wave+calculations

8/8/2019 Wave+Calculations

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Automatic Wave Loads Calculation of Wave Load Values

Overview of 9

7. Determine the amount of marine growth, if any, on the considered

object based on the defined marine growth parameters or the wave

overwrites.

8. Determine the drag and inertia coefficients for the considered object

based on the defined drag and inertia coefficient parameters or the

wave overwrites.

9. Apply the Morison Equation to calculate the force exerted by the wave

at a particular location on the object.

10. Calculate the buoyant forces acting on the object.

Wave Wind Load

The program calculates the force exerted by a wave wind load at a particular

location on a structural object using the following steps. Note that wave wind

loads are only applied to the portions of the structure that are above the

wave surface.

1. Calculate the design wind speed.

2. Determine the section dimensions (not including marine growth or ice)

based on the defined section properties or the wave overwrites.

3. Determine the amount of marine growth, if any, on the considered

object based on the defined marine growth parameters or the wave

overwrites.

4. Determine the amount of ice, if any, on the considered object based

on the wave overwrites. Note that if both marine growth and ice is

specified at a location, only the marine growth value is used.

5. Determine the shape coefficient used for wind loads for the considered

object based on the defined shape coefficient that applies to all

elements or the wave overwrites.

6. Determine the wind load shielding factor, if any, on the considered

object based on the wave overwrites. The wind load on the object is

multiplied by this shielding factor.

7. Calculate the wind drag at a particular location on the object.




Apparent Wave Period of 9

Apparent Wave Period

The wave period input in the wave definition data does not include the effect

of the current. The wave period used when calculating the wave water particle

velocities and accelerations must include the effect of the current component

in the direction of the wave. The wave period that includes the effect of the

current is called the apparent wave period, Tapp. The apparent wave period is

calculated by solving a system of three simultaneous nonlinear equations.

Those equations, which are documented in Section C2.3.1b1 of the

commentary of the API Recommended Practice (American Petroleum Institute

2000), are:

I

app

V

T T

+=λ λ

) / 2(tan

22

λ π

πλ

d gT app = C2.3.1b1

dzd z

zU d

V d

c I

+

= ∫ − λ

π

λ π

λ π )(4cosh)(

) / 4sinh(

/ 4 0

where

λ = Wave length.

T = Wave period as input by user (not considering the current).

appT = Apparent wave period (considers the current).

I V = Effective current speed in the direction of the wave.

g = Acceleration due to gravity.

z = Elevation referenced to the storm water level (positive above

storm water level).




Wave Kinematics of 9

)( zU c = Component of steady current profile at elevation z in the

wave direction and not multiplied by the current blockage

factor.

d = Storm water depth.

Wave Kinematics

Wave kinematics yield the wave water particle velocities and accelerations.

The velocities and accelerations are calculated from a specified wave theory

or they are user-defined. Regardless of which method is used to obtain the

wave water particle velocities and accelerations, they are then modified by

the wave kinematics factor, which is intended to account for wave directional

spreading and irregularity in the wave profile shape.

The modification consists of multiplying the horizontal velocities and

accelerations by the wave kinematics factor. The vertical velocities and

accelerations are not modified.

Current Profile

The user specifies the current profile (velocity and direction of current as a

function of height) from the mud line to the storm water level. The user

specifies that either a Linear or a Nonlinear current stretching method is used

to stretch or compress the current to the wave surface at a particular

location. The current velocity at a particular location determined from

applying the current stretching technique is multiplied by the current blockage

factor to obtain the current velocity that is combined with the wave velocity.

Linear Current Stretching

Linear current stretching is based on the following equation, which is found in

Section 2.3.1b-5 of the API Recommended Practice (American Petroleum

Institute 2000). The equation is solved directly for z'.

η++=+

d

d d zd z )()'( 2.3.1b-5

where




Current Profile of 9

z = Elevation of the location where the water particle current

velocity is desired referenced to the storm water level (positive

above storm water level).

z' = Elevation of the location in the user-specified current profile

where the current velocity should be obtained referenced to the

storm water level (positive above storm water level).

η = Elevation of the wave surface directly above the water particle

referenced to the storm water level (positive above storm water

level).


Nonlinear Current Stretching

Nonlinear current stretching is based on the following equation, which is

found in Section C2.3.1b-5 of the commentary of the API Recommended

Practice (American Petroleum Institute 2000). The equation is solved

iteratively for z'.

( )( )

( )n

n

d

d z z z

λ π

λ π η

/ 2sinh

/ '2sinh'

++= C2.3.1b-5

where

z = Elevation of the location where the current velocity is desired

referenced to the storm water level (positive above storm water

level).

z' = Elevation of the location in the user-specified current profile

where the current velocity should be obtained referenced to the

storm water level (positive above storm water level).

η = Elevation of the wave surface referenced to the storm water

level (positive above storm water level).


η = Wave length.




Morison Equation of 9

Morison Equation

The Morison equation is used to calculate the force exerted by the wave at a

particular location on an object. The equation is given in Section 2.3.1b-10 of

the API Recommended Practice (American Petroleum Institute 2000).

dt

dU V

g

wC U U A

g

wC F F F m D I D +=+=

22.3.1-1

where

F = Hydrodynamic force per unit length acting normal to the object

longitudinal axis.

DF = Drag force per unit length.

I F = Inertia force per unit length.

DC = Drag coefficient.

w = Weight density of water.

g = Gravitational acceleration.

A = Projected area normal to object axis per unit length. For pipesand circles this is the effective diameter of the object, including

marine growth. For other section type, it is the dimension of

the side of the rectangle that encloses the section (including

marine growth, if any) that is normal to the direction of the

load.

V = Displaced volume per unit length. For pipes and circles this is

π D2 /4 where D is the effective diameter of the object, including

marine growth. For other section types it is the product of thedimensions of two adjacent sides of the rectangle that encloses

the section (including marine growth, if any).

U = Component of the water particle velocity acting normal to the

axis of the object.




Buoyant Forces of 9

U = The absolute value of U.

M C = Inertia coefficient.

= Component of the water particle acceleration acting normal to

the axis of the object.

Buoyant Forces

Buoyant forces are only included when so indicated in the wave load

definition. Buoyant forces are only applied to objects (or portions of objects)

that lie above the mud line and below the wave surface. Buoyant forces

consist of a uniform projected Z direction load applied to objects that are not

vertical and concentrated compressive axial forces applied to the ends of all

objects.

Uniform Load

The magnitude of the uniform load is calculated as:

wV f z =

where

f z = A uniform load in the projected Z direction.

w = Weight density of the water.

V = Displaced volume per unit length of the object.

For pipes and circles the displaced volume V is calculated as V = π d2 /4,

where d is the diameter including marine growth, if any. For other sections V

is calculated as V = bd, where b and d are the width and height of a rectangle

that would enclose the section.

Concentrated Compressive Loads at Object Ends The magnitude of the concentrated compressive axial load at each end of

each object is calculated as:

cwAP =

where

dt

dU




Wind Loads of 9

P = A concentrated compressive axial load.

w = Weight density of the water.

Ac = Cross sectional area to which the load is applied.

The magnitude cross-sectional area to which the load is applied depends on

whether the object is flooded. All objects are assumed to not be flooded

unless the are specifically indicated to be flooded in the wave overwrites.

If the object is not flooded, for pipes and circles the cross sectional area Ac is

calculated as Ac = π d2 /4 where d is the diameter, including marine growth, if

any. For other sections, Ac is calculated as Ac = bd, where b and d are the

width and height of a rectangle that would enclose the section.

If the object is flooded, the cross-sectional area Ac is taken equal to the areaspecified for the section property that is assigned to the object.

Wind Loads

The wave wind loads are calculated based on Sections 2.3.2b-1 and 2.3.2c of

the API Recommended Practice (American Petroleum Institute 2000).

Design Wind Speed

The design wind speed is calculated using the following equations that are

taken directly from the API Recommended Practice.

−=

0

ln)(41.01)(),(t

t z I zU t zu u 2.3.2-1

where the one hour mean wind speed U(z) (ft/sec) at level z (ft) is given by:

+=8.32

ln1)( 0

zC U zU 2.3.2-2

00457.010573.0 U C +=

and where the turbulence intensity Iu(z) at level z is given by:




Wind Loads of 9

[ ]22.0

08.32

0131.0106.0)(

−

+=

zU z I u 2.3.2-3

Wind Drag Force

The wind drag force is calculated using the following equation that is takendirectly from the API Recommended Practice.

AC uF s

2

2

=ρ

2.3.2-8

where

F = Wind force

ρ = Mass density of air (slugs/ft3)

u = Wind speed (ft/sec)

Cs = Shape coefficient

A = Are of element (ft2)

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