Mechano mathematical modelling of floating structure dynamics

rab.

Technische Hog2school

y. Sheepsèouwkrnât

Deift

Svilen Apostolov Spassov

Sofia, 1987

2 9 JULI 1988

MECHANO- !4ATHEMATICAL MODELLING CF

FLOATING STRUCTURE DYNAMICS

SYNOPSIS

Ph.D.Thesis, Technical Sciences

ARCHIEF

GENERAL OUTLINES OF THE THESIS

ACTUALITY AND MOTIVATION OF THE THEME

The problem of the adoption of ocean resources has different aspects. In some of them, as for example the biological ones, there are centuries of tradition, while the adoption of mineral and energy resources has been extensively deve-loping only for the recent 15-20 years. This development has resulted in

turn-ing gas and mineral extraction into a new branch of economy. The difficulties occurring in solving new scientific and technical problems almost exclude the possibilities of achieving significant results in this field for a short pe-riod of time. For that purpose in the USSR, USA, Japar, Netherlands, Norway, etc. long-term programmes have been adopted for outstripping fundamental re-search investigations.

The declaring of a 200 mile area of particular Bulgarian interst along the Black sea coast and the first steps in the development of a perspective

prog-ramme for its resource utilization, combined with the active BSHC participa-tion in the internaparticipa-tional division of labour for investigaparticipa-tion and design of floating platforms, is still another stimulus to the development of foating

structures investigations.

As practice shows, it is necessary to create a new type of structures for solving the problem of the adoption of sea resources, the mast widespread being the floating platforms.

The influence of a complex of unfavourable and unstable factors, the high cost of the facilities and the strict requirements for their operation and

safety predetermine the importance of reliable prediction of their behaviour in real sea conditions.

The role of the model tests in this case is particularly great, but often on the one hand it is not possible to take account of all the influencing factors and ori the other, they can also be quite expensive. The most suitable way of

obtaining prompt and the same time multiple information seems to be the me-chano-niathematical modelling.

The first mechano-mathematical model of free floating structures is proposed by Hooft in 1972. All new developments are featuring a striving for taking

account of the complex hydrodynamic interaction of the elements of the con-struction on the basis of the linear potential theory of the fluid wave

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floating platforms presupposes exact knowledge of the motion characteris-tics, especially in the low-frequency range. This calls for a particular attention to the problem and necessitates going beyond the frames of linear potential theory. There is a strivng for complex consideration of all the

influencing factors.

Meanwhile, all the developed methods and their numerical realizations pro-vide good possibilities for practical application primarily at the early

stage of design.

Proceeding from the requirements abovementioned, the present work is direct-ed tu modelling the dynamics of floating structures, developing a program

sys-tem for its theoretical investigation and verifying the results by means of

complex experimental tests.

OBJECTIVE AND STRUCTURE OF THE THESIS

The main objective of the present thesis is improving the

mechano-mathema-tical model and creation of a numerical procedure for investigating the

dy-namics of floating structures, considering the force effects various in

na-ture. Thus it becomes possible that a series of numerical experiments _{can be} carried out and _{information can be obtained as for the influence of the}

de-sign parameters, which in itself is of vital fundamental and applied

import-ance.

Chapter one of the thesis is of Thtroductory character, giving discussion of the elements of the niechano-mathematical model for investigating the

dyna-inics of floating structures. _{On the basis of a detailed analysis of the}

na-ture of the various force interactions, a justified division is made of the

latter in dynamic _{and quasi-static ones. The general problem for defining} the velocity potential related to the dynamic loadings _{is formulated and} af-ter reviewing the references, a method is selected for deaf-termining the forces and moments of the hydrodynamic reaction and the wave loading, i.e. the inte-gral equations method. As for the quasi-static loadings - from hydrostatic

restoring forces and moments, from tension in the anchor lines, from wind and current influence - the available approaches are evaluated and it is proposed that combined theoretico-experimental methods should be used. The general for-mulations drawn of the dynamic and quasi-static loadings are unified in a ge-neral model for investigating the dynamics of floating _{structures. Considering}

waves as the basic external influence, determination is given of the problem for estimating the amplitude-frequency and phase-frequency _oscillation charac-teristics of floating structures.

Chapter two is dedicated to improving the model of dynamic loads and its

con-crete realization for seniisubmersibie crilling rigs. There are routine test procedures worked out for experimental determination of coefficients of added masses and damping, as well as of the ave forces and moments, taking account of the equipment available at EHC. The prccessing of the results, is carried out by means of Fourier's analysis.

The modellino of the structure of the hydrodynamic coefficients for equipments of complex hydrodynamic form is related primarily to the interaction of the ele-ments, the three dimensionality of the construction and the lcw-frequency

damp-ing. Frank's scheme and the strip theory is used for the numerical _estimation of the coeffcients of the addec mass and damping. The 3-D effects are taken

account of by rears of correction coefficients on th _{basis of the} achitec-ture peculiarities of the floating platforms, which are proved by series expe-rimental investigations. The problem of determining the drac force _{on the} har-monically oscillating submerged pontoon in a regime of symmetric _vor:ex exci-tation is solved for the purpose of estimating the low-frequerc. horizontal damping, using the dcrete vortices method.

For determination of the wave loading, a series of problems are solved for the wave forces and moments on the separate elements of the floating structures a sphere, a vertical cylinder crossing the free surface, a horizontal cylinder on and under the free surface. The structure of the forces and _{-ioments is} mo-delled from the loading on the floating platforms, _{taking account of the} inter-action between the elements and the low-frequency damping.

Experimental investigations are carried out at each step in studying the

dyna-mic loads for confirming the theoretical results.

In Chapter three estimation is made of the hydrostatic _{forces and moments fr-orn} the changes of the hydrostatic pressure, the tension in the anchor lines, the loads induced by the influence of wind and current on the floating structures.

In determining the restoring hydrostatic _{forces, estimation. is made of the}

cur-ves of the elements of the theoretical drawing. Applying the chain _{line theory} estimation is done also theoretically of the tension in two varieties of the states of the anchor lines _{- slack and taut - for the quasi-static reginìe'andof} the dynamic forces and mcments experimentally _{after the method of forced}

osci-llations.

In determining the forces and cments from the wind _{and current effect, a stress} is laid on the estimation of the relevant flow velocities and the resistance

coefficients. In determriining the vertical profile of the wind velocity,

consi-deration is taken of the gust _{actor and free surface roughness.}

The resista:

coeffcients are based on series aerodynamic _experiments.

Chapter four unifies the models developed and the numerical realizations for the different force effects in a joint model for studying the dynamics of the floating platforms. Routine test procedures are discussed for determination of motion parameters. An algorithm and a program package are worked out for nu-merical estimation of the characteristics _{of motions of free and moored}

float-ing platforms in regular and irregular waves at arbitrary headfloat-ing angle. A num-ber of comparisons are drawn of the results from model experiments, and in some

cases with full scale results for confirming the _{possibilities of the} numeri-cal procedure worked out. A numerinumeri-cal _{parametric analysis is carried out for} evaluation of the effect of the geometric and operation parameters _{on the} sta-tic and dynamic parameters and the _{motion characteristics of sernisubmersibles.}

By way of concluding, formulations _{are given of the thesis main results and}

contributions.

GENERAL ROUTINE TEST PROCEDURES

The complexity and versatility of the problems discussed, imposed _{that the}

up-drading of the rnechano-mathematical _{model of the floating structures}

dynamics should _{pass the following main stages:}

evaluation of the character of the force interactions and division of the

loads into dynamic and quasi-static _ones;

application of the hydrodynamic _{theory of oscillating body with}

six

de-gree of freedom;

modelling and numerical estimation of the dynamic loads, taking _{acount of} the interaction of the elements of the floating platforms;

modelling and numerical estimation of the damping at low-frequency _sway

motions;

application of the chain line theory for determination of the forces at the anchor lines;

experimental prooving of the theoretical _results;

application of the mathematical spectral _analysis;

effecting of numerical parametric analysis for evaluating the _influence of the geometrical and operation _parameters.

GENERAL CHARACTERISTICS OF THE SCIENTIFIC AND APPLIED RESULTS

As a result of the investigations carried out, a mathematical model of the dynamics of floating structures is developed, and general routine test pro-cedures are worked out, on the bsis of which a number of hydrodynamic prob-lems can be presented and solved, related to investigating technical means for adoption of ocean resources.

Software is developed for prediction of the dynamics of floating structures. A numerical parametric analysis is effected for studying the influence of the geometrical and the operation parameters on the oscillation characteristics

for a concrete floating platforin and relevant conclusions are drawn.

Complex experimental investigations are carried out for determining the iner-tia and damping forces, the wave forces, the dynamics of the anchor ropes and the characteristics of motions.

The rest of the thesis' contributions are related to:

- modelling the structure of the acting forces and moments at wave loads, hyd-rodynamic and hydrostatic reaction of tension at the mooring, of current and wind induced loads;

- numerical solution of a series of wave problems for the interaction of the elements of the structure and the fluid;

- numerical estimation of the vortex damping at low-frequency sway motion.

APPROBATION OF THE THESIS RESULTS

The main results of the thesis are reported to:

Joint Scientific Seminar between BSHC and Krylov Ship Research Institute, Leningrad, 1984.

International Scientific and Methodological Seminars on Ship Hydrodynamics, Varna, 1983, 1986.

Vth National Congress on Mechanics, Varna, 1985.

IVth IMAEM Congress, Varna, 1987.

The thesis is discussed in full length at:

BSHC Scientific Seminar under the leadership of Dr.P.Bogdanov, Honoured

Scientist.

Joint Seminar on Theoretical and Applied Mechanics under the leadership of Academician G.Brankov.

THESIS VOLUME

The thesis is comprised of ar introduction, four chapters and a conclusion.

The main text consists of 166 pages including 87 Figures and 3 Tables. The

List of References includes 126 titles.

The present Ph.D.thesis is dedicated to modelling and numerical investigation

of the floating structures' dynamics. The major results reached in the

the-sis are, as follows:

A mathematcal model of the dynamics of floating structures is proposed

and perfected in the direction of modelling sorne force interactions, including

the hydrodynaic reaction and the wave loads; the low-frequency vortex damping;

the quasi-static tension in the taut anchor lines.

Algorithms and programs are worked out, for determination of the static

pa-rameters, the hydrodyramic coefficients, the wave loads on floating structures,

as weil as for determination of the forces in the anchor lines. On ths basis

a program package is worked out for predicting the dynamics of floating

plat-forms in regular and irregular waves at arbitrary heading angle.

ir view 6f confirming the theoretical results, complex experimental

inves-tigations are carried out, for determination of the hydrodynamic coefficients,

the wave loads, the forces in the anchors and the motion charcateristics of

floating platforms.

Estimation is made of the effect of soma operation parameters for anchorec

floating platform and it is found out that the influence of the heading angle

is expressed in increasing those motions in the direction from which the waves

are coming; the increase in the tension at the anchor lines leads to decrease

of the motions amplitude and to reduction of the oscillations period of the

system platfonn - anchor, i.e. to increase in the probability of the system

to fall in resonance; the increase of the wind induced loads leads to a

cer-tain decrease of the sway motions' amplitude, i.e. there is a stabilizing,

effect in a certain range, after which the displacements increase imensely.

A numerical parametric analysis is effected for evaluation of the

influ-ence of the geometrical parameters. As a result of this, for the oscillation

characteristics, it is established that:

(a) for the practically most important cases the increase of draught leads to

decrcase of the amplitudes of the floating platforms;

- /

-the increase of -the clearance leads to decrease of -the amplitudes of roll

motion;

the increase of the diameter of the columns causes increase of the ampli-tudes of the horizontal motions and decrease of the ampliampli-tudes of the heave,

roll and pitch motions;

the increase of the height of the pontoons causes increase of the ampli-tudes in the vertical direction and to prevailing decrease

of

These conclusions are

of

of

structures design.

6. As a result of the invstigatic.ns carried out, general routine test pro-cedures are worked out, on the basis of which a series of specific hydrody-namic problems can be presented and resolved, related to the dyhydrody-namics of