eksperymentalna i numeryczna analiza niestabilności - PTES-ISES
Transkrypt
eksperymentalna i numeryczna analiza niestabilności - PTES-ISES
EKSPERYMENTALNA I NUMERYCZNA ANALIZA NIESTABILNOŚCI TERMICZNYCH POCHYLONEGO MODELU WYMIENNIKA CIEPŁA 5\dc]d^YP ./5+4ę9 <=;.<C,C.72. *[]bT^ũMX]bLcbKJMJĢYXM\]J`X`bLQJWJURcbWRN\]JKRUWXĵLRY[cNYũb`ß`]N[VRLcWbLQ`VXMNU^`bVRNWWRTJLRNYũJ9[JLJKJc^SNWJ`bWR TJLQKJMJĢNT\YN[bVNW]JUWbLQX[Jc\bV^UJLSRW^VN[bLcWbLQ[NJURcX`JWbLQ`Y[X\]XYJMũXĵLRNWWbVTJWJUNY[cNYũb`X`bVK¢MLbVVX MNUNVYXLQbUXWNPX`bVRNWWRTJLRNYũJCJ\]X\X`JWRNXY]bLcWbLQVN]XMYXVRJ[^YßUY[¢MTXĵLRR]NVYN[J]^[bYXc`XURũX`bXM[¢KWRî][cb YXM\]J`X`N[NŖRVbTXW`NTLSR`O^WTLSRT]JWJLQbUNWRJTJWJũ^`cJT[N\RNSNPXcVRJWXM" 9[cNY[X`JMcXWN\bV^UJLSNW^VN[bLcWNYX]`RN[McRũb]NXK\N[`JLSN8YRN[JSL\R¢WJ[Nc^U]J]JLQ\bV^UJLSRW^VN[bLcWbLQ`bcWJLcXWX`Yũb` T]JYXLQbUNWRJTJWJũ^WJURLcK¢7^\\NU]J7^XYR\^SLNONT]b`WXĵî`bVRJWbLRNYũJKJMJWNPXTJWJũ^<]`RN[McXWXŖNURLcK¢7^VXŖWJ c`R¢T\cbîT[X]WRNcVRNWRJSLT]WJLQbUNWRJTJWJũ^`cJT[N\RNcVRJWXM"JVJT\bVJUWb\][^VRNĢLRNYũJYXSJ`RJ\R¢MUJT]J YXLQbUNWRJϕ & @<=¡9 @ YJ\b`WbLQ `bVRNWWRTJLQ LRNYũJ YXM\]J`X`bV VN LQJWRcVNV][JW\YX[]^LRNYũJSN\]TXW`NTLSJWJ]^[JUWJ0ũß` WbVR YJ[JVN][JVR McR¢TR T]ß[bV VXŖWJ \]N[X`Jî NONT]b` WXĵLR `bVRJWb LRNYũJ SN\] YX`RN[cLQWRJ `bVRJWb R `J[]Xĵî \][^VRNWRJLRNYũJY[cNYũb`JSLNPXY[cNc`bVRNWWRT@`RNU^ Y[cbYJMTJLQ Y[cNVb\ũX`bLQ `bVRNWWRTß` LRNYũJ VXŖWJ Kb cJ\]X\X`JîTXUNSWbYJ[JVN][RLQXY]bVJURcJLSRJVRJWX`RLRN T] YXLQbUNWRJ YX`RN[cLQWR `bVRJWb 9[cbTũJMNV YXLQbUX WbLQ`bVRNWWRTß`LRNYũJ\TXUNT]X[b\ũXWNLcWN@UR]N[J]^ [cNVXŖNVbcWJUNŔîTRUTJY[JLMX]bLcLbLQ]NS]NVJ]bTRD1XU UJWM\" $;JR]QKb""!F CVRJWJT]JYXLQbUNWRJYX`RN[cLQWR`bVRJWbYX`XM^SN cVRJW¢ \][^T]^[b Y[cNYũb`^ YũbW^ [XKXLcNPX cWJSM^SLNPX \R¢ `N`W][c `bVRNWWRTJ 2\]WRNSN YX][cNKJ MXTũJMWRNS\cNPX cKJMJWRJ ]bLQ \][^T]^[ R RLQ `Yũb`^ WJ \][^VRNĢ LRNYũJ YX VR¢McbĵLRJWTJVRYXLQbUXWNPXVXMNU^`bVRNWWRTJLRNYũJ *WJURcX`JWb NT\YN[bVNW]JUWRN R W^VN[bLcWRN VXMNU `bVRNWWRTJ LRNYũJ SN\] Y[X\]XYJMũXĵLRNWWbV TJWJũNV Y[cN Yũb`X`bV -X XYR\^ YJ[JVN][ß` Y[cNYũb`X`bLQ cJ\]X\X `JWXURLcK¢;JbUNRPQnJ;J`cVXMb²TX`JWNS OX[VRN ;JcV ^`cPU¢MWRJSL \]X\^WNT `bVRJ[ß` `b\XTXĵLR MX Mũ^PXĵLR 15RcVRJW¢T]JYXLQbUNWRJTJWJũ^Y[cNYũb`X`NPX`cJ T[N\RNϕ "5RLcKb;JR;JcV`bcWJLcXWXcWJ\]¢Y^S LbLQcJUNŖWXĵLR# PMcRN#∆=ocJMJWJ[ßŖWRLJ]NVYN[J]^[bYXVR¢McbĵLRJW TJVR TJWJũ^ PY[cb\YRN\cNWRN cRNV\TRN β`\YßũLcbWWRT [Xc\cN[cJUWXĵLR LRNYUWNS 1`b\XTXĵî TJWJũ^ υ o `\Yßũ LcbWWRT UNYTXĵLR TRWNVJ]bLcWNS J o MbO^cbSWXĵî ]N[VRLcWJ 5oMũ^PXĵîTJWJũ^ϕ T]YXLQbUNWRJTJWJũ^ 9XWRŖNSWJ[b\cJY[NcNW]X`JWJSN\]cVRJWJURLcKb;JcV XMT]JWJLQbUNWRJϕ `bcWJLcXWJWJYXM\]J`RNYJ[JVN][ß` XYR\JWbLQ ` YXMY^WTLRN h.4<9.;B6.7=m CVXMb²TX`JWJ URLcKJ;JcV`b[JŔWRNVJUNSNRMUJϕ &MXϕ &"cVWRNS \cJ\R¢XM`J[c¢Mb`RNUTXĵLR`cJT[N\RNXMMX 6XŖWJ\R¢`R¢L\YXMcRN`JîŖN]JTM^ŖJcVRJWJ;JcVXMT]J WJLQbUNWRJϕ K¢McRNVRJũJ]JTŖNM^Ŗb`Yũb`WJcVRJW¢YJ [JVN][ß`LRNYUWbLQKJMJWNPXY[cNcWJ\YXLQbUXWNPXVXMNU^ `bVRNWWRTJLRNYũJ ;b\CJUNŖWXĵîcVXMb²TX`JWNS URLcKb ;JbUNRPQnJ ;JcVXMT]JWJLQbUNWRJϕ I I 4[cb\c]XO-.4*3Ũ8 2W\]b]^]9XM\]J`X`bLQ9[XKUNVß`=NLQWRTR9XU\TJ*TJMNVRJ 7J^T@J[\cJ`J ZYV]UK OXO\QO^cUK ]ĚYXOMdXK 9[cNY[X`JMcXWJ JWJURcJ \][^T]^[ Y[cNYũb`^ ` KJMJWbV VXMNU^`bVRNWWRTJLRNYũJ`bTX[cb\]^SNWX`XLcN\WN]NLQWRTR YXVRJ[ß`YXc`JUJSLNWJ`bcWJLcNWRN`Y[cNYũb`RNLJũXĵLRX `bLQYßUY[¢MTXĵLRR]NVYN[J]^[b+JMJWRJNT\YN[bVNW]JUWN `\YJ[]X\bV^UJLSJVRW^VN[bLcWbVRMcRNULMXVNW¢XKURLcN WRX` WJ ! ]b\R¢Lb XKS¢]XĵLR TXW][XUWbLQ MUJ [Xc`RcJWRJ ^TũJM^[ß`WJĢVNLQJWRTRYũbWß`RNWN[PRR UaSOMSOĜvMdO\aSOM ŵųųż .4<9.;B6.7= +JMJWRJNT\YN[bVNW]JUWNYXLQbUXWNPXVXMNU^`bVRNW WRTJ LRNYũJ Y[cNY[X`JMcXWX `Y[X\]XYJMũXĵLRNWWbV TJWJUN Y[cNYũb`X`bV`bTXWJWbVc9UNaRPUJ\^YX[[b\4JWJũ VRJũ`b\XTXĵî1&!VMũ^PXĵî5&VX[JcPũ¢ KXTXĵî-&!V9X\RJMJũM`RNY[cNLR`UNPũNRcX]N[VRLcWN ĵLRJWTRPß[WRMXUW`bTXWJWNcVRNMcRX[JcLc]N[bKXLcWN ĵLRJWTRJMRJKJ]bLcWN`bTXWJWNc9UNaRPUJ\^XP[^KXĵLRVV -cR¢TR M`ßV ]N[VX\]J]XV ]NVYN[J]^[b ĵLRJWNT RcX]N[VRLc WbLQ Kbũb ^][cbVb`JWN WJ \]JũbV YXcRXVRN MXUWJ LRNYũJ ĵLRJWTJ=&4RPß[WJcRVWJĵLRJWTJ=&""4;ßŖ WRLJ ]NVYN[J]^[b YXVR¢Mcb MXUW J Pß[W ĵLRJWT `bWX\RũJ ∆=&4`bV^\cJũJY[cNYũb`TXW`NTLbSWb`N`W][cTJWJ ũ^Y[cNYũb`X`NPX ;b\<LQNVJ]XPßUWbYXLQbUXWNPXVXMNU^`VRNWWRTJLRNYũJ 6NLQJWRcV VXL^SLb TJWJũ Y[cNYũb`X`b YXc`JUJũ WJ YũbWW[NP^UJLS¢T]JWJLQbUNWRJϕ `cJT[N\RNXMMX" ;b\^WNTcWJSM^SLb\R¢YXWRŖNSY[cNM\]J`RJOX]XP[J²¢ \]J WX`R\TJYXVRJ[X`NPXYXMLcJ\Y[JLb o4XVY^]N[9,cTJ[]JT`RcbLbSW !o4XUX[X`JTJVN[J[NSN\][^SLJXK[Jcb "o6NLQJWRcV^VXŖUR`RJSLbYũbWWcVRJW¢T]JYXLQbUNWRJ TJVN[b o9XcRXVJ\^`WRLJTJVN[b o<]ßũUJKX[J]X[bSWb 9XM\]XũNVUJKX[J]X[bSWbVcWJSM^S\R¢WRN`RMXLcWNWJ OX]XP[J²R M`J \]JKRURcJ]X[b ]N[VRLcWN ]N[VX\]J]b ²[Vb 3^UJKX /\]JKRURc^SLN]NVYN[J]^[¢M`ßLQRcX]N[VRLcWbLQĵLRJWNT TJWJũ^YXVRJ[X`NPX=NVYN[J]^[¢`XMbT[ŖLNS`^TũJMcRN YXVR¢Mcb ]N[VX\]J]NV J TXVX[JVR Y[cbUNPJSLbVR MX RcX ]N[VRLcWbLQĵLRJWNTTJWJũ^YXVRJ[X`NPXTXW][XUX`JũbM`J Lc^SWRTRXYX[X`N9] @TJWJUNYXVRJ[X`bVcWJSMX`JũJ\R¢XMPJcX`JWJ`XMJ MN\]bUX`JWJcMXMJ]TRNVcWJLcWRTß``YX\]JLRtVTJY\^ ũNTVJ]N[RJũ^LRNTũXT[b\]JURLcWNPX=5,JWP=QN[VXLQ[XVRL 5RZ^RM,[b\]JU\4XUX[X`JTJVN[J[NSN\][X`JũJXK[JcbcWJLc WRTß``ĵ[XMTX`NSYũJ\cLcbŔWRNTJWJũ^YXVRJ[X`NPXXĵ`RN ]UXWNS QJUXPNWX` UJVY hWXŖNV ĵ`RN]UWbVm YX[[b\ @bTXWJWX \N[R¢ NT\YN[bVNW]ß` ` cJT[N\RN cVRJW ϕ XM "cVRNWRJSLT]WJLQbUNWRJTJWJũ^YXVRJ[X`NPXLX 9XM\]J`X` VN]XM YXVRJ[X` KbũJ ]NLQWRTJ JWNVX VN][RRXK[JcX`NS92?JWP9J[]RLUN2VJPN?NUXLRVN][b@]NS VN]XMcRN TJVN[J [NSN\][^SN \NT`NWLSN XK[Jcß` ]bLQ cWJLc WRTß` ` ^\]JUXWbLQ XM\]¢YJLQ LcJ\X`bLQ 4X[NUJLSJ ]bLQ XK[Jcß` YXc`JUJ WJ `bcWJLcNWRN M`^`bVRJ[X`NPX YXUJ Y[¢MTXĵLR -X`bcWJLcNWRJ YXUJ ]NVYN[J]^[b cJ\]X\X`JWX VN]XM¢]N[VXVN][RRXK[JcX`NS92=JWP9J[]RLUN2VJPN=QN[ VXVN][b YXUNPJSLNS WJ JWJURcRN cVRJW KJ[`b cWJLcWRTß` LRNTũXT[b\]JURLcWbLQ=5,cWJSM^SLbLQ\R¢`KJMJWbVY[cNYũb `RN<cLcNPßũX`bXYR\]bLQVN]XMYXVRJ[X`bLQcWJSM^SN\R¢ `Y[JLbD4X`JUN`\TR=* F ;b\ /X]XP[J²J \]JWX`R\TJ YXVRJ[X`NPX$ `RMXT c Y[cXM^ YXLQbUXWNPX TJWJũ^RUJVYbXĵ`RN]UNWRX`NS ;b\ <LQNVJ] \]JWX`R\TJ YXVRJ[X`NPX RU^\][^SLb ]NLQWRT¢ JT`RcbLSR XK[Jcß` c `bTX[cb\]JWRNV hWXŖJ ĵ`RN]UWNPXm `b]`J[cJWNPX Y[cNc UJVY¢ 9XM\]J`X`bVRNUNVNW]JVR\]JWX`R\TJYXVRJ[X`NPX\# o1JUXPNWX`JUJVYJXĵ`RN]UNWRX`JXVXLbT@`b]`J [cJSLYũJ\cLcbcW¢ĵ`RN]UWMXJWJURcbYßUY[¢MTXĵLR]NV YN[J]^[bVN]XMJVR92?R92= o9RXWX`J\^`WRLJ\]N[X`JWJ\RUWRTRNVT[XTX`bV o9[cN`XMbMXY[X`JMcJSLN`XM¢c]N[VX\]J]ß`MXRcX]N[ VRLcWbLQĵLRJWNTTJWJũ^YXVRJ[X`NPX o@RNUXTJWJũX`b[NSN\][J]X[]NVYN[J]^[b9=69[NVJ MXT]ß[NPXYXMũLcXWX"]N[VXYJ[YXVRJ[X`bLQ o4JWJũYXVRJ[X`b o6NLQJWRcV^VXŖUR`RJSLbYũbWWcVRJW¢T]JWJLQbUNWRJ TJWJũ^YXVRJ[X`NPX UaSOMSOĜvMdO\aSOM ŵųųż QJUXPNWX`RTXUX[X`TJVN[¢ >c^YNũWRNWRNV XY]bLcWNS VN]XMb YXVRJ[^ YXUJ ]NV YN[J]^[b 92= Kbũ \b\]NV Y^WT]X`NPX YXVRJ[^ ]NVYN[J]^[b @]bVLNU^`TJWJUNYXVRJ[X`bV^VRN\cLcXWX"]N[VXYJ[ YXMũLcXWbLQ MX `RNUXTJWJũX`NPX [NSN\][J]X[J 9=6 9[NVJ<LQNVJ][XcVRN\cLcNWRJ]N[VXYJ[YXMJWXWJ[b\^W T^YXWRŖNS ZYV]UK OXO\QO^cUK ]ĚYXOMdXK ;b\;XcVRN\cLcNWRN]N[VXYJ[WJĵLRJWTJLQTJWJũ^YXVRJ[X`NPX =N[VXYJ[bXcWJLcXWN\bVKXUJVR#==== =!=" \]N[VXYJ[JVR\ũ^ŖLbVRMXTXW][XUR`J[^WTß`NT\YN[bVNW ]^>VRN\cLcXWNKbũb`MXUWNSX[JcPß[WNSĵLRJWLNTJWJũ^YX VRJ[X`NPX -cR¢TR XMLcb]XV c ]bLQ ]N[VXYJ[ VXŖUR`J KbũJ MXTũJMWJTX[NT]J`J[]XĵLR]NVYN[J]^[b^\]J`RJWNSWJ]N[VX \]J]JLQXMYX`RNMcRJUWbLQcJ^][cbVb`JWRNŖMJWbLQ]NVYN [J]^[WJĵLRJWTJLQTJWJũ^YXVRJ[X`NPX =N[VXYJ[bXcWJLcXWN\bVKXUJVR#===\]N[VXYJ[J VR YXVRJ[X`bVR >VRN\cLcXWN Kbũb WJ KXLcWNS ]bUWNS ĵLRJWLN TJWJũ^YXVRJ[X`NPX8MLcb]bc]bLQ]N[VXYJ[YX\ũ^ŖbũbMXMJU \cNS JWJURcb NT\YN[bVNW]ß` `bTXWb`JWbLQ MUJ [ßŖWbLQ T]ß` YXLQbUNWRJϕ YXLQbUXWNPXVXMNU^`bVRNWWRTJLRNYũJ 98-C2*Ũ7*;.ŕ26B *WJURcJ cVRJW \][^T]^[ Y[cNYũb`^ cJ[NSN\][X`JWbLQ `O^WTLSRT]JWJLQbUNWRJϕ TJWJũ^ YXVRJ[X`NPX YXc`XURũJ WJ`bXM[¢KWRNWRN][cNLQLQJ[JT]N[b\]bLcWbLQ[NŖRVß`XYR\J WbLQYXWRŖNS ;;J+Jo[NŖRV\][^T]^[]bY^;JbUNRPQnJo+NWJ[MJϕ & ;NŖRV \][^T]^[ ]bY^ ;JbUNRPQnJ o +NWJ[MJ cX\]Jũ `bXM [¢KWRXWb MUJ Y[cNYũb`ß` c cJT[N\^ cVRJW T]J WJLQbUNWRJ TJWJũ^ ϕ & *WJURc¢ [XcYXLcbWJVb XM ϕ & 3N\]]X\cLcNPßUWbY[cbYJMNTY[cNYũb`^Lc¢\]XWJcb`JWbSN\] TXVß[TJVR TXW`NTLbSWbVR ;JbUNRPQnJ o +NWJ[MJ \]M ]NŖ `cR¢ũJ\R¢WJc`J]NPX[NŖRV^4XVß[TR]N\SNMWbVcYXM\]J `X`bLQ\YX\XKß`X[PJWRcJLSRTXW`NTLSR`J]VX\ON[cN 7J[b\JDWJ`TũJMLNTXUX[X`NSFcJY[NcNW]X`JWXLQ`R UX`N YXUN ]NVYN[J]^[b WJ T]ß[bV `RMXLcWN \ VRNS\LJ YX `\]J`JWRJLRNYũbLQ]N[VRTß`TXUX[WRNKRN\TRT]ß[NXM[b`JS \R¢XMLRNYũNSMXUWNSĵLRJWTRTJWJũ^YXVRJ[X`NPXR^WX\c\R¢ MXPß[b7JPß[WNSĵLRJWLN\b]^JLSJSN\]XM`[X]WJcRVWN]N[ VRTRTXUX[LcN[`XWb\Yũb`JS`cMũ^ŖKXLcWbLQĵLRJWNTTJWJ ũ^9X`\]J`JWRNX[JccJWRTJWRN]N[VRTß`SN\]KJ[McX\cbKTRN >TũJM]NWLQJ[JT]N[bc^SN\R¢\RUWTXW`NTLSYX`\]JSNKUR\TJ \bVN][bLcWNS`R[X`J\][^T]^[JY[cNYũb`^9[cNYũb`SN\]\RUWRN cVRNWWb`LcJ\RNTRN[^WNTY[cNYũb`^`YX`\]JũbLQTXVß[ TJLQSN\]Y[cNVRNWWb 9X`\]J`JWRN TXW`NTLbSWbLQ TXVß[NT ]bY^ ;JbUNRPQnJ o+NWJ[MJVXŖNVb]JTŖNcJXK\N[`X`JîMUJT]ß`ϕ & Rϕ& 7RN`RNUTRN S^Ŗ YXLQbUNWRN TJWJũ^ YXVRJ[X`NPX `bV^\cJ WJ Y[cNYũb`RN [^LQ ` TRN[^WT^ ]NPX YXLQbUNWRJ 7RNcJ^`JŖJ\R¢S^Ŗ\bVN][bLcWNS\][^T]^[bM`^TXVß[TX`NS JSNMbWRN\][^T]^[¢WRN\bVN][bLcW9X`\]JSLNLRNYũNRcRVWN ]N[VRTRYX[^\cJS\R¢`TRN[^WT^YXLQbUNWRJĵLRJWNTTJWJũ^ ;b\^WNT DWJ `TũJMLN TXUX[X`NSF Y[NcNW]^SN `bWRTR X][cbVJWNMUJTXW²P^[JLSR ϕ &7J[b\^WT^]bVY[cNM \]J`RXWX YXUN ]NVYN[J]^[b `RMXLcWN ` KJ[`JLQ LRNTũbLQ T[b\c]Jũß`=5,R\][^T]^[¢Y[cNYũb`^9X`\]JSLNLRNYũN]N[VRTR ZYV]UK OXO\QO^cUK ]ĚYXOMdXK Y[cNVRN\cLcJSL\R¢`cMũ^ŖĵLRJWTRTJWJũ^YXVRJ[X`NPXc`R¢T \cJScJSVX`JWXKS¢]XĵîJŖMXVXVNW]^`T]ß[bVWJ\]YRRLQ \`XKXMWNXMN[`JWRNX[JcY[cNVRN\cLcNWRN\R¢T^Pß[cN 0ũß`WbVNLQJWRcVY[cNYũb`^MUJ]NSTXW²P^[JLSR Y[NcNW]^ SN[b\ K@RMcRVbWJWRVWRN\bVN][bLcW\][^T]^[¢M`^TXVß[ TX` 6WRNS\cJ TXVß[TJ cWJSM^SN \R¢ ` LRNYUNS\cNS Pß[WNS Lc¢ ĵLRTJWJũ^`RMXLcWJ`XK[JcRNLRNTũXT[b\]JURLcWbVSJTXXK\cJ[ XTXUX[cNWRNKRN\TRV@R¢T\cJTXVß[TJ`XK\cJ[cN]NVYN[J]^[ WRŖ\cbLQcWJSM^SN\R¢`MXUWbVXK\cJ[cNTJWJũ^RSN\]^`RMXLc WRXWJ Y[cNc LRNTũN T[b\c]Jũb TXUX[NV LcN[`XWbV YX[ [b\ J 9[cb ĵLRJWTJLQ cRVWNS R LRNYũNS `b\]¢Y^S ]N[VRTR T]ß[N Y[cb ĵLRJWLNPß[WNSXYJMJS`MßũMXY[J`NSMXUWNSY[cN\][cNWRTJWJ ũ^YXVRJ[X`NPXJY[cbĵLRJWLNMXUWNS^WX\c\R¢MXPß[b 9[cNYũb` ` [NŖRVRN ;;J+J SN\] WRN\]JLSXWJ[Wb ` LJũbV TJWJUN,NLQ^SNPXM^ŖJRW]NW\b`WXĵîVRN\cJWRJTXW`NTLbS WNPX @bVRJWJ LRNYũJ XKb`J \R¢ WJ M[XMcN \RUWNS TXW`NTLSR TXVß[TX`NS ;8<o[NŖRV\][^T]^[X\LbUJLbSWbLQϕ & ;NŖRV X\LbUJLbSWb ;8< cX\]Jũ `bXM[¢KWRXWb MUJ Y[cN Yũb`ß`ccJT[N\^cVRJWT]JWJLQbUNWRJTJWJũ^ϕ& 9XM\]J`X` [ßŖWRL YXVR¢Mcb \][^T]^[JVR c [NŖRV^ ; ;J+JR;8<SN\]`b\]¢YX`JWRN]bUTXSNMWNSY¢]URLb[T^UJLbS WNS`N`W][cTJWJũ^YXVRJ[X`NPX@VRJ[¢c`R¢T\cJWRJT]J WJLQbUNWRJ ϕ MUJ ]NPX [NŖRV^ Y¢]UJ Lb[T^UJLbSWJ cVWRNS\cJ WJ ]bUN \`XS Y[¢MTXĵî ŖN `RMXLcWJ SN\] SNS \][^T]^[J KUR\TJ \]JLSXWJ[WNS ,QJ[JT]N[b\]bLcWN WJ]XVRJ\] SN\] RW]NW\b`WN YX`\]J`JWRNLRNYũbLQRcRVWbLQ]N[VRTß`T]ß[N[X\WLY[cN VRN\cLcJS \R¢ `cMũ^Ŗ RcX]N[VRLcWbLQ ĵLRJWNT TJWJũ^ YXVRJ [X`NPXLRNYũN]N[VRTRYXMŖJSMXPß[bcRVWNcJĵ\Yũb`JS `MßũTJWJũ^,c¢ĵîcWRLQcMŖbWJ]bUN^[X\WîJKbXMN[`Jî \R¢RY[cNVRNĵLRîT^Pß[cNLc¢ĵîcWRLQ`YJMWRN`XK\cJ[cRV WRNS\cNPXU^KLRNYUNS\cNPXXK\cJ[^RYXY[X\]^`bPJĵWRN 9X`\]J`JWRNX[JccJWRTJWRNLRNYũbLQRcRVWbLQ]N[VRTß`SN\] Pũß`WbVVNLQJWRcVNVY[cNYũb`^MUJ]NPX[NŖRV^9XSJ`RJS \R¢McR¢TR]NV^X\LbUJLSNcVRJWYXUJY[¢MTXĵLRR]NVYN[J]^[bRWJ ]NSYXM\]J`RN[NŖRV]NWcX\]JũWJc`JWb[NŖRVNV\][^T]^[X\LbUJ LbSWbLQ;8<8\LbUJLSXV]X`J[cb\cb\][J]b²TJLSJ ]NVYN[J]^[b c`R¢T\cJSLJ \R¢ `[Jc cN `c[X\]NV T]J WJLQbUNWRJ ϕ TJWJũ^ YXVRJ[X`NPX @bVRJWJ LRNYũJ MUJ ]NPX [NŖRV^ XKb`J \R¢ WJ M[XMcN\ũJKWLNSTXW`NTLSRR[X\WLNV^Y[cN`XMcNWR^cJUNŖWN V^XM`c[X\]^T]JWJLQbUNWRJϕ TJWJũ^YXVRJ[X`NPX ;<=o[NŖRV\][^T]^[\]JLSXWJ[WbLQϕ & " ;NŖRV \][^T]^[ \]JLSXWJ[WbLQ ;<= cX\]Jũ `bXM[¢KWRXWb MUJY[cNYũb`ß`ccJT[N\^T]ß`WJLQbUNWRJϕ & " 9[cNYũb` ` ]bV [NŖRVRN LQJ[JT]N[bc^SN \R¢ ]bV ŖN WRN YX\RJMJ \][^T]^[ `R[X`bLQ Y[cNVRN\cLcJSLbLQ \R¢ `N`W][c TJWJũ^YXVRJ[X`NPX]JTSJT]XVRJũXVRNS\LNMUJYXY[cNMWRLQ [NŖRVß` ;;J+J R ;8< 7RN \ `RMXLcWN ]JTŖN VRNS\LJ YX `\]J`JWRJLRNYũbLQRcRVWbLQ]N[VRTß`9[¢MTXĵîY[cNYũb`^ ` LNW][JUWNS Lc¢ĵLR TJWJũ^ cJWRTJ WRNVJU MX cN[J 9XUN ]NV YN[J]^[b YX[ [b\ "J DWJ `TũJMLN TXUX[X`NSF `bPUMJ KJ[ McXLQJ[JT]N[b\]bLcWRNSN\]]X^`J[\]`RXWJWRNVRN\cJSLJ\R¢ \][^T]^[JCJ^`JŖJ\R¢M^ŖYRXWX`\][J]b²TJLS¢ ]NVYN[J]^ [b]JTRNPXY[cNYũb`^,Jũb[^LQTXW`NTLbSWbSN\]XP[JWRLcX WbMXLRNWTRNS`J[\]`bY[cbĵLRNWWNS@bVRJWJLRNYũJMUJ]NPX [NŖRV^XKb`J\R¢WJM[XMcN\RUWNPXY[cN`XMcNWRJ 9XWRŖNSWJ[b\^WT^DWJ`TũJMLNTXUX[X`NSFcJY[NcNW UaSOMSOĜvMdO\aSOM ŵųųż ]X`JWN \ cVRJWb ĵ[NMWRLQ [ßŖWRLN ]NVYN[J]^[ cVRN[cXWbLQ ]N[VXYJ[JVR = = R = ^VRN\cLcXWbVR `N`W][c TJWJũ^ YXVRJ[X`NPXCJWJURcb`bT[N\^`bWRTJŖNWJSVWRNS\cN[ßŖ WRLN]NVYN[J]^[b\MUJTXW²P^[JLSR ϕ&JWJS`R¢T\cNMUJ ϕ &"-UJ[NŖRV^;;J+J`J[]XĵLR∆==R∆==\ WJSVWRNS\cNRcVRNWRJS\R¢`cJT[N\RNĴ`RJMLcb]X XRW]NW\b`WNSTXW`NTLSRYũbW^`N`W][cTJWJũ^YXVRJ[X`N PX-UJ[NŖRV^;8<`J[]XĵLR∆==R∆==c`R¢T\cJS \R¢cM^ŖbVY[cbKURŖNWRNVURWRX`X`[JccN`c[X\]NVT]Jϕ Ĵ`RJMLcb ]X X [X\WLNS \][J]b²TJLSR ]NVYN[J]^[b KJMJWNPX YũbW^-UJ[NŖRV^;<=MUJϕ ' \][J]b²TJLSJ ]NVYN[J]^ [bSN\]WJS`R¢T\cJ@VRJ[¢`c[X\]^T]JWJLQbUNWRJϕ TJWJũ^ YXVRJ[X`NPX`J[]XĵLR∆==X[Jc∆==[X\WXM`J[ ]XĵLRRYXSJ`RJ\R¢NONT]Y[cNSĵLRJLQJ[JT]N[^Y[cN Yũb`^XMWRN\]JLSXWJ[WNPXMX\]JLSXWJ[WNPX <B6>5*,3.7>6.;B,C7. CJ\]X\X`JWRNTXMß`,/-JWP,XVY^]J]RXWJU/U^RM-b WJVRL\VJLX[Jc\cN[\cNcJ\]X\X`JWRN`WJ^LN4XMbW^VN [bLcWN\KJ[McXMXK[bVWJ[c¢McRNVMXYXPũ¢KRNWRJJWJURcb `bWRTß`^cb\TJWbLQM[XPNT\YN[bVNW]JUW,NUNV\bV^UJLSR W^VN[bLcWbLQY[cNY[X`JMcXWbLQ`]NSY[JLbSN\]YX]`RN[McN WRN R\]WRNWRJ [NŖRVß` Y[cNYũb`^ cJ^`JŖXWbLQ ` KJMJWRJLQ NT\YN[bVNW]JUWbLQ@bVJPJ]XMXKX[^XMYX`RNMWRNPXTXM^ W^VN[bLcWNPXX[JcXY[JLX`JWRNVN]XMXUXPRRXKURLcNWRX`NS @ XVß`RXWbLQ `bŖNS KJMJWRJLQ NT\YN[bVNW]JUWbLQ cJXK \N[`X`JWX ][cb [NŖRVb Y[cNYũb`^# ;;J+J [NŖRV \][^T]^[ Y[cNYũb`^;JbUNRPQnJo+NWJ[MJ;8<[NŖRV\][^T]^[X\Lb UJLbSWb R ;<= [NŖRV \][^T]^[ \]JLSXWJ[WbLQ -XRLQ JWJURcb W^VN[bLcWNS R\]WRNSN TXWRNLcWXĵî cJ\]X\X`JWRJ TXM^ W^VN [bLcWNPX ^VXŖUR`RJSLNPX YXY[J`WN XKURLcNWRN Y[cNYũb`ß` WRN\]JLSXWJ[WbLQ cVRNWWbLQ ` LcJ\RN CMNLbMX`JWX \R¢ WJ TXVYUN]WbYJTRN]TXVN[LbSWb/U^NW]-D/U^NW]FXYJ[]b WJ VN]XMcRN XKS¢]XĵLR \TXĢLcXWbLQ CJ\]X\X`JWX \][^T]^[JU WM`^`bVRJ[X`\RJ]T¢W^VN[bLcWX`bVRJ[JLQ]JTRLQSJT `NT\YN[bVNWLRNMũ^PXĵî5&VR`b\XTXĵî1&! V 8KURLcNWRJ Kbũb Y[X`JMcXWN ` XYJ[LR^ X YJ[JVN][b ²cb TXLQNVRLcWN`XMb`]NVYN[J]^[cN=&44]WJLQbUN WRJ ϕ Y[X\]XT]WNS MXVNWb XKURLcNWRX`NS Kbũ YJ[JVN][NV cVRNWRJWbV LX @bTXWJWX \bV^UJLSR W^VN[bLcWbLQ cVRNWRJSLT]WJLQbUNWRJϕ `cJT[N\RNXM"9XMLcJ\ VXMNUX`JWRJW^VN[bLcWNPXTXMNV/U^NW]-[Xc`Rcb`JWX [ß`WJWRJcJLQX`JWRJVJ\bY¢M^X[Jc[ß`WJWRNNWN[PRRM`^ `bVRJ[X`NPXWRN\]JLSXWJ[WNPX`LcJ\RNY[cNYũb`^ 8KURLcNWRJ W^VN[bLcWN YX]`RN[McRũb R\]WRNWRN XYR\b`J WbLQ ][cNLQ [NŖRVß` 9X[ß`WJWX `bWRTR NT\YN[bVNW]ß` c `bWRTJVR XKURLcNĢ W^VN[bLcWbLQ R\]`RN[McXWX ŖN `bWRTR ^cb\TJWNVXMNUNV/U^NW]-\`RJ[bPXMWNRVXPYX\ũ^Ŗbî MX MJU\cNS JWJURcb VXMNU^ YXLQbUXWNPX `bVRNWWRTJ LRNYũJ D-NTJSũX!F @BC7*,C.72.9*;*6.=;Æ@,2.957B,1 -5*;.ŕ26Æ@9;C.9ŨB@> cWJLcXWNWJYXM\]J`RNX\]J]WRLQ[Xc`RcJĢX][cbVJWbLQ `XM\]¢YJLQ\NT^WMX`bLQLcJ\^[cNLcb`R\]NPX\bV^UJLSR MUJ ` YNũWR [Xc`RWR¢]NPX Y[cNYũb`^ YX XT\ XKURLcNĢ WRN\]JLSXWJ[WNPXVXMNU^ -XXYR\^NONT]b`WXĵLR`bVRJWbLRNYũJKJMJWNPXVXMN U^`bK[JWXKNc`bVRJ[X`URLcK¢7^\\NU]J7^@b[JŖJXWJ \]X\^WNT][JW\YX[]^LRNYũJWJM[XMcN`WRTJWRJMXSNPX][JW\ YX[]^WJM[XMcNY[cN`XMcNWRJcX\]JũJ`bURLcXWJWJYXM\]J `RNWJ\]¢Y^SLbLQcJUNŖWXĵLR# PMcRN# PMcRN#QNɾoNONT]b`Wb`\YßũLcbWWRTY[cNTJcb`JWRJLRN YũJ T o `\YßũLcbWWRT Y[cN`XMcNWRJ LRNYUWNPX :ĵ[ĵ[NMWR \][^VRNĢ LRNYũJ =ĵLRJWTR o ]NVYN[J]^[J ĵLRJWTR =ĵ[o ]NVYN[J ]^[Jĵ[NMWRJYXVR¢McbRcX]N[VRLcWbVRĵLRJWTJVRTJWJũ^5o Mũ^PXĵîĵLRJWTRTJWJũ^ ;b\^WNT Y[NcNW]^SN cVRJW¢ URLcKb 7^\\NU]J 7^ `O^WTLSRT]JWJLQbUNWRJϕ TJWJũ^YXVRJ[X`NPX ;b\CJUNŖWXĵîURLcKb7^XMT]JWJLQbUNWRJϕ TJWJũ^YXVRJ[X`NPX @J[]XĵîURLcKb7^\\NU]J[XĵWRN`[JccN`c[X\]NVT]JWJ LQbUNWRJ ϕ TJWJũ^ YXVRJ[X`NPX -UJ ϕ& [NŖRV ;;J+JXK\N[`^SNVbURWRX`cVRJW¢URLcKb7^c`R¢T\cJ\R¢ XWJXWJTJŖMNc`R¢T\cJWNPXT]Jϕ@cJT[N\RNcVRJW ϕ&[NŖRV;8<XK\N[`^SNVbWRNURWRX`cVRJ W¢URLcKb7^cVRNWRJ\R¢XWJXTWJTJŖMNc`R¢T\cJ WNPXT]Jϕ6JT\bVJUW`J[]XĵîURLcKb7^cJXK\N[`X`JWX MUJ[NŖRV^;<=MUJϕ& -UJYXcX\]JũbLQT]ß`ϕ&! R ϕ&" c [NŖRV^ \]JLSXWJ[WNPX cJ^`JŖJ \R¢ WRNcWJLcW cVRJW¢`J[]XĵLRURLcKb7^cVWRNS\cJ\R¢XWJ`[JccN`c[X\]NV YXLQbUNWRJTJWJũ^YXVRJ[X`NPX2W]N[N\^SLNSN\]ŖNVJT\b VJUWN \][^VRNWRN LRNYũJ `b\]¢Y^S MUJ T]ß` cKURŖXWbLQ MX X8cWJLcJ]XcNUNTTRNYXLQbUNWRNYRXWX`NPX`bVRNWWRTJ LRNYũJVXŖNYXY[J`RîSNPXNONT]b`WXĵîWJ`N]XXTXũX 7JYXM\]J`RN\bV^UJLSRW^VN[bLcWbLQXKURLcXWX`J[]XĵLR \][^VRNWRLRNYũJ:][JW\YX[]X`JWNPXYXVR¢McbRcX]N[VRLcWb VRĵLRJWTJVRTJWJũ^@J[]XĵLR\][^VRNWRLRNYUWbLQMUJ][cNLQ `LcNĵWRNS cMN²WRX`JWbLQ [NŖRVß` Y[cNYũb`^ cJ\]Jũb `b UaSOMSOĜvMdO\aSOM ŵųųż ZYV]UK OXO\QO^cUK ]ĚYXOMdXK 98-<>68@*72. .T\YN[bVNW]JUWJ R W^VN[bLcWJ JWJURcJ WRN\]JKRUWXĵLR ]N[ VRLcWbLQYXLQbUXWNPXVXMNU^`bVRNWWRTJLRNYũJMX\]J[LcbũJ WJVLNWWbLQRWOX[VJLSRXYX`\]JSLbLQ\][^T]^[JLQY[cNYũb`^ 9Xc`XURũJ WJ YXMcRJũ ]bLQ \][^T]^[ WJ ][cb [NŖRVb 8T[NĵUXWX YXM\]J`X`N LNLQb SJTXĵLRX`N \][^T]^[b Y[cNYũb`^ LQJ[JT ]N[b\]bLcWNMUJTJŖMNPX[NŖRV^RRUXĵLRX`N\][^VRNWRNLRNYũJ URLcKJ7^VJSLN`Yũb`WJ`bMJSWXĵî`bVRJWbLRNYũJ ;NŖRV[Xc`RcJĢ]bY^;JbUNRPQnJ+NWJ[MJ;;J+JLN LQ^SN \R¢ \RUW TXW`NTLS ;NŖRV X\LbUJLbSWb ;8< SN\] [N ŖRVNV YXĵ[NMWRV `bVRJWJ LRNYũJ VJ LQJ[JT]N[ VRN\cJWb <TũJMJ \R¢ c TXW`NTLSR RY[cN`XMcNWRJ ;NŖRV \][^T]^[ \]J LSXWJ[WbLQ ;<= LNLQ^SN cJWRT Y[cNYũb`^ TXW`NTLbSWNPX J [^LQ LRNYũJ XMKb`J \R¢ Pũß`WRN WJ M[XMcN Y[cN`XMcNWRJ @]bV[NŖRVRN`J[]XĵLR\][^VRNWRLRNYũJ\WJS`R¢T\cNRNONT ]b`WXĵî `bVRJWb LRNYũJ URLcKJ 7^ X\RPJ WJS`R¢T\c `J[ ]XĵîMUJϕ & CY[cNY[X`JMcXWbLQKJMJĢ`bWRTJŖNMUJT]JWJLQbUN WRJϕ&URLcKJ7^`bWX\RJMUJϕ 'X\RPJ`J[]X ĵLRYX`bŖNS"-JSN]XY[J`RNVXŖUR`XĵLR[NP^UJLbSWN c`R¢T\cJWRJNONT]b`WXĵLR`bVRJWbLRNYũJcJT[N\RNcVRJWT]J WJLQbUNWRJXMϕ&" -UJ `bVRNWWRTß` YRXWX`bLQ PMcRN ϕ&" VXŖWJ c`R¢T\cbî NONT]b`WXĵî YXLQbUJSL YX`RN[cLQWR¢ `bVRJWb MX ϕ& McR¢TR LcNV^ ^cb\TJVb VJT\bVJUW `J[]Xĵî URLcKb 7^RX\RPWRNVbXT`c[X\]NONT]b`WXĵLR`bVRJWbLRNYũJ ZYV]UK OXO\QO^cUK ]ĚYXOMdXK 9XM\^VX`^SLVXŖNVb\]`RN[McRîŖN`\c¢McRN]JVPMcRN WRNVJVXŖUR`XĵLRWJXT[N\X`Nc`R¢T\cJWRNYX`RN[cLQWR`b VRJWbLRNYũJU^KWJcVRJW¢\][^VRNWRJY[cNYũb`^YũbW^[X KXLcNPXLcbWWRTJLQũXMcLNPXVXŖNVbcJ\]X\X`JîYXLQbũN `bVRNWWRTRLRNYũJ-cR¢TRcVRJWRNT]JYXLQbUNWRJYX`RN[cLQ WR`bVRJWbLRNYũJVXŖNVbMXMJ]TX`X\]N[X`JîRLQ`bMJSWX ĵLR;Xc`JŖJWb`]NSY[JLbVXMNUYXLQbUXWNPX`bVRNWWRTJ LRNYũJ\]JWX`R]bUTXLc¢ĵîTXUNT]X[J\ũXWNLcWNPX]SYXVR¢Mcb Y[cNc[XLcb\]X\ũXWJYũb]JK\X[KN[J 52=.;*=>;* 1XUUJWM\40="!6^U]Ro9[JWM]U7^VKN[,X[[NUJ]RXW.Z^J]RXW\OX[7J]^ [JU,XW_NL]RXWRW5JbN[\JWM.WLUX\^[N\2W]31NJ]=[JW\ON["!!"" ;JR]QKb0-1XUUJWM\40=""!7J]^[JULXW_NL]RXW2W@6;X\QNWX` 391J[]WN]]JWMB2,QXNMR]X[\1JWMKXXTXO1NJ]=[JW\ON[LQJY]N[ 6L0[J`1RUU7N`BX[T[MNMR]RXW /U^NW]>\N[\0^RMN_N[/U^NW]2WL5NKJWXW 71 4X`JUN`\TR =* =QN[VXLQX[VRL 5RZ^RM ,[b\]JU\ ` <Y[RWPN[ 1JWM KXXTXO.aYN[RVNW]JU/U^RM6NLQJWRL\=[XYNJ,$BJ[RW*5$/X\\3/.M\ RWLQJY+ YY! "" -NTJSũX 4 ! *WJURcJ <]JKRUWXĵLR 9[cNYũb`ß` =N[VRLcWbLQ ` 9XLQbUXWNS 0NXVN][RR 9[JLJ -XT]X[\TJ 9XU\TJ *TJMNVRJ 7J^T 2W\]b]^] 9XM\]J`X `bLQ9[XKUNVß`=NLQWRTRCJTũJM6NLQJWRTRR/RcbTR9ũbWß` UaSOMSOĜvMdO\aSOM ŵųųż