A study dy of Jumper r FIV due to multip iphas hase intern rnal al flow: w: under erst stan anding ding life-cy cycl cle fatig igue ue Alan n Muelle ler r & Oleg Voron onkov
Case e descrip cripti tion on [2] deformable jumper Main structural dimensions [1]: in Mixture on inlet out endings top half - air bottom half - water Case set-up: 1) water-air (50/50 % volume) mixture flow inside jumper; 2) the deformable jumper is clamped on its ends; 3) outside water is accounted as added mass and added damping. [1] 1] L. Chica. Fluid Structure Interaction Analysis of Two-Phase Flow in an M-shaped Jumper. University of Houston, College of Technology, Mechanical Engineering Technology. Star Global Conference 2012. January 28, 2012. [2] 2] Tie-in and structures. Brochure. Aker Solutions, 2010.
Applied ied physics ics & c charact acter eris istic tic param ameter ers Fluid side (STAR-CCM+): Structural side (Abaqus): Models: Step options: Implicit, 2-order time; Segregated flow, 2-order time; Eulerian Multiphase; VOF; Non-Linear Geometry (not a requirement) URANS k-omega SST turbulence; Gravity: [0,0,-1g]. Geometric parameters: Circular pipe; Flow parameters: D out = 10.75’’ (0.273 m); V in = 3.048 m/s; D in = 8.25’’ (0.210 m). water (incompressible): Mechanical characteristics: µ = 0.001 Pa·s; = 1000 kg/m 3 ; Steel: E = 205 GPa; Re(D in , V in ) = 6.4e+5; n = 0.29; air (ideal gas, isothermal): = 7800 kg/m 3 . µ = 2e-5 Pa·s; (P = 0) = 1.2 kg/m 3 ; Multi-phase internal flow leads to Re(Din, Vin) = 3.8e+4; range of forcing frequencies not air / water = 1.2e-3; found in single phase flows µ air / µ water = 2e-2. STAR-CCM+ v.9.02: ABAQUS v.6.13-1: 52 cpus: 82k cells per cpu; 4 cpu: 31.5k dof per cpu;
Poss ssible ible coupled ed solutio ution n approa oaches hes 1-way coupled 2-way coupled transient forces from the fluid solution are forces from the fluid side are transmitted to the structural side and transmitted to the structural solution; displacements of the structure are doesn’t account for vibration of the structure in the passed back to the fluid side; fluid solution; requires implicit coupling for stability; requires application of added mass and damping for added mass and damping from internal vibrations; internal flow is applied in a natural manner as a reaction for movement of the structure; Damping is applied Damping is applied two as as stiffness variants mass proportional proportional computationally more expensive; commonly used practice; potentially more accurate; needs minimum computational effort; How large is the difference in effort & What is a reasonable amount of added damping due accuracy from the 1-way coupled? to multiphase flow?
Abaqus s Stand andalo alone ne Analys ysis is: : Sti tiffn fness ess Static tic analys ysis is to evaluate e stiffne fness ss – 21K shell elements (S4), 126K DoF BCs: clamped ends
Abaqus s Stand andalo alone ne Analys ysis is: : Sti tiffn fness ess in X direction 2 forces (500 N each) applied def. x1000 in corresponding direction in Y direction X Y Z St., N/mm 575 56.5 489 def. x100 in Z direction Considerably weaker in Y (cross) direction def. x1000
Abaqus s Stand andalo alone ne Analys ysis is: : Natural ural Modes es Eigenvalu Ei lue e analys ysis s to evaluat uate e mode ode shapes pes and fun undamen damental tal frequenc encies ies Accounted mass: 1) structural mass (M s ); 2) mass of internal mixture (M im ): in assumption of uniform 50/50% air/water vol. fraction; 3) added mass of surrounding water: M e /M w = m* + Ca, m* = (M s + M im )/M w , Ca ≈ 1 [3], [4], M w – mass of displaced water; M e – effective structural mass mode #3 – Y mode #1 – Y mode #2 – Z [3] J.P. Pontaza, B. Abuali, G.W. Brown, F.J. Smith. Flow-Induced Vibrations of Subsea Piping: A Screening Approach Based on Numerical Simulation. Shell International Exploration and Production Inc., Shell U.K. Limited. SPE 166661. 2013. [4] J.P. Pontaza, R.G. Menon. Flow-Induced Vibrations of Subsea Jumpers due to Internal Multi-Phase Flow. Shell Projects & Technology. OMAE2011-50062.
Structural ructural mode e shapes es & natural ural frequen uencies cies Natural frequencies: Mode 1 2 3 4 5 6 7 8 … f, Hz 0.59 1.30 1.70 1.77 2.06 2.07 2.82 6.07 Considered in dynamic simulations mode #4 – X, Z mode #5 – Y mode #7 – Y mode #6 – X, Z
STAR-CCM+ CM+ VOF Standalo ndalone ne Struc ucture ture is rigid 4.2M polyhedral cells: Generalized Cylinder Mesh VOF Spatia tial resolut ution ion sufficie ient nt to reason onab ably ly capture ture water/a er/air r inter erfac ace e surfac ace Y+ near ar 1 to resolve e wall effects Time step limita tation tion : free surfac ace moves less than n 1 cell in 1 time step – D t f T 7 /50 (small fraction of highest mode considered) – Larger times step possible but leads to significant numerical diffusion Pressure Outlet Wall no slip Velocity Inlet
Fluid id Standa ndalo lone: ne: Volume ume Fractio tion n and Pressure essure Domina minate e Freq requenc ency y 0.09 9 Hz << Mode ode 1 Freq equenc ency y 0.59 9 Hz Pressure
1-way coupled Flui uid d – Same setup as in fluid standalone D t f T 7 /50 Struc uctu ture re – Structure resolution as in structure standalone – Same added mass for internal and external flow as in Eigenmode analysis – Time step chosen to resolve well 7 th mode D t=T 7 /60 – External fluid added damping – Internal fluid added damping • To correct ct for rigi gid d assum sumpti ption n in flui uid d model Explici Ex cit t Coupling ing – Fluid loads to structure once e per fluid d time e step Simulat ation ion over er 10 fun undamen damental tal flui uid d forci cing ng period iods
2-way coupled Flui uid d – Same conditions as in 1-way except fluid time step same as solid time step: D t f =T 7 /60 Struc uctu ture re – Same as 1-way but no added mass and damping for internal flow Implici mplicit t Coupl upling ing – Data Exchange once e per iterati tion on in a time e step • Fluid loads sent to structure • Structure displacements sent to fluid – Fluid and structure use identical time steps – Move to next time step when both structure and fluid residuals converge Simulat ation ion over er 10 fun undamen damental tal flui uid d forci cing ng period iods Under the stated conditions, the primary difference between 1-way and 2- way coupling: 2-way coupling requires more iterations within a time step: The elapsed time for 2-way is about 2 times the 1-way coupling
One-Way y Coupling pling : Intern ernal al Dampin ping Choice oice of f Damp mping ing – Mass Proportional C= a *M – Stiffness Proportional C= b *K e a,b to give dampi Size ping ng in Mode de 1 as s measured red in 2-way y coupl upling ing – ln(D) = 0.09 => ξ = ln(D)/sqrt[4·pi 2 + ln(D) 2 ] Stiffness proportional: 2ξ = βω Mass proportional: 2ξ =α / ω Mode 1 2 3 4 5 6 7 f, Hz 0.59 1.30 1.70 1.77 2.06 2.07 2.82 α =0.106Hz ξ : 1.43e-2 6.50e-3 4.97e-3 4.77e-3 4.10e-3 4.08e-3 3.00e-3 β =7.71e-3s ξ : 1.43e-2 3.16e-2 4.13e-2 4.30e-2 5.00e-2 5.03e-2 6.85e-2
Water er volume me fracti tion: on: evolutio ution of slugs gs bend before 2 nd lift: 1 st lift: formation of long slugs short slugs (1…3)D in long bend after 2 nd lift: long slugs ~(12…15)D in
Water er volume me fracti tion on 1-way coupled 2-way coupled cs #4 cs #4 cs #5 cs #5
Water er volume me fracti tion on (sec ectio tion n averaged aged) 2 1 6 5 ji jo 4 3 Dominant (slug) frequencies, Hz # 1 2 3 4 5 6 f, Hz 0.089 0.18 0.28 0.37 0.46 0.54
12 2 Pipe e vibrati rations ons 10 4 FFT (Ux), [25 s, tmax] 8 6 Fluid force
12 2 Pipe e vibrati rations ons 10 4 FFT (Uz), [25 s, tmax] 8 6
Pipe e vibrat rations ions 12 11 3 2 10 4 1 13 8 7 6 5 9 Dominant frequencies, Hz Mode - 1 2 3 4 5, 6 7 U (x200) U1-x 0.089 - 1.32 - 1.7-1.8 2.04 - U2-y 0.089 0.56 - 1.6-1.7 - 2.06 2.77 U3-z 0.089 - 1.32 - - 2.04 -
Stres ress s signal nal Def.: U (x200); Field: VM stress σ max (tension), max. amplitude Input for fatigue life calculation
Fatigue igue life e estim timat ate Rain flow counting results S-N curve [5] 1 repetition = ~79 s Applied modifications: thickness effect; stress gradient (bending); surface roughness. Palmgre gren-Min Miner r rule to compu pute te the damage and life estima imate te [5] Guide for the fatigue assessment of offshore structures. American Bureau of Shipping, Houston, TX, USA. November 2010.
Recommend
More recommend
