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 Tree Manifold www.oceaneering.com
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: 𝜖𝜍 𝜖𝑢 + 𝛼 ρV = 0 • Conservation of momentum: 𝜖(𝜍𝑣) + 𝛼 𝜍𝑣𝑊 = − 𝜖𝑞 𝜖𝑦 + 𝜖𝜐 𝑦𝑦 𝜖𝑦 + 𝜖𝜐 𝑦𝑧 𝜖𝑧 + 𝜖𝜐 𝑨𝑦 X Component: 𝜖𝑨 + 𝜍𝑔 𝑦 𝜖𝑢 𝜖(𝜍𝜉) + 𝛼 𝜍𝜉𝑊 = − 𝜖𝑞 𝜖𝑧 + 𝜖𝜐 𝑦𝑧 𝜖𝑦 + 𝜖𝜐 𝑧𝑧 𝜖𝑧 + 𝜖𝜐 𝑨𝑧 𝜖𝑨 + 𝜍𝑔 𝑧 Y Component: 𝜖𝑢 𝜖(𝜍𝑥) + 𝛼 𝜍𝑥𝑊 = − 𝜖𝑞 𝜖𝑨 + 𝜖𝜐 𝑦𝑨 𝜖𝑦 + 𝜖𝜐 𝑧𝑨 𝜖𝑧 + 𝜖𝜐 𝑨𝑨 Z Component: 𝜖𝑨 + 𝜍𝑔 𝑨 𝜖𝑢
Fluid Dynamics • Conservation of Energy: 𝜖𝑢 𝜍 𝑓 + 𝑊 2 + 𝛼 𝜍 𝑓 + 𝑊 2 𝜖 𝑊 2 2 = 𝜍𝑟 + 𝜖 𝜖𝑦 𝑙 𝜖𝑈 + 𝜖 𝜖𝑧 𝑙 𝜖𝑈 + 𝜖 𝜖𝑨 𝑙 𝜖𝑈 𝜖𝑦 𝜖𝑧 𝜖𝑨 − 𝜖 𝑣𝑞 − 𝜖 𝜉𝑞 − 𝜖 𝑥𝑞 + 𝜖 𝑣𝜐 𝑦𝑦 𝜖𝑦 𝜖𝑧 𝜖𝑨 𝜖𝑦 + 𝜖 𝑣𝜐 𝑧𝑦 + 𝜖 𝑣𝜐 𝑨𝑦 + 𝜖 𝜉𝜐 𝑦𝑧 + 𝜖 𝜉𝜐 𝑧𝑧 𝜖𝑧 𝜖𝑨 𝜖𝑦 𝜖𝑧 + 𝜖 𝜉𝜐 𝑨𝑧 + 𝜖 𝑥𝜐 𝑦𝑨 + 𝜖 𝑥𝜐 𝑧𝑨 + 𝜖 𝑥𝜐 𝑨𝑨 𝜖𝑨 𝜖𝑦 𝜖𝑧 𝜖𝑨 + 𝜍𝑔𝑊
Solid Mechanics • Elasticity equations 𝜖𝜏 𝑦 𝜖𝑦 + 𝜖𝜐 𝑦𝑧 𝜖𝑧 + 𝜖𝜐 𝑦𝑨 𝜖𝑨 + 𝑌 𝑐 = 0 𝜖𝜐 𝑦𝑧 𝜖𝑦 + 𝜖𝜏 𝑧 𝜖𝑧 + 𝜖𝜐 𝑧𝑨 𝜖𝑨 + 𝑍 𝑐 = 0 𝜖𝑦 + 𝜖𝜐 𝑧𝑨 𝜖𝜐 𝑦𝑨 𝜖𝑧 + 𝜖𝜏 𝑨 𝜖𝑨 + 𝑎 𝑐 = 0 http://en.wikiversity.org
Multiphase Flow 𝑊𝑝𝑚𝑣𝑛𝑓 𝑔𝑠𝑏𝑑𝑢𝑗𝑝𝑜 𝑝𝑔 𝑥𝑏𝑢𝑓𝑠(𝛽) = 𝑤𝑝𝑚𝑣𝑛𝑓 𝑝𝑔 𝑏 𝑞𝑗𝑞𝑓 𝑡𝑓𝑛𝑓𝑜𝑢 𝑝𝑑𝑑𝑣𝑞𝑗𝑓𝑒 𝑐𝑧 𝑥𝑏𝑢𝑓𝑠 𝑤𝑝𝑚𝑣𝑛𝑓 𝑝𝑔 𝑢ℎ𝑓 𝑞𝑗𝑞𝑓 𝑡𝑓𝑛𝑓𝑜𝑢 • Horizontal pipes Dispersed bubble flow Annular flow Plug flow Slug flow Stratified flow Wavy flow Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance
Multiphase Flow • Vertical Pipes Slug flow Churn flow Dispersed bubble 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 Outer Diameter (in) 10.75 Cross section Wall thickness (in) 1.25 Density (lb/in 3 ) 0.284 3x10 7 Carbon Steel Properties Young Modulus (psi) 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): 𝑀𝑃𝐺 = 𝜍𝑤 2 𝐺𝑊𝐺 𝐺 𝑤 Flow Section Value ρv 2 (kg/(m∙s 2 )) 4,649.5 FVF (Fluid Viscosity Factor) 1 Multiphase F v (Flow Induced Vibration Factor) 8,251.76 LOF 0.5634 • 0.5 ≤ LOF < 1 : main line should be redesigned, further analyzed, or vibration monitored. Special techniques recommended (FEA and CFD).
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 Exporting displacements and Fluctuating stresses Pressures FEA structural solution
Finite Element Analysis (FEA) Two-bend case parameters Linear elastic stress Element type hexahedral No. of elements 9,618 Time step 0.003 s Minimum Time 1.0x10e-9 s step:
Modal Analysis: Two-bend Model Determine the structural natural frequencies 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 Top view (1st mode) Isometric view (1st mode)
Modal Analysis: Jumper Model Mode Frequency Period No. (Hz) (s) 1 0.20485 4.882 2 0.34836 2.871 3 0.46962 2.129 4 0.52721 1.897 Isometric view (1st mode) Top view (1st mode)
Computational Fluid Dynamics (CFD) Two-bend case parameters Polyhedral + Element type Generalized Cylinder No. of elements 295,000 Time step (s) 0.003 Total physical time (s) 20 Physics Models Time Implicit Unsteady Reynolds-Averaged Turbulence 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 1.079 mode (Hz)
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 Volume Fraction of Water 0.7 0.6 0.5 Volume 0.4 Plane B Fraction 0.3 0.2 0.1 0 Plane A 0 5 10 15 20 25 30 Time (s) Plane A Plane B Volume fraction of water after 22.5 s
Jumper Simulation: Pressure Fluctuations 8 6 4 Pressure (psi) 2 3rd bend 0 0 5 10 15 20 25 30 35 -2 -4 Time (s) 1st bend 3rd bend 4rd bend 2nd 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 2 𝜏 2 − 𝜏 1 2 + 𝜏 3 − 𝜏 1 2 + 𝜏 3 − 𝜏 2 2 𝜏 𝑊𝑁 = 2 𝜏 1 , 𝜏 2 , and 𝜏 3 : principal stresses in the x, y, and z direction Maximum von mises stress: 404 psi < Yield strength: 65000 psi
Stress vs. Time Von Mises Stress vs Time 40 35 30 25 Stress (psi) 20 15 10 5 0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Time (s) 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
Recommend
More recommend
