w CaQU 'Q=Wi u}tND Qw_vtx@ u}kkLt 'xOvRer |Ov@xm@W w O} Q@}yTmwDU= � Q} w=v CqO=at R= 'CN=wvm} |OwQw u=} QH l} |xr=@vO =@ Q=N@ R=iO=O u=Wv xar=]t u}= R= pY=L G}=Dv [17]"OvDiQo xQy@ ?=@L l}t=v}O w Q=O}=B=vu; |xr=@vO uwQO Q=Wi u=Uwv O}rwD QO pt=a u} QDsyt lwv |@=OQo uw}U=D} w=m xmuwQO |xv=wQB Q=Wi R= pY=L CiW w xQB Tv=mQi MQv p}@k R= |D=YNWt w 'CU=V}=Ri= =@ xm OW xO=O u=Wv u}vJty "CU= Q@=Q@ pOt |UOvy |=yQDt=Q=B =@ xr=@vOw O@=}|t Vy=m xQB Tv=mQi l}ORv |Q=Wi |=yp=vo}U 'xv=wQB lU}O R= xrY=i

"OwW|t QD`} QU uw}U=D} w=m OOa w |wQW}B ?} Q[ Vy=m =@ h}a[D OvwQ|vw}U=D} w=m u=} QH GRr TmwDU= � Q} w=v Q=O}=B=v CqO=at VwQ R= xO=iDU= =@w k� " pOt R= |W=WDe= CqO=at |=Q@ w [13]'|UQQ@ Q=Ow}mU= |xv=wQB h=Q]=|xar=]t "OW xO=iDU= [18] ZGB |xOWKqY= pOt R= R}v Q=N@ R=i sQH p=kDv= |=Q@|xr=@vO QO xv=wQB |Q=m |=y|Q=O}=B=v OQmrta w uw}U=D} w=m |wQ w}mU= |x} w=R QF=xr�Ut u}= |=Q@ ZGB |xOWKqY= uw}U=D} w=m pOt xm O=O u=Wv CN=wvm} Q}eu}= |=Q@ ?=NDv= u} QDy@ xHQO 20 |w}mU= |x} w=R w xO=O s=Hv= |QDy@ |R=Ux}@Wu} QDsm xm CU= xOW XNWt xOvQ@ wrH |wQ}v =@ xOW |L=Q] |xvW=B |xr=@vO

"OQ=O R}v =Q wQ}v C=v=Uwv|}=} QO |xv=wQB l} h=Q]= QO Q=O}=B=v |vw}U=D} w=m |W=WDe= u=} QH R= u}kkLtxO=iDU= xOW l} QLD Q=Wi C=v=Uwv u}tND |=Q@ CN=wvm} Q}e |xr=@vO QO swUQtTmwDU= � Q} w=v CqO=at T=U=Q@ =Q |vw}U=D} w=m |xv=wQB |R=Ux}@W w [19]xOQm|Ov@xm@W R= xO=iDU= =@ w �K� ! SST pOt� sQH p=kDv= |vw}U=D} w=m pOt =@Q}}eD |wor= w Q=Wi C=v=Uwv u}@ \=@DQ= Qou=Wv xrY=L G}=Dv "OvO=O s=Hv= xOvRer|W=v ?=DW u=v; |xDiox@ "Ow@ xr=@vO O=} R CaQU s} SQ x@ =yxQB OwQw QO uw}U=D} w=mxv=wQB uw}U=D} w=m |xr}Uwx@ |m} QLD Q=Wi C=v=Uwv |rY= `@vt 'xQiL sHL Q}}eD R=|=yu=} QH |x@U=Lt |=Q@ x}=B Q=Wi |vt[ sD} Qwor= l} \U@ |] QO "CU=G=QNDU= sQH |=k@ uwv=k |=Q@ Q=Wi K}LYD |xrO=at l} [20]'|R=iwO |vw}U=D} w=mQ=Qk xO=iDU= OQwt u=} QH sm =L CqO=at pL |=Q@ CaQU � Q=Wi Ovw}B VwQ wu}= |@=} RQ= |=Q@ QB wU w |�RH uw}U=D} w=m u=} QH wO Qy 'Ov}=Qi u}= QO "CiQo|xDiox@ "OW |R=Ux}@W |vw}U=D} w=m |=yu=} QH Q=O}=B=v C=}YwYN j}kLD w VwQ|t=tD |=Q@ h=Y xe=tO |}xv=wDU= <=}W= |wQ |wk |DWoQ@ |=yCH u}kkLt|=yu=} QH |=Q@ xm OvO=O u=Wv =yv; "OQ=O OwHw |vw}U=D} w=m |=yu=} QH |R=Ux}@W|rY= Cra w OvwW|t Qy=_ ?w=vDt Qw]x@ |DWoQ@ |=yCH '|�RH |vw}U=D} w=m|DWoQ@ |=yCH 'uw}U=D} w=mQB wU |=yu=} QH |=Q@ &OvDUy uw}U=D} w=m V}=OH

"OvQ=O p@=kDt QF= <|W |xr=@vO |=yu=} QH =@ ,=U=U=

120

OvtOQN

O}aUw|

@w}==[Q

OtL=

[31]"k� " |W=WDe= pOt |=yC@=F "1 pwOHQ=Okt C@=F1 44 C1"1 93 C2"0 09 C�1 0 �k1 3 �"

|@ QHD C=aq]= |Q}oQ=mx@ =@ CqO=at u}= "OwW|t xO=iDU= Q[=L VwQ QO =yR=iCQ=@a |vw}U=D} w=m u=} QH |oDUw}B |xrO=at "OvwW|t xDU@ |@}mQD |=yx]@=Q QO

%R= CU=@�m@t

+r:(�m�!vm) = 0 (5)

|=Q@ sDvtwt |xrO=at "CU= \wrNt pOt QO Q}eDt u; x@ \w@ QtmT}Ov= u; QO xmCUO x@ R=i Qy |=Q@ sDvtwt |xv=o =OH CqO=at `tH =@ |vw}U=D} w=m u=} QH pL

%CWwv u}vJ u=wD|t =Q u; |xrO=at u}=Q@=v@ "O};|t@(�m�!vm)

@t+�!vm:r�m�!vm = �rp+ �mr2�!vm + F

+r:(nXk=1

�k�k��!vdr;k��!vdr;k) (6)

CaQU "CU= k R=i |tHL QUm �k w p=mU=B ?ULQ@ Q=Wi Qou=Wv p u; QO xm?}DQDx@ k R=i Vv=Q CaQU w \wrNt CHRr '\wrNt |r=oJ '|tQH \UwDt

%OvwW|t h} QaD 10 =D 7 |=yx]@=Q T=U=Q@

�!vm =

nPk=1

�k�k�!vk�m

(7)

�m =nXk=1

�k�k (8)

�m =nXk=1

�k�k (9)

�!v dr;k = �!vk ��!vm (10)

=@ Q=N@ w `}=t R=i wO u}@ sQH p=kDv= "CU= k R=i CaQU �!vk '10 |x]@=Q QO%OwW|t h} QaD [24]p=ynv}U |O=yvW}B uw}U=D} w=m pt=m pOt |xrO=at

@(�mf)@t

+r:(�m�!vvf) = r:( rf) +Re �Rc (11)

|x[w=at ?} Q[ w 'Q=N@ R=i CaQU Q=OQ@ �!vv 'Q=N@ R=i |tHL QUm f u; QO xmp=ynv}U VwQ w 7CUrB � |r}=Q |xDi=}Vy=m |xrO=at |Q}oQ_v QO =@ "CU= QF-wt13 w 12 |=yx]@=Q =@ Rc w Re |=yQDt=Q=B 'xvwtv ?=@L Q]k uOw@ xv}W}@ Q@ |v@t

%OvwW|t h} QaD Vr=oJ w Q=N@ O}rwD MQv |=yu=wva =@ ?}DQDx@

Re = cepkt

�s�l�v

s2(pv � p)

3�l (1� fv � fg); p i pv (12)

Rc = ccpkt

�s�l�l

s2(p� pv)

3�l fv; p h pv (13)

|y=oW}=tR; |=yxO=O =@ w G=QNDU= |R=Ux}@W u}= �Q=Wi?} Q[� |�RH w �OQmrta|OOa |R=Ux}@W "Ot; CUO x@ |@ wN ,=D@Uv j@=]D xm xOW |HvUQ=@Da= [14]OwHwtuw}U=D} w=m OOa QO [24]p=ynv}U pt=m uw}U=D} w=m pOt R= xO=iDU= =@ uw}U=D} w=m[15]u=U G}=Dv =@ Q=Wi ?} Q[ QDt=Q=B R= xO=iDU= =@ w 's=Hv= xv=wQB u}= pwL 1 02\@DQt |=yQDt=Q=B u}vJty "Ow@ VN@C}=[Q =yxU}=kt pY=L xm OW |HvUQ=@Da=syt QDt=Q=B xU C=QF= |UQQ@ j}kLD u}= QO "OW G=QNDU= uw}U=D} w=m |xO}OB =@w[wt QO �� xv=wQB Kw]U |Q@ R w xv=wQB |Q=m jta '|wQW}B ?} Q[ pt=W ��

Q=Wi ?} Q[ |=yptar=Tma uOQm ^=Lr w x]kv x@ x]kv |UQQ@ =@ uw}U=D} w=m|=y|}=Hx@=H w xQiL RmQt C}akwt 'sHL p}@k R= xQiL C=YNWt "CiQo s=Hv=OQwt x]w@ Qt |=yQ=Owtv =@ Cw=iDt \}=QW QO |UQQ@ CLD |=yQDt=Q=B R= QF-=Dt u;[25]uw}U=D} w=m w[wt QO |O=yvW}B |x]@=Q 'xwqax@ "CiQoQ=Qk xU}=kt w EL@

"OW Q=QkQ@

sm =L CqO=at "2<=k@ CqO=at R= '|D=@U=Lt Cq=}U l}t=v}O VwQ =@ p=}U u=} QH |R=Ux}@W |=Q@"OwW|t xO=iDU= [27] k � " |W=WDe= CqO=at R}v w [26]TmwDU= � Q} w=v 'sQH

%R= CU= CQ=@a |oDUw}B |xrO=at =} sQH <=k@ |xrO=at@�@t

+r:(��!v ) = 0 (1)

CaQU Q=OQ@ �!v w ?amt QDt Q@ sQowr}m OL=w =@ |r=oJ hQat � x]@=Q u}= QOCqO=at x@ hwQat |UQv}= `HQt x=oDUO QO CmQL <=k@ "CU= x}v=F Q@ QDt ?ULQ@

%CU= [26]TmwDU= � Q} w=v@(��!v )@t

+�!v :r��!v = �rp+ �r2 + F (2)

|=ywQ}v F w 'x}v=F Q@ `@ Qt QDt ?ULQ@ |m}t=v}O CHRr hQat � u; QO xmOQ=Ov=DU= pOt R= j}kLD u}= QO C=W=WDe= QF= |R=Ux}@W |=Q@ "CU= |HQ=NQO |}xrO=atwO |OQ@ Q=m pOt l} u=wvax@ pOt u}= "CU= xOW xO=iDU= [27] k� "|W@vH |SQv= [30�28w13]"CU= xDW=O u=w=Qi OQ@ Q=m u}kkLt Q}N= |=y|R=Ux}@W

%O};|t CUO x@ 4 w 3 |=yx]@=Q R= u; hqD= MQv w |W=WDe=@(�kt)@t

+r:(�kt) = r:[(�lam + �vt�k

)rkt] + �vtG� �" (3)

@(�")@t

+r:(�"�!v ) = r:[(�lam + �vt�"

)r"] + C1"�vtG"kt

� C2"�"2

kt(4)

MQv G 'pDv=QB � h=Qowtr)m CQ=@a vt '|W=WDe= |W@vH |SQv= kt '=yx]@=Q u}= QOQO pOt u}= |=yC@=F Q=Okt "CU= |W@vH |SQv= hqD= MQv " w 'V=WDe= O}rwD

"CU= xOt; 1 pwOHVwQ R= xv=wQB pwL |vw}U=D} w=m u=} QH |R=Ux}@W |=Q@ Q[=L j}kLD QO|xr}Uwx@ `}=t w Q=N@ |=yR=i 'VwQ u}= QO "OwW|t xO=iDU= |Qr} w= � |Qr} w=sHL xm =Hv; R= "OvwW|t |R=UpOt xDUw}B |Pwiv syQO CQwYx@ |[=} Q CqO=at|iQat |tHL QUm |m} R}i swyit 'OwW p=eW= =yR=i Qo}O =@ Ov=wD|tv R=i l}`tH xm OvwW|t ZQi u=mt w u=tR R= |}xDUw}B `@=wD |tHL |=yQUm "OwW|ts=tD |=Q@ x@=Wt Q=DN=U =@ |DqO=at xawtHt R= 'u}=Q@=v@ "CU= OL=w =@ Q@=Q@ =yv;

121

"""u=}QH

|OOa

|R=Ux}

@WQOQF

-wt|=yQD

t=Q=Bj}k

LD[36]"DTMB4119 xv=wQB |UOvy C=YNWt "2 pwOHQDt=Q=B Q=Okt xv=wQB QDt=Q=B0 3048 �QDt� Q]k

3 xQB O=OaD0 l} Q0 w}mU= |x} w=R

NACA 0066 a = 0 8 xQB `]kt

[36]"DTMB4119 |xv=wQB R= |}=tv "1 pmW

xm CU= |Q@ R `@=D f� "CU= 0 4187 Q=Okt =@ utQ=muw C@=F Q@=Q@ kv u; QO xm|Q@ R `@=D x]@=Q u}= "CU= |Q@ R C=QF= R= |W=v |Q}oyQ Q}}eD C}tm |xOvvmu}}aDxU CLD |=y|Q@ R `=iDQ= OQw;Q@ =@ Q=w}O l}ORv \UwDt CaQU |x@U=Lt QO =QQ=Po s} SQ "2 'k+ � 0 25 |m}t=v}OwQO}y h=Y s} SQ "1 %OyO|t Q}F-=D s} SQ

"k+ � 90 Q@ R ,qt=m s} SQ "3 '2 25 � k+ � 9022 |x]@=Q T=U=Q@ |Q@ R Oa@|@ QDt=Q=B R= 'u=} QH s} SQ wv X}NWD |=Q@

%OwW|t xO=iDU=k+ = �ksu�=� (22)

%O};|t CUO x@ 23 |x]@=Q =@ R}v u� "CU= |Q@ R |m} R}i `=iDQ= ks u; QO xmu� = c0 25

� kv0 5 (23)

"CU= xOW xOQw; u; Q=Okt 1 pwOH QO xm CU= C@=F OOa c�[36] DTMB4119 OQ=Ov=DU= pOt R= 'xv=wQB |xUOvy |=Q@ j}kLD u}= QOQO u}vJty "CU= xOW x�=Q= 2 pwOH QO xv=wQB u}= C=YNWt "CU= xOW xO=iDU=

"CU= xOW C@F xv=wQB l}D=tW |=tv 1 pmW

G}=Dv p}rLD "3|OOa VwQ |HvUQ=@Da= "1"3|vw}U=D} w=m Q}e u=} QH pL "1"1"3

\}=QW =@ DTMB4119 |xv=wQB 'xO=iDU= OQwt |OOa VwQ |HvUQ=@Da= Qw_vtx@"CU= xOW |R=Ux}@W Q_v OQwt `HQt �|v=QwO CaQU w |wQW}B ?} Q[� V}=tR;Q=Wi "OW xO=iDU= [14]AwU *H G}=Dv R= '|R=Ux}@W u}= G}=Dv |HvUQ=@Da= |=Q@

?} Q[ �s "OvDUy 0 01 w 0 02 |=yQ=Okt =@ |@ QHD |=yC@=F ?}DQDx@ cc w ceQ=N@ w `}=t R=i |r=oJ x@ \w@ Qt ?}DQDx@ �v w �l 'Q=N@ Q=Wi pv '|L]U VWm

"CU=SIMPLE VwQ R= "CU= xOW xDUUo [32]OwOLt sHLVwQ =@ sm =LCqO=atRmQt QO Qr=mU= Q=Okt l} |xDUUo Q}O=kt "OW xO=iDU= Q=Wi � CaQU pB wm |=Q@C=Q=@a |=Q@ Qr=mU= Q=Okt l} |}xLiY Q}O=kt xm |v=tR "OwW|t xQ}NP pwrUj}kLD u}= QO "OvwW|t |@=}uwQ@ =ypwrU Rm =Qt R= 'OW=@ R=}v CqO=at QO |}=Hx@=HswO x@DQt CkO |Dkw "CU= xOW xO=iDU= 8CUOq=@ OwOLt hqDN= VwQ R=|]N |R=Uwv VwQ R= xO=iDU= =@ =ypwrU |xLiY QO =Q =yC}tm 'OW=@ ?wr]t=ypwrU |xLiY QO |QDq=@ x@DQtCkO 'VwQ u}= QO "Ovvm|t x@U=Lt [33]|Oa@OvJR= "O};|t CUO x@ pwrU RmQt pwL =ypwrU |RmQt pL |=Q@ Qwr}D |QU \U@ =@pOt w sDvtwt '|oDUw}B |xrO=at |=Q@ swO |x@DQt CUOq=@ OwOLt hqDN= VwQhqDN= VwQ R= R}v �Q=N@ R=i� sQH p=kDv= |xrO=at |=Q@ w OW xO=iDU= |W=WDe=CQwYx@ '|}=Hx@=H C=Q=@a u}vJty "OW xDiQo xQy@ pw= |x@DQt CUOq=@ OwOLt|=yu=} QH QO Q=Wi QDt=Q=B |=Q@ "Ov=xOW xDUUo swO x@DQt CkO =@ |RmQt hqDN=swO |x@DQt VwQ w OQ=Ov=DU= VwQ R= ?}DQDx@ |vw}U=D} w=m w |vw}U=D} w=m Q}e

"CU= xOW xO=iDU=R= Q[=L j}kLD QO [34]'xv=wQB |OQmrta |=yQDt=Q=B |xOQDUo h}] u=}t R=?} Q[ w Qw=DWo ?} Q[ 'xOvQ@ wrH |wQ}v ?} Q[ '|wQW}B ?} Q[ |=yQDt=Q=B17-14 |=yx]@=Q T=U=Q@ ?}DQDx@ =Q =yQDt=Q=B u}= "CU= xOW xO=iDU= |yOR=@

%Ovvm|t h} QaDJ = va

ND(14)

kt = Tth�N 2D4 (15)

kq = Q�N 2D5 (16)

� = ktkq

J2� (17)

Tth 'xv=wQB Q]k D '|v=QwO CaQU N '|wQW}B CaQU va '=yx]@=Q u}= QO|xv=wQB Q=Wi ?} Q[ |x@U=Lt |=Q@ "CU= xv=wQB Qw=DWo Q w 'CU=QD |wQ}v

%OwW|t xO=iDU= `]kt Qy |=Q@ 18 |x]@=Q R= DTMB4119cp = pabs � p0

12�v2

a(1 + (�RrJ )2)(18)

xQB QO `=aW C@Uv Rr w '|Q=m w jr]t |=yQ=Wi ?}DQDx@ p0 w pabs u; QO xmQO uw}U=D} w=m wQW X}NWD |x]@=Q w uw}U=D} w=m OOa |i} QaD |x]@=Q "CU=

%R= Ov=CQ=@a ?}DQDx@ [34]|OOa C=k}kLD� = p0 � pv

12�2D2 (19)

�vi = �Cp (20)

xv=wQB Kw]U |m}ORv QO u=} QH |R=Ux}@W "CU= uw}U=D} w=m R=e; OOa �vi QDt=Q=B|UQQ@ |=Q@ j}kLD u}= QO "OQ}o|t s=Hv= [35]Q=w}O |O=yvW}B `@=wD R= xO=iDU= =@QF= uO}O |=Q@ "OwW|t xO=iDU= Q=w}O |xOWKqY= uwv=k R= xv=wQB K]U |Q@ R QF=

%OwW|t xi=[= |tD} Q=or uwv=k x@ 21 `@=D '|Q@ R�B = 1

kvln f (21)

122

OvtOQN

O}aUw|

@w}==[Q

OtL=

0 833 |wQW}B ?} Q[ |=Q@ `=aW 0 3 `]kt |=Q@ Q=Wi ?} Q[ `} RwD "2 pmW"O=R; uwtR; \}=QW QO

0 833 |wQW}B ?} Q[ |=Q@ `=aW 0 7 `]kt |=Q@ Q=Wi ?} Q[ `} RwD "3 pmW"O=R; uwtR; \}=QW QO

p@=kt QO |R=Ux}@W 7 |yOR=@ w Qw=DWo 'CU=QD ?}=Q[ G}=Dv |xU}=kt "4 pmW[14]"|y=oW}=tR; |=yxO=O

QDt Q@ sQowr}m 998 2 Q@=Q@ Xr=N ?; |r=oJ 'p=mU=B 101325 Q@=Q@ QiUtD="OW xDiQo Q_v QO 0 833 pO=at |wQW}B ?} Q[ w '?amt

xOW xO=iDU= Q=DN=U|@ |Ov@xm@W 1818604 O=OaD R= |R=Ux}@W u}= QOxQB `=aW 0 7 w 0 3 `]kt R= 'Q=Wi ?} Q[ |=yxO=O G=QNDU= |=Q@ "CU=QO "OW xU}=kt [14]AwU *H V}=tR; |=yxO=O =@ xrY=L G}=Dv TBU w OW xO=iDU=0 3 `]kt |=Q@ |y=oW}=tR; G}=Dv =@ Q[=L j}kLD |xU}=kt 3 w 2 |=ypmW|=yxO=O Q[=L |OOa pL '0 3 `]kt QO "CU= xOW xO=O u=Wv `=aW 0 7 wxv=wQB ?=yx@ l}ORv 0 3 `]kt "CU= xOR u}tND 0 7 `]kt x@ C@Uv =Q |QDnQR@&CU= QDOwyWt �� =yp}=iwQB QDOvr@ Ct=N[ Crax@ �� |RQt |x}q C=QF= w CU=Q=Wi u}tND 'OQ=O x}L=v u}= QO |tyt Vkv xm |[Qa u=} QH ?@U x@ u}vJtyQO 'Q[=L VwQ R= xO=iDU= =@ "CU= xOt; CUO x@ |@ QHD Q=Okt R= QDW}@ |}x]kvVwQ u}= R= xm |v}kkLt Qo}O C=k}kLD QO xm xOW O=H}= |mJwm VQ@ x@r |=yDv=|i=m |xR=Ov=x@ �RANS� Q[=L VwQ "OwW|t xOy=Wt R}v [37]Ov=xOQm xO=iDU=Q=Qi |x@r x@ l}ORv |x}L=v Q=Wi `} RwD |wQ |}=Hx@=H |RQt |x}q Ct=N[ QF=|[Qa u=} QH |=yCaQU VwQ u}= "CU= xO=Ov u=Wv |ak=w u=} QH x@ l}ORv =Qu}= "OvR|t u}tND =Q �nQR@ |vwQ}@ |a=aW CaQU |=yxir-wt |va}� |vwQ}@ |wkxm OW=@ xQB Q=Qi |x@r QO |RQt |x}q |v=yo =v Ct=N[ R= |W=v Ov=wD|t C=QF=u}= "Ovm|t |SQv=sm |x}L=v u}= R= ?=vDH= w VtN x@ Qw@Ht =Q xO}@UJ u=} QH

"OwW|t O}}-=D xQB |wQ l =m]Y= ?} Q[ Q=DiQ =@ xO}OB?} Q[ w Qw=DWo ?} Q[ 'CU=QD ?} Q[ p@}k R= xv=wQB syt ?}=Q[ 'C}=yv QO=D 0 5 R= |wQW}B ?} Q[ |xQDUo QO |R=Ux}@W 7 s=Hv= =@ xv=wQB u}= |=Q@ |yOR=@"�4 pmW� OW xU}=kt [14]AwU *H |y=oW}=tR; G}=Dv =@ 'O=R; uwtR; \}=QW QO 1 1x@ Q]k x@ s=o C@Uv V}=Ri= =@ |yOR=@ |vLvt |xrk 'OwW|t xOy=Wt xm u=vJ'Q]k x@ s=o C@Uv V}=Ri= =@ u}vJty "O@=}|t p=kDv= |wQW}B ?} Q[ QDnQR@ Q=Okt|x]kv j}kLD OQwt |xv=wQB QO "Ovm|t OwaY QDW}@ Q=Okt x@ |yOR=@ |vLvt |xrk

"CU= 0 833 |wQW}B ?} Q[ |L=Q]?U=vDt Cw=iDt |=y|wQW}BCaQU� Cw=iDt |x}rw= |=yxO=O =@ |R=Ux}@W Qy=@ xOW |] OvwQ Ck@=]t Qou=Wv =yxO=O u}= "CU= xOW xO=O �|wQW}B ?} Q[ =@|=y|wQW}B ?} Q[ pO=at xm nQR@ |=yxrtL x} w=R QO "CU= [14]AwU *H G}=Dv|@ QHD |=yxO=O x@ l}ORv Q=}U@ |OOa G}=Dv 'CU= u}ovU |Q=PoQ=@ =} QDlJwm

"CU=|vw}U=D} w=m u=} QH pL "2"1"3

QO "CU= CU=QD Vy=m 'uw}U=D} w=m CLD |=yxv=wQB QO |rY= p�=Ut R= |m}<=kDQ= Q]k x@ s=o C@Uv V}=Ri= =@ uw}U=D} w=m R=e; OOa 'C@=F |wQW}B ?} Q['|rm Qw]x@ "CU= xOW ?=NDv= 1 02 uw}U=D} w=m OOa j}kLD u}= |=Q@ &O@=}|tQ@ |}x}q uw}U=D} w=m "CU= uw}U=D} w=m OOa w |Q=PoQ=@ R= |a@=D xQiL l} Q=DiQx@ uw}U=D} w=m OOa Vy=m =@ w OwW|t wQW xQB lwv R= =yxQB CWB w wrH |xLiY|=DU=Q QO =Q xQiL pw] �RANS� Q[=L VwQ "OwQ|tV}B QDsm |=y`=aWCtUR= xm OW=@ |Q=wv uw}U=D} w=m Crax@ Ov=wD|t xm [38]"OvR|t u}tND QDW}@ |a=aWQ=}U@ |OOa VwQ QO |}x}q uw}U=D} w=m R= u; X}NWD w OwW|t wQW xrtL |x@r|vw}U=D} w=m \}=QW QO |R=Ux}@W u}= CLY |HvUQ=@Da= |=Q@ [34]"CU= CNUxU QO |R=Ux}@W u}= QO xrY=L Q=Wi ?} Q[ w xOW xO=iDU= [15]u}W}B G}=Dv R==Q |@ wN Ck@=]t xO}OB u}= |UQQ@ G}=Dv "CU= xOW xU}=kt G}=Dv u; =@ xQB `]ktuwtR; \}=QW |=Q@ '|R=iwO |=yu=} QH \wrNt pOt R= xO=iDU= =@ "OyO|t u=Wvs=Hv= |R=Ux}@W u}= 0 833 |wQW}B ?} Q[ QO w 1 02 uw}U=D} w=m OOa 'O=R;

123

"""u=}QH

|OOa

|R=Ux}

@WQOQF

-wt|=yQD

t=Q=Bj}k

LD

0 833 |wQW}B?} Q[ |=Q@ '`=aW 0 747 `]kt QO Q=Wi?} Q[ `} RwD "7 pmW"1 02 uw}U=D}w=m OOa w

0 833 |wQW}B ?} Q[ |=Q@ '`=aW 0 88 `]kt QO Q=Wi ?} Q[ `} RwD "8 pmW"1 02 uw}U=D}w=m OOa w

"1 02 uw}U=D}w=m OOa 0 833 |wQW}B ?} Q[ |=Q@ Q=N@ sHL Q=Owtv "9 pmW

xv=wQB CWB C=LiY |wQ Q=N@ R=i p}mWD |Oa@xU Q} wYD 5 pmW QO "CU= xOW"CU= xOW xO=O u=Wv

Vmt K]U =} xv=wQB CWB |xLiY |wQ Q=Wi ?} Q[ 8 =D 6 |=ypmW QO'0 613 |=y`]kt |=Q@ ?}DQDx@ 'OQ}o|t pmW |}x}q uw}U=D} w=m QDW}@ u; QO xm"Ov=xQiL p}mWD |]}Lt |=yRQt ,=OwOL xm xOW xO=O u=Wv `=aW 0 88 w 0 7476 pmW QO "CU= xOW l}ORv 1 02 OOa x@ Q=Wi ?} Q[ |ivt '=yQ=Owtv u}= QO?} Q[ u} QDsm Q=Okt '`]kt u}= QO "CU= xOW xO=O u=Wv `=aW 0 747 `]ktxOW p}mWD xQiL 'xrtL |x@r |m}ORv QO u}=Q@=v@ "OUQ|t uw}U=D} w=m OOa x@ Q=Wi'|R=Ux}@W uw}U=D} w=m OOa =@ Q@=Q@ O=Oa= Q=Okt QO Q=Owtv u}= R= xO=iDU= =@ "CU=`=aW 0 88 `]kt QO |HvUQ=@Da= |=Q@ "O=O X}NWD u=wD|t =Q xQiL |=yRQtQO `=aW 0 88 `]kt |=Q@ Q=Wi ?} Q[ 'xQiL uDiQ u}@ R= x@ l}ORv u}vJty wpw] 'xQiL |v=}=B RQt 'OwW|t xOy=Wt xm u=vJ "CU= xOW xO=O u=Wv 8 pmWw '�j}kLD u}= |=Q@ xOW xO=O uw}U=D} w=m OOa =@ Q=Wi ?} Q[ Q=Okt |Q@=Q@� xQiL

"CU= XNWt Q=Owtv u}= QO xrtL |x@r x@ l}ORv u=mtQ=Qi |x@r ?}DQDx@ 1 =D QiY R= |ki= QwLt �Q=N@ R=i sHL Q=Owtv� 9 pmW QOu} QDW}@ uDW=O Crax@ 'Q=Owtv u}= x@ xHwD =@ "CU= xOW xO=O u=Wv xrtL |x@r =D"O=OX}NWD `=aW 0 747 `]kt QO u=wD|t =Q xQiL RmQt ,=OwOL 'Q=N@ sHL Q=Oktw 0 613 `]kt QO 'CU= |}x]kv Q=Wi uw}U=D} w=m wkw w wQW Q=}at xm =Hv; R=0 866 pLt QO �xQiL Q]k u} QDW}@� |tHL *QUm Q=Okt u} QDW}@ '`=aW 0 747u} QDW}@ R}v `=aW 0 880 `]kt QO &CU= 0 389 w 0 313 =@ Q@=Q@ ?}DQD x@ w 'QDw

"CU= 0 234 =@ Q@=Q@ w QDw 0 703 pLt QO Q=N@ R=i |tHL *QUm Q=Okt

"xv=wQB CWB C=LiY |wQ Q=N@ R=i |tHL QUm "5 pmW

0 833 |wQW}B?} Q[ |=Q@ '`=aW 0 613 `]kt QO Q=Wi?} Q[ `} RwD "6 pmW"1 02 uw}U=D} w=m OOa w

124

OvtOQN

O}aUw|

@w}==[Q

OtL=

OOa w 0 747 `]kt |=Q@ |vw}U=D}w=m u=} QH QO Q=Wi ?} Q[ `} RwD "10 pmW"1 02 uw}U=D} w=m

u=} QH |R=Ux}@W xU |yOR=@ w Qw=DWo 'CU=QD ?}=Q[ G}=Dv |xU}=kt "11 pmW"|vw}U=D}w=m u=} QH p@=kt QO |vw}U=D} w=m Q}e

"0 747 `]kt |=Q@ |vw}U=D}w=m u=} QH QO Q=Wi ?} Q[ `} RwD "12 pmW

uw}U=D}w=m QO QF-wt |=yQDt=Q=B |xar=]t "2"3|wQW}B ?} Q[ QF= |xar=]t "1"2"3

|R=Ux}@W xU 'u}ovU |Q=PoQ=@ \}=QW |=Q@ |wQW}B ?} Q[ QF= |xar=]t Qw_vtx@x@ ,=@} QkD xm Qw]u=ty |Q=PoQ=@ V}=Ri= |xt=O= xm CU= K[=w "CU= xOW s=Hv=j}kLD |=Q@ "OyO|t V}=Ri= R}v =Q lwv |x@=OQo CQOk OwW|t O=} R xQB lwv CtU|v=QwO CaQU sy OQwt u}= QO "s}vm|t O=} R =Q |wQW}B CaQU '|wQW}B ?} Q[ QF=9 76 '8 365 j}kLD u}= |=Q@ |wQW}BCaQU "CU= xOW xDiQo Q_v QOC@=F xv=wQB"CU= 0 833 w 0 7 '0 6 |=y|wQW}B ?} Q[ |=Q@ ?}DQDx@ x}v=F Q@ QDt 11 61 w'�QDsm |wQW}B ?} Q[� QDW}@ |=y|Q=PoQ=@ QO xm xOW xO=O u=Wv 10 pmW QO?} Q[ |vLvt CmQL Q}U |Q}oQ_v QO =@ "O@=}|t V}=Ri= uw}U=D} w=m CLD |x}L=vxDio `]kt QO =Q xQiL |xaUwD |L=wv u=wD|t '1 02 OOa x@ uO}UQ QO Q=WiQDl}ORv xrtL |x@r x@ xQiL |=yRQt 0 747 `]kt QO 'u}=Q@=v@ "OQm xOy=Wt xOW

"OwW|t'xH}DvQO w |wQW}B ?} Q[ V}=Ri= QO CaQU V}=Ri= QF= |m} R}i u}}@D |=Q@CaQU uDW=O xov C@=F pO=at =Q u; u=wD|t '=yxQB |wQ uw}U=D} w=m COW Vy=m?} Q[ 'Cr=L u}= QO "CiQo Q_v QO xv=wQB CiW |v=QwO CaQU V}=Ri= w |OwQwCaQU V}=Ri= =@ "O@=}|t V}=Ri= uw}U=D} w=m xH}DvQO w O@=}|t Vy=m |wQW}BQ=Wi xH}DvQO w O@=}|t V}=Ri= R}v =yxQB K]U |wQ |rLt CaQU 'CiW |v=QwOuw}U=D} w=m V}=Ri= |=Q@ \}=QW uOW Oa=Ut |xv=Wv u}= &O@=}|t Vy=m |}x]kvQ=Wi Vy=m '|rLt CaQU V}=Ri= x@ QHvt |v=QwO CaQU V}=Ri= 'xH}DvQO "CU=

"OwW|t uw}U=D} w=m |xO}OB V}=Ri= ,=D}=yv ww |vw}U=D} w=m Q}e u=} QH wO QO xv=wQB u}= |OQmrta ?}=Q[ 11 pmW QOuw}U=D} w=m uDW=O =@ 'OwW|t xOy=Wt xm u=vJ "CU= xOW xO=O u=Wv |vw}U=D} w=mxm u=vJ "CU= xDi=} Vy=m |yOR=@ ?} Q[ xH}DvQO w xDi=} Vy=m |OQmQ=m ?}=Q[xDi=} Vy=m u=} QH wO u}= u}@ hqDN= |wQW}B ?} Q[ V}=Ri= =@ OwW|t xOy=Wt?wN sy |vw}U=D} w=m u=} QH QO |L=Q] |wQW}B ?} Q[ xm OyO|t u=Wv w CU=Vy=m QDsmuw}U=D} w=m 'QDnQR@ |=y|wQW}B ?} Q[ CtU x@ R}v w CU= xO=O ?=wH|wQW}B ?} Q[ R= uw}U=D} w=m O}OWD Qou=Wv xOW xO=O u=Wv |L=wv "CU= xDi=}w lJwm |xrtL |x} w=R QO '=R=Q@ p} wi l} |=Q@ '|rm Qw]x@ "CU= u}}=B x@ 0 7=Q} R 'OwW|tv =Q@ Vy=m Ea=@ xW}ty uw}U=D} w=m |xO}OB 'pO=aDt uw}U=D} w=m OOal}ORv =Q@ Vy=m u=} QH CUOu}}=B CtU x@ 'Q=Wism s} SQ |va} xQiL VQDUo?}=Q[ x@ QHvt ?re= QDlJwm |=yxQiL pw] 'u}=Q@=v@ "Ovm|t u=Q@H =Q xrtL |x@r

"OwW|t QDlJwm |=Q@jta QF= |xar=]t "2"2"3

'xQiL C=YNWt w =yxQB |}x}q uw}U=D} w=m |wQ xv=wQB |Q=m jta QF= |UQQ@ |=Q@Q=Wi ?} Q[ 12 pmW QO "OW s=Hv= Cw=iDt |=y`=iDQ= QO |R=Ux}@W Q=yJ`]kt QO QDw ?ULQ@ Q=Wi ?} Q[ "CU= xOW xO=O u=Wv `=iDQ= Q=yJ u}= |=Q@QO "CU= xOW x�=Q= QDt 1 5 w 1 0 '0 5 'QiY ?; `=iDQ= Q=yJ |=Q@ 0 747|R=Ux}@W u}= "CU= xOWv xDiQo Q_v QO |R=Ux}@W u}= |=Q@ |a=iDQ= 'Q=Owtv u}rw=|U=}kt Ov=wD|t =Hv}= QO xm CU= xv=wQB l} |=Q@ ?; O=R; uwtR; \}=QW u=ty`=iDQ= V}=Ri= =@ OwW|t xOy=Wt 12 pmW QO xm u=vJ "OW=@ Qo}O |=yjta |=Q@QO QiY ?; `=iDQ= |=Q@ xm |Qw]x@ 'OwW|t sm xQiL pw] 'xv=wQB |q=@ QO ?;?; `=iDQ= |=Q@ 'QDw 0 85 pLt QO QDt 0 5 ?; `=iDQ= |=Q@ 'QDw 0 1037 pLt?} Q[ QDw 0 74 pLt QO QDt 1 5 ?; `=iDQ= |=Q@ w 'QDw 0 78 pLt QO QDt 1

125

"""u=}QH

|OOa

|R=Ux}

@WQOQF

-wt|=yQD

t=Q=Bj}k

LD

'|vw}U=D} w=m u=} QH QO xv=wQB |xQBCWB QO `=aW0 7 `]kt QO Q=N@ sHL "14 pmW"1 02 uw}U=D}w=m OOa w 0 833 |wQW}B ?} Q[

CWoR=@� h=Y pOt x@ C@Uv |QDW}@ pw] C pOt xm |DQwY QO "CU= �QiY|vLvt CWoR=@� OQ=O B w A |=ypOt w �OwW|t wQW QDw 0 89 pLt R= |vLvt`=iDQ= QF=Q@ Q=Wi ?} Q[ C=Q}}eD u}= "�OwW|t wQW QDw 0 9 pLt R= Q=Wi ?} Q[[39]u}kkLt xm u=vJ 'Ovm O=yvW}B |Q@ R uDW=O |=Q@ |}xv}y@ Cr=L Ov=wD|t |Q@ Rl} uDW=O u}=Q@=v@ "OvOQm O=yvW}B uW C=QP |xR=Ov= =@ uw}U=D} w=m uOW QF-=Dt |wQu=wD|t QDW}@ j}kLD =@ "OyO|t Vy=m xQB |wQ =Q uw}U=D} w=m COW |Q@ R |Q=OktQF= |m} R}i u}}@D QO "OQm =O}B |}=} QO |=yxv=wQB OQ@ Q=m |=Q@ =Q QD?U=vt |=ypOt'CUv=O Q=Wism l}B QO Q@ R K]U |wQ =Q u; wkw u=wD|t uw}U=D} w=m |wQ |Q@ R|=yu=tr= |x]U=wx@ =Q=mW; \=kv u}= "uw}U=D} w=mlJwm \=kv |xr}Uwx@ ,=YwYNtu}= &Ovm|t Rw=HD |Q@ R |=yu=tr= |xR=Ov= R= =yv; |xR=Ov= w OwW|t O=H}= |Q@ R"CU= Q=N@ Q=Wi x@ l}ORv |RQt |x}q uwQ}@ QO Q=Wi \UwDt xm CU=vat u=O@uw}U=D} w=m O=H}= lQLt =Q |Q@ R |=yu=tr= QO |rLt V}=OH wkw u=wD|t xH}DvQO

"CUv=OpOt 'QiY |Q@ R pOt Q=yJ |=Q@ 0 7 `]kt |wQ Q=N@ R=i sHL 14 pmW QO1 =D QiY R= |ki= QwLt 'pmW u}= QO "CU= xOW xO=O u=Wv C pOt w B pOt 'ACw=iDt `]kt xU |=Q@ Q=Owtv u}= "OyO|t u=Wv =Q xrtL |x@r =D Q=Qi |x@r ?}DQDx@x@ C@Uv |Q@ R V}=Ri= =@ pmW u}= QO "CU= xOW xO=O u=Wv QDw pw] =@ xOW Oa@|@|Q@ R |OwOL=D u=wD|t xH}DvQO "s} Q=O =Q Q=N@ R=i |tHL QUm Vy=m 'h=Y pOtA |=ypOt Q=N@ |tHL *QUm "CUv=O uw}U=D} w=m Vy=m |=Q@ |O}it |QDt=Q=B =Q|vLvt u}vJty "CU= 0 37 w 0 36 |=yQ=Okt Q@=Q@ w xR=Ov= l} x@ ,=OwOL B wh=Y pOt =@ xm OQ=O =Q |v=Um} sHL B w A |=ypOt =@ QDw 0 6 OwOL =D C pOt0 44 |tHL *QUm |=Q=O w CU= Cw=iDt ,qt=m �CU= 0 48 Q@=Q@ u; |tHL *QUm �

"CU=

|Q}oxH}Dv "4VwQ =@ DTMB4119 |xv=wQB pwL |vw}U=D} w=m w |vw}U=D} w=m Q}e u=} QH wO|=Q@ "OW |R=Ux}@W [24]p=ynv}U |O=yvW}B sQH p=kDv= pOt w RANS

'CU=QD 'Q=Wi ?}=Q[ |=yQDt=Q=B R= |vw}U=D} w=m Q}e u=} QH pL |HvUQ=@Da=R= |vw}U=D} w=m u=} QH pL |HvUQ=@Da= |=Q@ u}vJty "OW xO=iDU= |yOR=@ w Qw=DWo

?} Q[ u} QDsm Q=Okt V}=Ri= u}vJty "Ovm|t CmQL QDW}@ |=yQ=Okt x@ Q=Wi|=yDv= 'CU= XNWt R}v pmW QO xm u=vJ "CU= uw}U=D} w=m Vy=m Qou=Wv Q=Wiu}= R= w OQ=O Q=Qk u; u} QDsm R= Q=Wi ?} Q[ |OOa Q=Okt u} QDW}@ QO xQiL |RQtVy=m Ea=@ xm ?; `=iDQ= V}=Ri= |m} R}i Cra "OQ=Po|t p=wR x@ wQ xQiL 'x]kvQHvt xm CUv=O l}D=DUwQO}y Q=Wi V}=Ri= u=wD|t =Q OwW|t uw}U=D} w=m COWxm OwW|t uw}U=D} w=m OOa V}=Ri= R}v w Q=N@ Q=Wi =@ u; Q=Wi hqDN= V}=Ri= x@|=Q@ "CU=yxQB |wQ ?; Q=N@ R=i |tHL *QUm w xQiL Vy=m |xOvyOu=Wv u}=?=y w lwv |@=OQo uw}U=D} w=m |=yxO}OB |wQ =Q =yQDt=Q=B QF= u=wD|t QDW}@ C=k}kLD

"OQm j}kLD|Q@ R QF= |xar=]t "3"2"3

R= xO=iDU= =@ 0 833 |wQW}B ?} Q[ QO |Q@ R QDt=Q=B C=QF= CtUk u}= QOQ=Qk |UQQ@ OQwt OW x�=Q= sm =L CqO=at CtUk QO xm |Q@ R |xOWh} QaD `@=DQ}O=kt w \UwDt CaQU '|WQ@ VvD Q}O=kt '`@=D u}= R= xO=iDU= =@ "CU= xDiQo[35]j}kLD u}= QO |O=yvW}B |=ypwtQi "OwW|t OQw;Q@ K]U |m}ORv QO |W=WDe=|Q}oR=Ov= \UwD xOWx�=Q= pOt xU "CU= xOW P=ND= xRO=Qwm}v |=yxO=O Q@ |vD@tQO "CU= xDW=O OQ@ Q=m xv=wQB Kw]U |Q@ R |R=Ux}@W QO [34]CQ*@=Q |xOvvmxU}=kt|=Q@ Q=Wi `} RwD 13 pmW QO "CU= xOW x�=Q= pOt Q=yJ u}= C=YNWt 3 pwOHxQB CWB QO C pOt w B pOt 'A pOt 'QiY |Q@ R pOt Q=yJ QO `=aW 0 7|R=Ux}@W Q=yJ |=Q@ Q=Wi ?} Q[ 13 pmW QO u}vJty "CU= xOW xO=O u=Wv=@ xQiL pw] V}=Ri= 'OwW|t xOy=Wt xm u=vJ "CU= xOW xU}=kt xQB |wQ |Q@ RQ=Okt QO Q=Wi ?} Q[ |vLvt j@=]D xm |Qw]x@ 'OQ=O x]@=Q |Q@ R `=iDQ= V}=Ri=A |=ypOt xm u}= Qo}O |xDmv "CU= Qo}O pOt xU R= QDW}@ C pOt |=Q@ 1 020 848 pLt R= Q=Wi ?} Q[ |vLvt CWoR=@� Ov=j@]vt sy Q@ |OwOL=D B wA pOt Q@=Q@ wO R= QDW}@ B pOt |Q@ R `=iDQ= xm |DQwY QO �OwW|t wQW QDw

"CU=|Q@ R `=iDQ=� h=Y pOt R= QDsm B w A |=ypOt |=Q@ xQiL pw] u}vJty

[34]"|R=Ux}@W pOt Q=yJ |=Q@ Q@ R Kw]U |=y`=iDQ= "3 pwOHC B A h=Y pOt

31 7 14 2 6 7 0 �QDtwQm}t� |Q@ R `=iDQ=

OOa w 0 7 `]kt |=Q@ |vw}U=D} w=m u=} QH QO Q=Wi ?} Q[ `} RwD "13 pmW"1 02 uw}U=D}w=m

126

OvtOQN

O}aUw|

@w}==[Q

OtL= 'QDt=Q=B u}= OQwt QO u}=Q@=v@ "O@=}|t Vy=m xQB lwv |@=OQo uw}U=D} w=m p=tDL=

u;Cra xmCU= |}x}q uw}U=D} w=m R= QDW}@ xQB lwv |@=OQo uw}U=D} w=m |Q=oOv=t"CUv=O xQB |x@r x@ u; VQDUo w lwv R= |@=OQo uw}U=D} w=m wQW x@ u=wD|t =Q'xv=wQB K]U |Q@ R Q=Okt V}=Ri= =@ %xv=wQB Kw]U |Q@ R QDt=Q=B |UQQ@ G}=Dv ��uw}U=D} w=m CL=Ut B w A |=ypOt "OQm =O}B =Q |}xv}y@ |=ypOt u=wD|tCL=Ut C pOt QO xm |DQwY QO 'OvyO|t u=Wv h=Y K]U x@ C@Uv |QDsm*QUm Q=Okt 'xv=wQB K]U |Q@ R Q=Okt V}=Ri= =@ "CU= xDi=} V}=Ri= |vw}U=D} w=mQO "OQ=Po|t V}=Ri= x@ wQ K]U uOW QDQ@ R =@ w Vy=m =OD@= QO Q=N@ R=i |tHLCLD CL=Ut xwqax@ "Ov=xDW=O |v=Um} G}=Dv B w A |=ypOt sy OQwt u}=C@=F ,=@} QkD |Q@ R pOt Qy |=Q@ w xDi=} Vy=m h=Y pOt x@ C@Uv uw}U=D} w=m|wQ Q=N@ R=i |tHL *QUm |=yQ=Okt 'xv=wQB K]U |Q@ R Q=Okt V}=Ri= =@ "Ov=t|t"O@=}|t V}=Ri= C pOt |=Q@ xQiL |xrk =t= CU= |D@=F Q=Okt 0 6 OwOL =D QDw

|@=}u=mt 'Q=Wi ?} Q[ QDt=Q=B R= xO=iDU= =@ "OW xO=iDU= `]kt xU QO Q=Wi ?} Q[|x@r |m}ORv QO xQiL |rw] |oO}Wm "OW s=Hv= u; |=yRQt |xOwOLt w xQiL|UQQ@ |=Q@ "OW xO=O u=Wv QDw 0 88 w 0 747 '0 613 |=ypLt QO xrtLC}=aQ =@ |vw}U=D} w=m u=} QH |=y|R=Ux}@W 'uw}U=D} w=m COW QO QF-wt |=yQDt=Q=B

%R= Ov=CQ=@a xrY=L G}=Dv xm OW s=Hv= xv=o =OH Qw]x@ X=N QDt=Q=B Qy QF=|x}L=v |wQW}B ?} Q[ V}=Ri= =@ %|wQW}B ?} Q[ QDt=Q=B |UQQ@ G}=Dv ��"OwW|t nQR@ �u; |=yRQt� xQiL |xOwOLt w O@=}|t V}=Ri= |vw}U=D} w=mx@ C@Uv xQiL CL=Ut G}=Dv 0 7 w 0 833 |wQW}B ?}=Q[ u}@ QO 'xwqax@V}=Ri= xQiL |=yRQt 0 6 Q=Okt =D u; Vy=m w CU= QDsm 0 6 |wQW}B ?} Q[

"CU= xDW=O |Q}osWJCL=Ut '?; jta V}=Ri= =@ %xv=wQB QwLt |q=@ ?; jta QDt=Q=B |UQQ@ G}=Dv ��w OQ}o|t xrY=i xQB |xrtL |x@r R= xQiL RmQt 'u}vJty "O@=}|t Vy=m xQiL

=yCWwv=B1. laser Doppler Velocimetry2. span3. viscous/inviscid interaction4. rotor and stator5. large eddy simulation (LES)6. volume-of- uid (VOF)7. Rayleigh-Plesset8. upwind

�References� `@=vt1. Wright, M.M., Epps, B., Dropkin, A. and Truscott, T.T.

\Cavitation of a submerged jet", Experiments in Fluids,54(6), pp. 1-21 (2013).

2. Hattori, Sh., Taruya, K., Kikuta, K. and Tomaru, H.\Cavitation erosion of silver plated coatings consider-ing thermodynamic e�ect", Wear, 300(1-2), pp. 136-143(2013).

3. Lee, H., Taenaka, Y. and Kitamura, S. \Mechanism forcavitation in the mechanical heart valve with an arti�-cial heart: Nuclei and viscosity dependence", Arti�cialOrgans, 29(1) pp. 41-47 (2005).

4. Mohammad noori, M., Riahi, M. and Valipour, A. \Us-ing perturbation method to obtain scaled numericalmodel for analyzing noise of supercavitation", ModaresMechanical Eng. Journal, 12(5), pp. 146-153 (1391).

5. Kinns, R., Thompson, I., Kessissoglou, N. and Tso, Y.\Hull vibratory forces transmitted via the uid and theshaft from a submarine propeller", Ships and O�shoreStructures, 2(2), pp. 183-189 (2007).

6. Paik, B.G., Kim, K.S., Kim, K.Y., Ahn, J.W., Kim,T.G., Kim, K.R., Jang, Y.H. and Lee, S.U. \Test method

of cavitation erosion for marine coatings with low hard-ness", Ocean Eng., 38(13), pp. 1495-1503 (2011).

7. Ye, J.M. and Xiong, Y. \Prediction of podded propellercavitation using an unsteady surface panel method", J.of Hydrodynamics, Ser. B, 20(6), pp. 790-797 (2008).

8. Kanemaru, T. and Ando, J. \Numerical analysis of cav-itating propeller and pressure uctuation on ship sternusing a simple surface panel method \SQCM"", J. ofMarine Sc. and Tech., 18(3), pp. 294-309 (2013).

9. Behbahani-nejad, M. and Changizian, M., Reduced- or-der modeling of unsteady partial cavity ows using theboundary element method", Modares Mechanical Eng.Journal, 13(6), pp. 140-152 (1392).

10. Lee, H. and Kinnas, S.A. \Application of a boundaryelement method in the prediction of unsteady bladesheet and developed tip vortex cavitation on marine pro-pellers", J. of Ship Research, 48(1), pp. 15-31 (2004).

11. Lee, H.S. and Kinnas, S.A. \A BEM for the modelingof unsteady propeller sheet cavitation inside of a cavita-tion tunnel", Computational Mechanics, 37(1), pp. 41-52(2005).

12. Young, Y.L. and Kinnas, S.A. \Analysis of supercavi-tating and surface-piercing propeller ows via BEM",Computational Mechanics, 32(4-6), pp. 269-281 (2003).

13. Liu, Y., Zhao, P.F., Wang, Q. and Chen, Z.H. \URANScomputation of cavitating ows around skewed pro-pellers", J. of Hydrodynamics, 24(3), pp. 339-347 (2012).

14. Jessup, S.D. \An experimental investigation of vis-cous aspects of propeller blade ow", PhD Thesis, TheCatholic University of America, Washington DC (1989).

15. Sun, H. \Performance prediction of cavitating propulsorsusing a viscous/inviscid interaction method", PhD The-sis, The University of Texas at Austin, Austin (2008).

16. Ji, B., Luo, X.W., Wu, Y.L., Liu, S.H., Xu, H.Y. and Os-himab, A. \Numerical investigation of unsteady cavitat-

127

"""u=}QH

|OOa

|R=Ux}

@WQOQF

-wt|=yQD

t=Q=Bj}k

LD

ing turbulent ow around a full scale marine propeller",J. of Hydrodynamics, 22(5), pp. 747-753 (2010).

17. Zhu, Z.F., Fang, S.L. and Wang, X.Y. \Characteristicanalysis of unsteady viscous ow around a cavitatingpropeller", Science China Technological Sciences, 53(7),pp. 1983-1993 (2010).

18. Zwart, P.J., Gerber, A.G. and Belamri, T. \A two-phase ow model for predicting cavitation dynamics", Inter-national Conference on Multiphase Flow, Yokohama,Japan (2004).

19. Ji, B., Luo, X., Peng, X., Wua, Y. and Xu, H. \Numeri-cal analysis of cavitation evolution and excited pressure uctuation around a propeller in non-uniform wake", In-ternational J. of Multiphase Flow, 43, pp. 13-22 (2012).

20. Zhang, L.X. and Khoo, B.C. \Computations of par-tial and super cavitating ows using implicit pressure-based algorithm (IPA)", Computers & Fluid, 73, pp. 1-10 (2013).

21. Yang, Q.F., Wang, Y.Sh. and Zhang, Z.H. \Scale e�ectson propeller cavitating hydrodynamic and hydroacousticperformances with non-uniform in ow", Chinese J. ofMech. Eng., 26(2), pp. 414-427 (2013).

22. Lu, N.X., Bensow, R.E. and Bark, G. \Large eddy sim-ulation of cavitation development on highly skewed pro-pellers", Journal of Marine Science and Technology,19(2), pp. 197-214 (2014).

23. Lee, K., Lee, J., Kim, D., Kim, K. and Seong, W. \Pro-peller sheet cavitation noise source modeling and inver-sion", Journal of Sound and Vibration, 333(5), pp. 1356-1368 (2014).

24. Singhal, A.K., Athavale, M.M., Li, H. and Jiang, Y.\Mathematical basis and validation of the full cavita-tion model", ASME J. Fluids Eng., 124(3), pp. 617-62(2002).

25. Franc, L.P. and Michel, J.M., Fundamentals of Cavita-tion, Kluwer Acadamic Publishers, New York (2005).

26. Batchelor, G.K., An Introduction to Fluid Dynamics,Cambridge Univ. Press, Cambridge, England (1967).

27. Launder, B.E. and Spalding, D.B., Lectures in Mathe-matical Models of Turbulence, Academic Press, London,England (1972).

28. Kim, S., Choi, Ch., Kim, J., Park, J. and Baek, J.\Tip clearance e�ects on cavitation evolution and headbreakdown in turbopump induce", J. of Propulsion andPower, 29(6), pp. 1357-1366 (2013).

29. Kellett, P., Turan, O. and Incecik, A. \A study of nu-merical ship underwater noise prediction", Ocean Eng.,66, pp. 113-120 (2013).

30. Yue, Ch., Guo, Sh. and Shi, L. \Hydrodynamic analysisof the spherical underwater robot SUR-II", InternationalJ. of Advanced Robotic Sys, 10, pp. 1-12 (2013).

31. Launder, B.E. and Spalding, D.B. \The numerical com-putation of turbulent ows", Computer Methods in Ap-plied Mechanics and Eng., 3, pp. 269-290 (1974).

32. Coutier-Delgosha, O., Deniset, F., Astol�, J.A. and Ler-oux, J.B. \Numerical prediction of cavitating ow on atwo-dimensional symmetrical hydrofoil and comparisonto experiments", ASME J. Fluids Eng., 129(3), pp. 279-292 (2007).

33. Barth, T.J. and Jespersen, D. \The design and applica-tion of upwind schemes on unstructured meshes", AIAA27th Aerospace Sciences Meeting, Reno, Nevada (1989).

34. Carlton, J., Marine Propeller and Propulsion, 2nd e.,Elsevier Ltd, USA (2007).

35. Cebeci, T. and Bradshaw, P., Momentum Transfer inBoundary Layers, Hemisphere Publishing Corporation,Washington D.C. (1977).

36. Ghassemi, H. \A study on hydrodynamic analysis of pro-pellers and cavitation prediction of hydrofoils by the ap-plication of surface panel method", PhD Thesis, Yoko-hama National University, Yokohama, Japan (1997).

37. Villa, D., Gaggero, S. and Brizzolara, S. \RANS andPANEL method for unsteady ow propeller analysis",9th International Conference on Hydrodynamics, Shang-hai, China (2010).

38. Bertetta, D., Brizzolara, S., Canepa, E., Gaggero, S.and Viviani, M. \EFD and CFD characterization of aCLT propeller", International J. of Rotating Machinery,2012, pp. 1-22 (2012).

39. Wu, J.H. and Gou, W.J. \Critical size e�ect of sandparticles on cavitation damage", J. of Hydrodynamics,Ser. B, 25(1), pp. 165-167 (2013).

128