Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Study on the CFD Application for VLCC Hull-Form Design K.-S. Min. J.E. Choi, D.~. Yum, S.H. Shon, S.H. Chung, D.W. Park (Hyundai Mantime Research Institute) ABSTRACT Flow characteristics around very large oil carriers with 3 different aft-body hull forms have been investigated by 4 different CFD codes and compared. Hull forms were prepared by modifying the existing form of 309,000 TOW VLCC recently designed by Hyundai Heavy Industries, and classified as the basic form, extreme U-form and extreme V-form. Model tests were conducted to verify the results of numerical analysis. Test results have shown that the extreme V- shape aft-body hull form has the most superior propulsion characteristics to the other two hull forms. Presently, even the qualitative prediction of ship's propulsive performance as well as the quantitative prediction is not possible by the numerical method, and hence, model test should be conducted to evaluate superiority of hull forms. Therefore, much further study should be performed for CFD to be utilized in the hull form design. INTRODUCTION The processes of hull-form design at initial stage are performed by the creation of totally new hull or by the modification of existing hull form. The latter is generally used in shipyards. Therefore, it is necessary to predict the changes of flow characteristics due to hull-form variations. The prediction of the flow characteristics is traditionally carried out by experimental method, that is, model test. The experimental method has a merit of accuracy, but demerits of longer time and higher cost. Recently, it is possible to predict flow characteristics using computational method so called computational fluid dynamics(CFD) through highly developed computer and CFD codes, and so, CFD has been applied from the initial design stage at some shipyards. This method is not only economical in time and cost, but also able to estimate some characteristics which are not possible to be measured by model tests. In general, however, the computational method does not have sufficient accuracy and reliability yet for the practical applications. This is a disadvantage of the computational method. In order to utilize CFD for useful tool of hull- form design, the CFD results should be accurate and credible, and show the differences of the flow characteristics according to the variations of hull form. The studies to improve the CFD technology for the prediction of flow characteristics around ship hull have been actively carried out in the world through the International CFD Workshops which have been held four times in last two decades(Larsson, 1980, Larsson et al., 1991, Kodama, 1994, Larsson et al., 2000~. Following the worldwide trend and necessity, Hyundai Maritime Research Institute(HMRI) has established the long term R&D Program on this subject and carried out the study. The flow characteristics of five different ships in four different ship types were investigated through the computational method using four CFD codes(HMRI-SNU home code, STAR-CD, FLUENT, SHIPFLOW) and the experimental method(Min et al., 2000~. The objected ships were VLCC, bulk carrier, LPG carrier, container carrier, and destroyer, which were recently manufactured or studied at Hyundai Heavy Industries Ltd.(HHI). The purpose of this paper is to predict the differences of the flow characteristics due to the hull- form variations through the experimental and the computational method. The basic hull form is a 309,000 TDW VLCC recently designed at HHI. After selecting basic hull form, the frame lines of stern are changed to extremely U- and V-shaped hull. For the computations, four CFD codes(WAVIS, COMET, STAR-CD, FLUENT), which gave relatively good results at the previous work of Min et al.~2000), were utilized. Model tests were carried out at the deep-water towing tank of HMRI. The contents of model tests were resistance and self-propulsion test, wake measurements on a propeller plane, and paint test for visualizing limiting streamlines on a hull. This paper includes the following contents: - Systematic hull-form variation of the stern of slow speed full-ship - Selection of CFD codes - Model tests to predict flow characteristics including resistance and propulsion performance - Calculation of flow characteristics - Evaluation of different stern hull form
NUMERICAL METHOD The dual coordinate systems have been adopted as shown in Figure 1. The global coordinate system~x,y,z) is defined to represent the flow patterns Turbulence model around hull as positive in the flow direction, positive y starboard, and positive z upward where the origin is at the bow and undisturbed free surface; while the local coordinate system~x',y',z') to enhance the usefulness of the calculated wake patterns in the propeller design where the origin is at the center of propeller. ~ v ~ y ._ Figure 1 Coordinate System Governing equation The governing equations for turbulent flow in the present study are the continuity equation for mass conservation and Reynolds-averaged Navier-Stokes equations for momentum transport. All the physical quantities are non-dimensionalized by the ship length(Lpp), ship speed(Vs), and fluid density" p ). Continuity equation auf = o axi Momentum transport equation aUi+u~aUi = ap + a ~ 1 aUi UP) (2) al ax, axi ax, Rn ax, where Ui(=U,V,W) are velocity component in xi=(x,y,z) directions, while p, Rn, and u ju ~ are static pressure, Reynolds number, and Reynolds stress, respectively. Turbulent kinetic energy transport equation Dk a c k2 Ok Ok auto Do ax, ( k £ ax,+ Rn ax/)-Ui2l~ ax -£ (3) Dissipation of turbulent energy equation Dt ax, ~ £ axe Rn aX' ) Cal k uju/ a £2 -Ce2 k where k and ~ represent turbulent kinetic energy and dissipation rate of turbulent kinetic energy, respectively; and Ck, C e, Cal, and Cc2 are model constants. For turbulence closure, Reynolds-stress (FLUENT, 2000) and eddy-viscosity model are applied. For the eddy-viscosity model, Chen's(COMET, 2001), cubic(STAR-CD, 2000), and realizable(WAVIS, 1999) k-£ turbulence model are utilized. ReYnolds-stress model Reynolds stresses are expressed as the form of partial differential equation deduced from Navier-Stokes equation; Du,z`~ 2 D = Dig + Gig 3 ~ij£ + PS (5) where Dij, Gij, and PS are diffusion, generation, and pressure strain term, respectively; and dij is Kronecker delta. a k2auiuj 1 aujuj D = (Ck + ) 'I axe £ axe Rn OX I ~ i ~ ax, i ~ at ) (6) PS=-C~ k (uiuj - 3 dijk)-C2(Gij - 3 dijGk) where Cat and C2 are model constants. EddY-viscositY model Reynolds stresses can be written using Boussinesq's isotropic eddy viscosity hypothesis; -uiu/ =-3k~y+2v,si; (7) where v,(=C,u) is turbulent eddy viscosity and Sij[= 2(aa i + a j)] is rate of strain. In the Chen's k- ~ model, Cu has constant value of 0.09 while in realizable k- ~ model, C,u is expressed using Sij and Qij[=2(a i_ a j) ], where Qii is (4) vorticity.
An +Asu( ) where the terms are defined as U( ) =4SijSij + Q`yQij ~ An =4.,0 As = JO cos A, ~ =arccos(~W), ~ f S = ~SijSij In the cubic k- ~ model, Reynolds stresses are expressed with considering anisotropic and non- linear relationships between Reynolds stresses and rate of strain. - u juj = - 3 k~ij + V,sij Cat v'(Sik Skj3 id Ski Sk! ) C2v,(Qik Sky + Q jk Ski ~ C3 V,(Q ik Q jk3 id Qk! Q k! ) C4 Vt 2 (Ski Q I + Sky Q y ) Sk! CsV, 2 (SkiSk~ + QkIQ~)Sij where Cat, C2, C3, C4, and C5 are model constants. Computational method (9) To solve the governing equations, the flow domain is subdivided into a finite number of cells and these equations are changed into algebraic form via the discretization process. Finite volume method is used for the discretization. Temporal derivative in the governing equations is ignored by putting very big time value. The convective terms are discretized using QUICK(Quadratic Upwind Interpolation for Convective Kinematics), LUD(Linearized Upwind), or MARS(Monotone Advection and Reconstruction Scheme). Central difference scheme is utilized for diffusion terms. Then the algebraic form becomes Ap~p=~Am~m+ m where Maui (i = 1,2,3), k,£] (8) represents convective and diffusion terms, s ~ is source term, and Ap =~Am . For the velocity- m pressure coupling, SIMPLE(Semi-Implicit Methods for Pressure-Linked Equation) or SIMPLEC (SIMPLE Consistent) is utilized. The characteristics of the utilized four CFD codes are summarized at Table 1. Table 1 Characteristics of CFD codes WAVIS COMET STCADR- FLUENT Turbulence Realizable Chen's Cubic Reynolds model k-e k-e k-e stress Convection QUICK WD MARS QUICK Velocity- pressure SIMPLEC SIMPLE SIMPLE SIMPLE coupling Boundary conditions and grid generation Wall function is utilized for hull-surface boundary condition. Symmetry condition is applied for free-surface boundary condition by assuming double body model. Uniform flow condition for the inlet and the outer plane, symmetry condition for the centerplane, and Neumann condition for the exit plane are applied. The same girds are applied for the calculations using four CFD codes. The grids are composed of single block with O-H type. The number of grids is 253,831 with 3,900 on the hull surface. The space of the 1st grid from the hull is y+~45. The calculations are carried out at model scale with Rn=6.918xlO4. SELECTION OF OBJECT SHIPS AND MODEL TESTS (10) is variables, Am Three kinds of hull form are investigated to predict the change of hydrodynamic characteristics due to hull-form variation. After selecting basic hull form, frame lines of stern are changed to extremely U- and V- shaped hull form with constraints of the same principal particulars and the same bow shape. Hereinafter, the extremely U- and V-shaped stern hull form is called "extreme U-hull" and "extreme V-hull", respectively. The basic hull form is a 309,000 TOW VLCC which was recently designed at HHI. The model tests are carried out to predict the resistance and propulsive performances of ship, and to validate the computational results. The contents of model tests are resistance and self-propulsion tests, wake measurements at a propeller plane, and paint tests to investigate the limiting streamlines on the hull.
Selection of object ships For the basic form, the shape of bow bulb is middle bulb of plank type and frame line of stern is moderate U-form. The plank typed bow bulb is recently applied for slow speed full-ship because the variation of ship performance due to the change of draft is small and it is possible to generate hull-form with moderate curvature. The constraint of extreme U- form is to maintain the shape of sectional area curve if possible, to satisfy the width for engine room, and to maintain the width of the upperpart of propeller of basic form. The constraint of extreme V-form is to maintain the minimum of width for engine room. The depth of transom is the same for three ships. The body plans, side profiles, and sectional area curves for three ships are shown in Figure 2. As shown in Figure 2, the breadth of extreme U-form is relatively wide at the - Figure 2 Body plan, side profile and sectional area curve of 309,000 TDW VLCC (red: basic form, green: extreme U-form, blue: extreme V-form) Table 2 Hull form characteristics Basic | Extreme l Extreme form U-form V-form LWL. (m) 326.50 LPP (m) 320.00 B (mj 58.00 T (m) 20.95 1` (tonnage) 322 314 322 651 1 322 168 . _ . , , , , S (m') 27 621 27 603 1 27 271 . , , . , LCB (m, fwd +) 9.952 CB 0.8089 1 0.8095 1 0.8083 CM 0.9978 lower part of propeller and nearly same at the upper part of propeller. The breadth of extreme V-form is narrow at the lower part of propeller and wide at the upper part of propeller compared with those of basic form. The principal particulars of ships and propeller are shown in Table 2 and 3, respectively. Model tests The model tests were conducted at the deep water Towing Tank of HMRI. The size of the tank is 210x14x6 m in length, width, and depth, respectively, with maximum carriage speed of 1 lm/sec. During the resistance test, the model ship was provided with no appendages and free in vertical motion. The resistances acting on the towing point of model ship at various speeds were measured. The towing point was located at (LCB, O. KB)- ,,/' /! \ Fug. Table 3 Characteristics of model propeller Diameter (mm) 210.26 No. of Blades Section Type ~~ ~ ~ ~ NACA Chord Length at 0 7R(mm) 56.03 P/D at 0.7R 0.7451
During the self-propulsion test, the model ship was provided with a rudder and a stock propeller. The model ship was propelled with its own electrometer and free in vertical motion. In order to compensate for the model's excessive frictional resistance it was additionally towed by the resistance dynamometer. The tests were conducted at 6 carriage speeds. For each speed, the propeller relative speed was varied to cover at 3~4 loadings around a self-propulsion point. The resistance, propeller relative speed, thrust and torque acting on propeller were measured. The fluid velocities were measured at propeller plane using a rake consisting of five two-hole Pitot tubes. The model ship was free in vertical motion at design model speed of 1.171m/s. The rake was attached to model ship. The center and side holes of Pitot tubes were connected to pressure gauges through vinyl tubes. The angular interval to be measured was 5° to 15° at five radii. The flow-line test was conducted by using paint. The model ship was free in vertical motion at design model speed of 1.171m/s. The paint was an appropriate mixture of dye, oil paint, wax, and thinner. The mixture rate was dependent on the local velocity close to the hull. The results of resistance and self-propulsion test were analyzed to full scale by the method recommended by ITTC Performance Committee(1978~. RESULTS AND COMPARISONS The computational and experimental results of three varied hull forms of 309,000 TDW VLCC are compared. The computations have been conducted using four selected CFD codes, i.e., WAVIS, COMET, STAR-CD, and FLUENT. The changes of hydrodynamic characteristics to be investigated are as follows; - Resistance and propulsion performance - Limiting streamline on the hull - Hull pressure - Wake on propeller plane Resistance and propulsion performance The viscous resistance coefficients(CvM) at Rn=6.916X 106 of three hull forms from the computations and experiments are summarized in Table 4. The magnitude order of CVM obtained from the experiments is CVM (B) < CVM (V) < CVM (U), where B. V, and U represents basic form, extremely U- and V- form, respectively. The computational results show the same tendencies, but their values are lower than those of experiments. Table 4 Comparison of viscous resistance characteristics in model scale Exp. WAVIS COMET STAR-CD FLUENT Basic form CVM X103 3.914 3.583 3.856 3.854 3.65 1 Comp. (%) 100.0 91.54 98.52 98.47 93;28 CVM X103 . 4.189 3.722 4.073 3.953 3.856 Extreme U-form . Comp. (%) 100.0 88.85 97.23 94.37 _ 92.05 Extreme V-form CVM Comp. X103 (%) 4.004 100.0 3.665 91.53 3.865 96.53 3.919 97.88 3.749 93.63 The wave resistance coefficients(Cw) and effective horse powers(EHP) obtained from the experiments at various speeds are shown in Table 5. The magnitude order of Cw is Cw~v)<cw~u)<cw(B). And the magnitude order of EHP is EHP(VJ<EHP(BJ<EHP(UJ. The EHP of extreme U- form and extreme V-form increases 3.6% and decreases 2.1%, respectively. Note that the resistance performance of extreme V-form is superior to others not because of viscous resistance but because of wave resistance performance. Table 5 Comparison of resistance characteristics in full scale Test condition VM=0.970m/s Fn=0.1 19 Rn=1.801 x 106 VM=1.044m/s Fn=0.129 Rn=1.939 x lo6 VM=1.1 l9m/s Fn=0.138 Rn=2.078 x 106 VM=1.193m/s Fn=0. 1 47 Rn=2.216X 106 VM=1.268m/s Fn=0.156 Rn=2.3SSX106 VM=1.343m/s Fn=0.165 Rn=2.496X 106 Hull form Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V CWX lo3 0.026 0.026 0.021 0.047 0.024 0.019 0.070 0.03 1 0.025 0.099 0.05 1 0.039 0.134 0.087 0.063 0.179 0.144 0.097 | EHP 1 I 1 1477 1 12176 I 11534 I 14377 1 I 15071 1 14278 rl7763 I 18467 I 17485 1 21727 1 1 22473 1 1 21230 :263S9 1 27250 1 25611 1 31801 1 33031 1 30739 | Comp. | of EHP 1 '%' I 100.0 I 106.1 I 100.5 1 loo.o I 104.8 I 99.3 I 100.0 I 104.0 I 98.4 I 100.0 I 103.4 I 97.7 T loom T 103.4 I 97.2 I 100.0 T 103.9 I 96.7 The propeller relative speed(RPM), advance ratio of propeller(J= ( /)), thrust deduction fraction(t), effective wake fraction(wS), hull efficiency( n H), relative relative efficiency( IT R),
Table 6 Comparison of propulsive performance coefficients Test condition VM=0.970m/S Fn=0.119 Rn=l.8Ol X 10 VM= 1 .044m/S Fn=O. 129 Rn=1.939X 106 VM=1. 11 9m/S Fn=0.138 Rn=2.078X 106 V~1.193m/S Fn=O. 147 Rn=2.216X 106 V~1.268m/S Fn=0.156 Rn=2.355 X 106 V~1.343m/S Fn=0.165 Rn=2.493 X 106 Hull form Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V Basic forth Extreme U Extreme V Basic form Extreme U Extreme V Basic form Extreme U Extreme V RPM 57.11 _ s7.23 58.22 .- . 61.52 61.57 .- 62.55 66.03 65.98 66.95 70.55 70.48 .- 71.44 75.22 75.13 76.04 79.97 79.97 80.78 0.441 0.427 0.478 0.442 0.422 0.477 0.445 0.419 0.475 0.446 0.418 0.475 0.447 0.419 0.475 0.448 0.422 0.475 T 0.224 0.190 0.237 . 0.238 0.197 0.233 0.247 0.201 0.228 0.249 0.203 0.221 0.244 0.202 0.214 0.230 0.197 propulsive efficiency in open-water( n, o), and propulsive efficiency rl p) at various speeds are shown in Table 6. Here hull surface roughness is assumed to be 150 ~m. Note that r,p includes the effect of transmission efficiency~rc'=O.99), i.e., rip = llH X II R X 11 o X ~ ~ and the brake horse power(BHP) is obtained on the condition of Cp=1.00, CN=1.00. The magnitude order of ws is ws~v)<ws(B)<ws~lJ). We can consider advance ratio of propeller, which has inverse relationship to ws if propeller relative speeding is not so much changed. It seems to be reasonable because the same propeller is used for model tests of three hull forms. Therefore, the magnitude order of r,o is rl,o(U) < r,o(B) < n.,o(V) because the value of J becomes larger as that of ws becomes smaller. The value of t (=1-R/T, where R and T is ship resistance and propeller thrust, respectively) becomes smaller as that of J becomes larger since R/T is proportional to J2. This relationship can be deduced from dimensional analysis. So, the magnitude order of t is t(V) < t(B) < t(U). The magnitude order of the hull efficiency n H), which shows the interaction effect between hull and propeller, is II H(V) < II H(B) < II H(U)' since n H is generally proportional to ws. The magnitude order of relative relative efficiency (rlR), which shows the ratio of behind to open efficiency of propeller and is dependent on the radial load ws 0.373 0.391 0.306 0.370 0.399 0.310 0.365 0.403 0.313 0.363 0.404 0.314 0.59 0.401 0.312 0.355 0.392 0.310 _ IIH 1.207 1.274 1.168 1.210 1.267 1.165 1.209 .2652 1.162 1.213 1.259 1.161 1.214 1.261 1.162 1.219 1.267 1.163 IIR 0.987 1.017 1.026 1.006 1.022 10.31 1.022 1.027 1.036 1.031 1.032 1.039 1.035 1.037 1.042 1.032 1.042 1.044 to 0.579 0.566 0.611 0.581 0.561 0.610 0.584 0.557 0.609 0.585 0.556 0.608 0.586 0.557 0.608 0.587 0.561 0.608 1 Be 0.683 0.725 0.725 .7oo 0.718 0.724 0.714 ro.7l4 r 0.725 0.724 0.715 0.726 1 0.729 1 0.721 1 0.728 T 0.731 1 0.732 1 0.731 3 r 16640 1 1 1 16632 5756 20307 1 20785 T 19515 T 24622 1 T 25588 1 1 23887 29716 1 31109 28957 35760 37432 34826 43037 44656 1 41611 1 Comp. of BHP (%) 100.0 100.0 94.7 100.0 102.4 96.1 100.0 103.9 97.0 100.0 104.7 97.4 100.0 104.7 97.4 100.0 103.8 96.7 distribution of propeller, rlR(B) < rlR(U) < rlR(V), but the differences are small. Considering all the efficiencies of r,O, rl'H, r,R and rut, the magnitude order of r p is rl p(U) < rl p(V) ~ n, p(B). At the design speed of 15.70knots, the value of BHP is increased by 4.5% and is decreased by 2.6% for the extreme U-form and the extreme V-form when compared with the basic form, respectively. Therefore, the extreme V-form is superior to the others with respect to resistance and propulsive performance. Velocity distribution Figure 3 shows the results of WAVIS code for the axial velocity and velocity vector at the propeller plane of the basic form, extreme U-form and extreme V-form. The "hook-shape", which is the characteristics of the axial velocity contours, is shown at all three hull forms. Other computational results using COMET, STAR-CD, and FLUENT codes also show same tendencies although their shapes and the lowest values are a little different from each other. The core of secondary flow becomes close to the hull as the hull form of stern becomes V-form. The magnitude order of boundary layer~or wake) thickness ~ ~ is ~ (V) < b(B) < b(U). More details will be described at wake at propeller plane).
-0.02 -0.06 -0.08 7. -0.06 -0.08 . o -0.02 z -0.08 . . C. (~b,01~/ ~ -0.02 nn4 is. 0 0.02 0.04 0.06 0.08 y A! ~o.9~/ ,,·,1,,,,1,,,,1,,,,1, 0 0.02 0.04 0.06 0.08 y /~ ~~ l ,,,,1,,,,1,,,,1,,,,1. 0 0.02 0.04 0.06 0.08 y (a) Basic form z (b) Extreme U-form non non (c) Extreme V-form 0.5 Rt, I 1~'I 1~ , 1` ~ ~ ~ 0 0.02 0.04 0.06 0.08 y -0.04 -n no 1 ', , ', , 1' 0 0.02 0.04 0.06 0.08 y '`\ .,',\,,1,,,,1,, 0 0.02 0.04 0.06 0.08 y Figure 3 Axial velocity contours and velocity vectors at the propeller plane (WAVIS)
Limiting streamline Figure 4 shows the results of experiment and calculation using COMET for limiting streamline in the forward and afterward part. Same shapes of streamlines in the forward part are shown for three hull forms since the bow shapes are the same. For the upper part of bow, the streamlines are parallel to the direction of ship. However, the limiting streamlines are directed a little upward for the upper region of bulb, and downward for the lower region because of rapid change of hull form. Other computational results using WAVIS, STAR-CD, Experiment - - ._ - _ and FLUENT codes also show same tendencies. In the afterward part, the limiting streamlines of three hull forms are quite different from each other. From the experiments, the limiting streamlines incoming to lower propeller plane are not clear, so the fluid velocity near this region can be expected to be very slow. For the case of extreme V-form, this region is the largest. All the computational results are similar in tendency, except for the WAVIS results showing reverse flow in this region of extreme V-form. Calculation (COMET) (a) Bow - _! - (b) Stern of basic form _ _. my. _ 1 _ . 1 ~ ; (c) Stern of extreme U-form (d) Stern of extreme V-form Figure 4 Limiting streamline .
(a) Bow (c) Stern of U-form Figure 5 Pressure contours on the hull (STAR-CD) Pressure distribution Figure 5 shows the computed pressure contours in the forward and afterward part of the hulls using STAR-CD. The shapes of the pressure contours on the forward part of the basic form are the same as those of U- and V-form. Other computational results using WAVIS, COMET, and FLUENT codes are the same shapes. The bow region dashed against flow shows very high pressure. At the lower part of bulbous bow a rapid pressure gradient region exists. Passing through this region, the fluid flow acceleration occurs due to the change of hull curvature, so very low pressure region exists. There is a little change of pressure at the middle of hull. Pressure is increased at the region of stern due to the hull curvature, but there is no great pressure gradient region such as that of bow. This may be due to the less hull curvature comparing to the region of bow and thicker boundary layer. However, the differences of pressure distribution are clear. Very low pressure region exists at the lower part of extreme U-form due to hull curvature. In the case of V-form, such a low pressure region is relatively small and locates at the stern region. Wake(at the propeller plane) The axial velocity contour on the propeller plane is shown in Figure 6. The computational results are from those using FLUENT code. The characteristics of wake at the propeller plane show clear differences. For the extreme U-form, wide region of hook shape exists, the value of minimum velocity in this region is relatively high, the radial gradient of the (d) Stern of V-form circumferentially averaged axial velocity is gentle, and the value of nominal wake is larger. For the extreme V- form, narrow region of hook shape exists, the value of minimum velocity in this region is relatively low, the radial gradient of the circumferentially averaged axial velocity is steep, and the value of nominal wake is smaller. The characteristics of wake at propeller plane are very much dependent on the turbulence model. The results applying Reynolds stress turbulence model show good agreement with those of experiment. The results applying realizable k- ~ turbulence model are also good agreement, but the minimum axial velocity is expected by 0.1 less at the hook-shape region. The results applying Chen's and cubic k- ~ show similar tendency, but decrease in accuracy. Note that the unclear region of limiting streamline from the paint test is coincident with the region of very low velocity . . Incoming.
Experiment Calculation (FLUENT) (at Basic form (b) Extreme U-form (c) Extreme V-form Figure 6 Axial velocity contour on the propeller plane The control plane for nominal waketwN) is a circle located at propeller plane with the same center of propeller, and with minimum and maximum radius of r~=0.380 and r2=1.141, respectively, where r is radial distance non-dimensionalized by propeller radius. So, the nominal wake at control plane is N A MA where A is area of control plane. The nominal wake at the control plane is shown Table 7. The values of WN can be assumed to be proportion to those of ws because the same propeller is used. Therefore, we can estimate the propulsion performance of ship using the values of WN as described in the previous section of Resistance and propulsion performance. Table 7 Comparison of nominal wake fraction \\ WAVIS COMET STAR-CD FLUENT I Basic form WN 0.457 0.435 . 0.425 0.419 . 0.434 . Extreme . U-form WN Miff.* . - ~ ~,~.~ ~~ 1` A 0 ~ I: ~.~.~: Jo: -- A:.::: ~- V.~tOV i.:'::. ~'':: ~~:~:~i~ ~~.~i . 0.510 6.30 0.5 16 7.40 0.475 -0.98 0.484 0.94 Diff .(%) = N ( 1-) WN (exp.) x 100 WN (exp ·) DISCUSSIONS AND CONCLUSIONS Extreme V-form WN I Diff.* : ~~ ~~ ~ ~.~: i. . ~ . - ~: tot A ~ ~ .:: ~:~:~ I: -I : ~:~:~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ V.~4V i:. I'd i :~i:~.:':i'- f:~: :: ~~:~ ~,~ ~~ :. : -I ~:~:~ ~:~ 0.410 -3.70 0.363 -14.87 0.374 -12.19 0.410 -3.63 The differences in flow characteristics according to the variations of hull form, i.e., basic form, extreme U- and V-form, are predicted by the computational method and verified through the experiments. The basic form is a 309,000 TOW VLCC, which is recently developed as a standard full slow- speed ship at HHI. For the computations, four CFD codes, i.e., WAVIS, COMET, STAR-CD, and FLUENT are used. The values of viscous resistance from the computations are generally lower than those from the experiment. The predictions of wake at the propeller plane are dependent on turbulence models. The results applying Reynolds stress and realizable k- ~ turbulence model are similar to those of experiments. The results applying Chen's and cubic k- ~ show similar tendency, but decrease in accuracy. All the results qualitatively show the differences due to the changes of hull form, but are still quantitatively different from those of experiment. From the experimental studies, the V-form hull is superior to both the basic and the U-form hull form with the respect to the resistance and propulsion performance. The propulsion performance according to the hull-form variations cannot be evaluated from the computational results only. To apply CFD technology on the development of fuel-economic hull-form at the initial design stage, not only viscous resistance performance but also wave resistance and propulsion performances should be promptly predicted with accuracy. To predict the propulsion performance, the flow around a hull attached with propeller and rudder should be analyzed in full scale. However, there may be many problems to
carry out computation in full scale, such as grid generation and the lack of verification data, etc. Further study will be necessary for the prediction of flow characteristics in full scale using the results in model scale. REFERENCES Larsson, L.(editor), "SSPA-ITTC Workshop on Ship Boundary Layers" SSPA Publication No 90 1980 , . . . Larsson, L., Patel, V.C., and Dyne, G(editor), "Ship Viscous Flow: Proceedings of 1990 SSPA-CTH-IIHR Workshop", Flowtech International AB, Gothenburg, Sweden, 1991. Kodama, Y.(editor), "Proceedings of CFD Workshop Tokyo 1994", Japan, 1994. Larsson, L., Stern, F., and Bertram, V.(editor), "Proceedings of CFD Workshop Gothenburg 2000", Sweden, 2000. Min. K.S., Choi, J.E., Yum, D.J., Chung, K.N., Chang, B.J., Chung, S.H., Han, B.W., "Study on the Prediction of Flow Characteristics around a Ship Hull", Proc. of the 23rd ONR Symposium on Naval Hydrodynamics 2000. "WAVIS User's Guide", KRISO, 1999. "COMET User Manual", ICCM, 2001. "STAR-CD User Manual", Computational DYnamics Limited, 2000. "FLUENT User Manual", Fluent, 2000. "Report of the Performance Committee", Proc. of the 1 5th ITTC, Hague, 1978 Prohaska, C., "A Simple method for the Elevation of the Form factor and Low Speed wave Resistance", Proc. of the 11th ITTC, Tokyo, 1966
DISCUSSION Chi Yang George Mason University, USA Authors should be congratulated for their detailed study on the CFD application for VLCC hull-form design. The authors have used systematic hull-form variation to study the change of hydrodynamic characteristics due to hull-form variation. However, the CFD tools have only been used to predict the hydrodynamics characteristics for given hull forms. The next step would be the compiling of CFD tools with optimization techniques, such as gradient-based method, to optimized hull form automatically. I would like to have authors' comments on the hull form optimization using CFD tools together with optimization techniques. AUTHORS' REPLY Thank you very much for your comment. I agree with your comment to utilize the coupling of CFD tools with optimization technique. However, the object function is the speed-power performance. This means not only resistance but also propulsion performance is important. To get this object function, I think, the flow characteristics around a hull attached with propeller and rudder should be predicted and analyzed to full scale with sufficient accuracy and reliability. It is possible at present stage to make local hull-form variation based on CFD by utilizing restricted object functions, i.e., wave resistance or local vorticity, etc. Unfortunately, however, it is impossible to apply CFD technology on the hull-form optimization considering the speed-power performance. We hope you could send us your proposal or idea on the hull form optimization utilizing CFD technology in the view point of powering performance. We will strongly think over the cooperative research project. Thank you.
