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' H   0޽h ? 33___PPT10i.oq+D=' )= @B +   0 `(0(  (x ( c $Xr'gt   ~ ( s *8s I   (0  `A P? ?"` P  (0  `A Q? ?"`   Q 4 (  ` \GgjJ?"6@ NNN?N+/ f Primary (direct) field variables!! ! 2 ( Zb\jJ?"6@ NNN?N V  j$Secondary (indirect) field variables%% % H ( 0޽h ? 33___PPT10i.\@+D=' )= @B +  0 $ Note `N6(  r  S |\ `}  \ x  c $l\ ` \   `C  N #"&r `C  G3 # T b jJ?"6@ NNN?N J`C  i free enthalpy   @` " Tb jJ?"6@ NNN?N J C  temperature and pressure (T,p)B&    @`. ! TL  jJ?"6@ NNN?N 6`J denthalpy     @`   T jJ?"6@ NNN?N 6 J enthropy and pressure (s,p)B4     @`1  TT jJ?"6@ NNN?N #`6 g free energy     @`  T jJ?"6@ NNN?N # 6 <temperature and volume (T,1/)B   @`5  TD jJ?"6@ NNN?N `# kinternal energy   @`  T# jJ?"6@ NNN?N  # 6enthropy and volume (s,1/)B   @`6  TD  jJ?"6@ NNN?N ` l TD potential     @`P  Td\ jJ?"6@ NNN?N   &Representation (independent variables)'' '  @`B $ No ?"0@NNN?N `B & H1 ?"0@NNN?N #`#B ' H1 ?"0@NNN?N 6`6B ( H1 ?"0@NNN?N J`JB ) No ?"0@NNN?N C `C B * No ?"0@NNN?N  C B + H1 ?"0@NNN?N  C B , No ?"0@NNN?N``C B A H1 ?"0@NNN?N `<  c $ ? 33___PPT10i.ft+D=' )= @B +Q  0 h`(  r  S DK `}  K r  S pK$ K t  s *A ? ?"`  t  s *A ? ?"`   t  s *A ? ?"`q N $"  T̳KjJ?"6@`NNN?N$ bStoksean fluid  E"   T̢KjJ?"6@`NNN?Nq$ #compressible (or barotropic) fluid$$&    2   N0jJ?"6@`NNN?NI& | cmodels for complex fluids  ""   Z\jJ?"6@`NNN?N @  Zgeneral simple fluid  |F   h   '"  T$jJ?"6@`NNN?N h ]fluid dynamical equations  -"  TjJ?"6@`NNN?N  h cheat transport equation (1PDE)      ZjJ?"0@NNN?N~8  & h   -"   ZbjJ?"6@`NNN?N h ]fluid dynamical equations  +"   ZjJ?"6@`NNN?N & h [heat transport equation     fjJ?"0@NNN?NB   fDjJ?"0@NNN?N/ $/B   fDjJ?"0@NNN?NN!B   fDjJ?"0@NNN?Nc  c B   fDjJ?"0@NNN?N & H  0޽h ?/@   33___PPT10i.Oc+D=' )= @B +  0 @ (  x  c $H `}   x  c $P{    X  0A? yXB  0D3Ԕc )c XB  0DfԔc s XB  0DԔC9XB  0D33ԔCXB   0DԔcXB   0DԔ3 XB   0DfԔ 3 f XB   0DԔf  H  0޽h ? 33___PPT10i.\++D=' )= @B +  0   `(   r  S `w9  X  0A?7   0F   q 2In equilibrium 1, 2 or 3 phases can exist together3% 3   Bp3jJ"`[* o+Complete mechanical and thermal equilibrium,, , RB  s *D3I  <>"`<  y3Several solid phases (crystal structures) may exist44 4 XB  0DjJ7RB  s *DfjJ`   c $A ?? 8  H  0޽h ? 33___PPT10i.\얀+D=' )= @B +   0  Pd(  dr d S t3  `}   x d c $T4  0    r d S 45 0 `   H d 0޽h ? 33___PPT10i.+D=' )= @B +I  0 `X(  x  c $ɸ `}   ~  s *Ѹ `   0  `A ? ?"`3   t  s *A ? ?"` &'  t  s *A ? ?"` &  H  0޽h ? 33___PPT10i.\ЪC+D=' )= @B +O  0 $ Note B:0(  x  c $ظ `}   ~  s *(ݸ',%   0 3 rA ? ?"` $%   0 3 rA ? ?"`6    <  c $ ? 33___PPT10i.\0y+D=' )= @B +Q  0 h` (  x  c $ `}   ~  s * `   0  `A ? ?"` 3   H  0޽h ? 33___PPT10i.\u+D=' )= @B +o    0  ~ 0  (       <T>) c"$`  `}  ) ~   s * ` ) 8 J 5r   J5rh   c $A ??J 5r B   TDjJ?"0@NNN?N  B   TDjJ?"0@NNN?N  B   TDjJ?"0@NNN?N rB  B TDjJ?"0@NNN?N ] B  B TDjJ?"0@NNN?N  ] B  B TDjJ?"0@NNN?N f ] B  B TDjJ?"0@NNN?N  B  B TDjJ?"0@NNN?N  B  B TDjJ?"0@NNN?N rH   0޽h ? 33___PPT10i.+D=' )= @B +  0 S(  x  c $ `}   ~  s *p `   0 C xA ?8c ?"`  ;  # lTKG(HIJjJ?"6@`NNN?N aTD limit on the # of phases  H  0޽h ? 33___PPT10i.+D=' )= @B +  0 L(  x  c $ `}     s * `  "P@08XH  0޽h ? 33___PPT10i.\ЪC+D=' )= @B +d  0 {s (  x  c $;G `}  G x  c $XG   G x  c $Gp ` G S  # lhKGHoI J%jJ?"6@`NNN?N < y3Topological limit on the # of phases (always local)44 4 H  0޽h ? 33___PPT10i.\+D=' )= @B +}  0 t$(  tr t S ( `}   r t S # `  H t 0޽h ? 33___PPT10i.\P$+D=' )= @B +. 0 8>(  8X 8 C 4    8 S  4 0   @ Update me!H 8 0޽h ? 3380___PPT10.N 0 zr< (  <X < C 4   r < S T4 0   H < 0޽h ? 3380___PPT10.7>  0 D(  DX D C 4    D S |c4 0   XTODO: 1/rho=spec volume, viscosity, chemical potential. Write equations of equilibrium.    H D 0޽h ? 3380___PPT10. 0 zr (  X  C 4   r  S R4 0   H  0޽h ? 3380___PPT10. Akj 0 zr (  X  C 4   r  S x4 0   H  0޽h ? 3380___PPT10. D( 0 T(  ^  S 4     c $Ā4 0   JTODO: concentrationsH  0޽h ? 3380___PPT10.w=* 0 ~(  ^  S 4   x  c $4 0   H  0޽h ? 3380___PPT10.w= 0 80@(  X  C 4   0  S 4 0   0This should be recast to the multicomponent case~H  0޽h ? 3380___PPT10.K: 0 PJ(  X  C 4   G  S G4 0  G L(p,T) represaentattionH  0޽h ? 3380___PPT10.`1 0 D<@$(  $^ $ S 4   )6 $ c $\)4 0  ) 0This should be recast to the multicomponent case~H $ 0޽h ? 3380___PPT10.KxYMlE~3Nz㶉[JUbe()n898$EPI։Qb:_*~$z@)\@#Hz0 8PO8 Uؼ7vb7V?kۙylֿ7n@= >(Ww=XtrRG>,=Pt 23AsP6{>{,e!%yݷ_Gm: `44Hzyg/d \y F=L0ԔT}Oy`: _6;?Q ?..J~Dpw|C[n @RKv<؉zjjeSkLm^j~;vvPLg~tNO|6.,~=p^$fFf*VZqob/1>xPŏ|kGÁê§i" VL/ C[T A_' Xfgx_c*UF188՛!AGǺ焗RXO?Q.=:K%ҩ̌O½q 􌡱/hU8k7[m!ex78A#ӹ,a|~oaDsoNo: ׿4lj%7?jhwOG˵~d cRAJ37{cK+!MiMfɂB]ӻ5Mv7?J>T"ҦÊCB}'>C)lϙ{e6+-3gsf3̽uo& iT.:2o2NS%]BQb~b= LSW4@s?ްxw|Ǫ(6 @K*Z}=ny\ [6f,(,W5v,%JEoѯT:T8pKxI:S//Pד @꽯?jfwƍXr QLkv iy"\H\@ɡh臏[?y!srmF;O\g񯫯w86 5{I=:ǵD(~G bQ%Ѿ~rfˬ6ѺDUe| >X6?e<084k&n>I,.m{dhWo\vo߅{i{-?7]QxiC:t{H`_!{JbjbpᔾV99,eݧsl\>nlȥ4%9jr: xX]h[UsIvmuZ!v.ؚZ BҚj]#˃V>$v2A 2_R21xoҤ]?|NV+W/}R{ 2qP bS%pm jRlh_i/!IHfB^@"? 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GborSzab K. Gbor39Microsoft Office PowerPoint@e;@00Y\@`6۪G';  ``&WMFColx EMF~Qr F(GDICx!b $$==% % V0xx x % % $$AA" FGDICF(GDIC &FGDICRp@"Arial<t̘_btlL`X _b x 0  A0U00h\t^bh\dv%    T 0 B BLMultiphase and Reactive Flow  % ( Rp@"Arial0<Arial x 8z@"Arial 0 | x 0  A0U00@ P T=+Ab\Pp*Abdv%    T;e#0 B B;! L`Modelling  % ( F(GDIC(dFGDICRp@"Arial9<Arial`D8z@"Arial 0  `Dp  A0U00@ P T=+Ab\Pp*Ab$dv%    Tl5*M00 B B50LXBMEGEe % ( Rp@"Arial9<@"Arial 0  `Dp  A0U00@  `Dp  A0U00$dv PNDC0 B BC(LDept. of Hydraulic and Water Management  % ( Rp@"Arial <Arial`D8z@"Arial 0  `Dp  A0U00@ P T=+Ab\Pp*Abldv%    TBE^J0 B BBJ LdEngineering, % ( Rp@"ArialC<Arial`D8z@"Arial 0  `Dp  A0U00@ PT=+Ab\Pp*Abldv%    T0LoQ0 B B0QLFaculty of Civil Engineering % ( Rp@"ArialK<Arial`D8z@"Arial 0  `Dp  A0U00@ PT=+Ab\Pp*Abldv%    T,Uu[0 B B,[LxSpring semester, 2012  % (   x--$xx--'@"Arial??-. 32 Multiphase and Reactive Flow . 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(2 [,Spring semester, 2012 .-՜.+,D՜.+,,     YDiavetts a kpernyreBME~ ' ArialSymbolTimes New RomanAlaprtelmezett tervMicrosoft Equation 3.0(Multiphase and Reactive Flow Modelling IntroductionBasic notions and terminology Properties and models of solids Models and properties of fluidsModelling Simple Fluids Thermodynamical representationsSome models of fluidsPhase transitions10. diaTConditions of local phase equilibrium in a contact point in case of a pure materialMultiple components-Notations to be used (or at least attempted)/Material properties in multicomponent mixturesXConditions of local phase equilibrium in a contact point in case of multiple components/Phase equilibrium in a multi-component mixture Miscibility"Topology of phases and interfaces Special Features to Be Modelled Hasznlt bettpusokTervezsablonBegyazott OLE kiszolglk Diacmek 8@ _PID_HLINKSA 263,2,Outline263,2,Outline&_OhSzab K. GborSzab K. 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