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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
• 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
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: 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
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.