numerical simulation of slug generation at a v...

Numerical Simulation of Slug Generation at a

V-Shaped Elbow Between Inclined Pipes

Motoki Irikura 1,2

Munenori Maekawa 1

Shigeo Hosokawa 2

Akio Tomiyama 2

1 Chiyoda Corporation

2 Graduate School of Engineering, Kobe University

13th

International Conference on

MULTIPHASE FLOW IN INDUSTRIAL PLANTS

17-19 September 2014, Sestri Levante (Genova), Italy

http://www.kobe-u.ac.jp/

13th International Conference on MULTIPHASE FLOW IN INDUSTRIAL PLANTS Numerical Simulation of Slug Generation at a V-Shaped Elbow Between Inclined Pipes Sep. 18th, 2014

1

Contents

1. Background and Motivation

2. Previous Experimental Work

3. Numerical Method

4. Slug Generation and Flow Patterns

5. Slug Characteristics

Gas Liquid

Slug generation at a V-shaped elbow



2

(Image: Marc Shandro via flickr.com , http://gasline.alaska.gov/)

(Image: http://www.offshore-mag.com, http://www.dpoperators.org,

http://pipeliner.com.au)

Oil and Gas Transport Pipeline

Background

Overland pipeline Offshore pipeline



3

Background

In such hilly-terrain pipelines, there are V-shaped elbows

between descending and ascending pipes.

Flow pattern and flow characteristics of oil and gas two-phase

flow varies at V-shaped elbow

Liquid slugs are often generated at V-shaped elbows



4

Gas

Liquid

Significant pressure fluctuation

Overflow in separator

Reduction of transport performance

For the piping design and execution of appropriate operation procedure, predicting slug generation and their characteristics is important

Slug flow in horizontal, vertical and inclined piping have been received much attention.

Knowledge on the slugging at a V-shaped elbow is scarce.

Background

Liquid Slugs at a V-shaped Elbow



5

To give reasonable predictions for this phenomena,

three-dimensional simulation is required

Gas

Liquid

Background

Liquid Slugs at a V-shaped Elbow

Flow field of terrain induced slugging is three-dimensional



6

[Numerical Method]

• Two-fluid model

• The free-surface model for the interfacial area density

Objectives

Three-dimensional numerical simulation was carried out to

examine its applicability to prediction of slug generation at a V-

shaped elbow and slug characteristics.

Gas

Liquid



7

θ θ

Test section

Ring type electrode

Mixing section

Flow meter Valve Mhono

pump

Tank

Filter Critical flow nozzle

Pressure regulator valve

Air filter

Cooler

Compressor

Tank

θ θ

l Insulant

Electrode 1 2 1

50mm 50mm

400 mm 800 mm

12 00 mm

Ring-type electrode

Flow

Test Fluids: Water and Air D = 20 mm

θ = 3˚, 5˚, 7˚

JG = 0.095 – 1.041 m/s

JL = 0.087 – 1.034 m/s

Air

Water

Separator Plate

Previous Work (Hosokawa and Tomiyama, 2003)

Experimental Apparatus

Test Section



8

0.5 1

0.5

1

0

Stratified-Slug

Stratified-Plug

Stratified-Semi-Slug Slug-Slug

Slug-Plug

<JL> (m/s)

<JG

> (m

/s)

D =20mm

θ = 5˚

Ascending pipe Descending pipe

Flow direction


Flow Pattern in the Ascending Pipe

Flow direction

Stratified-Slug


Flow Pattern Map Target



9

θ θ

50mm 50mm

400 mm 800 mm

12 00 mm

Flow


Measured Liquid Profile

l

0 1 20

10

20

= 20 mm = 5° = 0.61 m/s = 0.22 m/s

= 800-25 mm = 800+25 mm

Time (sec)

Liq

uid

lev

el (

mm

)

D

JG

JL

ll



θcos056.0log135.0θsin35.0ρ

ρ07.1 10

Eo

gDJJV

L

LGS

94.32.3exp,

LG

LU

U

SS

JJ

J

D

L

L

Vf 　　

S

G

GU

S

V

J

L

L

α

11

Slug Velocity VS :

Slug Frequency fS :

Slug Length LS :

(Gas Volume Fraction αG ) 227.0625.0α

LG

G

GJJ

J

D = 20, 30, 40 mm

θ = 3˚, 5˚, 7˚

JG = 0.087 - 1.034 m/s

JL = 0.095 - 1.041 m/s

10


Correlation for Slug Characteristics



11

)(||ρ8

1LGLGGLifL iG i AC VVVVFF

LiA α

LGGL ρ5.0ρ5.0ρ

5.3fC

])([ν T

kktk t VV τ

δκσ nF ss

Mass :

Momentum :

Governing Equations

Closure Models

Interfacial force :

Area density :

Density :

Friction coeff. :

Numerical Method

kk

s

kk

k ik t

T

kkkk

kk

kkk τP

t αραρ]})({[να

α

1

ρ

1)(

FFgVVVV

V

0

kk

k

tV

where k : gas or liquid

Turbulent stress :

Surface tension :

Free-surface treatment (Egorov, 2004; Vallée et al., 2005; Höhne et al., 2011)

Commercial Software CFX13 was used.

The k-ε model for the two-phase mixture was used for

turbulent viscoisity νt .

The Continuum Surface Force Model (Brackbill, 1992) was used for the

surface tension.



12

100D 100D Inlet

z

x

z

y

Water

Air

Number of cell ： 54,000

Time step： 0.005 s

Time duration： 30 - 60 s

Calculation time： 4 – 6 d / run

CPU： Intel Xeon(2.9GHz, 4GB-RAM)

Parallel Core： 4 cores

Simulation Model

Calculation Model

Mesh

θ θ

Inlet

Constant velocity

Outlet

Constant pressure D = 20, 30, 40 mm

θ = 3˚, 5˚, 7˚

Close-up of V-section



13

D = 20 mm

θ = 5˚

JG = 0.60 m/s

JL = 0.22 m/s

Result Computed Liquid Distribution


Stratified-Slug

0

Tim

e (s

)

1

2

αL 1 0

l/D 40 50 60 70 80 90 30 20 10 0

0.5 1

0.5

1

0

Stratified-Slug

Stratified-Plug


Slug-Plug

<JL> (m/s)

<JG

> (m

/s)



14

Measured Predicted

Result Computed Liquid Profile @ l/D = 40

0 1 20

10

20

= 20 mm = 5° = 0.61 m/s = 0.22 m/s

= 800-25 mm = 800+25 mm

Time (sec)

Liq

uid

lev

el (

mm

)

D

JG

JL

ll

0 1 20

10

20

= 20 mm = 5° = 0.61 m/s = 0.22 m/s

= 800-25 mm = 800+25 mm

Time (sec)L

iquid

lev

el (

mm

)

D

JG

JL

ll



15

D = 20 mm

θ = 5˚

JG = 0.2 m/s

JL = 0.4 m/s



Stratified-Plug

0.5 1

0.5

1

0

Stratified-Slug

Stratified-Plug


Slug-Plug

<JL> (m/s)

<JG

> (m

/s)

0

Tim

e (s

)

1

2

l/D 40 50 60 70 80 90 30 20 10 0

αL 1 0



16

D = 20 mm

θ = 5˚

JG = 1.0 m/s

JL = 0.2 m/s



Stratified-Semislug

0.5 1

0.5

1

0

Stratified-Slug

Stratified-Plug


Slug-Plug

<JL> (m/s)

<JG

> (m

/s)

0

Tim

e (s

)

1

2

l/D 40 50 60 70 80 90 30 20 10 0

αL 1 0



17

Flow Pattern Map

Stratified-Plug

Stratified-Slug

Slug-Slug Stratified-Semi-slug

Slug-Plug

0 0.5 10

0.5

1

(m/s)

(m/s

)

JL

J G

Predicted flow pattern Stratified-Plug Stratified-Slug Stratified-Semi-slug

D = 20 mm

θ = 5˚



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Slug Characteristics

0 1 20

1

2 = 20 mm = 5°

(m/s)

(m/s

)

=0.2 m/s Correlation Predicted



D

JL

JL

JL

JG

VS

0 1 20

10

20 = 20 mm = 5°

(m/s)

(1/s

)




D

JL

JL

JL

JG

f S

0 0.5 1 1.5 20

0.5

1 = 20 mm = 5°

(m/s)




D

JL

JL

JL

JG

LS /L

U

Slug Velocity Slug Frequency Slug Length

(non -dimensional)

Dependence on JG and JL D = 20 mm

θ = 5˚



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Slug Characteristics

Slug Velocity Slug Frequency

Comparison between measured and predicted results

0 1 20

1

2

Measured and predicted (m/s)

Co

rrel

atio

n (

m/s

)

VS

-15%

+15%

Measured Predicted

= 20 mm = 3°, 5°, 7°

D

0 10 200

10

20

Measured and predicted (1/s)

Corr

elat

ion

(1

/s)

fS

+20%

-20%

Measured Predicted

= 20 mm = 3°, 5°, 7°

D

0 0.5 10

0.5

1

Measured and predicted

Co

rrel

atio

n

LS/LU

Measured Predicted

+20%

-20% = 20 mm = 3°, 5°, 7°

D

D = 20 mm

θ = 3˚, 5˚, 7˚

Slug Length

(non -dimensional)



20

Summary Three-dimensional numerical simulation of slugs generated at a V-shaped

elbow was carried out. The results are summarized as follows:

The two-fluid model with free surface treatment was able to

predict the slug generation at the V-shaped elbow and slug

growth and collapse in the ascending pipe.

The model gave reasonable predictions for the effects of the

gas and liquid volume fluxes on slug characteristics.

Since the pipe diameters studied here are relatively small compared with those

in practical systems, validation of the method for slug flow in large-size pipes is

required in the future.



21

END



22



23

Effect of Mesh

0 0.50

0.5

Predicted

Corr

elat

ion

LS/LU

54,000 cells 320,000 cells

+20%

-20% = 20 mm = 5°D

0 0.5 1 1.50

0.5

1

1.5

Predicted (m/s)

Co

rrel

atio

n (

m/s

)

VS

-15%

+15%

54,000 cells 320,000 cells

= 20 mm = 5°D

0 5 100

5

10

Predicted (1/s)

Corr

elat

ion

(1

/s)

fS

+20%

-20%

54,000 cells 320,000 cells

= 20 mm = 5°D


(non -dimensional)

D = 20 mm

θ = 5˚



24

Effect of friction coefficient Cf


(non -dimensional)

D = 20 mm

θ = 5˚

0 0.50

0.5

Predicted

Corr

elat

ion

LS/LU

= 0.5 = 3.5 = 10 = 50

+20%

-20%

Cf

0 0.5 1 1.50

0.5

1

1.5

Predicted (m/s)

Co

rrel

atio

n (

m/s

)

VS

-15%

+15%

= 0.5 = 3.5 = 10 = 50

Cf

0 5 100

5

10

Predicted (1/s)

Corr

elat

ion

(1/s

)

fS

+20%

-20%

= 0.5 = 3.5 = 10 = 50

Cf



Slug Velocity VS :

Slug Frequency fS :

Slug Length LS :

(Gas Volume Fraction αG )

25


Correlation for Slug Characteristics

θcosθsinρ

ρhv

L

LGoS FrFrgD

JJCV

Based on the drift flux model:

D = 20, 30, 40 mm

θ = 3˚, 5˚, 7˚

JG = 0.087 - 1.034 m/s

JL = 0.095 - 1.041 m/s

Slip Velocity (Bendiksen, 1984)

θcos056.0log135.0θsin35.0ρ

ρ07.1 10

Eo

gDJJV

L

LGS

94.32.3exp,

LG

LU

U

SS

JJ

J

D

L

L

Vf 　　

S

G

GU

S

V

J

L

L

α

11

227.0625.0α

LG

G

GJJ

J

Dimensionless slug unit length LU/D was assumed to

relates to the dimensionless liquid volume flux JL/(JL+JG)

Based on mass conservation of slug unit

Measured αG was proportional to the dimensionless gas

volume flux JL/(JL+JG)



26

)(||ρ8

1LGLGGLifL iG i AC VVVVFF

LiA α

LGGL ρ5.0ρ5.0ρ

5.3fC

])([ν T

kktk t VV τ

δκσ nF ss

Mass :

Momentum :

Governing Equations

Closure Models

Interfacial Force :

Area Density :

Density :

Friction Coeff. :

Numerical Method

kk

s

kk

k ik t

T

kkkk

kk

kkk τP

t αραρ]})({[να

α

1

ρ

1)(

FFgVVVV

V

0

kk

k

tV

where k : gas or liquid

Turbulent Stress :

Surface Tension :

Free-surface treatment (Egorov, 2004; Vallée et al., 2005; Höhne et al., 2011)

Commercial Software CFX13 was used.

The k-ε model for the two-phase mixture (ANSYS, 2010) was

used for turbulent viscoisity νt .

The Continuum Surface Force Model (Brackbill, 1992) was used for the surface

tension.



27

])σ

νν[(ε kk

kk

k

tmm P

tV

m

T

mmtP VVV ])([νk

]ε)σ

νν[(

εεε

ε 2

2ε1ε

k

kkk

tmm CPC

tV

m

GLLGGGm

ρ

ραρα VVV

m

LLLGGGm

ρ

ναναν

εν μ

2kCt

Numerical Method

Turbulence Model : k-ε Model for Two-Phase Mixture (ANSYS, 2010)

Turbulent Kinetic Energy k:

Turbulent Dissipation Rate ε:

where

Turbulent Kinematic Viscosity νt:

Production Rate of Shear-induced Turbulence Pk:

Mixture Kinematic Viscosity νm:

Mixture Velocity Vm:



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|α|δ L

LL

L

L

LL

L α|α||α|

α

|α|

1

|α|

ακ n

Numerical Method

Surface Tension Model : Continuum Surface Force Model (Brackbill et all., 1992)

where

Unit vector normal to the interface n:

Curvature of the interface κ:

Delta function δ:

δκσ nF ss Surface Tension Fs :

|α|

α

L

L

n

(The liquid volume fraction αL was used as a phase

indicator function.)

Contact Angle nw: 70˚ ww sincos θθ ww tnn @Cells adjacent to wall



29

Past research in onset of slugging

In a straight pipe

In a hilly-terrain pipeline

• Kordyban and Ranov, 1970

• Wallis and Dobson, 1973

• Mishima and Ishii, 1980 ,etc.

• Mishima and Ishii, 1993

• Zheng, Brill and Shoham, 1993

• Hosokawa and Tomiyama, 2003

• Masella et al., 1998

• Issa et al., 2003

• Bonizzi et al., 2003

In a V-shaped elbow • Fitremann, 1975

For such hilly-terrain pipeline,

knowledge on a onset of

slugging is still rudimentary.

In particular, there are few

studies on a slug flow in a V-

shaped elbow.



30


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