Prediction of water level motion and forces acting on a diving bell during launching through a moonpool

ARCH1EF

Deift

Skìbsteknîsk La

ratorium

t

Danish Ship Research Laboratory

MEDDELELSE

APRIL 1980

BULLETIN NO. 45

PREDICTION OF WATER LEVEL MOTION AND

FORCES ACTING ON A DIVING BELL DURING

LAUNCHING THROUGH A MOONPOOL

BY

NIELS FL. MADSEN

Technische Hogeschoof

w

ADDRESS: HJORTEKRSVEJ 99 DK-2800 LYNGBV DANMARK

SKIBSTEKNISK

LABORATORIUM

Danish Ship Research Laboratory

PREDICTION OF WATER LEVEL MOTION AND

FORCES ACTING ON A DIVING BELL DURING

LAUNChING THROUGH A MOONPOOL.

by

Niels Fi. Madsen

nkcFo -oqesc -' -- t

NOMENCLATURE

ABSTRACT

INTRODUCTION 2

METHODS TO CONTROL THE BELL MOTION 3

The Bell Compensator 3

Subsurface Diving Gear 3

Bell Guided by Cursor 6

Moonpool Diving System 6

THE THEORITICAL MODEL 10

Equations of Motion for the Bell 11

Equilibrium of Liquid in a Moonpool 12 Solution of the Equations of Motion 17

The Computer Program 18

MODEL TESTS 19

Hydrodynamic Coefficients 19

Model Tests in Waves 26

NUMERICAL RESULTS 38

Water Level Motion in Fixed Moonpool 38

Influence of Winch Strategy 49

CONCLUSIONS . 57

REFERENCES ₅₈

APPENDIX A. Data Sheets for Program Belirnoon

APPENDIX B. Post-Processing Time Histories

APPENDIX C. Example, Program INPUT/OUTPUT

a = Fourier components.

n

g = Acceleration of gravity.

h = Draught of moonpool.

h' = Equivalent length of added water column below moonpool.

k = Stiffness of hoist rope / winch.

m = Mass of diving bell.

p = Froude-Krylov pressure at bottom of moonpool.

t = Time.

u = Bell motion relative to ship.

y = Bell motion relative to earth.

w = Wave motion relative to earth.

y = Liquid motion at bell position relative to earth.

z = Ship motion relative to earth.

Ab = Projected area of bell perpendicular to the flow direction.

A = Choke area. c

A = Cross-sectional area of moonpool.

CD = Drag coefficient for bell.

C = Added mass coefficient for bell.

m

F = Hoist rope force.

Fa = Damping force from arbitrary damping device.

F = Damping force at bottom opening.

F = Restoring force. r

F = Wave force. w

H = Wave height (peak to peak).

Ç)

V = Volume of bell.

p = Damping coefficient for arbitrary damping device.

Y = Damping coefficient for damping at the bottom of the

moonpool.

= _{Natural frequency for bell oscillations.}

= _{Natural frequency for moonpool oscillations.}

= Frequency of n'th Fourier component.

4' = Phase angle of ntth Fourier component.

P _{= Density of water.} d( )

dt

d2( ₎ 2 dt

ABSTRACT

This report describes a numerical method for the determination of forces acting on a tethered subsea unit such as a diving bell during launching. The launching or retrieving operation is assumed to take place either exposed to the open sea or through a moonpool.

The liquid motion in a moonpool with a bell in it is studied in detal, and a mathematícal model for the system is established. The bell

motion and wire force are investigated for a number of operating situ-ations and for different strategies for rope force control.

Model tests have been carried out in order to verify the mathematical model, and the hydrodynamic coefficients have been measured for models of three typical diving bells in tubes with different diameters.

1. INTRODUCTION

The ability to launch and retrieve diving bells safely in a rough seaway has become one of the important aspects of offshore activities. _{The safe}

launching or retrieving depends on systems having the ability to withstand

the hydrodynamic forces on the bell caused by large, relative velocities and accelerations between the support vessel and the surface waves.

If the weight of the bell in water is too small compared to the hydrodynamic forces there is a risk of slack wire with subsequent jerk forces which _may

lead to excessive vertical accelerations of the bell, collision between the subsea unit and the offshore vessel, or the hoist wire may even burst.

The report revíews briefly some existing design concepts which are intended to minimize the hydrodynamic forces or to prevent the bell from being exposed to excessive forces due to slack wire.

A theory has been developed for the prediction of water level motion in a

moonpool and the forces acting on a diving bell either situated ín a

moonpool or exposed to the open sea. A special attention has

been given to devices for control of the hoist rope force, and the theory is able to predict wire forces during the period of slack wire followed by a sudden jerk in the rope.

Model test were carried out in order to confirm the theory, and the hydro-dynamic coefficients have been measured for three models of diving bells, situated in tubes with different diameters. For one of the diving bells a comparison has been made with full-scale measurements.

2. METHODS TO CONTROL THE BELL MOTION

A variety of solutions has been suggested or employed in practice to minimize the bell motion and to minimize or eliminate the risk of slack in the hoisting wire.

For some of the systems, which are briefly outlined below, safety and / or the ability to dive under rough weather conditions can be further increased. Slack wire will not occur or the consequencies of slack wire

with subsequent large vertical bell accelerations will be less severe, if the hydraulic bell winch system is fitted with a device for maintaining a certain minimum tension, a relief valve to limit the maximum tension or a

device for maintaining constant wire force or if the equivalent spring stiffness of the hoist rope and winch is sufficiently small.

Safety also depends on the complexity of the system. As a general rule,

systems containing a minimum of moving parts submerged in salt water should be preferred.

The Bell Compensator

The bell compensator as described in Ref. (1) and roughly sketched in Fig.

i has been claimed to have the ability to eliminate the heave motion over

a total heave of 13 metres. The solution is, however, limited to the case

where the weight can be placed on the sea floor approximately vertically below the diver's work site.

Subsurface Diving Gear

The diving system of Fig. 2, known as Subsurface Diving Gear, Ref. (2), can be built into one of the columns of a semisubmersible or in the bottom of a mono-hull vessel. This system has the advance, that the bell does not pass the air/sea interface at all.

Cc2)5.TA%-)T TL5 to

V)C44

"-J

-4cST Rc'PE

'.' I -Ca

/

,-ot

r

C_41

C.L) tEL* F4 L

\'E_l C H -r

Figure 1. The Bell Compensator. A system for compensating the heave motion of the bell.

Figure 2. Subsurface Diving Gear. The diving bell does not pass

the surface at all.

Bell Guided by Cursor

Fig. 3 shows a system where the bell is trapped in a cursor (3). The

bell is exposed to the open sea, but the bell is enforced to follow the motion of the cursor.

Noonpool Diving Systems

The conventional moonpool approach as shown in Fig. 4 has the advantage that the outside waves will appear in a filtered version, the short waves

being filtered away more effectively than the larger ones, so the motion left in the moonpool is relatively slow. Furthermore, waves with large

amplitudes are damped more efficiently than small waves since the damping is nonlinear. See Fig. 9.

However, the natural frequency of the liquid oscillating vertically in the moonpoon will often coincide with frequencies contained in wave spectra met in the North Sea.

Within draughts of 5 - 15 metres resonance occurs at sea-states from Force 3 to Force 6, and the water motion may be amplified by a factor

3 - 5 or even more.

For this reason the designer will often prefer to introduce a device which has the ability to increase damping such as choke decks or flanges

as shown in Fig. 5, an airtight casing above the moonpool as described in Ref. (4) and Fig. 6, or the arrangement shown in Fig. 7, Ref. (5), in which damping is provided by horzontal baffles and the perforated wall.

In addition, the buoyancy of the bell is decreased by use of an air injection system.

Finally, Fig. 8, Ref. (6) shows a moonpool arrangement where the bell is guided by a cursor. After the bell and cursor assembly has reached its

lower position the bottom door is opened and the bell can then be released from the cursor. At this moment the pumping effect of the water column in

the moonpool caused by the heave motion of the ship will only be small since the roof of the cursor nearly fills the cross-section of the

Figure 4. _{The moonpool approach.}

¿2

)

Figure 5. Moonpool fitted with choke decks for damping the liquid motion. The moonpool has been installed in a leg of a Semisubmersible Support Vessel.

Figure 7.

,a. r

r t

4-jr

C,A.

! L)(i

Figure 6. _{Moonpool with an airtight casing.}

t L L) c r C.- -.

£...

\' I T -4

' j_T

_{E_}

LT E Z. C. . E.

.LE r--E5.

Moonpool with damping chamber and a system for air injection.

7.0 f- ,.o

5.0

3.0 £ 2.0 L Figure 9. -I- 1-c.

'

-.

Moonpool wave to outside wave versus wave frequency showing the effect of wave height and draught of the moonpool. The height of the moonpool wave is

calcu-lated by use of the numerical procedure described in this report. The figure also shows frequencies met in the North Sea for different significant wave heights.

Figure 8. Moonpool with cursor.

o

_0.6

4.0 4. E. 2.o

3. THE THEORETICAL MODEL

The wave motion and the ship motion are assumed to be known

as

determi-nistic functions of time.

We only consider the vertical components of

the wave motion w(t) and the ship motion z(t) at the location of the

moonpool.

_{So, the motions of the moonpool and the point of suspension}

of the hoist rope are given by z(t).

The system consists of a tethered unit which may either be situated in

the open sea or in a moonpool, or the system may consist of a moonpool,

only.

For the case where a tethered unit is included it is possible to

study the bell response on different devices built into the hoisting winch.

The system bell - moonpool is described mathematically by the two degrees

of freedom, bell motion and water level motion in the moonpool.

The bell is restricted to

be fully submerged for two reasons:

- It is not expected that slaiuining alone may cause

a slack wire when the bell is handled through a

moonpool since the high frequent wave components

are filtered away.

- For a partly submerged bell the prediction of

hydro-dynamic coefficients including a coefficient for

slam-ming is believed to be highly inaccurate.

However, the effect of slamming could, of course, be included in the

equations of motion for the bell.

For a further discussion of the problem of penetrating through the splash

zone, see Ref. (7).

The bell is treated as a point mass with concentrated forces acting on it. The wire force must keep equilibrium with acceleration forces, gravity forces, buoyancy forces and hydrodynamic forces.

According to Morison's formula, the hydrodynamic forces acting on the bell can be calculated by:

FH = pV (1+C ) -

pv C ii ApAb C

_('Cr-r)I-7I

m m

where y and y are the liquid motion and bell motion, respectively. p is the density of water, V is the volume of the bell and Ab is the projected area perpendir'iilar to the flow. The virtual mass coefficient and drag coefficient ar denoted by Cm and CD, respectively.

For the case where the bell is situated in a moonpool, y is recognized as the water level motion, and Cm and CD are values which are valid for the bell in the moonpool.

Application of Newton's second law leads to the following expression for the force in the hoist rope:

F = nrJ + mg-PVg - pv (1+C) + _{V Cm i + pAb CD}

_(VY

_HT-I

where g is the acceleration of gravity and m is the mass of the bell.

The bell motion and the force in the hoist rope depend to a large extent on the response of the hoist system. A number of standard strategies for

rope force control has been included in the computer program, and any new device may easily be added. At present, the following possibilities exists:

- Inelastic winch / wire. The bell is subjected to a given

motion u(t) relative to the ship. The bell motion is de-termined by:

- Elastic winch / wire. The bell motion is determined

by the wire force:

F = k(z + u -

y)

where k is the combined stiffness of the wire and winch. The program includes the possibility to simulate slack wire by putting F equal to zero in case that the

right-hand side of equation (4) is negative.

- Ability to maintain a certain minimum tension in the hoist

rope. Such a device is introduced by adding a value to u

in eq. (4) which gives the specified tension.

- Relief valve in the hydraulic system. The device is in-troduced by subtracting the value from u in eq. (4) which

gives the specified tension in the rope.

- Constant tension winch. The bell motion is determined by

the constant tention T:

F=T

Equilibrium of Liquid in a Moonpool

The moonpool geometry is shown in Fig. 10. The moonpool has a constant

cross-sectional area At over the draught h. The moonpool may be fitted with choke decks or beams welded to the wall in a direction normal to

the flow. The effects of such damping devices are included by adding an

equivalent damping of the water level motion, and the hydrodynamic

coeffi-cients for the bell must be adjusted to be valid for themodified moonpool.

The liquid in the moonpool consists of three parts:

- the constant part determined by A and h minus the

volume occupied by the bell,

- the variable part determined by At and the water level motion y in the moonpool,

- the added mass determined by A and an equivalent

length h' of an imaginary water column below the bottom opening.

Fukuda (8) suggests the formula:

which is included in the computer program.

The momentum for the above three contributions becomes:

P = pA

(h + h' +

y) S

-

pVi

The last term is explained by the fact, that the momentum in the surrounding liquid caused by the bell moving upwards with the velocity is equivalent

to that of the same volume of water moving downwards with the same velocity.

The equilibrium equations are derived by using:

= kall external forces,

or (h + h') ₊

pA2 + pAy

- pV ₌

4 L

-w I I

-L----J

Figure 10. The moonpool geometry.

y

h

The external forces acting on the water column in the moonpool are:

- Restoring force acting at the bottom opening

(10) _{Fr = -ypg A}

- Wave forces. The Froude - Krylov hypotheses is assumed,

i.e. the pressure p at the bottom opening is equal to the dynamic wave pressure and the excitation force from the waves then becomes:

F =pA

w t

The dynamic pressure is evaluated by Fourier decomposing the wave motion:

w(t) = Z a cos ( _{t - 4' )}

n n n

n

where a, and 4, are Fourier amplitudes, frequencies

and phases, respectively.

When the sea is deeper than a half wave length, the dyna-mic pressure becomes: ₂

n

p(t) = pg

ae -

(h - z) cos ( t - 4, )

n n

n

- Damping force due to energy loss at the bottom opening. The

bottom opening is regarded as a tube which has an abrupt enlargement, see Fig. 11, and the flow is assumed to be stationary. When the flow runs out of the moonpool the velocity is approximately uniform over the cross-section of the moonpool. At the abrupt enlargement, the flow forms

turbulent eddies in the corner which result in an energy loss.

Sufficiently far away downstream from the enlargement, the velocity will again be uniform.

/

p-t

cQ

L) Q L.

-,.- ,

ec'rrc-/

W L_L.

cr

"J

E-Figure 11. Idealization of the flow at the bottom opening of the moonpool.

Figure 12. Proposed damping coefficients for the bottom opening.

o

The radial accelerations over the horizontal surface (the bottom surface of the ship) are very small, a fact which leads to the experimentally supported evidence, that the pressure at the horizontal surface is equal to

that found in the bottom opening.

Using the above assumptions, the momentum equation for a

steady flow, the equations for continuity and energy conservasion for a constant density flow and letting the larger diameter go to infinity, the total force becomes:

F=-pA (-)

-J

where the factor y = i for the flow running out of the

moon-pool. See Ref. (9).

When the flow runs into the moonpool, the flow forms a

contraction just above the bottom opening, after which the stream widens again to fill the moonpool, as shown in Fig.

lib. The damping force caused by loss in the turbulent

eddies between the contraction and the wall of the moonpool follows eq. (14), but with values of y being dependent on the geometry of the bottom opening, see Fig. 12. The

usually accepted values for y are taken from Ref. (9).

- Device giving additional damping. An additional term allowing for quadratic damping due to damping giving devices such as appendages or choke decks are also allowed for.

The general expression is:

F _{p A -}

-According to Ref. (10), p. 23, the damping coefficient due to a choke deck can be derived as:

= 1)2

where Ac is the open area, andoK can be approximated by:

A ₂ = 0.598 + 0.4 (i-)

C

Collecting all force contributions, eq. (9) is rewritten by:

pAt y + pAt S2 + pAt (h + h') =

(18) v(1 + Cm) (j - + p Ab -

--Y +

2 pA

(S -

)

' -

-

y p + p At

Solution of the Equations of Motion

Numerical techniques are used to solve the initial value problem consisting of the two non-linear second order differential equations

(2)

and (18) and the intial values y(t),

t), v(t) and c(t).

By substituting from eq.

(2)

into eq. (18), the differential equations can be written:

= f (y, y, , ) (equilibrium for liquid)

(19)

= g (y, y, Çr,

î,

₎ (equilibrium for bell) Furthermore, we introduce the parameters:

(20)

r=y

s =v

such that eq. (19) can be rewritten by:

y=r

(21)

= f (y, y, r, s) = g (y, y, r, s,

which is a system of first order ordinary differential equations the solution of which is performed by use of fourth order Runge-Kutta formulae, see (11).

k

=

m+ PVC

m

This formula can be used to estimate k by use of vibration tests if Cm is known or to measure C if k is known.

Neglecting the influence from the bell and non-linearities due to the variable mass in the moonpool, the natural frequency for undamped free moonpool oscillation becomes:

()

g m

h+h'

The Computer Program

The above theory has been programmed and tested on several examples.

The input data for wave motion and ship motion may either be results from model tests or results from a seakeeping program.

The output from the program is given as time histories for motions, velo-cities, accelerations and forces. The numerical results can then be post-processed by use of SL's standard programs for spectrum analysis,

statistics, plots, etc.

The initial values for motions and velocities are to be specified by the program user.

For the cases where the wire force is determined by the stiffness of the hoist wire and winch system the bell will vibrate with a small amplitude

Model tests were carried out in order to verify the numerical procedure and in order to obtain values for the hydrodynamic coefficients for typical diving bells in moonpools with different diameters.

Hydrodynamic Coefficients

The three typical diving bells shown in Fig. 13 were manufactured on the scale of 1:20. The main characteristics of the three bells are given in

Table 1. The bell denoted by III is especially interesting since data

from full-scale measurements are available for this diving bell (7).

The models were tested in open-water and in four plastic tubes having the inner diameter 127, 144, 173 and 194 mm.

Added Mass Coefficient C m

The added mass coefficients were measured by use of vibration tests. From eq. (22) we have:

k m (23) C

m

PV

The diving bells were attached to a spring with stiffness k = 61.50 N/m and the natural frequency _{b =Wb/2U} was read from the signal from a

force gauge connected to the spring. 4. MODEL TESTS

Table 1. Diving Bell Data.

Bell Mass (kg) Volume (ms) Projected Area (2) i: 5 504 4.568 3.020 II 6 608 4.160 3.834 III 5 200 4.576 3.611

Figure 13. Diving bell I, II and III.

Table 2. Added Mass Coefficients for Three Diving Bells Shown in Fig. 13. Bell Draught (m) Tube diam. (m) Frequency (Hz) Cm 0.65 0.127 1.140 0.89 0.65 0.144 1.176 0.77 0.65 0.173 1.205 0.67 0.65 0.194 1.220 0.63 1.246 0.55 0.55 0.194 1.223 0.62 0.75 0.194 1.209 0.66 0.65 0.127 1.014 1.34 0.65 0.144 1.061 1.07 0.65 0.173 1.106 0.86 0.65 0.194 1.126 0.77 II 1.150 0.68 0.55 0.127 1.029 1.76 0.75 0.127 0.993 1.45 0.65 0.144 1.147 0.93 0.65 0.173 1.211 0.72 0.65 0.194 1.224 0.67

co

_cc

1.232 0.66

The measured values for Cm are summarized in Table 2. The natural

frequencies are obtained as the average of three independent measure-ments each being the average taken over about 25 cycles.

As a test on the accuracy. tests have also been performed with a sphere

of radius 54 mm and the mass 835 g. The natural frequency b = 1.142

gives Cm = 0.55 which is ten per cent above the theoretical value Cm = 0.5 for a sphere. The discrepancy is assumed to originate from the boundary layer around the sphere.

For diving bell No. III vibrating in open water, the measured added mass

coefficient Cm 0.66 could be compared to the full-scale value Cm = 0.9 0.25% which has been evaluated by Mellem (7).

The following conclusions may be drawn from Table 2 and Fig. 14:

- The added mass coefficient Cm increases approximately with the projected bell area to the cross-sectional area of the tube as:

C m

1.9 ()

2.25 (24)

- =

1 + C m

- Cm depends on the tube length for the ratio

being close to 1, but not for small ratios of

Drag Coefficient CD

For a diving bell moving with constant velocity in a fluid at rest, equation (2) can be rewritten by:

2F (25) _CD

1.8

1<.

Table 3 shows the measured drag coefficients based _{on the projected area}

given in Table 1.

Q O

02

_{03 o5 O 01}

_os

_{oo TTJ}

O

Figure 14. Increase in added mass coefficient versus blockage

ratio.

The experimental test set-up is shown in Fig. 15. The diving bell is attached to a servo winch by use of an articulated rod.

The servo winch is trigged by a tringular signal such that the

bell has a constant velocity over a total length of 0.30 m when moving upwards or downwards . The force is recorded by use of a ring gauge

fitted on the connection rod.

A typical force signal is shown in Fig. 16. The drag coefficients for upwards and downwards velocity are recognized from the nearly stationary

Fig. 15a. The servo winch which is used to give the specified motion of the

bell.

Fig. 15b. _{Diving bell I in one of} the tubes.

Table 3. Drag Coefficients for Models of the Three Diving

Bells Shown in Fig. 13.

Bell Frequency (Hz) Tube diam. (m) F F up down (N) (N) C up C down, D D 0.30 0.127 0.424 0.485 3.47 3.97 0.30 0.144 0.294 0.312 2.40 2.55 0.30 0.173 0.242 0.240 1.98 1.96 0.30 0.194 0.164 0.175 1.34 1.43 0.20 0.052 0.054 0.96 0.99 0.25 0.072 0.082 0.85 0.97 0.30 - 0.104 0.113 0.85 0.92 0.35 0.138 0.139 0.83 0.83 0.30 0.127 1.004 1.039 6.47 6.69 0.30 0.144 0.571 0.623 3.68 4.01 0.30 0.173 0.312 0.329 2.01 2.12 0.30 0.194 0.260 0.268 1.67 1.73

U

_{0.20 0.078 0.078 1.13 1.13} 0.25 0.121 0.113 1.12 1.05 0.30 0.168 0.173 1.08 1.11 0.35 0.251 0.225 1.19 1.06 0.30 0.144 0.554 0.658 3.79 4.50 0.30 0.173 0.260 0.346 1.78 2.37 0.30 0.194 0.208 0.249 1.42 1.70 III 0.20 0.061 0.078 0.94 1.20 0.25 0.095 0.104 0.94 1.02 0.30 0.147 0.156 1.01 1.07 0.35 0.164 0.208 0.82 1.04

For ce

Figure 16. _{A typical signal from the force gauge. The figure} also shows the position of the diving bell.

F

down up

The drag coefficient CD = 1.08 for downwards motion of bell _{III in open}

water corresponds to CD = 1.47 based on a projected area taken as the

cross-section of the pressure hull, instead of the entire projected area.

This value could be compared to the full-scale value _{CD = 1.9 12%}

obtained by Mellem (7).

The difference is partly explained by auxiliary equipment below the diving bell from (7).

Fig. _{17 shows the drag coefficients versus bell to tube area Ab/At. The}

drag coefficients in Fig. 17 are the average for upwards and downwards

values.

From Table 3 and Fig. 17 the following has been concluded:

- The drag coefficient CD increases approximately with the projected bell area to the cross-sectional area of the tube

as:

CD Ab

(26) = i + 9.2

CD

n=

- CD is nearly the same for upwards and downwards motion.

- CD does not depend on velocity.

Model Tests in Waves

2.25

The testing arrangement is shown in Fig. 18. The tube with diameter

173 min is fixed with the opening 1 m below the water surface. SL's large

model basin was used for these tests and the waves were produced by a digitally controlled pnumatic wavemaker.

Three signals were recorded and stored on disk for further analysis:

- outside wave

- moonpool wave

- force acting on diving bell I situated inside or outside the tube.

Figure 18. Testing arrangement for tests in waves. The diving bell is shown both inside and outside the tube.

Tests were carried out with two regular waves:

Wave height (peak to peak)

H1.60

m Wave frequency

C=

0.660 rad/s.

Wave height

H1.73

m

Wave frequency w= 0.890 rad/s.

and the irregular wave spectrum in Fig. 20 with significant _{wave height}

1.35 m and the peak period 7.76 sec. _{A list of runs is given in Table 4.}

The time histories are shown in Fig. 19.

The small ripples on the wire force signals are due to the elasticity in the hoist string.

Table 4. List of Runs in Large Model Basin. Data are given in full scale.

The frequency of wave I was chosen to be close to the natural frequency of the water column (m = 0.680), and for this case it was not possíble

to perform measurements with the bell in the moonpool.

For resonant excitation the wave amplitude was enlarged by a factor 4.7, and the moonpool wave was very stable.

The moonpool wave shows a kind of unstable beating, which is also met in the theoretical model, when being exposed to excitation frequencies away from the resonance frequency, see Fig. 19 b and c. The enlargement factor is only 0.3 for wave II which has a frequency that is 30 per cent above the natural frequency of the moonpool.

When comparing wire forces in run Nos. 958/959 and 960/961 it should be noticed, that the hydrodynamic forces acting on the bell decays exponen-tially with the distance from the water surface. Thus, being reduced to

the surface, the variable part of the wire force must be multiplied with a factor 2.5, and the variable part of the wire force then is smallest when the bell is in the moonpool. The draught and diameter of the

moon-pool could of course be optimized to meet a given set of wave spectra in a much more favourable way.

Spectra and response amplitude operators for force and moonpool waves are shown in Fig. 20 and 21. The response amplitude operators (RAU) should

be taken only as an illustration of the filtering effect of the moonpool since the RAO-analysis is only valid for linear systems.

RUN NO. Wave Height (m) Wave Frequency (rad/sec.) Remarks

957 1.60 0.660 Bell outside 14 m below surface. Resonance in moonpool.

958 1.73 0.890 Bell inside 12 m below surface.

959 1.73 0.890 Bell outsidemoonpool 12 m below surface.

960 Irregular wave

0. 838 (peak) Bell outside. 12 m below surface. 961 JH1/3 = 1.34 Bell inside moonpool 12 m below

2.00 UT51D( UPV (n) 2.50... 0.00. d -2. 50... 0.00 C -2. 00_ ¿0 _.00

Ai AAíÀÀAÄaAAAAAAAIAIA AAAAAA

y,,

y,,,

J I . 25 S, \; Figure 19a.

Measured Values. Bell outside 14 m below surface. H = 1.60 m

= 0.66 rad/sec T1n IN OINUT(s 1N)'. I.UIVE 1)1) 2 50 2.50 1111 IN F1INUTES J J 3.15 3. 15 J r' TESTS (resonance). SKI 5ST[KN 15K LFB0RPT0R I UM DIVING SELL 00E SCALE Ii LYNG6'I DRNMPÇ RUN 957 0RWN -5.00... TitlE IN rUNUTES FACE UP) i .00 0. 00 00 -.00 -2. 00 5. 00_ 2.00... .10 i. 00...

2.00 1.00 0.00 _{-1.00 -2.00} -2. 00_

f

OUTSIDE IJPVE (li)

I

«

1.00 MOONP. IJVE (rl) -1.00 2.00j FOMCE INN) '10 0.00 1.00 -1 . 00_ Figure 19b.

J

Measured Values. A

A

hAlA 1111111

fof

111

1

TITlE IN MINUTES 0.50

A

A

A A

A A

A &

£

A £ £

.

£ &

à £

A A A

£ A

A A A A à A A

A &

s,0D,.y,v,v,y,Iy,vvvyv,vTv5!vvvvT

V

175 1VVVVV'V50

TIME IN MINUTES

Bell inside 12 m below surface. H = 1.73 m

= 0.89 rad/sec.

TIllE IN MINUTES

ÍLRBÛBATOR J UM

DIVING BELL TESTS

OMOEM SL- SCPLE Ii 20.000

1.25

II

11 11!

VI s 1.25 rigure i...

Measured Values. Bell outside 12 m below surface.

A

111111

11ff!! 1 11

TitlE IN r1JNUTES 2.00.. tlUTSIUE IJAVE uu 1 00... 000

II

doIf

py

-i. 0o -200... 1.00. rl0NP. llAVE 1)11 0.50.

A A

-L

A

T

-o.5o_ - I. 00.. 2.00... fOACE (KNI .10 i . 00 0 00 C 00 -2.00..

,..

-AA £-AA*-AA-AA-AA-AA-AA4lh-AAA*4Ê-AA-AA14I-AA

_VYV2YVVVWVY

y

w

w'

y

,,

--V YVVVVVVVVVV

50 TitlE IN IIJNUTES 2.50 TitlE IN MINUTES 3.75 H = 1.73 m = 0.89 rad/sec. SKI BSTEKN 15K DJVJNG BELL TESTS OFIOEFI SL-LAB OHR T OH J UM SCALE i. 20.000 LYNG6'! DANNARK HUN 959 DRWN

2.00 OUTSIOE WOVE IF1 1. 00

000k.L

Lé

L_ L

L

L

L*

L AAAA

MLAaLL

l

A

Li'

k

'

i

'

!

W

r

'

!.

IV''

Y

I

Y

'

' I !.

!

J t Y

-1.00 -2. 00 4.00 1NP. 0000 (II) 2. 00

DALA

!OYV

Vvv.v5VyVyy

-2.00 -4. 00 FMCE INN) 1.00 0.00 -:o.00 -l.00_ -2. 00_ 1 .75 Figure 19d.

Measured Values. Bell outside 12 m below surface. 111,3 = 1.34

= 0.838 rad/sec.

peak

TIllE IN MINUTES Tirio IN MINUTES

3.50 TIME IN MINUTES SÇJBSTEKNJ SF LR5OBPTOHIUM 5.25 DJVJNG BELL TESTS 0000M SL- SCALE u 20.000

2. OO_ OOQA

£AA

A

AIa*i.

gj

AL

A A

AL

a&

L AA

'1

'''V', I I I

'

i

I r' ii'

'

' '

'2S

i

T

'II' I

"

O 00

UTSIOE UPVE IN)

00 Figure 19e. TitlE IN MINUTES r10NP. UVE In) 1.75 3.50

Bell inside 12 m below surface. H113 = 1.34 m L)

= 0.838 m. peak SJBSTEKNJ s"; [ABURRIDA J UM ...-L'YNGBT OANMAMI(

DIVING BELL TESTS

0MOEM SL- SC8LE i RUN 961 DARUN -'L OO_ TIME IN MINUTES FOMCE KHI Measured Values. TitlE IN MINUTES 2.00... 'lo i i .00__ 0 00 _{-1.00 -2. 00} -2. 0Q_ 'LOO 2. 00 5.25

(N LQQ

r

cL 2.00 Li D (n 0.50 0.00 0.00 0.00

RUN 960

0.00

RUN 960

¡¡1

I 3.75 FEQ. T-FERK S 7.58 T02 5 7.36 SIGN.VAL. 1.3L1E+00 TEST TInE 7.00 1.50 PRO/S Ui

s: 2.00

t'

:i

Q-z

0.00 T-PEK s 9.27 TO S 9.21 SI .VPL. 2.95E+00 T S TIME 7.00

\

SKI BSTEKN 15K

LPBOI9PTOP .1 UM

DIVING BELL TESTS

OFlOEFl SL-SCRLE L 20.000

L'NG6 ORNr1RFlK Figure 20a. Power spectra. OFlPN 0O3l3 0.00

RUN 960

0.75F FlEO. 1 .50 1 .50 CN 0.75 FREQ. RPO/S LOO D

tI

a: N. (fI 1-PERK S 7.50 102 S = 7.60 SIGN. L. 2.16E+00 TEST TI E 7.00

N '-1.00 i O

-(n

z

w 2.00 w D (n t-0.00 2.00 0.00 T-PEAP S 7.50 102 S 7.29 SJGN.VIRL. i.32E+OO TEST TIME 7.00 0.00 RUN 961 ST .VRL.

9.t5E-00

T

I

TJME = 7.00 E ('J

> 2.00

a-D D E 0.00 0.00 RUN 961 9.47 STGN.VRL. 2.36E+0B TEST TIME 7.00

S}KIBSTEKNISK

LAB OHR IOPiIUN

LYNG8Y 04NMA9K

Figure 2Db.

DIVING BELL TESIS

090E9

SC9LE 1: 20.000

Power spectra.

O9RWN 800313

0.0.

0.75 1 .50 RUN 961 FfiEQ. 990/S _N

p-L00

T-PER( S 8.27 T-PERPÇ S D 102 S S.2'4 102 5 0.75 F9EQ. 1 .50 990/S 0.75 F9 EQ. 1.50 990/S

2.00

I . 00

0.00

E E 2.5CL

z

0.00

HPO i

iii,,

i'' t

i r t i i i i r r r i r r i

SKIB5TENJSK

DIVING SELL TESTS

LBDRTOH JUM

/

L'INGBI oRNr1RR

Figure 21a.

OVIOF9 SL-SCALE 1 2 ORPLN 8 0.000 00313

0.50

0.00

RUN 960

I . 00

1.50

2.00 FREQ. t APD/SEC

0.50

1.00

1.50

FF9EQ. t VIRO/SEC 2.00

0.00

RUN 960

2.00 -10 1 .00 0.00 4.00 w

> 2.OIL

0.00 RUN 961 HAD 0.00 RUN 961 0.50

5 J55TEKNIS

LAOHATOH JUM

1.00 1.50 FREQ. ( RFLJ/SEC 2.00 0.00_ t

II

ii

i i i

I 1111 t

i i

iii i

i

iii

i 0.50 1.00 1.50 2.00 FFIEQ. ( HAD/SEC

DIVING BELL TESTS

060E6

SL-SCALE 1: 20.000

5.

NUMERICAL RESULTS

The numerical method has been tested on a number of different examples, some of which will be shown here.

Water Level Motion in Fixed Moonpool

As a test on the accuracy of the method, the program has been tested on the model test series from the previous section of this report, Fig. 22 a-e.

Fig. 23 shows a comparison between measured and calculated results for

run No. 957 previously shown in Fig. 19a. The agreement is very satisfactory.

For the measured values, the velocity and acceleration are obtained by numerical differentiation of the moonpool wave motion after having smoothed the signal by use of the low-pass digital filter shown in Fig. 24

For the run Nos. 960 and 961 the outside wave has been approximated by 99 Fourier terms, the highest frequency of which being 1.5 rad/sec.

The best agreement between measured and theoretical results was found for run No. 957. _{For this case, the amplitude of the moonpool wave is}

much larger than for run Nos. 958-961, since the wave frequency has been chosen to be close to moonpool resonance. _{The idealized model of the}

flow at the bottom opening as shown in Fig. 11 is thus believed _{to be a}

better approximation for large amplitudes than for the small ones of run Nos. 958-961

Discrepancies between measured and predicted results may also be due to model scale effects such as:

- wall friction - laminar separation

- damping from the wave probe

- formation of axisyrmnetric surface waves in the moonpool.

A comparison between the measured and calculated moonpool wave for run No. 960 is shown in Fig. 25. The calculated moonpool wave is both

shown for (y , 3 ) = (1,0) which is the theoretical value for the bottom

damping and for (y , = (1,1) which is twice the theoretical value.

The validity of Morison's formula is found to be excellent both for the bell inside and outside the moonpool.

The results shown in Fig. 26 are obtained by using the measured moonpool wave from run No. 961 as input to the computer program. The figure also

00 LOO _{-t .00} -2.00 URVE M0TII3F Ut)

AA AAAAAAAAAA AAAAAAAAAAAAAAAAA

5.00.. t'ARTJOLE rtflTttON li) 00 I . 25 Figure 22a.

Numerical Results as Run

957.

Bell outside 14 m below surface. H

1.60 m = 0.66 rad/sec. (resonance) TitlE IN MiNUTES So TIME IN MINUTES 2.00 WtME FOFICE tFOJt 10 2.50 TItlE IN MINUTES

li

i LP5ONRTOHIUM 3.75 D1VN BELL TESTS 0RUE

-2. 00_. i .00 0.50 t. 00_. 0,00_ :o.00 -2. 00.. FfFtT1CLE r10T10 (It] o.00 A

L

L

A A

ALA

AA.

A A

ALA £AA.AAAA

i p y"

iyryyvyyyv.9vvflvvflvvflyyyv.o

-0.50 (flaE FOF.CE UÇUI i . 25 Figure 22b.

Numerical Results as Run 958. Bell inside 12 m below surface.

1111f IN FUMiJTES lIftE 1M IUMUTES

2.50 T1rE IM MJMiJTES 3.75 H = = 1.73 m 0.89 rad/sec. SFIBSTEKNISK LIRBODRTOPLI UM LS.KG8'( UPNMRIIK

DIVING 8ELL TESTS

2.00 SR n0T1 rtj I . 00 o co -1 00 -2.00 1 00 O 50 0 00 -0. 50_. -1 . 00_ 2.00...: _.10 0.00

I

IAAAAA

A

AA

A

AA AA

AA

AA

u

1111111

2j

7

1121711171

11

;.

177111

1

o _{0.10 0. 00} PRftTICL[ r10TJ04 II)

WIflE I09C{ (KNI

I . 25

Figure

22c.

Numerical Results as Ruii 959. Bell outside 12 m below surface. H = 1.73 m

= 0.89 rad/sec.

TINI IN MiNUTES TINE IN tIINUTE

2.50

TINt IN rilNuTEs

rì

SFc I OSTERN J SR LP500PTOO I UtI

DIVING BELL TESTS

5L-2.00 UTSI0E UPVE (11) 1. 00

000AM4

£ £ .

,.T

''11

V1.'5 wvv!r!

V

y -I .00 -2.00 H113 = 1.34 m = 0.838 rad/sec. peak 1111E IN luNUlES

SKI AST EKrJ 15K L A B D B A TO A JIJ M LING8'Y

OPNMAMK

DIVING BELL TESTS

00ER SOPLE li ORIIUN

-4.00 11(10 IN MINUTES 2 . 00. UlME FISIICE (KW) .10 I . 00_. 0 00 1000 1. 75 3.50 5.25 -1 . Fi;ure 22cl.

Numerical Results as Run 960.

-2. 00..

TIrIO IN luNUlES

Bell outside 12 m below surface.

9. 00..

MNP. IJRVE

2 0O_ i .00.. 0 00 _{-1.00 -2. 00..} 9. 00.2 2.00... 0 00 _{-2.00_ -4.00} 1.00 0 00 _-1,00 0.0 OUTSIDE I4Í1VE ill) 00 LJOUIIJ MOT (M) 2.00

lUME FOMCE (liN)

.10 TIME IN MINUTES

A.

LAAA

LLLAAAAAAA

',T,'''Y51,

U''!'''

TIME IN MINUTES 1.75 3.50 5.25 -2.001 Figure 22e.

Numerical Results as Run 961. Bell inside 12 ni below surface. H113 = 1.34 m _LI

0.838 rad/sec. peak 1111E IN MINUIES ' SKJBSTEKNJSK

DIVING DELL TESTS

OMOEM

SL-LRBU9RT0D1UM

I. 00 0. 50 o 00 -0.50 -1.00 3. 00 2.00 I. 00 C 0G -1.00 -2.00 -3.00 2.00 t. 00 O 00 -t .00 -2.00 2.00 I . 00 0 00 -1.00 -2.00 t .00 .10 0.50_ 0 CII 0.0 Measured values - - - - Numerical results

OUTSIDE WAVE ¡II)

U1E FONCE (KN)

TINE IN SEC.

1111E IN EEC.

15.0

SKIBSTEKNISK

DIVING BELL TESTS

ORDER

SL-LABORRTOH JUN

SCALE It 20.000

LINGS'( DANMARK Figure 23. DRAWN 600122

DIGITAL FILTER DESIGN

TYPE OF FILTER

LP

CUTOFF (ON) FREQ.

( HZ ) 1.500

S1MP. JNTERVFL

( SEC ) 0.OLIO

NO OF COEFFS.

161.

FILTER CODE (INDEX)

18.

(Model scale)

- r -

r

_-

- - -2.50 3.75 5.00 FAEQ M

SKJBSTEKNJSK

LP6ORRTOR JUM

LING6Y DRNMRfl

Figure

24. ORDER SL DRAWN 800121

0.00 2.00J t1NF. WPVF UI) I . 00 0.00 TillE IN llINUTES

-Calculated with P = O Calculated with 3 =

SKIBS TE N IS L RB BRAT OR IUM

DIVING BELL TESTS

ûR0 SCALE LING61 CANIIARK RUN 960 ouN 1. 0U_ OuTsI0 IJAVE (Ii

Measured moonpool wave.

9 .1J0_ o jio PP.MTICL M0I (MI 0 00 -0. - i . oo i.00.. DMRG F6F(CE (KNI -io o. so_ 0. 00 1111E IN MINUTES WIBE FORCE (NH) TIME IN MIMJT5 dy

Y V

V

V Y Y Y Y

' !

Y '

Y 0! Y Y

V '

' Y

Y!CY V V '

TIME IN MJN(.TES

-AAAAA AAA&

£AA

', V V V y V V

y y

V -2.00 .00 Figure 26.

Calculated wire force based on measured moonpool wave from Run 961.

TIME IN MINUTES 6.00 -i. 00__ _{-2 .D0_} I.00_, MRS 0-So-1Z9C (liN) SKJ5STE)(NJS

DIVING BELL TESTS

LRB O FIR T OFIJ UM -$.-Uo--2. 00_ 10 i. oo__ 0.00 2.00 '(.00 6 .0D

Influence of Winch Strategy

The influence of the response of the hoisting system on bell motion and wire force has been studied numerically for a number of different winch

types.

The diving bell III with Cm and CD taken from Ref. (7) is suspended 8 m below the still water level in a moonpool built into a ship with the draught 10 m.

The cross-sectional area is 30 m2 and the bottom opening is not protruding into the flow.

The wave height is 3.4 m and the wave frequency is 0.6 rad/sec. The total

vertical motion of the ship at the point of suspension is 1 .4 m and the

ship and wave are 30 deg. out of phase.

The initial values for the moonpool wave motion are y(0) = 1.5 and (0) = O

and the simulated time was 20 seconds.

The above parameters were chosen such that slack would occur in the hoist rope after 5 seconds unless any action was taken to prevent the wire from being slack.

The following cases were studied, see Fig. 27 a-f.

Bell fixed.

Bell in wire with stiffness k = i . 107N/m. The wire

becomes slack, and the bell undergoes several sudden

jumps.

The maximum wire force is 43 . 104N which is nearly

eight times the dry weight.

C Bell in flexible wire (k = 1 . 106N/m). The bell

accele-rations are less severe. The maximum wire force is more than halved compared with case b

d . Bell in stiff wire and winch fitted with relief valve

Bell in stiff wire and winch fitted with a device to maintain a mínimum wire tension of 1000 N.

The bell undergoes small vibrations after the moment,

where the winch has stopped.

Bell suspended in constant tension winch with the tension

.00.4 MONP. WAVE (M) 2.00.. 0.00 -2.01LO.O -4.00: WAVE M5TJtN (M) 0.0 ShIP MT1tN ((1) BELL M(TJ0N (rl)

'4.00 BELL ACC. (tl/SEC2)

2.00 WIRE F(FLCE (W 'iP. 010 10.0 TIME IN SEC. TIME IN SEC. TIME IN SEC. TIME IN SEC. TIME IN SEC. TIME IN SEC. 20.0 20.0 20.0

SKIBSTEKNISK

DIVING BELL TEST

OADEA

SL-LRB O F1R T O Fi UM

L1NGBL DRNMAAK

Figure 27a.

Fixed bell.

OHAWN 800130

'.. 20.0 ' I 5.0 0.0 10.0 15.0 5.0 10.0 15.0 20.0

LOO

0.00 -t. 00 -2.00 4. 00. 2. 00.. 0.00 -2.0O -'4. 00 1.. i: 1cfso...E 0.00 -0. 5cLE -1 . O0_ k50 0.00 -2.50 -5.00 0.00 -2.50 -5.00 0.0 0.0 WAVE t1OTIN (M) MNP. 1-JAVE (M) 0.0 SELL MTJN (M) 5.00 WIRE FORCE (KN) 2 50 ' I 5.0 10.0 TIME IN SEC. TIME IN SEC. t I t 10.0 TIME IN SEC.

2.00... SELL VEL. (ti/SEC)

i . 00_ 0.00_ k

V-.4

T 1 -

-.

-i.0cL.0.0 5.0 10.0 15.0 20.0 -2. 00 TIME IN SEC.

5.00J bELL ACC. (M/SEC2)

' I ' I

i

J 0.0 5.0 10.0 15.0 20.0 TIME IN SEC. 0.0 5.0 10.0 TIME IN SEC. 20.0 20.0 2G.0 15.0 20.0 OROEh

SL-SKIBSTEKNISK

DIVING BELL TEST

LABORPTOI9IUM

2.00 WAVE (WTIN (M) 1.00 0 00 -1.00 0.0 -2.00 8.0 SHIP IWTIt1 (M) -1 i -0.0 _LI.Q .13.0 8.0 -q.00.... 2. 00 0.00: -2.00.. _LLQO_ i.00_.

j:

kR 5o 0 00 -0. 50.. -1.00.. MWN'. URVE (M) 0.0 BELL MtTIN (M)

2.00.! BELL ACC. (M/SEC2)

lia. (it0__ 0.00: - V T -, -l.0O.0.0 5.0 -2. 0O_

cD

10.0 TINE IN SEC. TIME IN SEC. 10.0 TIME IN SEC. TIME IN SEC.

2.00 BELL VEL. (M/SEC)

1.00 0.00 -1.00 0.0 5.0 10.0 -2.00 TitlE IN SEC. 15.0 20.0 20.0 20.0 15.0

'20.0

I -. _I__J 10.0 15.0 20.0 TINE IN SEC. 2.00 WIRE F0ACE (KN)

A

A

n

g g _{i i} i i i g -1.00 0.0 5.0 10.0 15.0 20.0 -2.00 TIME IN SEC.

SK1BSTEKF'SF

OJVJNG BELL TEST

OffiJER

SL-LRBÚFRTOHIUM

L'YNGB'Y DANtIARK

Figure 27c.

Flexible wire.

DRAWN 800128

I ( 10.0 u i g 15.0 0.0 20.0 i r 5.0

2.00

1.. 00

URVE MtTItTh (ti)

0.00 P1IÍh.

-i.00..EO.0 5.0 10.0 15.0 20,0

-2. OQ.E

TINE IN SEC.

8.0 J SHIP MTIN UI) --q.o ..0.0 5.0 10.0 5.0 20.0 -8.0 TIME IN SEC. q.00 tIONP. L1RVE (M) 2.00.. -2.00.EO.0 5.0 10.0 15.0 20.0 -q.00 TIME IN SEC. 1.00. BELL MTJ6N (M) kP.51o4 0.00: - I I I I t I I I I I -0.500.0 5.0 10.0 15.0 20.0 -1. TItlE IN SEC.

2.00 BELL VEL. Ui/SEC)

LOO

0 00

--1.00 '.0 5.0 10.0

" '

15.0 20.0

-2.00

TIME IN SEC.

2.00....6 _{BELL ACC. (M/SEC2)}

--i.0O..0.0 5.0

-10.0 15.0

-20.0 -2. 00.. TIME IN SEC. 2.00 UIIiE FRCE (KN) I

1Cco1

I A I I I I J I I I I J I I I I

0.OI

-1.00 6.0 5.0 10.0 15.0 20.0 -2.00 TitlE IN SEC.

SKIBSTEKNISK

DIVING 8ELL TEST

0A0E

SL-LR5OI9PTOI9IUM

_{Figure 27d.}

_{Stiff wire}

2.00 1.00 0.00 -1.00 -2.00

6.0 ... Sill? MTItTh UI)

-1

-a1tp ₄

-8.0

4.0Q_ MINF. I.JRVE UI)

2.Q0..

Q 00

-2. O0...0. O

-9. 00_

BELL I(TJ0N UI)

i:

kP5o4

0.00

-0. 5Q

-l.00-8.0 BELL VEL. II/SEC)

-1 a'p.0

0.0 -9.0 -6.0

l.00.. BELL ACC. (M/SEC2) 0. 50.. 0.00: -0. 50 -i. QQ_E 2.00 WJI9E FI9CE (KN) i 5.0 -2. oo..E 0.0 0.0 0.0 0.0

WAVE tItTIN UI)

J I 5.0 5.0 10.0 TIME IN SEC. 10.0 TIME IN SEC. TIME IN SEC. t -J- t 10.0 TIME IN SEC. TIME IN SEC. '

i

-t 10.0 TIME IN SEC. TIME IN SEC. 1 15.0 15.0 15.0 20.0 20.0 20. 0 20.0 20.0 0.0 I i 20.0

SKISTEKNISK

DIVING 6ELL TESTS

OflOEh

SL-LRSOI9RTORIUM

LThGBY OANMRAK

lIIl*lii4

gv, , , iv, _'V,

Figure 27e. Stiff wire

2.00 WAVE MT1N (M)

i 00

0.00

-1.00 0.0

-2.00

6.0 SHIP MOTIN (M) 0.0 -4.0 0.0 -6.0 2. 00... t: .1100-0.00: -2.QcL 2.00...: l.00-0 l.00-0l.00-0

-i. 00_i

-2.00_

cU

q.00: t1ONP. WAVE (M) 2. 00.. 0 00 -2.00..0.0 -q.00-BELL FrnTJN (rl)

2.00..1 BELL VEL. (ti/SEC)

i.00-0 00: -i. 00.. 0.0 -2. 00 BELL RCC. (ll/SEC2) .0 5.0 1111E IN SEC. 10.0 TIME IN SEC. TIME IN SEC. 10.0 1111E IN SEC. TINE IN SEC. TIME IN SEC. 20.0 20.0 20.0 20.0 15.0 20.0 ' i ' ' i '

0.01

-9.0 0.0 5.0 10.0 15.0 20.0

-8.0

1111E IN SEC. 6.0 .. WIRE F0RCE (KN)

q.0J

SKIBSTEKNISK

DIVING BELL TESTS

ORDER

SL-LPBOARTOFfl UM

L'(NGB'Y DANMAIiK Figure 27f. Constant tension winch.

r _I J- I -r

6. CONCLUSIONS

The launching / retrieving procedure for a diving bell has been studied theoretically and experimentally.

A variety of solutions to minimize the necessary wet weight of the diving bell to avoid slack in the hoist wire has been reviewed briefly,

and a special attention has been given to the moonpool approach.

A numerical símulation procedure has been developed for the prediction of the non-linear water level motion in a moonpool and the forces acting on the diving bell.

The necessary hydrodynamic coefficients for this procedure were measured for models of three diving bells in tubes with different diameters.

Both the added mass coefficient °m and the drag coefficient CD appeared to increase with the blockage ratio in a systematic way.

Model tests were carried out in regular and irregular waves with one of the diving bells situated in a tube. The moonpool wave and wire force were predicted theoretically using the measured values for Cm and CD, and a good agreement was found in most cases.

A number of simulated operating situations showed that the wire force and bell motion depend very much on the control strategy for the winch response.

The present investigation confirms that it is possible to treat the problem of launching a diving bell through a moonpool theoretically in a satisfactory way. Only moonpools with smooth wall were considered in the numerical examples, but more complex configurations may be treated by modifications of the input parameters or by slight modifications of the theory.

(8)

"New Diving Bell Compensator for Heavy Seas",

Ocean Industry, March 1979.

"Rough Weather Diving System",

Ocean Industry, February 1977.

Busby, R.F.: "Houlder's Semisubmersible Support Vessel",

Journal of Naval Architects, January 1976.

Kuo, C.: "A Controlled Handling Method for Effective Offshore Supported Operations",

OTC Paper No. 3318, 1978.

(5) Huges, D.: "MOOnpOO1 Design for Diving Support Vessels", Underwater Systems Design, October 1979.

British Patent No. 1226319, Norwegian Patent No. 19814.

Mellem, T.: "Surface Handling of Diving Bells and Submersibles in Rough Sea",

OTC Paper No. 3530, 1979.

Fukuda, K.: "Behaviour of Water in Vertical Well With Bottom Opening of Ship, and its Effects

of Ship Motion",

Journal of the Society of Naval Architects of Japan, Vol. 141, June 1977.

Massey, B.S. : "Mechanics of Fluids",

Van Nostrand Reinhold Company, 1975.

Prandtl, L.: "Strömungslehre",

Friederick Vieweg & Sohn, Braunschweig, 1965.

Ralston, A. and Wilf, H.S.: "Mathematical Methods for Digital Computers",

Wiley, New York / London, 1960. REFERENCES

A program to predict water level motion and forces acting on a diving bell during launching through a moonpool.

The following data sheets may be taken in any order. The last data sheet must be followed by _l:EODI

Moonpool Data

Name of data sheet, check No.

Draught of moonpool (m)

Cross-sectional area of moonpool (m2)

Bottom opening protruding into flow YES/NO Damping coefficient

I for quadratic damping

Wall friction included (Blasius), model scale only YES/NO Kinematic viscosity (m2/sec) (only if wall friction)

Start amplitude of moonpool wave (m), pos. upwards Start velocity of moonpool wave (m/sec)

MOON,

New data sheet (PRO) BELLMOON

INPUT (file name)

#TEST (file name)

\

L

Name of data sheet,Check No.

Mass of bell (kg) Volume of bell (m3)

Projected area (m2)

Added mass coefficient Cm

Drag coefficient CD

Start position of bell (< O and rei, to ship)

Start time for launching / retrieving (sec.)

Bell motion determined by constant tension winch Tension of constant tension winch (N)

Bell motion determined by constant velocity Launching / retrieving velocity pos. up (rn/sec)

Connection type bell-ship inelastic

Connection type bell-ship as elastic rod Stiffness of connection (N/rn)

Initial elongation pos. downwards (rn)

Connection type bell-ship as elastic wire Stiffness of connection bell-ship (N/rn)

Specified max. wire force (N)

Ability to specify min. wire force YES/No Specified min. wire force (N)

:BELL, CTENSIO C. VELO (INELAST I ROI) WIRE

The bell is fixed until the wire becomes slack or the specified

min. or max. wire force has been exceeded.

new data sheet

new data sheet

new data sheet

new sheet if NO new data sheet

(t

Name of data sheet, Check No.

Ship fixed

Regular ship motion: z = a cos (t-4,) Amplitude a (m)

Frequency (rad/sec.)

Phase

4, (deg)

Irregular ship motion

Irregular Ship Motion _{(Only to be filled-in if ship motion = IRREG)}

Name of data sheet, Check No.

N

Irregular ship motion: z = a

cos 4t-

4)

n= i

Number of Fourier terms N (max. 300)

The following data may be output from program RHARN.

:SHIP,

FIX

REG

IRREG new data sheet

f :FOUSH,

new data sheet

new data sheet

new data sheet Frequency (rad/sec) Amplitude (m) a n Phase (deg) 4, n

\

Irregular wave

Irregular Wave (Only to be filled-in if wave motion = IRREG)

Name of data sheet, Check No.

N

Irregular wave: w = Z a cos t- 4' ₎

n n n

n= i

Number of Fourier Terms N (max. 300)

The following data may be output from program REARM.

new data sheet

new data sheet Frequency (rad/sec) Amplitude (m) a n Phase (deg) 4'_n Check No.

Name of data sheet, :WAVE,

Density of water

Still water

(kg/rn3)

new data sheet STILL

Regular wave;

w = a cos (t-

4i) REG Amplitude a (m)

Frequency (rad/sec)

Name of data sheet, Check No.

Start time for integration (sec.)

Stop time (sec.)

Time increment (sec.)

Accuracy of solution e.g.

iO3iO6

Max. lines to be printed (number of time steps)

Type of response to be printed

:OUTPU,

EOA

The following possibilities exists:

WNO Wave motion (m)

PMO Particle motion (m), i.e. moonpool wave or liquid motion at the bell position if no moonpool

PVE Particle velocity (m/sec)

PAC Particle acceleration (m/sec2)

SMO Ship motion (m)

SVE Ship velocity (m/sec)

SAC Ship acceleration (m/sec2)

BMO Bell motion (m)

BVE Bell velocity (rn/sec)

2 BAC Bell acceleration (rn/sec )

FWI Wire force (N . iO)

FDR Drag force (N . iO)

FMA Mass force (N 103)

RNO Relative motion (m) Moonp. wave - ship.

Max. 6 types for upright A4 format.

Max. 7 types for output to be used as plot data file. Max.1O types for wide paper format.

The time increment gets halved up to 10 times to obtain the desired accuracy. The required step size will especially be small for the case of slack wire. If equidistant time steps are required, a sufficiently small initial step length may be chosen, or result lines for intermediate time steps may be deleted.

Time history No. Name of time history

Min. of max. value at y-axis

Give input to plot file #IN

The following possibilities exist for time history names:

WMO Wave motion (m)

PMO Particle motion (m)

PVE Particle vel. (ni)

2

PAC Particle acc. (rn/sec )

SMO Ship motion (rn)

SVE Ship vel. (m/sec)

SAC Ship acc. (m/sec2)

BMO Bell motion (ni)

BVE Bell vel. (m/sec)

BAC Bell acc. (rn/sec2)

FWI Wire force (KN)

FDR Drag force (KN)

FMA Mass force (KN)

ENO Relative moonp. wave (m) (between moonpool wave and ship)

NEW New text to be defined by the user.

The output from program 1tBELLMOON" stored on a symbol file must contain

a max. of 7 time histories and 2500 time steps. All lines except those

for the time solution must be deleted.

Two possibilities exist:

Post-processing by use of the SLAFO database.

The data are transferred to SLAFO by use of the program REALSL. The time solution must be given

for equal time steps.

Plot of time histories by use of the program THIST:

(at present only available for interactive use).

(PRO) THIST

TS S

Viewport (= i for scale 1:1)

X-length of frame e.g. 21.-29.7-42 cm Y-length of frame e.g. 21.-29.7-42 cm

Text identifying plot

Length of x-axis ( x-length of frame minus

Length of pos. y-axis (cm)

Start time (sec)

Stop time (sec)

Number of time histories on file (max. 6)

Number of time histories to plot (max. 6)

>

5$43 $3 $333

$3333

DIVING

ELL - MOONPUOL

VERSION 05.02,1980/NM

s s s s s s sss sss 533 s $ $ s $ 3$ £$ $3 $ 3$ 3$ $ $3333$ SS $33$ $33$ $33333333$ SS S $

FAM'ETRS OF THE PRO8LEM:

DATA FO

SHIP MOTION;

THE SHIP IS FIXED.

DATA Qk SELL:

MASs OF SELL (KG)

VOLUME yF SELL (M3)

PRO1)ECTc.D AREA UF SELL (M2)

ADDED MASS COEFFICIENT

CRAG COEFFICIENT

STMRT POSITION OF

LL (i1)

STAtT TME FOR LAUNCHING/RETRIEVING (SEC)

LAUNCHING/RETRIEVING VELOCITY (M/SEC)

8ELL 1NtLASTICALLY ATTACHED TO SHIP

CMT FO WAVES

DENSITY OF WATER (KG/M3)

REGULAR WAVES.

sAVE AMfLITUUE (M)

MVE FREQUENCY (RAD/SEC)

WAVt. PHASE (DEG)...

DATA FOk MOONPOOL:

DkAUGrT 0F MUONPOOL

(M.)

CROSS-S.CTIONAL AREA

OF

MOCNPOOL (M2)

OTTUM OPENING PROTRUDING INTO FLOW

CAMPING COEFFICIENT FOR OUACRATIC DAMPING

START AMPLITUDE OF LIUIO (M)

STT VELOCITY UF LiUIU (M/SEC)

DATA FQ

OUTPUT CONTROL:

START T1M

FOR I,TERATION (SEC)

STOP TI-E (SEC)

TIME INUREMENT (SEC.) ACCURACY OF 5OLLiTIO

RESUL1 S:

RESULTS FOR FR

MOONPOOL

CSCILLATIONS

EQUIV. COLUMN LENGTH OF ADDED MASS (M),

NATURAL FREQUENCY (RAD/SEC)

NATURAL PERIOD (SEC)

5504.0000

4,5680

3.0200

0,6100 1. 9700

12.0000

0.0000 0.0000

1000.0000

0.8650 0,8900 0.0000

20.0000

9.2400 0.0000 0,0000 0, 0000 0, 0000

300.0000

0,2500 i

0000E-04

1.2463

0,6795

9.2467

0.000

0.5O

0.ò4'. 0.001

8,914

O,7b1 0,004

b.969

0.679

0,010 9,057 0.544 0.016 9,172 0,383

0.02

9.306

1N.Mfr Ai'4() MAXDuM VALUES;

MOTION (M)

PAkTICL. MOTION

(M)

FMRTICL

VELOCITY (,'i/SEC)

FMFT1&L.

MCCELERATICN (1/SEC2)

SiI

1OTION (M)

SiiW VELOCITY (M/bEC)

StiIP ACCLEkATIOF

(M/5EC2)

L#.T1Vt. MOTION (M) MOONP. WAVE - ShIP

LL ¡'lOTION (M)

BELL VELOCITY IM/SEC)

EELL McELERMTI0f

(il/SEC2)

hI. FOC

(P'N)

CRA,

FQkCE AT BELL

<N)

SASS

FOtCS AT 8ELL (KN

-0.8650

0,8650

-0.6467

0,4244

-0.4102

0,4221

-0,3067

0,3450 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

-0,6467

0,4244

-12.0000

-12,0000

0.0000 0,0000 0.0000 0.0000

6,5505

11,b19

-0.5299

0,5006

-2,6317

2,3397

c99,00

-0,767

0.037 10.157

¿99,750

-Q

0.045

10.238

300. uCD

-0, ø6+ 0,045 10,258

ML)U., i

ç

Q o ¡

cLL, i

550'i.

'e

0.67

1. .97

o Ç .'VLLLÌ o i N r_L. A $ T

:SHLP, i

FIX

:

i

1uuu

iEy

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