Khaled Qdaeh

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JORDANIAN - GERMAN

WINTER ACADEMY

2006



Typical Study Of Two-phase

Flow IndustrialApplications

Pressure Drop and FlowRegimes.

Dr. . Al-Shanna!

"ng. #h. Al-$udah



Basic Definition of Two-Phase Flow

•A phase is simply one of the state of matterand can be either a gas , a liquid or a solid.

•ultiphase flow is a simultaneous flow of se!eral

phases . Two-phase flow is the simplest case of

multiphase flow .

•"as-liquid mi#tures are referred to as two-phasetwo-component flow where as liquid -!apor

mi#ture referred to as two-phase single-

component mi#ture.



•common e#amples of two-phase flows, some

such as rain, clouds , smo$e ,fog ,snow ,dust

storms are occur in nature . %thers such as

boiling water, coo$ing are frequent occurrences

and se!eral e!ery day processes in!ol!e a

sequence of different two-phase flowconfiguration or flow patterns .

•Two-phase flow in!ol!ing a mi#ture of gas or

!apor and liquid is !ery common in !arious

industrial and scientific applications, and there

ha!e been many e#perimental and theoretical

studies



Two-phase Flow ApplicationsThe practical importance in many common

engineering and industrial applications are:

&team generators and condensers, steam

turbines ' Power Plants (.

)efrigeration .

*oal fired furnaces .

Fluidi+ed bed reactors .

iquid sprays .

&eparation of contaminants from a carrier fluid



Free surface flows, where sharp interfaces e#ist .

pumping of slurries .

pumping of flashing liquids .

raining bed driers .

oil industry two phase flow occurs in pipelinescarrying oil and natural gas.

energy con!ersion .

paper manufacturing .

food manufacturing .

medical a lications .



•-The laws go!erning two phase flow are

identical to those for single phase flow.

owe!er, the equations are more comple#andor more numerous than those of single

phase flow.



•The description of the two-phase flow iscomplicated due to the existence of

interface between the phases dependingon a large number of variables such as :

quality '#(.

phase physical properties .

flow patterns .

pipe geometry .

orientation of flow .



A general classifications di!ide two-phase flow into

four groups depending on the mi#tures of phases in

the flow. The four groups are the flow of gas-

liquid, gas-solid, liquid-solid and immiscible liquid-

liquid mi#tures. The last case is technically not a

two-phase mi#ture, it is rather a single phase two-

component flow, but for all practical purposes itcan be considered as a two-phase mi#ture.



Two-Phase Flow )egimes

The description of two-phase flow in tubes iscomplicated by the e#istence of an interface

between the two-phases. For gas /liquid two-

phase flow the interface e#ists in a wide !ariety of

forms, depending on the flow rates and physical

properties of the phases, and also on the

geometry and orientation of the tube.

The different interfacial structures are called

flow patterns or flow regimes.



There are !arious flow patterns common in two-phase flow system, each ha!ing different

characteristics and associated pressure drops. A

number of different methods ha!e been proposedfor the recognition of flow patterns, ranging from

!isual obser!ation to characteristic fluctuation in

hold up.



Flow )egimes 0n ori+ontal Flow

1. Bubble flow .

2. Plug flow .

3. &tratified flow 'layered, separated( .

4. 5a!y flow 'ripple flow, cresting( .

6. &lug flow .

7. &emi-annular flow .

8. Annular flow 'ringed( .

9. &pray flow 'mist, froth, dispersed( .



:ertical flow )egimes

1. Annular flow.

2. Bubble flow.

3. &lug flow.

4. *hurn flow.

6. )ipple Flow.

7. ist Flow .



Slug Bubble Separate A!!ular



Two Phase Flow )egimes apping

apping of flow patterns that occur in pipe flow

has always been a popular means of describing thebeha!iors of flow at different conditions. The

superficial !elocity of the gas and liquid are usually

put on the two different a#es, and supply anefficient method of comparing and contrasting the

effects of different flow conditions.



D"#per#e Bubble

Ma!$a!" et al Map%&'()(



Analysis of two-phase flows*+, + ,e a!al.e t,+-p$a#e /l+,#

T$e 1a"! a!al#"# te$!"3ue# "4"e "!t+ t$e/+ll+,"!g ateg+r"e#5

A-S"1ple C+rrelat"+!#

• ba#e +! eper"1e!t 5

•+/te! 3u+te "! "1e!#"+!le## /+r15

•1a +r 1a !+t $a4e #"e!t"/"7p$#"al ba#"#5

•+/te! re#tr"te "! area +/ appl"at"+! 5



B-&imple Analytical odels .

Due t+ t$e large !u1ber +/ appl"at"+!# ,$ere

1ult"p$a#e /l+, +ur#8 "t "# "1p+rta!t t+ $a4eaurate 1+el#5

1-omogeneous model 5

Su"table a4erage pr+pert"e# are eter1"!e a! t$e1"ture "# treate a# a #"!gle /lu" "! t$e

•ta9e a4erage +/ pr+pert"e# /+r b+t$ p$a#e# 5

•u#e8 e5g58 /+r #u#pe!#"+!8 /+a18 1"#t8 "#per#e

bubble5

•!+ eta"l +/ t$e /l+, +!#"ere 5



/r"2t1+12#tat"t+tal

P P P P ∆+∆+∆=∆

θ ρ #"!*#tat" g P H =∆

α ρ α ρ ρ G L H +−= :&%

( )

−+

=

L

G

L

G

x

x

u

u

ρ

ρ α

&&

&



dz

md

dz

dP H total

mom

55

:7% ρ =

tp

total p

d

m L f P

ρ "

25

2

/r"t

2=∆

2;502

Re

0('50= p f



LG p x x µ µ µ :&%2 −+=

p

total im2

5

Re µ

=

2 & t d fl d l



2-&eparated flow model 5

•a##u1e p$a#e# /l+, #"e b #"e 5

•u#e #eparate e3uat"+!# /+r ea$ p$a#e 5

•+!#"er "!terat"+! bet,ee! t$e p$a#e# 5

3-Drift flu# model .

•focuses on relati!e motion between phases .

*-0ntegral Analysis .

•a##u1e 4el+"t8 te1perature +r +!e!trat"+! pr+/"le

•/"t t+ b+u!ar +!"t"+!# a! appl "!tegrate /lu"

1e$a!"al e3uat"+!#



/r"t1+1#tat"t+tal P P P P ∆+∆+∆=∆

θ ρ #"!*2#tat" g P H =∆

( ) ( )

+

−

−−

+

−

−=∆

inG Lout G L

total

x x x xm P

α ρ α ρ α ρ α ρ

222225

1+1t:&%

&

:&%

&

[ ]

&

5

;5025

2;50:%:&%&<5&&::&%&250&%

−

−−+

−+−+=

L

G L

LGG

m

g x x x x

x

ρ

ρ ρ σ

ρ ρ ρ α

D Diff i l A l i



D-Differential Analysis.

•use of time-a!eraged equations of motion .

;-<ni!ersal Phenomena .

•certain phenomena apply regardless of the

regime, e.g. wa!e theory

T*E N=MERICA> MODE>S



T*E N=MERICA> MODE>S

•T$e !u1er"al #"1ulat"+! +/ "!u#tr"al /l+,# "# a!

"!rea#"!gl "1p+rta!t 1ea!# t+ #+l4e a large 4ar"et+/ /lu" /l+, pr+ble1# #u$ a# "!ter!al /l+,#8 eter!al

aer+!a1"#8 #pra ++l"!g8 /"l1 +at"!g8

e!4"r+!1e!tal a! b"+l+g"al /l+,#8 a! p+,er

ge!erat"+!5 Se4eral ge!eral-purp+#e +e# a! a large

!u1ber +/ #pe"/" ?@I +e# are !+, a4a"lable5



•I! +!tra#t t+ t$e #ta!ar +!e-"1e!#"+!al

lu1pe para1eter #"1ulat"+! a! 1+el"!g +/

t,+-p$a#e /l+,#8 t$e 1+re ge!eral 1et$+# +/+1putat"+!al /lu" !a1"# %CD: are ba#e +!

t$e +!#er4at"+! e3uat"+!# +/ 1a##8 1+1e!tu1

a! e!erg "! t$e t$ree #pat"al "1e!#"+!# +/ a/l+, /"el5 CD-1et$+# are !+, e#tabl"#$e a#

e!g"!eer"!g t++l# /+r reat+r #a/et a!al#"#5

•+ur ba#" appr+a$e# a! be appl"e "! t$e CD1+ell"!g +/ 1ult"p$a#e /l+,#5 T$e#e are t$e

porous medium, t$e agrangian8 t$e ;ulerian

and the interface models.

lti h d l i F<;=T



ultiphase models in F<;=T

•D"#rete $a#e M+el %DM:5

•M"ture M+el 5

•?+lu1e +/ lu" M+el %?O: 5

•Euler"a! Mult"p$a#e l+, M+el 5



Ca#e StuModeling and Experimental investigation ofTwo-phase flow contraction coefficient and

pressure drop at the branching pipes .

PhD Proposal

Supervised By:

r . ! . Salaymeh.

r . B. Shanna" .



1

3

2

Ac-12

Ac-13

&tream ines



r+ble1W$e! t$e /ull e4el+pe8 t,+-p$a#e /l+, pa##e#

t$r+ug$ a! "!let +/ t$e bra!$"!g u!t"+!8 t$e /l+,#eparate# /r+1 t$e ,all at t$e e/let"!g leg#

%bra!$e#: a! rea$e# !arr+,e#t r+## #et"+! t$at

alle +!trat"+! reg"+!5 T$e#e #eparat"+!# a!+!trat"+! reg"+!# au#e $"g$ pre##ure l+##e# a!

t$ere/+re a $"g$-e!erg "##"pat"+!5 T$e re#"#ta!e t+

/l+, +//ere b T-u!t"+! "# larger t$a! t$at "1pl"e

b t$e e3uat"+!# /+r t$e #"!gle p$a#e /l+,5

C+!#e3ue!tl8 t$e la,# +/ /r"t"+! "! T-u!t"+! are +/

great prat"al "1p+rta!e8 a! eper"1e!tal ,+r9 +!

t$e1 "# 4er !ee##ar5

D e to the lac$ of readil a ailable standard



-Due to the lac$ of readily a!ailable standard

design methods to calculate pressure drop and

mass flow rate in two-phase flow applications,

design methodologies ha!e been routinely based on

pre!ious e#periences. Depending on the strength of

the interaction between phases, different modeling

approaches ha!e been proposed for two-phaseflows but !ery little of these conducted the two-

phase flow contraction .



&o the present study will also e#pand our

$nowledge of the state-of-the art of

contraction coefficient and pressure drop oftwo-phase flow in pipe branching.

Obet" e



Obet"4e

T$e +4erall +bet"4e +/ t$e pre#e!t #tu "# t+ /+u#

#+1e #$e# +! t$e 1+el"!g a! "!4e#t"gat"+!# +/ t$econtraction coefficient and predict the two-phase

flow pressure drop and mass flow rate at t$e

bra!$"!g u!t"+! "! +rer t+ pr+ue a !e, rel"able

+1putat"+!al relat"+! /+r t$e +!trat"+! +e//""e!t

a! t+ e4el+p a! e1p"r"al 1+el /+r pre##ure r+p

T$e rele4a!e +/ t,+-p$a#e /l+, pr+ble1# "!

"!u#tr"al appl"at"+!# $a4e 1+t"4ate t+ t$"#"!4e#t"gat"+! 5 Ne, /+r1ula 1a be pr+ue relate

t$e pre##ure r+p 8 1a## /l+, rate# a! +!trat"+!

+e//""e!t relat"+!#5



ethod of Analysis



T$e +!trat"+! +e//""e!t #$+ul beM+ele ,"t$ t$e $elp +/ t$e /+ll+,"!g

la,#5C+!#er4at"+! la, +/ 1a## 5

•+!#er4at"+! la, +/ 1+1e!tu15

•+!#er4at"+! la, +/ e!erg5



1

3

2

Ac-12

Ac-13

&tream ines

1-The general principle of conser!ation of mass



1 The general principle of conser!ation of mass

that the mass within the system remains constant

with time >

050=+∂∂ ∫ ∫

cscv

VdAdvt

ρ ρ

050=∂

∂

t

( ) ( ) ( )[ ] 050:2%

2FFF22222&&& ==+−⇒ ph

ph ph phdt

dmV AV AV A ρ ρ ρ

( ) ( ) ph ph ph

V AV AV A2FFF22222&&& ρ ρ ρ +=⇒

/+r #tea #tate /l+,

5here , , represent a!erage !elocities

o!er the cross sections.&V 2V FV

2-;nergy *onser!ation



2-;nergy *onser!ation

&2* E-EW-G =

dAeV edvt dt

dE

cscv

∫ ∫ +∂∂

= ρ ρ

dAeV edvt dt

dw

dt

dQ

cscv

∫ ∫ +∂∂=− ρ ρ



%2p$:

2

&

&&&

&

"! 2

++++−

V

gz u

P

dmdwsdq ρ

%2p$:

2

F

FFF

F

2

2

222

2

+ut 22

++++

+++−

V

gzu

P V

gzu

P

dm ρ ρ

#-#te1

2

2

++= V gz umd

:HHHHHHHH)%

3-*onser!ation of momentum



3 *onser!ation of momentum

∫ ∫ ∑ +∂

==cscv

dAVV Vdvdt dt

5%14:

A ρ ρ

#ur/ae b+ F F dt

dV

+= ρ

( )

== ∫ ∑

sysdt

d m

dt

d F ?1?

( ) ( )?md Fdt =

∑ ∫ = sys

dmm

tA51 ∆= nV ρ

∫ ∫ ∫ ∫ =

∆∆

+

=

→∆ csout csout cst sys

dAV V t t dAV V dAV V Vdm

dt d :5%:5%:5%

550l"1 ρ ρ ρ

( ) ∫ ∫ ∑ =

==⇒

cs sys

dAV V dt

d m

dt

d F :5%?1? ρ



( )

∫ ∫ ∑ =

==⇒

cs sys

dAV V

dt

d m

dt

d F :5%?1? ρ

:2%

2

&&& :#"!%0 phV A Fy θ ρ ∑ ==

:2%

2

222 :%0 phV A Fx ρ ∑ ==

:2%

2

&&&:2%

2

FFF :+#%:% ph ph V AV A θ ρ ρ −−

defined the contraction coefficient as>



defined the contraction coefficient as>

2

2:2&%

A

Acc =

−

F

F

:F&% A

Acc

=−



T$e +!trat"+! +e//""e!t C a! be repre#e!te a#

ph AV p f c 2:8888% θ ρ =

All t$e#e pr"1ar "!/lue!"!g para1eter# #$+ul be

ta9e! "!t+ +!#"erat"+! /+r t$e e4el+p1e!t +/ a!e,

pre##ure l+## /+r1ula5

*omparison will be made between model and

e#perimental data .



&tream

lines

?

&8A&

28A2

A&2

A&F

Khaled Qdaeh

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