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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

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SLIDE 1

Jumper Analysis with Interacting Internal Two-phase Flow

Leonardo Chica University of Houston College of Technology Mechanical Engineering Technology March 20, 2012

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SLIDE 2

Overview

  • Problem Definition
  • Jumper
  • Purpose
  • Physics
  • Multiphase Flow
  • Flow Induced Turbulence
  • Two-way Coupling
  • Conclusions
  • Future Research
  • Q & A
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SLIDE 3

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

  • n fatigue life of the jumper.
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SLIDE 4

Jumper

Types:

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

www.oceaneering.com

Manifold Tree

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SLIDE 5

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.

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SLIDE 6

Fluid Dynamics

  • Conservation of mass:
  • Conservation of momentum:

X Component: Y Component: Z Component:

πœ–πœ πœ–π‘’ + 𝛼 ρV = 0 πœ–(πœπ‘£) πœ–π‘’ + 𝛼 πœπ‘£π‘Š = βˆ’ πœ–π‘ž πœ–π‘¦ + πœ–πœπ‘¦π‘¦ πœ–π‘¦ + πœ–πœπ‘¦π‘§ πœ–π‘§ + πœ–πœπ‘¨π‘¦ πœ–π‘¨ + πœπ‘”

𝑦

πœ–(πœπœ‰) πœ–π‘’ + 𝛼 πœπœ‰π‘Š = βˆ’ πœ–π‘ž πœ–π‘§ + πœ–πœπ‘¦π‘§ πœ–π‘¦ + πœ–πœπ‘§π‘§ πœ–π‘§ + πœ–πœπ‘¨π‘§ πœ–π‘¨ + πœπ‘”

𝑧

πœ–(𝜍π‘₯) πœ–π‘’ + 𝛼 𝜍π‘₯π‘Š = βˆ’ πœ–π‘ž πœ–π‘¨ + πœ–πœπ‘¦π‘¨ πœ–π‘¦ + πœ–πœπ‘§π‘¨ πœ–π‘§ + πœ–πœπ‘¨π‘¨ πœ–π‘¨ + πœπ‘”

𝑨

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SLIDE 7

Fluid Dynamics

  • Conservation of Energy:

πœ– πœ–π‘’ 𝜍 𝑓 + π‘Š2 2 + 𝛼 𝜍 𝑓 + π‘Š2 2 π‘Š = πœπ‘Ÿ + πœ– πœ–π‘¦ 𝑙 πœ–π‘ˆ πœ–π‘¦ + πœ– πœ–π‘§ 𝑙 πœ–π‘ˆ πœ–π‘§ + πœ– πœ–π‘¨ 𝑙 πœ–π‘ˆ πœ–π‘¨ βˆ’ πœ– π‘£π‘ž πœ–π‘¦ βˆ’ πœ– πœ‰π‘ž πœ–π‘§ βˆ’ πœ– π‘₯π‘ž πœ–π‘¨ + πœ– π‘£πœπ‘¦π‘¦ πœ–π‘¦ + πœ– π‘£πœπ‘§π‘¦ πœ–π‘§ + πœ– π‘£πœπ‘¨π‘¦ πœ–π‘¨ + πœ– πœ‰πœπ‘¦π‘§ πœ–π‘¦ + πœ– πœ‰πœπ‘§π‘§ πœ–π‘§ + πœ– πœ‰πœπ‘¨π‘§ πœ–π‘¨ + πœ– π‘₯πœπ‘¦π‘¨ πœ–π‘¦ + πœ– π‘₯πœπ‘§π‘¨ πœ–π‘§ + πœ– π‘₯πœπ‘¨π‘¨ πœ–π‘¨ + πœπ‘”π‘Š

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SLIDE 8

Solid Mechanics

  • Elasticity equations

πœ–πœπ‘¦ πœ–π‘¦ + πœ–πœπ‘¦π‘§ πœ–π‘§ + πœ–πœπ‘¦π‘¨ πœ–π‘¨ + π‘Œπ‘ = 0 πœ–πœπ‘¦π‘§ πœ–π‘¦ + πœ–πœπ‘§ πœ–π‘§ + πœ–πœπ‘§π‘¨ πœ–π‘¨ + 𝑍

𝑐 = 0

πœ–πœπ‘¦π‘¨ πœ–π‘¦ + πœ–πœπ‘§π‘¨ πœ–π‘§ + πœ–πœπ‘¨ πœ–π‘¨ + π‘Žπ‘ = 0

http://en.wikiversity.org

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SLIDE 9

Multiphase Flow

  • Horizontal pipes

Dispersed bubble flow Annular flow Plug flow Slug flow Stratified flow Wavy flow π‘Šπ‘π‘šπ‘£π‘›π‘“ π‘”π‘ π‘π‘‘π‘’π‘—π‘π‘œ 𝑝𝑔 π‘₯𝑏𝑒𝑓𝑠(𝛽) = π‘€π‘π‘šπ‘£π‘›π‘“ 𝑝𝑔 𝑏 π‘žπ‘—π‘žπ‘“ π‘‘π‘“π‘•π‘›π‘“π‘œπ‘’ π‘π‘‘π‘‘π‘£π‘žπ‘—π‘“π‘’ 𝑐𝑧 π‘₯𝑏𝑒𝑓𝑠 π‘€π‘π‘šπ‘£π‘›π‘“ 𝑝𝑔 π‘’β„Žπ‘“ π‘žπ‘—π‘žπ‘“ π‘‘π‘“π‘•π‘›π‘“π‘œπ‘’

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

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SLIDE 10
  • Vertical Pipes

Multiphase Flow

Dispersed bubble flow Slug flow Churn flow Annular flow

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

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SLIDE 11

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

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SLIDE 12

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

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SLIDE 13

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

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SLIDE 14

Geometry Models

  • Two-bend model: Two-way coupling simulation
  • Jumper model: CFD simulation
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SLIDE 15

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
  • f vibration.
  • Assessment for avoidance induced fatigue

failure.

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SLIDE 16

Flow Induced Turbulence Assessment

  • Likelihood of failure (LOF):

𝑀𝑃𝐺 = πœπ‘€2 𝐺

𝑀

πΊπ‘ŠπΊ

  • 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/(mβˆ™s2)) 4,649.5 FVF (Fluid Viscosity Factor) 1 Fv (Flow Induced Vibration Factor) 8,251.76 LOF 0.5634

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SLIDE 17

Engineering Packages

  • Computational Fluid Dynamics (CFD)

– STAR-CCM+ 6.04

  • Finite Element Analysis (FEA)

– Abaqus 6.11-2

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SLIDE 18

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

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SLIDE 19

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

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SLIDE 20

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

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SLIDE 21

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)

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SLIDE 22

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)

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SLIDE 23

Two-bend Case: Volume Fraction

Volume fraction of water after 7.4 s

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SLIDE 24

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

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SLIDE 25

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
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SLIDE 26

Jumper Simulation: Volume Fraction

0.1 0.2 0.3 0.4 0.5 0.6 0.7 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

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SLIDE 27

Jumper Simulation: Pressure Fluctuations

  • 4
  • 2

2 4 6 8 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

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SLIDE 28

Displacements

Maximum displacement: 0.0725 in after 8.28 s

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SLIDE 29

Von Mises Stress

πœπ‘Šπ‘ = 2 2 𝜏2 βˆ’ 𝜏1 2 + 𝜏3 βˆ’ 𝜏1 2 + 𝜏3 βˆ’ 𝜏2 2

𝜏1 , 𝜏2, and 𝜏3: principal stresses in the x, y, and z direction Maximum von mises stress: 404 psi < Yield strength: 65000 psi

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SLIDE 30

Stress vs. Time

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

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SLIDE 31

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.

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SLIDE 32

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).
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SLIDE 33

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

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SLIDE 34

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. β€œInvestigations 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.

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SLIDE 35

Questions?