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Two Phase Flows(Section 6)
By: Prof. M. H. Saidi
Center of Excellence in Energy ConversionSchool of Mechanical EngineeringSharif University of Technology
Two Phase Flows
Homework set#2
Problems 5-9; Chapter 1, Collier and Thome.
Due to next Tuesday
Homework set#2
Problems 5-9; Chapter 1, Collier and Thome.
Due to next Tuesday
Methods Used with HM and SFM
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
Baroczy (1965 )
Baroczy Method
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
Baroczy (for flux of mass flow rate 1365 kg/m2.s)
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
22
( 1356)2( ) fo f
fo Gf Gdp F
dz Dν
== Φ Ω
Baroczy method has the satisfaction results for liquid
metals and refrigerants.
Chisholm method
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
22
11fCX X
φ = + + 0.5 0.5 0.52( )( ) ( ) ( )fg g f
g f g
v v vC Cv v v
λ λ
= + − +
(2 )0.5(2 2)nλ −= −
n
f f ff f
f
u Df K ρµ
−
=
For rough pipe: n=0 and λ=1
For smooth pipe: n=0.25 and λ=0.68
at critical pressure vf =vg and vfg=0For rough pipe: C=2
For smooth pipe: C=1.36
A
Chisholm method
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
Chisholm proposed this method for water-steam flow in the pipe at high pressure
*for G G≤* 6
2 22000 1.47 10. .
kg lbG orm s h ft
= ×
for rough pipe:
for smooth pipe:
C is calculated by equation A with λ=0.75 and C2=G*/G
* 62 21500 1.1 10. .
kg lbG orm s h ft
= ×
C is calculated by equation A with λ=1 and C2=G*/G
Chisholm method
22
1(1 )fCX X
φ ψ= + +
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
*for G G≤
for smooth and rough
pipe
2 21 1(1 ) /(1 )C C
T TT Tψ = + + + +
0.5 0.5( ) ( )g f
f g
v vCv v
= +
1 0.52 2( ) ( ) ( )1
n nf f
g g
vxTx v
µµ
−=
−
for smooth pipe C is calculated by equation
A with λ=0.75 and C2=G*/G
For rough pipe C is calculated by equation
A with λ=1 and C2=G*/G
Comparison of experiment with Chisholm and Baroczy theory
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
Baroczy theory can be used directly for the other systems
Chisholm theory must be corrected
with property index when it used for the
other systems
0.2( )( )f f
g g
vv
µµ
Index of property
Friedel Theory
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
2 2 31 0.045 0.035
3.24( )fo heated TubeA AA
Fr Weφ = +
2 21
0.78 0.2242
0.91 0.19 0.73
2
2
2
(1 ) ( )
(1 )
( ) ( ) (1 )
f go
g fo
g gf
g f f
fA x x
f
A x x
A
GFrgDG DWe
ρ
ρ
µ µρρ µ µ
ρ
ρσ
= − +
= −
= −
=
=
Friedel (1979) is one of the exactest relation for two phase flow
Whalley (1980) recommendation for separated flow
ØFor μf/μg<1000:
Friedel theory (1979)
ØFor μf/μg>1000 and G>100 kg/m2.s: corrected theory of Chisholm (1973)
ØFor μf/μg>1000 and G<100 kg/m2.s:
theory of Lockhart- Martinelli(1949) and Martinelli- Nelson(1948)
Two phase flow in inclined pipes
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
Beggs and Brill1973
Effect of heat flux on the void fraction and pressure gradient
Multiphase Flow Research GroupSchool of Mechanical Engineering The Basic Model
2 2 3 0.7( ) ( ) [1 4.4*10 ( ) ]fo heated Tube fo Unheated Tube Gφ
φ φ −= +
Tarasova (1966) and Leont’ev (1965 ) find a relationship between heat flux and pressure gradient
Tarasova and Leont’ev proposed a empirical equation for friction multiplayer in the isolation pipe for water-steam system
