Jumper Analysis with Interacting Internal Two-phase Flow

Leonardo Chica

University of Houston

College of Technology

Mechanical Engineering Technology

March 20, 2012

Overview

• Problem Definition

• Jumper

• Purpose

• Physics

• Multiphase Flow

• Flow Induced Turbulence

• Two-way Coupling

• Conclusions

• Future Research

• Q & A

Problem Definition

A fluid structure interaction (FSI) problem in which the internal two-phase flow in a jumper interacts with the structure creating stresses and pressures that deforms the pipe, and consequently alters the flow of the fluid.

This phenomenon is important when designing a piping system since this might induce significant vibrations (Flow Induced Vibration) that has effects on fatigue life of the jumper.

Jumper

Types:

• Rigid jumpers: U-shaped, M-shaped, L or Z shaped

• Flexible Jumpers

www.oceaneering.com

Manifold

Tree

Purpose

• Couple FEA and CFD to analyze flow induced vibration in jumper.

• Assess jumper for Flow Induced Turbulence to avoid fatigue failure.

• Study the internal two-phase flow effects on the stress distribution of a rigid M-shaped jumper.

• Find a relationship between the fluid frequency, structural natural frequency, and response frequency.

Fluid Dynamics

• Conservation of mass:

• Conservation of momentum:

X Component:

Y Component:

Z Component:

𝜕𝜌

𝜕𝑡+ 𝛻 ρV = 0

𝜕(𝜌𝑢)

𝜕𝑡+ 𝛻 𝜌𝑢𝑉 = −

𝜕𝑝

𝜕𝑥+

𝜕𝜏𝑥𝑥

𝜕𝑥+

𝜕𝜏𝑥𝑦

𝜕𝑦+

𝜕𝜏𝑧𝑥

𝜕𝑧+ 𝜌𝑓𝑥

𝜕(𝜌𝜈)

𝜕𝑡+ 𝛻 𝜌𝜈𝑉 = −

𝜕𝑝

𝜕𝑦+

𝜕𝜏𝑥𝑦

𝜕𝑥+

𝜕𝜏𝑦𝑦

𝜕𝑦+

𝜕𝜏𝑧𝑦

𝜕𝑧+ 𝜌𝑓𝑦

𝜕(𝜌𝑤)

𝜕𝑡+ 𝛻 𝜌𝑤𝑉 = −

𝜕𝑝

𝜕𝑧+

𝜕𝜏𝑥𝑧

𝜕𝑥+

𝜕𝜏𝑦𝑧

𝜕𝑦+

𝜕𝜏𝑧𝑧

𝜕𝑧+ 𝜌𝑓𝑧

Fluid Dynamics

• Conservation of Energy:

𝜕

𝜕𝑡𝜌 𝑒 +

𝑉2

2+ 𝛻 𝜌 𝑒 +

𝑉2

2𝑉

= 𝜌𝑞 +𝜕

𝜕𝑥𝑘

𝜕𝑇

𝜕𝑥+

𝜕

𝜕𝑦𝑘

𝜕𝑇

𝜕𝑦+

𝜕

𝜕𝑧𝑘

𝜕𝑇

𝜕𝑧

−𝜕 𝑢𝑝

𝜕𝑥−

𝜕 𝜈𝑝

𝜕𝑦−

𝜕 𝑤𝑝

𝜕𝑧+

𝜕 𝑢𝜏𝑥𝑥

𝜕𝑥

+𝜕 𝑢𝜏𝑦𝑥

𝜕𝑦+

𝜕 𝑢𝜏𝑧𝑥

𝜕𝑧+

𝜕 𝜈𝜏𝑥𝑦

𝜕𝑥+

𝜕 𝜈𝜏𝑦𝑦

𝜕𝑦

+𝜕 𝜈𝜏𝑧𝑦

𝜕𝑧+

𝜕 𝑤𝜏𝑥𝑧

𝜕𝑥+

𝜕 𝑤𝜏𝑦𝑧

𝜕𝑦+

𝜕 𝑤𝜏𝑧𝑧

𝜕𝑧+ 𝜌𝑓𝑉

Solid Mechanics

• Elasticity equations

𝜕𝜎𝑥

𝜕𝑥+

𝜕𝜏𝑥𝑦

𝜕𝑦+

𝜕𝜏𝑥𝑧

𝜕𝑧+ 𝑋𝑏 = 0

𝜕𝜏𝑥𝑦

𝜕𝑥+

𝜕𝜎𝑦

𝜕𝑦+

𝜕𝜏𝑦𝑧

𝜕𝑧+ 𝑌𝑏 = 0

𝜕𝜏𝑥𝑧

𝜕𝑥+

𝜕𝜏𝑦𝑧

𝜕𝑦+

𝜕𝜎𝑧

𝜕𝑧+ 𝑍𝑏 = 0

http://en.wikiversity.org

Multiphase Flow

• Horizontal pipes

Dispersed bubble flow Annular flow

Plug flow Slug flow

Stratified flow Wavy flow

𝑉𝑜𝑙𝑢𝑚𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟(𝛼) =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑝𝑖𝑝𝑒 𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑤𝑎𝑡𝑒𝑟

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 𝑠𝑒𝑔𝑚𝑒𝑛𝑡

Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance

• Vertical Pipes

Multiphase Flow

Dispersed bubble flow Slug flow Churn flow Annular flow

Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance

Slug Flow

• Terrain generated slugs

• Operationally induced surges

• Hydrodynamic slugs

– Instability in stratified flow

– Gas blocking by liquid

– Gas entrainment

http://www.feesa.net/flowassurance

Jumper Model

Feature Value

Cross section Outer Diameter (in) 10.75

Wall thickness (in) 1.25

Carbon Steel Properties

Density (lb/in3) 0.284

Young Modulus (psi) 3x107

Poisson Ratio 0.303

Flow Selected Parameters

• Velocity: 10 ft/s

• 50% water – 50 % air

Volk, M., Delle-Case E., and Coletta A. Investigations of Flow Behavior Formation in Well-Head Jumpers during Restart with Gas and Liquid

Geometry Models

• Two-bend model: Two-way coupling simulation

• Jumper model: CFD simulation

Flow Induced Turbulence

• Formation of vortices (eddies) at the boundary layer of the wall.

• Dominant sources:

– High flow rates

– Flow discontinuities (bends)

• High levels of vibrations at the first modes of vibration.

• Assessment for avoidance induced fatigue failure.

Flow Induced Turbulence Assessment

• Likelihood of failure (LOF):

𝐿𝑂𝐹 =𝜌𝑣2

𝐹𝑣𝐹𝑉𝐹

• 0.5 ≤ LOF < 1 : main line should be redesigned, further analyzed, or vibration monitored. Special techniques recommended (FEA and CFD).

Flow Section Value

Multiphase

ρv2 (kg/(m∙s2)) 4,649.5

FVF (Fluid Viscosity Factor) 1

Fv (Flow Induced Vibration Factor) 8,251.76

LOF 0.5634

Engineering Packages

• Computational Fluid Dynamics (CFD)

– STAR-CCM+ 6.04

• Finite Element Analysis (FEA)

– Abaqus 6.11-2

Two-way Coupling

• CFD and FEM codes run simultaneously.

• Exchange information while iterating.

• Work for one-way coupled or loosely-coupled problems.

CFD flow solution

Exporting Fluctuating Pressures

FEA structural solution

Exporting displacements and

stresses

Finite Element Analysis (FEA)

Two-bend case parameters

Element type Linear elastic stress

hexahedral

No. of elements 9,618

Time step 0.003 s

Minimum Time step:

1.0x10e-9 s

Modal Analysis: Two-bend Model

Determine the structural natural frequencies

Top view (1st mode)

Isometric view (1st mode)

Mode No. Frequency (Hz) Period (s)

1 1.079 0.927

2 2.320 0.431

3 3.289 0.304

4 5.366 0.186

Modal Analysis: Jumper Model

Mode

No.

Frequency

(Hz)

Period

(s)

1 0.20485 4.882

2 0.34836 2.871

3 0.46962 2.129

4 0.52721 1.897

Top view (1st mode)

Isometric view (1st mode)

Computational Fluid Dynamics (CFD)

Two-bend case parameters

Element type Polyhedral +

Generalized Cylinder

No. of elements 295,000

Time step (s) 0.003

Total physical time (s) 20

Physics Models

Time Implicit Unsteady

Turbulence Reynolds-Averaged

Navier-Stokes (RANS)

RANS Turbulence SST K-Omega

Multiphase Flow Volume of Fluid (VOF)

Two-bend Case: Volume Fraction

Volume fraction of water after 7.4 s

Two-bend Case: Slug Frequency

Two-bend case

Slug Period (s) 0.96

Slug Frequency (Hz) 1.0417

Natural Frequency 1st mode (Hz)

1.079

Jumper Simulation

• Similar flow patterns in first half of jumper as one-bend and two-bend cases

• Mesh: 640159 cells

• Time step: 0.01 s

• Total Physical time: 30 s

Jumper Simulation: Volume Fraction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25 30

Volume Fraction

Time (s)

Volume Fraction of Water

Plane A Plane B

Plane A

Plane B

Volume fraction of water after 22.5 s

Jumper Simulation: Pressure Fluctuations

-4

-2

0

2

4

6

8

0 5 10 15 20 25 30 35

Pressure (psi)

Time (s)

1st bend 3rd bend 4rd bend 2nd bend

3rd bend

4th bend Section Max. Pressure (psi)

3rd bend 7.2

4th bend 7.1

Displacements

Maximum displacement: 0.0725 in after 8.28 s

Von Mises Stress

𝜎𝑉𝑀 =2

2𝜎2 − 𝜎1

2 + 𝜎3 − 𝜎12 + 𝜎3 − 𝜎2

2

𝜎1 , 𝜎2, and 𝜎3: principal stresses in the x, y, and z direction

Maximum von mises stress: 404 psi < Yield strength: 65000 psi

Stress vs. Time

0

5

10

15

20

25

30

35

40

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

Stress (psi)

Time (s)

Von Mises Stress vs Time

Time History in 2nd bend

Period between peaks (s) 6

Response frequency (Hz) 0.167

Conclusions

• For Flow Induced Turbulence assessment, modal analysis and CFD is required to check stability and likelihood of failure.

• Slug frequency falls close by the structural natural frequency for the two-bend model.

• A sinusoidal pattern was found for the response frequency.

• Two-way coupling is a feasible technique for fluid structure interaction problems.

Future Research

• Further FSI analysis for the entire jumper.

• Apply a S-N approach to predict the fatigue life of the two-bend model and the entire jumper.

• Include different Reynolds numbers, free stream turbulence intensity levels, and volume fractions.

• Couple Flow-Induced Vibration (FIV) and Vortex-Induced Vibration (VIV).

Thank You

• University of Houston: – Raresh Pascali: Associate Professor

– Marcus Gamino: Graduate student

• CD-adapco: – Rafael Izarra, Application Support Engineer

– Tammy de Boer, Global Academic Program Coordinator

• MCS Kenny: – Burak Ozturk, Component Design Lead

• SIMULIA: – Support Engineers

References

• Banerjee. Element Stress. Wikiversity. 22 Aug. 2007. Web. 17 Jul. 2011. <http://en.wikiversity.org/wiki/File:ElementStress.png>

• Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance. 2010. Web. 14 Oct 2011. <http://www.drbratland.com/index.html >

• Blevins, R. D. Flow Induced Vibration. Malabar, FL: Krieger Publishing Company, 2001. Print

• Energy Institute. Guidelines for the avoidance of vibration induced fatigue failure in process pipework. London: Energy Institute, 2008. Electronic.

• Feesa Ltd, Hydrodynamic Slug Size in Multiphase Flowlines. 2003. <http://www.feesa.net/flowassurance>

• Izarra, Rafael. Second Moment Modeling for the Numerical Simulation of Passive Scalar Dispersion of Air Pollutants in Urban Environments. Diss. Siegen University, 2009. Print.

• Mott, Robert. Machine Elements in Mechanical Design. Upper Saddle River: Pearson Print

• ---. Applied Fluid Mechanics. Prentice Hall 6th edition, 2006. Print. • Timoshenko, S. and Goodie, J. Theory of Elasticity. New York: 3rd ed. McGraw-Hill, 1970.

Print. • Volk, M., Delle-Case E., and Coletta A. “Investigations of Flow Behavior Formation in

Well-Head Jumpers during Restart with Gas and Liquid”. Office of Research and Sponsored Programs: The University of Tulsa. (2010): 10-41.

Questions?