Post on 07-Jul-2018
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Le!" P#$"
Discussed Topics Course Outcome Course Learnin(Students should be a
Chapter 4Two-phase fow• Flow regimes and
fow patterns or
horizontal andvertical fow• Hold-up• Pressure,
momentum andenergy relations
• Practical methodsor evaluatingpressure drop
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Se/!"+$ - +iee+ i*.i" *.e /!"*i"! .$e
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I6!*$"/e !, M#*i.$e F#!
Flow patterns — the ways in which the phases are distribut
cross section !, *.e ie ! +/*7 I" +ei8"& i* i "e/e$ *! )e $)#e *! predict pressure dro
$##& +ee"+ "!* !"# !" *.e ! $**e"& )* $#! !" *.ee#!/i* !, *.e .$e *.i slip velocity will infuence the holraction o the pipe volume .i/. i !//ie+ ) $ $*i/#$
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*.ee /!6#e@ 6i@*e7%1' T.e ! $**e"7
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%3' T.e e#$*i!".i )e*ee" ee 8$+ie"* i" $ ie $"!$*e $"+ .i/$# !e*ie !, *.e .$e
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I6!*$"/e !, M#*i.$e F#!
T.e +i>ee"/e i" +e"i* )e*ee" *.e .$e i i6!
+e*e6i"i"8 ! $**e"7 8$ 8$D#ii+ #i #iD!#i+ !#i+ !ertical upward fow
#i8.*e .$e i## ie 6!e i/# *.$" *.e +e"e .$ee#!/i*7
Horizontal fow ! $**e" 6!e /!6#e@
8$i*$*i!"$# ,!/e i## $/* ee"+i/#$ *! *.e ie $@i& *.e +i
+e"e /!6!"e"* *! ! e,ee"*i$## "e$e *.e )!**!6ie7
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Two-phase "as #!apour$ - %iFlow T.e !i)#e comination !, *! .$e ! $e
gas'li&uid gas'solid li&uid'solid
Be/$e !, *.e ee"/e !, *.e *! .$e& *.ee $e /!"i+e$)#e com+e/i)i"8 $"+ $"*i,i"8 *.e "$*e !, *.e !
I" 6!* /$e *.e 8$ .$e& .i/. 6$ )e !i"8 i*. $ much great*.$" *.e #ii+& /!"*i"!# $//e#e$*e *.e #ii+ *. i"!#i"8 $ *$"
Ei*.e .$e 6$ )e i" streamline ! i" turbulent fow, though the most imporin which both phases are *)#e"*7
I, *.ee i "! .e$* *$",e *! *.e !i"8 6i@*e& *.e 6$ $*e !, ! !, e$/. .$e e6$i" )*$"*i$## /!"*$"*
!#6e*i/ !$*e %$"+ e#!/i*ie' i"/e$e !8eie# $ *.e 8$ e@$"+ee7
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Two-phase "as #!apour$ - %iFlow I" $ )!i#e ! e$!$*!=
!8eie $!i$*i!" !, *.e #ii+ +e/e$e+ 6$ !$*e !, #ii+
I"/e$e+ 6$ !$*e *.e $!
*!*$# 6$ $*e !, ! e6$i"i"8 /!"*$"*7
T.e !#6e*i/ !$*e i"/e$e e $i+# $ $ e#* !, *.e /!6)i"e+,$##i"8 ee $"+ i"/e$i"8 $!#ii+ $*i!7
C!"i+e$*i!" i## "! )e 8ie" *! *.e $i! ! e8i6e .i/. 6
.! *.e 6$ )e eee"*e+ !" $ F#! P$**e" M$ *! *.e /$#/e+i/*i!" !, .!#+- !, *.e *! .$e +i"8 ! $"+ *! *.e /$#/ee 8$+ie"* ,! 8$-#ii+ ! i" ie7
I" $++i*i!"& .e" 8$-#ii+ 6i@*e ! $* .i8. e#!/i*ie ei!!)#e6 /$" $ie $"+ i* i "e/e$ ,! *.e +ei8"e *! e*i/*
*! $!i+ ei! +$6$8e *! ei6e"*7
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Flow (egimes and Flow Patt
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L! $#e i* ,!6 *.e +iee.$e
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Flow (egimes and Flow Patt
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RiCHAR;SON )$e+ !" *.!eei!# ee"*e+ ) MAN;HANE etal $"+ WEISMAN et $#7
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Flow (egimes and Flow Patt
Vertical fow
A@i$# 66e* e@i* $"+! $**e" *e"+ *! )emore stale7
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I" 8e"e$#& *.e ! $**e"6$ i $#! $#i/$)#e *!e*i/$# !
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H!#+-
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LOCHART $"+ MARTINELLI = e@ee+ .!#+- i" *e6 !, $ $$6e*e J& /.*.e e#$*ie !$*e !, #ii+ $"+ 8$& +e
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H!#+-
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H!#+-
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6!+i
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Pee& M!6e"*6& $"+ E"e8 Re#$
Me*.!+ ,! +e*e6i"i"8 *.e +! i" ee
*$* i*. $ .i/$# 6!+e# !, *.e *!-.$e *e6 $"$#i i +ee#!e+ $ $" e@*e"i!" !, *.$* e+ ,! i"8#e-.$e !
I" *.e separated fow model
the phases are "rst considered to fow separately
their /!6)i"e+ e>e/* i *.e" e@$6i"e+7
T.e *!*$# ee 8$+ie"* i" $ .!i:!"*$# ie& #- dP$P% & dl '& /!"
/!6!"e"* .i/. eee"* *.e ,i/*i!"$# $"+ *.e $//e#e$*i!" e8$+ie"* ee/*ie# !=
.ee 'dP$P% T!*$# ee +! ,! *! .$e !
-dP Pee +! +e *! ,i/*i!"
-dPa Pee +! +e *! *.e $//e#e$*i!"
dl
dP
dl
dP
dl
dP a f TPF −+
−
=−
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Pee& M!6e"*6& $"+ E"e8 Re#$
T.e .e$ $* *.e $## i !!*i!"$# *! *.e *!*$# $*e !, 6!6e"*6
$ii"8 ,!6 riction and acceleration& ! *.$* *.e *!*$# +! i" is given by(
-∆P TPF = ( -∆P f ) + (-∆P a )
T.e ee +! +e *! acceleration i i6!*$"* i" *!-.$e
*.e 8$ i "!6$## !i"8 6/. ,$*e *.$" *.e #ii+& $"+ *.ee,!e@$"+ *.e #ii+ .$e i## $//e#e$*e i*. /!"ee"* transer
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$//e#e$*i!" #!e
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Pee& M!6e"*6& $"+ E"e8 Re#$
M!6e"*6 )$#$"/e $"+ $" e"e8 )$#$"/e - i**e" i" e@$
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+e"i*ie $e "!* "!"7
S!6e i6#i
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Pee& M!6e"*6& $"+ E"e8 Re#$
Me*.!+ ,! e*i6$*i"8 *.e +! i" ee +e *! ,i/*i!" ) LOC
MARTINELLI $"+ #$*e 6!+ie/* ,!6#$*e+7
T.e *!-.$e ee +! +e *! ,i/*i!" -∆P TPF i *$e" $ *.
+! -∆P L ! -∆P G *.$* !#+ $ie ,! ei*.e .$e !i"8 $#!"e
*.e *$*e+ $*e& 6#*i#ie+ ) !6e ,$/*! 2G ! 2
L 7
F"/*i!" !, *.e $*i! !, *.e i"+ii+$# i"8#e-.$e ee +!7
2
G
G
TPF
P
P Φ=
∆−
∆− 2 L
L
TPF
P
P Φ=
∆−
∆−
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P$/*i/$# Me*.!+ ,! E$#$*i"8 Pe
T.e e#$*i!" )e*ee" G $"+
L $"+ ' %igure ).* Se$$*e /e - $//!+i"8 *!
*.e "$*e !, *.e ! !, *.e*! .$e7
F! 6$ !$*e e "i* $e$!, L! and G+ or the liuid and
gas, ee/*ie#& Re"!#+"6)e eL #L! d& L / and eG
#G+d & G / may be used as
criteria ,! +e
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Ci*i/$# !
C!6ei)#e i+ C!"+i*i!" !, !"i/ e#!/i* 6$ )e e$/.e+ Li6i*i"8 *.e 6$@i66 !$*e ,! $ 8ie" *e
ee7
C$" $#! !// i*. *!-.$e !&
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E@$6#e
S*e$6 $"+ $*e ! *.!8. $ Q5 66 i7+7 i
!$*e !, 0705 $"+ 175 8 ee/*ie#7 I, **e6e$*e $"+ ee $e 330 $"+ 120 .$* i *.e ee +! e "i* #e"8*. !, i$6i"8 $+i$)$*i/ /!"+i*i!"
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S!#*i!"
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S!#*i!"
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)ummary
M#*i.$e F#!
;EFINITIONS
IMPORTANCES
GAS LIKUI;FLOW
-M$*ei$# i*. +i>ee"/*$*e ! .$e
-M$*ei$# i*. +i>ee"*
/.e6i/$# !e*ie )**.e $6e *$*e ! .$e
-;i*i##$*i!"& A)!*i!E$!$*i!"&C!"+e"$*i!"&S!#e"* e@*$/*i!"
17 T.e fow patterns.27 T.e hold-up !, *.e i"+ii+$# .$e
$"+ *.ei e#$*ie e#!/i*ie737 T.e e#$*i!".i )e*ee" pressure gradient i" $ie
$"+ *.e !$*e $"+ .i/$# !e*ie !, *.e
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T*!i$#
571
572