Jumper Analysis with Interacting Internal Two-phase Flow

Transcription

1 Jumper Analysis with Interacting Internal Two-phase Flow Leonardo Chica University of Houston College of Technology Mechanical Engineering Technology March 20, 2012

2 Overview Problem Definition Jumper Purpose Physics Multiphase Flow Flow Induced Turbulence Two-way Coupling Conclusions Future Research Q & A

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 on fatigue life of the jumper.

4 Jumper Types: Rigid jumpers: U-shaped, M-shaped, L or Z shaped Flexible Jumpers Tree Manifold

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.

6 Fluid Dynamics Conservation of mass: ρ t + ρv = 0 Conservation of momentum: X Component: (ρu) t + ρuv = p x + τ xx x + τ xy y + τ zx z + ρf x Y Component: (ρν) t + ρνv = p y + τ xy x + τ yy y + τ zy z + ρf y Z Component: (ρw) t + ρwv = p z + τ xz x + τ yz y + τ zz z + ρf z

7 Fluid Dynamics Conservation of Energy: t ρ V2 e ρ e + V2 2 V = ρq + x up x + uτ yx y + ντ zy z + ρfv k T x + y νp y + uτ zx z + wτ xz x wp z k T y + z + ντ xy x + uτ xx x + wτ yz y k T z + ντ yy y + wτ zz z

8 Solid Mechanics Elasticity equations σ x x + τ xy y + τ xz z + X b = 0 τ xy x + σ y y + τ yz z + Y b = 0 τ xz x + τ yz y + σ z z + Z b = 0

9 Multiphase Flow Volume fraction of water(α) = volume of a pipe segment occupied by water volume of the pipe segment Horizontal pipes Dispersed bubble flow Annular flow Plug flow Slug flow Stratified flow Wavy flow Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance

10 Multiphase Flow Vertical Pipes Dispersed bubble flow Slug flow Churn flow Annular flow Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance

11 Slug Flow Terrain generated slugs Operationally induced surges Hydrodynamic slugs Instability in stratified flow Gas blocking by liquid Gas entrainment

12 Jumper Model Cross section Carbon Steel Properties Feature Value Outer Diameter (in) Wall thickness (in) 1.25 Density (lb/in 3 ) Young Modulus (psi) 3x10 7 Poisson Ratio 0.303

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

14 Geometry Models Two-bend model: Two-way coupling simulation Jumper model: CFD simulation

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 of vibration. Assessment for avoidance induced fatigue failure.

16 Flow Induced Turbulence Assessment Likelihood of failure (LOF): LOF = ρv2 F v FVF Flow Section Value ρv 2 (kg/(m s 2 )) 4,649.5 Multiphase FVF (Fluid Viscosity Factor) 1 F v (Flow Induced Vibration Factor) 8, LOF LOF < 1 : main line should be redesigned, further analyzed, or vibration monitored. Special techniques recommended (FEA and CFD).

17 Engineering Packages Computational Fluid Dynamics (CFD) STAR-CCM Finite Element Analysis (FEA) Abaqus

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 displacements and stresses Exporting Fluctuating Pressures FEA structural solution

19 Finite Element Analysis (FEA) Two-bend case parameters Element type Linear elastic stress hexahedral No. of elements 9,618 Time step Minimum Time step: s 1.0x10e-9 s

20 Modal Analysis: Two-bend Model Determine the structural natural frequencies Mode No. Frequency (Hz) Period (s) Top view (1st mode) Isometric view (1st mode)

21 Modal Analysis: Jumper Model Mode No. Frequency (Hz) Period (s) Isometric view (1st mode) Top view (1st mode)

22 Computational Fluid Dynamics (CFD) Two-bend case parameters Element type Polyhedral + Generalized Cylinder No. of elements 295,000 Time step (s) Total physical time (s) 20 Time Turbulence RANS Turbulence Multiphase Flow Physics Models Implicit Unsteady Reynolds-Averaged Navier-Stokes (RANS) SST K-Omega Volume of Fluid (VOF)

23 Two-bend Case: Volume Fraction Volume fraction of water after 7.4 s

24 Two-bend Case: Slug Frequency Two-bend case Slug Period (s) 0.96 Slug Frequency (Hz) Natural Frequency 1st mode (Hz) 1.079

25 Jumper Simulation Similar flow patterns in first half of jumper as one-bend and two-bend cases Mesh: cells Time step: 0.01 s Total Physical time: 30 s

26 Jumper Simulation: Volume Fraction Volume Fraction of Water Volume Fraction Plane B Time (s) Plane A Plane A Plane B Volume fraction of water after 22.5 s

27 Jumper Simulation: Pressure Fluctuations Pressure (psi) rd bend -2-4 Time (s) 1st bend 3rd bend 4rd bend 2nd bend Section Max. Pressure (psi) 4th bend 3rd bend 7.2 4th bend 7.1

28 Displacements Maximum displacement: in after 8.28 s

29 Von Mises Stress σ VM = 2 2 σ 2 σ σ 3 σ σ 3 σ 2 2 σ 1, σ 2, and σ 3 : principal stresses in the x, y, and z direction Maximum von mises stress: 404 psi < Yield strength: psi

30 Stress vs. Time Von Mises Stress vs Time Stress (psi) Time (s) Time History in 2nd bend Period between peaks (s) 6 Response frequency (Hz) 0.167

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 twobend model. A sinusoidal pattern was found for the response frequency. Two-way coupling is a feasible technique for fluid structure interaction problems.

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).

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

34 References Banerjee. Element Stress. Wikiversity. 22 Aug Web. 17 Jul < Bratland, O. Pipe Flow 2: Multi-phase Flow Assurance Web. 14 Oct < > Blevins, R. D. Flow Induced Vibration. Malabar, FL: Krieger Publishing Company, Print Energy Institute. Guidelines for the avoidance of vibration induced fatigue failure in process pipework. London: Energy Institute, Electronic. Feesa Ltd, Hydrodynamic Slug Size in Multiphase Flowlines < Izarra, Rafael. Second Moment Modeling for the Numerical Simulation of Passive Scalar Dispersion of Air Pollutants in Urban Environments. Diss. Siegen University, Print. Mott, Robert. Machine Elements in Mechanical Design. Upper Saddle River: Pearson Print ---. Applied Fluid Mechanics. Prentice Hall 6th edition, Print. Timoshenko, S. and Goodie, J. Theory of Elasticity. New York: 3rd ed. McGraw-Hill, 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):

35 Questions?