wave, current, and wind forces
TRANSCRIPT
An offshore structure is
designed to withstand
the 100-year storm
(wave/current/wind). A
mono-chromatic wave of
height Hmax is assumed.
Wave, current, and wind forces
CE358-Introductory Ocean Engineering, UT Austin 1 Copyright: Prof. S.A. Kinnas, 2012
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 2
OFFSHORE PLATFORMS are comprised of
many cylindrical or prismatic components
(structural elements, floatation parts, risers,
tendons, mooring lines, etc)
Fixed
Platform
(FP)
(to 1650 ft) Compliant
Tower
(CT)
(1500-3000 ft) Sea Star
(SStar)
(600-3000 ft)
Floating
Production
Systems
(FPS)
(1500-600 ft)
Tension
Leg
Platform
(TLP)
(1500-7000 ft)
Subsea
System
(SS)
(to 7000 ft)
SPAR
Platform
(SP)
(2000-10,000 ft)
Figure from BOEMRE, U.S. Department of the Interior CE358-Introductory Ocean Engineering, UT Austin 3 Copyright: Prof. S.A. Kinnas, 2012
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 4
What inflow velocity would a pile be subjected to?
Movie here!
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 5
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 6
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 7
Study steady flow around 2-D cylinder (circle)
subject to steady inflow
Study unsteady flow around 2-D cylinder (circle)
subject to accelerating inflow
Apply the study and the formulas developed in
the previous steps, on “slices” of the 3-D cylinder,
subject to wave and current, and integrate along
its length to determine total forces and moments
Steps to take:
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 8
22
2
1yx
RUx
sin222 Uvuqs
2
2
0 1
2
1
U
q
U
PPC SS
P
Velocity potential:
Surface
velocity
Surface
pressure
coefficient
Inviscid Flow
Around a Circle
D’Alembert “paradox”: The force on a body subject
to inviscid steady flow is equal to zero!
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 9
Re=9.6
Re=2,000
Re=26
Photos from Album of Fluid
Motion of M. Vandyke
UDRe
D
U
viscositykinematic/ =10-6 m2/s for H2O at 20o C. If D=20cm
for Re=2000, U should be 0.01 m/s
Reynolds
Number
Effect of viscosity on flow around circle
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 10
From Engineering Fluid Mechanics of Crowe et al, 2009
Physical properties of air and water circle
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 11
Effect of Re on the
pressure distribution
on surface of circle
Inviscid Flow
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 12
Drag
UDRe
=dynamic viscosity
= friction (shear stress) acting on
the body
0cos Drag Friction ds
U
p
0sin Drag ) formor ( Pressure dsp
Total Drag = Friction Drag + Pressure Drag
DU
CD2
2
1
hunit widtper force Drag
Drag Coefficient (in 2-D):
proj
D
AU
C2
2
1
force Drag
(in 3-D): Aproj is the projected area of the body on
a plane normal to the direction of inflow
z u
dz
du
pressure
(normal stress)
velocity profile
p
Drag and Drag coefficient
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 13
D U
DUDlUAU
C
proj
D222
2
1
unit widthper force Drag
2
1
force Drag
2
1
force Drag
Drag force on a cylinder subject to uniform current U
DlAproj
l
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 14
Effect of Re on Drag coefficient on Cylinder
Drag “crisis”
2
1
hunit widtper force Drag
2DU
CD
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 15
Effect of roughness on Drag coefficient on Cylinder
k
d
k/d= relative
roughness
From Engineering Fluid Mechanics of Crowe et al, 2009
smoothDC ,
roughDC ,
CE358-Introductory Ocean Engineering, UT Austin Copyright: Prof. S.A. Kinnas, 2012 16
Drag coefficients for some other 2-D shapes
From Engineering Fluid Mechanics of Crowe et al, 2009
