Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
Currently Skimming:
Pages 863-881
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 863... ...
and Pidikn tic (1962) w re among the first to obtain experimental data for k flat plate in icillating flow Even though the mit igation effect of bilge keels on ship motion Han been known from the time of William F oude, who pro posed the usage of "bilge pieces" in 1865 and later measured its of ii tance, very little dvancf i, baled on fluid mechani i fir t principles he f9 taken place The modeling of unsteady viscous forces by sEk p edge -- 3 he f9 been k did cult one Amid the long history of the subject on roll mo tion, we will mention k few recent references which is not an f hauetive list Robinson and Stoddart (1987)
|
From page 864... ...
provided related, and zimilnrly in teresting features of the oscillating fl ws about bilge keels Poll damping of ships is not strictiJ related only to fl w separation around the bilges and keels Of equal importance is that bilge keels, if present, also generate lift like n low aspect wing because of the forward speed of the hull it is primarily the first aspect that we address in this paper, even though the latter aspect could be eflectiveiJ modeled by the first without n full fledge three dimensional so lotion An extensive amount of literature exists in motion predictions -- inviscid fluid theories it is gener ally assumed that inviscid fluid ship motion theory (WeEnusen, 1971) can be la gely improved -- in cluding viscous effects as ad hoc hydrodynamic co efl cients On the other hand there are good rear sons to believe that viscous effects could be fully coupled to the inviscid fluid motion The nature of this inviscid and viscous coupling was fir t ex Mined by (Yeung and Wu, 1991)
|
From page 865... ...
Geometry of bilge keel and bilge corner Figure 1: Geometry of cylinders with bilge keels. y Damplng ODF Damplng layer ~ ~~ layer ~ ~ O ~ \ hi ~G~ \/~ODb Dt ~ = V ~ JJ ED = ~Db lJ IF U0 ~,jj= -A Figure 2: Computational domain and definitions for FSRVM.
|
From page 866... ...
and (12) is zero except in the damping Infers L < xl < Xl and L > at > x, on the lefi and right ends of the free Surface, and zO is the initial local tion of the lend free surface node of the Infers at t = 0 (Israeli and Orssag, 1981, Cointe et cl 1991, Lino and Roddier, 1998)
|
From page 867... ...
Free surface elevation, 71~i, t) , the two Cartesian velocity components (ui)
|
From page 868... ...
, the shear tress was found to be of secondary importance in trongiJ separated fi w the pressure is the domi pant dynamic stress contributing to the total fluid force and moment H waver, BFFDM can provide the shear tress as part of the solution procedure, and both component of the stress are used to com pute the force and moment integrals (Eqns 25 27) The hydrodynamic coed cients will be dire tlJ ob twined from these time histories as explained further in Section 3 2 3 Experimental Setup and Hydrodynamic Coefficients The experiment were conducted at the ichmond Ship Model Is ting Facility of the University of Cal if ornin at Berkeley A 2 54 x 0 3 x 0 3 m rectangu Inr acrylic cylinder as shown in Fig 4 was hinged at the water level by the sides of the tank Bilge keels of 1 25 and I 90 cm were mounted on the bilge corner of the cylinder at n 45° angle The model w ighted 100 kg and displaced 0 11 m3 The rolling motion was induced by n hydraulic cJ5nder that can accept n random motion input (Random Mo tion MechaDi m, Hodges and Webster, 1986)
|
From page 869... ...
Figure 4: Experimental apparatus and setup MY' A (Q Drivi g Rod 1 \ W rod b' ~ o \x ~ E- at' \~L Figure 5: Free body di gram or measured at the roller bearing 0, 'the cylinder and the X' and Y' refers to the forcm in Ax'y coordinate system as sh wn in Fig 5 Force transducers are adjusted to zero and calibrated when the cylinder is installed on the hinges and in the upright position Their outputs are zeroed when no motion is present even though there may be static loads When the cylin der is in motion, the transducer respoonse are pro po tional to the additional forces present There fore, thetotal force applied m -- - cylinder at n hinge can be expressed as F=F OF, (3o) where F can be either X or Y and the second term 'm' is proportional to the output voltage of the transducer BJ making use of Eqn (30)
|
From page 870... ...
solution when the vortical psrt of the strenm function corrmpond ing to Eqn (8) is not 'turned on " in Figs 6 to 9, the inviscid fluid hJdrodJnamic cc6fl cient6 nr6 pr+ mnted The solution for n rectangular crm6 section (with n smnll bilge rndiu6, s66 Fig 1)
|
From page 871... ...
I nviscid Roll Added Momem d Ine ria C efficiem Figure 6: Added moment of ine tin, inviscid fluid solution o~ os os ~ Inviscid RolPSway Coupled Added Momem Coefficiem 032 028 024 020 p15015 ~ 012 ~// 008 'i~ 004 .< O ~ 0 5 Figure 7: Added m dS of roll into swnJ, inviscid fluid solution Inviscid Roll Damping Coefficieni 2 S 2V M, r n ~ i s c id, 20 K ee l s 252VM, rnViscid' 4t Keels 252VM, rnViscid' 6t Keels 252VM, rnViscid' 0t Keels \ \\ ,,." . " ' /~/', ~ ~" 04 05 08 ~ 10 12 14 Figure 8: Dnmping coeflicient of roll, inviscid fluid 2snM' rnVircid' b Keels 02 <^\ 2snM' rnVircid' 4t Keels / ~ 251ZI'M, rnViscid' 6t Keels 024 i_ ~ i~ 2snM' rnVircid' 0t Keel~ 02 {/~/ 'n'\ //,/ ,~'~'., ?
|
From page 872... ...
The diagonal term of the coed cients Figs 13 16 are grouped separntelJ from the coupling terms, Figs 17 20 Numerical results obtained using BFFDM are ndded to Figs 13 and 15, when KD = 470 and coo = 2 85 for comparison purposes it is grntifJing to see these two very defied ent and independent methods yield very predictions close to each other These predictions also tend to agree well, for the most part, with the experimental result Generally speaking, FSPVM and BFFDM do agree better in the diagonal terms than the cou Fling coed cients in the case of comparisons with experiments, one should keep in mind that the reli ability of the experimental measurements decreases with an increase in frequency because of vibration of the test apparatus Detail examination of this e tensive set of data will suggest the toll wing trends e An increase in keel depth (ado to Who) w uld in crease both the ndded inertia and damping for the entire range of frequency This is expected intuitiveiJ and from the computations The inertia measurements indicate otherwise even though the change is not seen as substantial e With bilge keels size fixed, experiments and real fluid theory suggest that an increase in roll amplitude lead to a decrease in the inertia coed cients for both di gonal and off diagonal term, or at least up to the largest angle of 5 75° investigated here Larger roll amplitude yield an appreciably larger damping coed cients e The agreement betw en theory and experi 10
|
From page 873... ...
oo6r 0.05 0.04 0.03 0.02 Q 0.01 Q O -0.01 -0.02 -0.03 -oo4 -0.05 -0.06 -- BFFDM - FSRVM — Experiment 0.1 r VT = 4 -- -- -- -a -- -- -- - BFFDM -- -I -- FSRVM _ i;/; 1/ (i t/T Figure 10: Moment MW(t) history, ~ = 0.8 ~ Q 0.05 _ 0.025 a)
|
From page 874... ...
k i kttributabie to memory effect of the stk ting swing In Fig 22, the vo ticity fields obtained using both numericki models are di played kVi color contour plot The vortex method predicts larger and more di tinct vortices, kVi well kVi larger distances from the 5: d:, once they become ceparkted from the keel A stronger dissipation apnea i to he f9 taken place in the BFFDM As in most finite diflerencing schemes, numericki (krtifleiki) damping is always present The grid free method of FSPVM does not direction of roll motion k fly half period, the fore keel be comes the aft keel, md ic~versa Experimental and theoretical studies of the forced roll motion hJdrodJnkmim of k cylinder with bilge keels are conducted The theoreticki model includes the use of two free su face Napier Stokes Solvers (FSRVM & BFFDM)
|
From page 875... ...
o. 1 Figure 14: Added moment of inerti 4 coef cient, 4O = 5 75° Figure 16: Equi 41ent line 4r d 4mping coef cient of roll, 4O = 5 75° 13
|
From page 876... ...
Roll-Sway Coupled Added Moment d Inedia Coeffiaent 08 ~ 10 12 14 Figure 17: Roll s 4J coupled 4dded inerti 4 coef ficient, 4O = 2 85° Ro -Sway Coup ed Added Mom ent of nert a Coeff c ent 030 026 / /~ \ ~ 020 / .\ ~ ~ ~ ~ /y '\ u1416 ~N 010 ~ t 06 ~ ~ ~: ~ 04 06 OS ~ 10 12 ~4 Figure 18: Roll s 4J coupled 4dded inerti 4 coef ficient, 4O = 5 75° 14 ~ ~ ~ ~.. ~ DU 04 oc od ~ Jo 12 14 Figure 19: Roll s 4J coupled d 4mping coefi cient, 4O = 2 85° Roll-Sway Coupled Damping Coefficient ~.,.
|
From page 877... ...
2C 1C y C -1 C -2C -3C -4C 2C 1C y C -1 C -2C -3C -4Ce — 20 10 _ y O— -10 -20 _ -30 -40 -40 -30 -20 -10 VorticityVectors,ocO=5.75°, w=0.8 Vorticity Vectors, oc0 = 5 75°, ~ = 0.8 -40 -30 -20 -1 0 VorticityVectors,ocO=5.75°, w=0.8 - ;,~,`~-i-~ -- I-.; -40 -30 -20 t/T = 5 1/6 ~ -10 0 X VorticityVectors,ocO=5.75°, w=0.8 30 40 -40 -30 -20 t/T = 5 1/2 , 1, .
|
From page 878... ...
s3~] -10 ~ 10 20 30 Figure 22: Vorticity contours for a rolling cylinder with 4/ bilge keels at one instant of time, TO = 5.75° The contour scale is based on a non-dimensional vorticity defined by (3/~.
|
From page 879... ...
Grosenba gh, M A and Yeung, F W (f333) "Nom /ffiear free surface d w at a tw dimensional bow", I Flmd Moch, 909, pp f 7 7f [fJ]
|
From page 880... ...
(f960) 'Noffiinear, tw dimensiona/ ship motions", Tech F pt.
|
From page 881... ...
AUTHORS' REPLY he amount of time thm c particohr solution takes to attain c periodical stecdy-state behavior depends on the frequency of excitation Lower frequency excitation generally takes more time to achieve steady state Figure 10 of the pa r indicates that it took about 4 to 5 periods to cttam c steady behavior for the f equency in questmn It is worthwhile to note thm while the roll moment curve might not cppe to vary signific mtly in amplitude during the "tr msient state", the phasing of the moment rektive the to roll male contim e to adjust itse f es more vorticescreshedoffthe keels his phcsmg m~tmclly demean es the damping Ed added moment of ine tic DISCUSSION M Kcshiwagi Ky shu University, Up m In the classical potential theory, the conservation principles c m be used to check the validity of mmffical remits without resorting to comparison with experiments I wonder if the same kind of principles c m be used to validate the m mericcl results in this paper What is the relation between the coupled coefficient of roll into sway Ed the coefficient of sway into roll? AUTHORS' REPLY Unlike classical potenticl-flow theory, the flows being considered in this paper are governed by the fully nonlinear Navier-Stokes equations hus, none of the non cl conservation or reciprocity relations, such es She wave-cmplitude to damping relation, symmetric of hydkodynamic coefficients, would be applicable he FSRVM method contains no artificial or m medical viscosity in the fluid domain, aside from the sponge layer used to damp out reflected waves on She f ee surface its a gray was e lier tested out by c n mber of experiments Ed n mericcl solutions repo ted in the references he nonlinear mature of the solution, particularly the importmce of convective effects in the flow, renders the sway-roll coupling coefficients to be non- mmetriccl About c decade ego, w developed c viscousflow formulation IYenng & '.\ a, R f [35]
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.