Vortex Induced Vibration-Oil Platform Riser (English Units)

CROSS FLOW VORTEX INDUCED VIBRATION ANALYSIS
Global Variables - Input
Prepared by:				Checked by:
Pipe Outside Diameter, Do =						18	in
Pipe Wall Thickness,t =						0.562	in
Concrete weight coating thickness, tc =						1.5	in
Young Modulus -Steel, E =						2.90E+07	psi
Sea current velocity for a 100 yr Return period storm, U =						3	ft/s
Specified minimum yield strength of pipe, Sy =						52000	psi
Strouhal number, St =						0.219
Kinematic viscosity of sea water at 70oC, vk						0.0000113	ft2/s
End fixity constant, C =(kπ)/2						2.55
Added mass coefficient, Cm						1
Concrete weight coating density, ρoc =						140	lbs/ft3
Density of Steel, ρos =						490	lbs/ft3
Density of Seawater, ρow =						64	lbs/ft3
Logarithm Decrement, δ						0.05
ψT =	Normal Safety Class coefficient					2
ψD =	Period transformation Factor					1
ψR =	Natural frequency Reduction Factor					1
ψU =	Extreme Current Variability factor					1
Pipe Inside Diameter, Di = Do - 2t						16.876	in
Total pipe outside diameter with concrete coating, Dtot = Do+2tc						21	in
Moment of inertia of cross section, I						1171.637829	in4
Damping ratio, ζ = δ2/(δ2+4π2)						0.007956464
Weight of displaced water, ww =(π/4)*Dtot2*ρow						153.958	lbs/ft
Weight of contents, wocn =(π/4)*Di2*ρocn						99.4266266	lbs/ft
Dry weight of pipe with concrete coating, ws
=(π/4)*((Do2-Di2)*ρos +(Dtot2-Do2))*ρoc						194.1292651	lbs/ft
Specific weight of pipe, (ρs/ρw) = (ws/ww)						1.260923532
Dynamic mass, wd =(ww + wocn + ws) / g						13.89794695	slugs/ft
Stability Parameter, Ks =π2 ζ ((ρs/ρw) -Cm)						0.020494895
Free Span Reduced Velocity, VR,ONSET CROSS FLOW
=((π3)*((ρs/ρw + Cm)/(1.5+St2+(ρs/ρw + Cm)-1.5Ks2)))^0.5						3.797567143
Limiting criteria for the onset of Cross flow Vibration,
fn ≥ (U/(VR,ONST*Dtot))*ΨT *ΨD*ΨR*ΨU						0.902833656	Hz
Maximum Allowable Free Span length, L							ft
=(((C*((EI/M)^0.5)))/fn)^0.5)						107.8787189	ft