Questions on Ship nd Offshore Hydromechnics (in progress of formtion) JMJ Journée Contents: Question 1 Stnding Wves Question Regulr Wve Observtion Question 3 Axes Systems in Ship Motion Clcultions Question 4 Lod Superposition Question 5 Dissiption of Energy Question 6 Model Tests3 Question 7 Eqution of Motion3 Question 8 Heve Resonnce of Verticl Cylinder 3 Question 9 Irregulr Motions 3 Question 1 Irregulr Motions of Spr Buoy4 Question 11 Men Wve Lods on Wll4 Question 1 Wve Drift Forces5 Question 13 Cummins Equtions5 Question 14 Potentil Theory Applictions 6 Question 15 -D Velocity Potentils of Ursell nd Tsi6 Question 16 -D Velocity Potentils of Frnk 7 Question 17 -D versus 3-D Approches7 Question 18 Forced Oscilltion Tests7 Question 19 Wve Lod Mesurements8 Question Symmetric nd Anti-Symmetric Motions8 Question 1 Experimentl Determintion of Mss nd Dmping8 Question Viscous Roll Dmping8 Question 3 Froude-Krilov Force for Heve 8 Question 4 Coupled Heve nd Pitch Motions 8 Question 5 Nturl nd Resonnce Frequencies9 Question 6 Free-Surfce Anti-Rolling Tnk 9 Question 7 Added Resistnce9 Question 8 3-D Diffrction Computtions 1 Question 9 Non-Liner Behviour of Ships1 Question 3 Men Wve Drift Forces 11 Question 31 Wve Set Down 11 Question 3 Stiffness of Mooring System 11 Question 33 Sttion Keeping1 Question 34 Sustined Se Speed 1 JMJ Journee Pge 1
Question 1 Stnding Wves The velocity potentil of simple regulr deep-wter wve is given by: ζ g k z Φ = e sin ( k x ω t) ω ) Using this definition, determine the velocity potentil of stnding wve b) Determine for both, the simple wve nd the stnding wve, the pths of the fluid prticles c) Sketch the wve elevtion of the stnding wve s function of x nd t How lrge is its mplitude? d) Determine for both, the simple wve nd the stnding wve, the energy in the wves per unit wve surfce re Question Regulr Wve Observtion The mst of smll floting rft is observed to oscillte with period of 7 seconds nd mplitude from the verticl of ± 8 degrees, due to the pssge of trin of (more or less regulr) deep-wter wves Find of these wves: ) wve height ( H = 339 m) b) wve length, ( λ = 765 m) c) phse velocity of wves ( c = 19 m/s) Question 3 Axes Systems in Ship Motion Clcultions ) Mention nd explin the three xes systems, used in ship motion clcultions S x, y z Determine the wve elevtion b) Wves re defined in n erth-bound xes system, (, ) in the stedily trnslting xes system, O ( x, y, z) c) Determine the generl reltion between the frequency of encounter, ω e, nd the wve frequency, ω Question 4 Lod Superposition The lods on body - oscillting in wves - re divided in two seprte contributions ) Mention nd explin these two contributions b) Show these seprte contributions in n uncoupled eqution of motion for heve c) Explin the terms ''hydrodynmic mss'' nd ''hydrodynmic dmping'' Question 5 Dissiption of Energy The hydromechnicl lods on floting structure consist of inerti, dmping nd spring terms ) Show for trnsltions, such s heve motions, tht only the dmping term dissiptes energy b) Show the sme for rottions, such s roll motions c) Show, in cse of non-liner dmping behviour, how n equivlent liner dmping coefficient cn be obtined JMJ Journee Pge
Question 6 Model Tests ) Describe briefly model experiments to determine the hydrodynmic mss nd dmping of heving verticl cylinder by free decy test Explin - by presenting the relevnt equtions - how these coefficients cn be determined from the mesured motion signl b) Describe briefly model experiments to determine the hydrodynmic mss nd dmping of heving verticl cylinder by forced oscilltion tests Explin - by presenting the relevnt equtions - how these coefficients cn be determined from the mesured force signl c) Describe briefly model experiments to determine the wve lod mplitude nd phse lg of heving verticl cylinder Explin - by presenting the relevnt equtions - how these phenomen cn be determined from the mesured wve lod signl Explin nd determine the mgnitude of the so-clled Froude-Krylov contribution in these lods Question 7 Eqution of Motion Consider verticl cylinder - dimeter D nd drft T, upright in wter with density ρ - heving in regulr wves with mplitude ζ nd frequency ω The hydrodynmic mss,, nd dmping, b, re known ) Give the eqution of motion for heve b) The spring coefficient, c, follows from the dimensions given bove Show this c) Determine t frequency ω the wve lod mplitude, F / ζ, nd phse shift, ε F ζ d) Determine t frequency ω the heve mplitude, z / ζ, nd phse shift, ε z ζ e) Determine t frequency ω the reltion between the heve motion nd the wve lod, z / F nd ε zf f) Determine the nturl frequency for heve, ω Question 8 Heve Resonnce of Verticl Cylinder Consider circulr cylinder with rdius R, floting upright with drft T in wter with density ρ ) Give n pproximtion of the wve length in short (deep wter) wves t which resonnce in heve cn occur b) Discuss the effect of dmping on the frequency chrcteristics of heve t different R / T rtios Question 9 Irregulr Motions ) Show how one cn determine the heve spectrum, S zζ motion, z /, nd the wve spectrum, S ζ ζ, when the trnsfer function of the, re given Prove the reltion used for this JMJ Journee Pge 3
b) Define the Root Men Squre vlue, z RMS z 1/ 3, the men period bsed on the centroid of the spectrum, T 1 z, of this motion, the significnt heve mplitude,, nd the men zero-crossing period, T z c) Determine the probbility tht the significnt heve mplitude, z 1/ 3, will be exceeded in this se stte defined by S ζ d) Show how this heve spectrum bsed on circulr frequency ω cn be trnsferred to spectrum bsed on the frequency f in Hz Show these spectr in one relistic grph e) Give the reltion between the heve velocity spectrum, S zζ & spectrum, S zζ f) Give the reltion between the heve ccelertion spectrum, S zζ & displcement spectrum, S zζ, nd the heve displcement, nd the heve g) Which of the zero, first nd second order moments m, m 1 nd m of the displcement, velocity nd ccelertion spectr re similr? Question 1 Irregulr Motions of Spr Buoy The response mplitude opertor of the heve motion, ζ D clcultions The wve spectrum of the irregulr wves, S z /, of Spr buoy is known from 3- ζ, is given too Using this, show how one cn determine: ) the significnt mplitude nd verge zero-upcrossing period of the: verticl reltive displcements verticl bsolute displcements verticl bsolute velocities verticl bsolute ccelertions b) the probbility of exceeding threshold vlue by the verticl ccelertions c) the number of times per hour tht this will hppen Question 11 Men Wve Lods on Wll The velocity potentil nd elevtion of regulr wve in deep wter - progressing in the positive x direction - re given by: ζ g k z Φ = e sin ( k x ω t) ω ζ = ζ ( k x t) cos ω The time-verged wve lod on verticl wll - in regulr wves perpendiculr to this wll - is: 1 ρ g ζ per meter length of the wll ) Show the principle of the determintion of this vlue b) How lrge is this lod in irregulr wves with significnt wve height H 1/ 3? c) Wht ssumption hs been mde when this formul is pplied s n pproximtion for the men wve lods on crude oil crrier, moored in bem wves? Is the ctul lod on the ship lower or higher thn this pproximtion? Why? JMJ Journee Pge 4
Question 1 Wve Drift Forces Floting bodies in wves re not only loded by oscillting forces with frequencies in the wve frequency rnge, but lso by men second order forces s well s low-frequency forces in irregulr wves ) Which simple experiment proofs the presence of men wve drift force on body in regulr wves? Give n explntion for the presence of this force According to Mruo nd to others, the men (time-verged) wve drift force in regulr bem wves per unit length cn be defined by: 1 F d = ρ g R ω ζ ' { ( ) } in which R is reflection coefficient nd ζ is the mplitude of the incident regulr wve b) Show, using the potentil theory, the vlidity of Mruo's expression with =1 R for the cse of verticl wll Consider now the cse of moored tnker in irregulr hed wves c) Explin the low-frequency behviour in irregulr wves of the wve drift forces on this tnker d) Explin why - nevertheless tht second order wve drift forces re smll when compred to first order wve forces - reltively high second order motions cn pper in irregulr wves e) Sketch time history of the surge motion in irregulr wves nd show in this figure the vrious cuses, which led to this motion Question 13 Cummins Equtions The so-clled Cummins-eqution in the time domin is given by: with: in which nd ( M + A) x( t) + && B( τ ) x& ( t τ ) dτ + C x( t ) = X ( t) B( τ) = π b( ω) cos 1 A = ( ω) + ω ( ωτ ) dω B( τ) sin ( ωτ ) dτ b re the hydrodynmic mss nd dmping determined in the frequency domin ) Which term(s) in this Cummins-eqution re liner en which one(s) cn be non-liner? b) Discuss the physicl mening of the individul terms c) Becuse mny computer progrms fil t very high frequencies, the high-frequency ''til'' of the 3, is often pproximted by = β/ω, where β is determined from the dmping t the highest successful frequency in the clcultions d) Explin the origin of this pproximtion nd reproduce derivtion of the used reltion F / ω, nd wve spectrum, dmping curve, b e) Show, given the frequency chrcteristics of the wve force, ζ ( ), how time history of the (liner) wve force cn be generted S ζ f) How cn the effect of non-liner spring be dded to this Cummins-eqution? g) How cn this Cummins-eqution be solved? h) Discuss the mutul ''pros nd cons'' of frequency-domin nd time-domin equtions JMJ Journee Pge 5
i) Give three exmples of problem tht cn not be solved in the frequency-domin, by which one is forced to solve this problem in the time-domin Question 14 Potentil Theory Applictions Consider the totl velocity potentil to describe the motions of the fluid prticles round n oscillting body in wves ) In which three individul prts cn this potentil be divided nd why is this division permitted? Why is the hydrosttic contribution ignored? Wht is for ech of these potentils the motive for the ppernce of the relted motions of the wter prticles Discuss the division in spce nd time dependent terms b) Discuss nd explin the requirements nd boundry conditions, tht hve to be fulfilled when defining these velocity potentil(s) Which of these requirements or boundry conditions re similr to those used when defining the velocity potentil of simple regulr wve? c) Wht is the reltion between the rdition potentil nd the hydrodynmic mss nd dmping coefficients? Which symmetry properties hold for the hydrodynmic mss nd dmping coefficients? From which ppers this? d) Explin why the integrtion of the rdition potentils over lrge closed surfce of volume with fluid cn be simplified to integrtion over the wetted surfce of the body only e) Give the expression for the wve lods bsed on n integrtion of the pressures on the body ccording to the linerized Bernoulli eqution f) Explin why + Φ w / n is equl to Φ d / n in the definition of the wve lods g) The so-clled ''Hskind reltions'' provide the opportunity to clculte the wve lods without using the diffrction potentil Whereupon is this bsed? h) Explin the physicl mening of the potentil mss coefficients M 35 nd M 53 nd their relted hydrodynmic force nd moment i) Explin why the potentil mss coefficients M 3 nd M 3 nd their relted hydrodynmic forces do not exist for crude oil crrier Question 15 -D Velocity Potentils of Ursell nd Tsi Consider cross section of horizontl cylinder, oscillting in the surfce of fluid ) Ursell ssumed two types of wves, which were produced by this oscillting cylinder Describe the physicl chrcteristics of these two wve systems b) Which potentil flow element combintions (source, sink, doublet, etc) re used for the simultion of the verticl motions of this cylinder nd which ones for the simultion of the horizontl motions Explin the different pproches for the verticl nd horizontl motions briefly c) Which requirements nd boundry conditions re fulfilled lredy by these potentils nd which one(s) re depending on the prticulr cross section of the body itself d) Describe how the potentil mss nd dmping for heve cn be determined, s the velocity potentil is known e) Describe some cses where the conforml mpping method will fil? f) Describe the (non-) similrities of ''Lewis'' cross section nd the ctul cross section g) Determine the Lewis coefficients ( M s, 1 nd 3 ) of hlf circulr cross section with dimeter of 1 m JMJ Journee Pge 6
h) Describe the principle of method, which cn be used to obtin the N -prmeter close-fit conforml mpping coefficients of cross section? i) Consider now rectngulr cross section Explin why Lewis trnsformtion gives much more poor results for roll thn it gives for swy nd heve Question 16 -D Velocity Potentils of Frnk ) Bsed on work of Wehusen nd Litone, the complex potentil t z of pulsting pointsource of unit strength t the point ζ in the lower hlf plne of cross section ws given by Frnk s: ik ( z ζ e ) * 1 G ( z, ζ, t) = ln ( z ζ ) ln ( z ζ ) + PV dk cos( ω t) π ν k ik { e ( z ζ )} sin ( ω t) where: z = x + iy ζ = ξ + iη ζ = ξ iη In here: ζ is defined in the lower hlf plne of the cross section ζ is defined in the upper hlf plne (mirrored) ν = ω / g is the wve number in deep wter ik ( z ζ e ) PV dk is principle vlue integrl with vrible k ν k Discuss the possible singulrities in this Green's function b) In which cses would one prefer Frnk's pulsting source method bove the method of Ursell nd Tsi with 1-prmeter conforml mpping? c) Wht is the mjor disdvntge of Frnk's method, when compred with the method of Ursell nd Tsi? Question 17 -D versus 3-D Approches ) Mention some prcticl exmples in offshore pplictions for which -D pproch suffices nd some exmples for which 3-D pproch is required b) Discuss the mutul (dis)dvntges of the -D nd the 3-D pproches when determining the potentil coefficients Question 18 Forced Oscilltion Tests ) Describe briefly model experiments to verify the results of potentil clcultions on the hydrodynmic mss nd dmping for heving nd pitching crude oil crrier for rnge of frequencies b) Wht re the scle-fctors for these coefficients c) Explin how - by using Fourier nlysis - the in-phse nd out-of-phse terms cn be found from the mesured signl JMJ Journee Pge 7
Question 19 Wve Lod Mesurements Describe briefly model experiments to verify the results of wve lod clcultions for heving nd pitching crude oil crrier Question Symmetric nd Anti-Symmetric Motions Sometimes distinction will be mde between symmetric nd nti-symmetric motions of ships ) Explin the difference between these two types of motion b) Wht is the effect of this distinction on the equtions of motion of ship for 6 degrees of freedom? c) Wht cn possible influence of mooring be on this distinction? Question 1 Experimentl Determintion of Mss nd Dmping The frequency dependent hydrodynmic mss nd dmping for heve nd pitch of floting structure cn be determined experimentlly by mens of model tests ) Describe to types of model experiments for this purpose Wht re the mutul ''pros nd cons'' of these two methods? b) Which scling lw(s) hve to be used c) The model is scled by α Determine the scle fctors of the time, the mplitude nd frequency of oscilltion, the forwrd speed, the length of the rdited wves, the mesured forces, moments nd phse shifts nd the obtined hydromechnicl coefficients d) When plys the so-clled ''scle-effect'' significnt role? Question Viscous Roll Dmping ) Explin why (generlly) viscous dmping of norml ships plys role in the roll motions nd not in the heve or pitch motions In which cse(s) cn the viscous prt of the roll dmping be ignored? b) Describe the vrious cuses of viscous roll dmping c) Sketch nd explin the reltion between the roll dmping nd the bredth to drft rtio, B / T, of ship Question 3 Froude-Krilov Force for Heve ) Discuss the so-clled Froude-Krilov force for heve on cross section of ship b) Where on the cross section is the center of this force locted? Question 4 Coupled Heve nd Pitch Motions Consider the coupled equtions of motion for heve nd pitch of floting structure in regulr hed wves ) Reproduce these two equtions of motion When re the so-clled coupling terms in these equtions zero nd explin why JMJ Journee Pge 8
b) In which cse(s) hs the use of the strip theory gret dvntge on the use of the 3-D diffrction method nd in which cse(s) hs the lst one preference? c) Which methods cn be used in the strip theory to clculte the hydromechnicl coefficients of cross section? Discuss the benefits nd limittions of ech method d) Describe briefly model experiments to verify the results of clcultions on the hydrodynmic mss nd dmping for heving nd pitching crude oil crrier e) Reproduce the clcultion principle of the three terms in the wve lods on ship, s used in the strip theory method Hint: mind the reltive velocity principle f) Describe briefly model experiments to verify the results of wve lod clcultions for heving nd pitching crude oil crrier Question 5 Nturl nd Resonnce Frequencies ) A box-shped vessel hs length of 5 m, bem of 1 m, drft of 3 m nd freebord 6 m The height of the CoG bove the bottom, KG, is 45 m Assuming tht the vessel's mss is uniformly distributed throughout the length nd section of the vessel, nd neglecting the effects of ssocited wter, clculte the nturl periods of heve, roll nd pitch in slt wter ( ρ = 15$ t/m b) A vessel, length meter, whose nturl periods of roll nd pitch re 15 nd 1 seconds respectively, is siling t knots in (more or less regulr) se with wve length of 5 meter Clculte the hedings on which the lrgest roll nd pitch mplitudes re likely c) When the mplitude chrcteristics of for instnce heve shows resonnce t certin frequency of oscilltion, this frequency is not necessrily the nturl frequency of the floting structure Explin this sttement Question 6 Free-Surfce Anti-Rolling Tnk The uncoupled eqution of motion for roll of n FPSO in regulr bem wves is given by: + φ&& + b φ& + c φ = X cos ω t ε while the wves re given by: ( ) ( ) Ixx 44 44 44 4 + X 4ζ ( t) ζ = ζ cos ω Becuse of too hevy roll motions, it is decided to investigte the reduction of roll by free-surfce nti-rolling tnk in the vessel The hrmonic exciting moments on its environment of this nti-rolling tnk is given by: ( ω ε ) K = K cos t + Kφ The mplitude K / φ nd phse lg ε K φ s function of ω hs been determined by forced roll oscilltion tests with tnk model Show how the effect of this tnk cn be included in the coefficients, in the left hnd side of the eqution of motion for roll of the FPSO Question 7 Added Resistnce The resistnce increse of ship siling in regulr wves cn be obtined by model experiments or be computed Then, with known wve energy spectrum, the men dded resistnce in irregulr wves cn be found JMJ Journee Pge 9
) Wht is the reltion between the men dded resistnce in regulr wves, R ( ) w ω, nd the wve mplitude, ζ? Is this liner or non-liner reltion? How cn this be concluded from results of model tests? b) Show the principle of the clcultion of the men dded resistnce in regulr wves either by: the rdited energy method (Gerritsm \& Beukelmn), nd the integrted pressure method (Boese) c) Determine the reltion between the men dded resistnce in regulr wves - trnsfer function Rw ζ ( ωe ) spectrum, S / - nd the men dded resistnce in irregulr wves, R AW, s the wve energy ζ, is given d) Determine the reltion between the men dded resistnce in irregulr wves, R AW, nd the significnt wve height, H 11/ 3 of Bretschneider wve spectrum e Question 8 3-D Diffrction Computtions 3-D diffrction clcultions re crried out to determine the behviour of rbitrrily shped floting structures in wves; the computtion method is bsed on the clssic potentil theory ) Which velocity potentils ply role here nd describe the physicl bckground of ech of these potentils b) How re the potentils described which re relted to the presence of the floting body? Give generl eqution of the potentil s distribution of sources over the men wetted surfce of the body nd explin the different terms in this eqution Which mgnitudes in here cn be clculted directly nd which one(s) re unknown so fr? c) The formultion of the Green's function (or influence function) in this eqution is chosen in such wy tht these potentils fulfil utomticlly number of requirements or boundry conditions Mention these requirements or conditions d) Bsed on which - still missing - boundry condition re the source strengths being clculted nd which (integrl-)eqution needs then to be solved? How cn this eqution be discretized - to restrict the number of unknowns - nd wht does this men for the description of the (under wter) hull form of the body? e) As the solutions of the source strengths hve been found, then number of mgnitudes - required for determining the body motions - cn be clculted Mention these mgnitudes f) Give the linerized equtions of motion of the floting body nd explin the physicl mening of the different terms in these equtions Question 9 Non-Liner Behviour of Ships For the determintion of the first order wve lods, the ''body-in-wves'' hs no motions (zero order) in the erth-bound xis system The wves re pproching restrined body For the determintion of the second order wve lods, the ''body-in-wves'' is crrying out first order hrmonic motion, forced by first order wve lods The wves re pproching hrmonic oscillting body nd - using perturbtion methods - the O X, X X system of xes becomes: orienttion of surfce element reltive to the fixed ( ) 1, N = n + εn The prmeter ε is some smll number, with ε << 1, which denotes the order of oscilltion If the velocity potentil: ( 1) ( ) Φ = εφ + ε Φ + JMJ Journee Pge 1 ( 1) 3
is known, the fluid pressure t point is determined using the Bernoulli eqution: Φ 1 p = ρ g X ( ) 3 ρ ρ Φ t Assuming tht this point is crrying out smll - first order - wve frequency motions, men position, X ( ) ( 1) X, bout, nd pplying Tylor expnsion to the pressure in its men position, yields: ( ) ( 1) ( ) p = p + ε p + ε p The instntneous wetted surfce, S, is split into two prts: constnt prt, S, up to the sttic hull wterline nd n oscillting prt, s, the splsh zone between the sttic hull wterline nd the wve profile long the body ) Show (without presenting very detiled formuls) tht the fluid force on the oscillting body cn be split into three prts: hydrosttic fluid force, ( 1) ( ) F nd second order fluid force, F b) Discuss this pproch nd its results F ( ), first order oscilltory fluid force, Question 3 Men Wve Drift Forces Floting structures in wves re not only loded by oscillting forces with frequencies in the wve frequency rnge, but lso by men second order forces s well s low-frequency forces in irregulr wves ) Wht does these different lods men for: the resulting ship motions (show the motion components), nd the mooring forces b) Wht is the reltion between the men drift force in regulr wves nd the wve mplitude? Is this liner or non-liner reltion? How cn this be concluded from results of model tests? c) Determine the reltion between the men drift forces in regulr wves (trnsfer function) nd S ω, is given the men drift forces in irregulr wves s the wve energy spectrum, ( ) d) Determine the reltion between the men drift force in irregulr wves nd the significnt wve height e) Drift forces cn be clculted by using the potentil theory Show the principle of this clcultion Which terms in the men drift forces re similr to the dded resistnce terms clculted by the integrted pressure method (Boese) ζ Question 31 Wve Set Down Discuss (by using prcticl exmple) the phenomenon ''wve set-down'' nd its effect on the heve motions of vessel Question 3 Stiffness of Mooring System Discuss the phenomenon tht s the stiffness of mooring system increses, so does the RMS vlue of the low frequency mooring force too JMJ Journee Pge 11
Question 33 Sttion Keeping Thrusters my be used to keep vessel in its desired position ) How cn the propulsive chrcteristics of thruster be presented? b) An importnt thruster-hull interction effect is the Cond effect Explin this Cond effect nd its influence on the efficiency of the thruster c) Show how the thruster forces of dynmic position system re ccounted for in the eqution of motion for surge of floting structure in wves d) Discuss the problems tht cn pper when thruster of dynmic positioned floting structure in wves comes too close to the free surfce e) For tunnel thrusters, the thruster forces re ffected by the flow of current pst the inlet nd outlet Discuss the effect of this current on the performnce of bow thruster Question 34 Sustined Se Speed A crude oil crrier is siling in rough to very rough sewy ) Explin briefly - for crude oil crrier siling in irregulr wves - the different resistnce nd propulsion components, which cuse: involuntry speed reduction voluntry speed reduction b) Discuss the phenomen (relted to the ships motions) which cn be reson for the ship's cptin to reduce speed nd/or chnge heding Account in your considertions for the loding of the ship, fully loded or bllst condition JMJ Journee Pge 1