Vol. 45 . No. 1 Februaiy 1998
T E C H N I S C H E I J N I V E R S I T E I T
Scheepsfaydromechanica A r c h i e fMekelweg 2, 2628 CD D e l f t
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Computation of R u d d e r Force and Moment in U n i f o r m F l o w by Shiu-Wu Chau
Model E x p e r i m e n t s with Surface Piercing Propellers by Wojciech Miller and Jan Szantyr
M e m o r y - B a s e d L e a r n i n g Approach to Selection of Basis Ship in Conceptual Design
by Dongkon Lee, Jaeho Kang, Kwang-Ryel Ryu and Kyung-Ho Lee
N u m e r i c a l Simulation of Hull-Propeller Interaction Using Force Fields W i t h i n Navier-Stokes Computations
by David Hally and Jean-Marc Laurens
P u b l i s h e d b y
S c h i f f a h r t s - V e r l a g „ H A N S A " , H a m b u r g
D a s F a c h b u c h
für Schiffbau,
Schiffsmaschinenbau
und Schiffstechnik
H e r a u s g e b e r P r o f . D r . - l n g . H . K e i l 3 5 0 S e i t e n , F o r m a t 1 4 , 5 x 2 1 , 5 c m , z a h i r e i c h e S k i z z e n u n d T a b e l l e n , E f a l i n , D M 9 7 , 5 0 z z g l . V e r s a n d k o s t e n , i n k l . M w S t . I S B N 3 - 8 7 7 0 0 - 0 9 1 - 6 ¥1D[L D T E I L 11 SCHIFFBAU - SCHIFFSMASCHINENBAU Betriebsfestigkeit schiffbaulicher Konstruktionen - BeispieleProf. Dr.-lng. H. Petershagen, Dr-Ing. W. Fricke, Dr-Ing. H. Paetzold
Angewandte Schiffsakustik, Teil II
Prof. Dr.-lng. H. Schwanecke
Technologie der Schiffskörperfertigung
Dipl.-Ing. H. Wilckens
Binnenschiffe für extrem flaches Wasser -Ergebnisse des VEBIS-Projektes
Dipl.-Ing. H.-G. Zlbell, Prof. Dr.- r Ing. E. Müller
Kühiwassersysteme auf Motorschiffen
Dr.-lng. K.-H. Hochhaus
Verzeichnis der deutschen Schiffswerften
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- Boots- und Kleinschiffswerften - Spezlalbetriebe für Schiffsreparaturen
T E I L I I I
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SHIP Ï E C H I O W RESEARCH
J o u r n a l f o r Research i n S h i p b u i l d i n g a n d Related SubjectsSHIP T E C H N O L O G Y RESEARCH/SCHIFFSTECHNIK was founded by K . Wendel in 1952. I t is edited by H. Söding and V. Bertram in collaboration w i t h experts from universities and model basins in Berlin, Duisburg, Hamburg and Potsdam, from Germanischer Lloyd and other research organizations in Germany.
Papers and discussions proposed for publication should be sent to Prof. H. Söding, Institut für Schiff-bau, Lammersieth 90, 22305 Hamburg, Germany; Fax -|-49 40 2984 3199; e-mail soeding@schiffbau. uni-hamburg.de. Rules for authors, newest abstracts, keyword index and editors' software see under http://www.schiffbau.uni-hamburg.de
Vol. 45 No. 1 • F e b r u a r y 1998
Shiu-Wu Chau
Computation of R u d d e r Force and Moment in U n i f o r m F l o w Ship Technology Research 45 (1998), 3-13
The turbulent flow around ship rudders in uniform inflow is computed by solving the Reynolds-averaged Navier-Stokes equations. The standard k — e turbulence model w i t h wall function is applied. The conservation equations are discretized by a (nearly) second-order finite volume method in a block-structured body-fitted grid and solved by the SIMPLE method. The three-dimensional flow around rudders of different aspect ratio and profile shape was computed at different Reynolds numbers. I n general the results agree well w i t h measurements below the stall angle. The HSVA MP73-xx profile is found to be superior to the standard NACA OOxx profile w i t h respect to l i f t slope, maximum l i f t and drag as a function of l i f t .
Keywords: rudder, turbulent flow, manoeuvring, hydrofoil, RANSE, stall, lift
Wojciech Miller, Jan Szantyr
M o d e l E x p e r i m e n t s with Surface Piercing Propellers Ship Technology Research 45 (1998), 14-21
The paper presents a series of model experiments conducted i n the Gdansk Model Basin w i t h a pair of surface piercing propeller models. These relatively little known propellers are regarded as efficient propulsors for small fast craft. A series of model experiments was arranged w i t h propellers designed for a patrol boat to gain first hand experience. The experiments included measurement of thrust, torque, efficiency, transverse forces and unsteady blade bending moments for a number of conditions characterized by varying propeller immersion, shaft inclination and yaw, both in single and twin screw configurations.
Keywords: fast ship, surface-piercing propeller, propeller, model, thrust, torque
Dongkon Lee, Jaeho Kang, Kwang-Ryel Ryu, Kyung-Ho Lee
M e m o r y - B a s e d L e a r n i n g Approach to Selection of Basis Ship in C o n c e p t u a l Design Ship Technology Research 45 (1998), 22-27
A memory-based learning (MBL) technique is apphed to build automatically an indexing scheme to access reference designs during the conceptual design stage. The M B L method can build an effective indexing scheme for retrieving good reference designs from previous ship designs. Empirical results show that the indexing scheme generated by M B L outperfcrins those by other learning methods such as the decision-tree learning.
Keywords: design, concept design, basis ship, learning
David Hally, Jean-Marc Laurens
N u m e r i c a l Simulation of H u l l - P r o p e l l e r Interaction Using Force Fields W i t h i n Navier-Stokes Computations
Ship Technology Reserach 45 (1998), 28-36
The pressure distribution obtained by a time-dependent potential flow simulation at the surface of the propeller blades is converted into a force field which can then be imposed within a steady Navier-Stokes simulation of the viscous fiow around the hull. Iterative coupling between the two codes allows the effective wake to be included i n the calculation. I t is shown that, due to the displacement effect of the blades, the force field must be calculated from the difference between the pressure on the outside of blade surface and a virtual pressure inside the blade, or the mass conservation equation must be corrected by adding source terms to the Navier-Stokes solver.
Keywords: propeller, Navier-Stokes, ship, effective wake, panel
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Computation of Rudder Force and Moment i n U n i f o r m Flow
S h i u - W u C h a u , United Ship Design and Development Center^
1. Introduction
Rudders are hydrofoils used to control ship direction and path. They are normally put at the ship's stern behind the propeller. A rudder gear can rotate the rudder around a vertical axis (stock) to produce controllable side forces due to the forward ship motion and/or the propeller slipstream. The rudder drag increases the required propulsion power. The necessary size of the rudder gear is determined by the rudder stock moment. L i f t , drag and stock moment, being functions of the attack angle a of the rudder, characterize the rudder performance. They may be expressed by non-dimensional coefficients
6*^(0;),
Cuipi) and Cm(o;). These are useful not only to evaluate the manoeuvring ability of ships, but also for designing the rudder and the rudder gear.High Reynolds number Rn and strong turbulence characterize the flow around the rudder behind a ship and its propeller. A typical ii^j is 5 • 10^ for a large ship, and the strong turbulence acts similar as a large R^- Viscous effects are important in determining the stall (maximum lift) attack angle. Potential theory is widely used to investigate the rudder characteristics; however, i t is unable to give the stall condition due to neglecting viscosity. A remedy for this drawback is to introduce a boundary layer calculation to take the viscous effect into account.
Tamashima et al. (1993) have computed the propeller-rudder system with a hybrid (potential
and viscous) approach. A viscous approach using the Navier-Stokes equations should be a better alternative to analyze the flow around rudder because it considers the pressure change due to viscous (especially separation) effects. However, the high Reynolds number flow with strong turbulence cannot be computed directly using the Navier-Stokes equations. Instead, the Reynolds-averaged Navier-Stokes (RANS) equations combined with a turbulence model are used to compute high Reynolds number flows with satisfactory precision. Only a few au-thors have used this approach to study rudder performance. Suzuki et al. (1994) calculated the flow around a rudder behind a propeller, presuming laminar flow, w i t h zero rudder angle. I will investigate rudder forces and moments by solving the RANS equations together w i t h the continuity equation and transport equations of turbulent kinetic energy k and its dissipation rate e for the flow around rudders. The influence of the ship hull and the propeller on rudder inflow will not be considered.
2. Governing Equations
2.1 Reynolds-Averaged Navier-Stokes Equations
The steady RANS equation for incompressible flow can be expressed as
Index i denotes a component in the direction of the Cartesian coordinate x f , Ui and are mean and fluctuating part of the velocity, P the mean pressure, p the density, u the kinematic viscosity, u'^u'j the time average of u[u'y The symmetrical tensor pu'-u'j is the Reynolds stress tensor. The Reynolds-averaged continuity equation can be expressed as
(1)
(2)
2F, 174-7 Lane 1, Ji-Jing 2nd Road, Keelung, Taiwan, R.O.C.
2.2 Turbulence Model
The Boussinesq model is adopted to determine the Reynolds stresses in RANSE:
Ut is the eddy viscosity which is not a fluid property, but depends on the local turbulence. 5ij
is the Kronecker delta, which is 1 for i = j , otherwise 0. Eq. (3) is built i n analogy to the molecular stress and implies isotropic eddy viscosity, ut is expressed using the turbulent kinetic energy k and its dissipation e:
i^t = c^ —• (4) Cn is an empirical constant. The transport equations for k and e are
d{kUj) d dxj dxj d{eUj) d dxj dxj ut\ dk CTfc/ OXj GE) dxj + (5) + CslPk^-Ce2^. (6)
(Tfc, (TE, Cei, are constants mainly obtained from the comparison between experiments and computations. The production of turbulent kinetic energy Pk is deflned as
ft = - « H ^ . (7) The constants used in (4), (5) and (6) are = 0.09, Ck = 1, cr^ = 1.3, c^i = 1.44, and
= 1-92. The transition from laminar to turbulent flow is neglected: the flow is treated as turbulent along the whole rudder surface. A wall function is applied to bridge the viscous sublayer along the solid wall (rudder surface). The velocity on solid walls must satisfy the no-slip condition, i.e. the velocity is zero relative to the wall, k should be zero, too. To specify e on solid walls is not obvious; i t is non-zero there. The flow region near the wall can be subdivided into three subregions: laminar sublayer, overlap layer, turbulent layer. The turbulence model mentioned before, i.e. Eqs. (4), (5) and (6), is applicable only to turbulent flow regions; thus it cannot be applied within the laminar sublayer. Therefore the wall function approach proposed by Launder and Spalding (1974) is used to bridge the laminar sublayer near the wall. Experimental evidence shows that the velocity profile i n the viscous layer follows the linear viscous relation
u+ = ^ = y^=y+. (8) Up is the local velocity component parallel to the waU, y the distance normal to the wall,
the wall shear stress. The friction velocity Uj is defined as SJTIUIP- The velocity in the overlap
layer varies logarithmically w i t h y (known as logarithmic law of the wall):
?x+ = - l n y + + 5 (9) AC
K = 0.41 and 5 w 5. The valid range of (8) is 0 < y+ < 5, and (9) holds for 30 < y+ < 800. There is no known analytic function which describes the velocity distribution between ^ + = 5 and 30. I f the turbulence is in local equilibrium so that the production Pk is equal to the dissipation rate e and the shear stress is constant along the wah, the following relations can be deduced: k = 4 = , (10) e = u^ (11) ny
Eqs. (8), (9), (10) and (11) are applied near solid walls in the wall function approach. Eq. (11) is used as the boundary condition near solid walls for e. I n the numerical computation the dependent variables at certain points, usually known as nodes, are stored. Because y — 0 makes (11) singular, e is specified in the nodes next to solid walls instead of on solid walls. A simplified practice bEised on the wall function approach is adopted to calculate i n the computations:
= M e ^ , i f y + < 1 2 , (12)
y
Tu, = if y + > 1 2 . (13)
/ig is the effective viscosity ( = M + Mt)- The direction of T^J is assumed as opposite to Up. The normal stress T„ on the solid walls is zero due to the vanishing normal velocity component u„. y+ of the nodes next to solid walls can be up to 800 in the wall function approach; but the typical value of y"*" of the nodes next to solid walls is 40 ~ 80 in the computations.
3. N u m e r i c a l Method
A l l vector quantities, e.g. position vector, velocity and moment of momentum, are expressed in Cartesian coordinates. The governing equations are written and solved in the primary vari-ables, i.e. velocity components and pressure. The finite volume method is adopted to discretize the governing equations into a system of algebraic equations which is solved by Stone's (1968) SIP method. A second order scheme results from the deferred correction procedure by blending upwind and central difference scheme. The SIMPLE algorithm, Patankar (1980), is applied to compute the velocity and pressure updates. The non-staggered variable arrangement is used to define dependent variables in the cell centres. The pressure is interpolated at cell faces according to the procedure proposed by Rhie and Chow (1983) to avoid unrealistic pressure oscillations. I n Peric's (1985) practice, the cell-face velocity depends on the under-relaxation factor au which is used for solving the momentum equations. This results in an a„-dependent solution. A simple practice to obtain an «„-independent solution is proposed by Chau (1997) to determine the cell-face velocity. A multi-block grid structure is used for the computational grids. Each block is a structured sub-grid having curved grid lines defined by spline functions and fitted to the bodies and/or block interfaces within the computational domain. The stretch-ing function proposed by Vinokur (1983) is adopted to determine the grid point distribution on grid lines. See Chau (1997) for the details of the above discussed procedure.
4. E x i s t i n g Measurements
Experimental data to compare w i t h the numerical results are mainly taken from Whicker
and Fehlner (1958) and Thieme (1963). Whicker and Fehlner tested rudder models with
different profiles at i?„=1.0...3.0-10^; the Mach number ranged from 0.07 to 0.21, which allows comparisons w i t h incompressible flow calculations. The maximum thickness of the profiles is 15% of the chord length. The models had either a square (plane) or a faired (rounded) t i p . The test section of the wind tunnel was 6 by 10 feet while the largest height of the models was 3 feet. The models were mounted on a ground board in this closed wind tunnel. Therefore, the models were considered as only one half of the investigated rudders. Tunnel corrections proposed by Swanson and Toll (1943) were applied to convert the data measured in the wind tunnel to free-stream conditions. The form parameters used by Whicker and Fehlner to specify a model are deflned as follows. Fig. 1:
mean chord length Cm = —T T - ^ (14)
z
Cr and Ct are the chord length at the root and t i p of a rudder model; respectively
taper ratio
Cr h
aspect ratio Ar
Cm
h is tlie height of the whole rudder. Different aspect ratios Ar and sweep angle /3 were used i n
the experiments, but the taper ratio Tr=0.45 remained constant.
quarter chord axis
Fig. 1: Definition of rudder geometry
Thieme (1963) tested his rudder models at i?„ = 10^...10^. His wind tunnel had a circular
nozzle with 1.0m diameter. The models had an eispect ratio Ar = 1.0 and a taper ratio Tr = 1.0 (i.e. they were rectangular) according to the definition of Whicker and Fehlner; the height of his models was 0.4m. No tunnel corrections were applied to his results while his models are relatively close to the jet boundaries compared with the tests by Whicker and Fehlner.
The drag coefficient CD and the lift coefficient CL of a rudder are defined as
CD 2D
O.bpUlcmh ' CL =
2L
0.5pUlcmh (15)
D and L denote the drag and lift force, and Uoo the uniform infiow velocity. Rudder stock
moments M0.25 refer to the vertical axis 1/4 Cm behind the rudder nose. The moment coefficient about the quarter-chord axis is defined as
C M .
2Mo 25
0,25
0.5pUlclh (16)
5. E m p i r i c a l Formulae
Söding (1993) proposed the following formulae based on potential theory and measurements:
27r-A - (A + 1)
CT =
CD =
sin a + Cn • sin a • I sin a\ • cos a
CLI -|-Cq|sina|^-|-CDo CD2 CL2 (17) (18)
CM,O.25 = -{CLI • cosa-f CDI • sina) • I 0.47 A + 2
4(A + 1),
-0.75 • {CL2 • COS a 4- CD2 • sin a) + 0.25 • ( C L • COS a C D • sin a) (19) A is the aspect ratio, Cq = 1.0 is used for rudders with a sharp upper and lower edge and CDQ
is calculated from
CDO = 2.5 0.075
( l o g i ? „ - 2 ) ^ (20)
These formulae are applicable only below the stall angle, and except for the small influence of CDO they do not take account of the Reynolds number and profile shape. The C L , CD, and Cjvf,o.25 calculated from Söding's formulae will also be compared w i t h the numerical and experimental results.
6. N u m e r i c a l Results
The three-dimensional flow around rudders with square tip (i.e. plane upper and lower ends) is investigated. Here only rudders w i t h zero sweep angle are studied. The most important factors influencing the rudder performance are Reynolds number, section shape and aspect ratio. Rudder forces and moments are investigated depending on these three parameters. Only one half of the rudder is considered due to the symmetry i n height direction. Three blocks with together about 80000 control volumes are used to discretize the computational domain. Figs. 6 and 7. The functions (7^(0;), CD{ot) and CM,O.25(O;) of each rudder are presented to compare the computed and measured rudder characteristics where a is the rudder angle.
0.20 0.15 0.10 0.05
Profile shape of NACA 0015 Fig. 3: Profile shape of NACA 0025
0.20 0.15 0.10 0.05 0.00 •0.05 •0.10 •0.15 •0.20 0.20 0.15 0.10 0.05 0.00 •0.05 •0.10 •0.15 •0.20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XI c
Fig. 4: Profile shape of IfS 62TR25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 5: Profile shape of HSVA MP73-25
Fig. 6: Block arrangement for rudder flow Fig. 7: Grid used for N A C A 0025 rudder flow calculations
6.1 Aspect R a t i o Effects
Three rudders all w i t h the profile shape NACA 0015, Fig. 2, are studied at i?„ = 1.82 • 10*^ with three different aspect ratios ^^=1-0) 2.0 and 3.0. A l l three rudders have the taper ratio 0.45. Figs. 8, 10, and 12 compare the computed C L ( Q ; ) , Cnia) and CM,O.25(Q;) to measurements by Whicker and Fehlner. For all Ar investigated, the computed CL agree very well w i t h the measurements for a < a stall,measured^ Fig. 8. CL calculated from (17) agrees also well w i t h the measurements except near the stall angle. Fig. 9. The errors of the numerically predicted
CL,max are 10%, 7% and 14% for ^4^=1.0, 2.0 and 3.0 respectively, whereas the predicted Ustaii
values differ by 14%, 12% and 12% from the measured ones. The stall data depend, however, substantially on details of the measurements, e.g. whether the attack angle was increased from small or decreased from large absolute values, from the turbulence level of the inflow and the surface roughness. The rudders w i t h ^^=2.0 and 3.0 produce 48% and 78% more l i f t , respectively, than the rudder w i t h ^^=1-0 for a given a < agtall, but the stall angle and also
CL,max are smaller for larger Ar¬
No substantial influence of aspect ratio on CD for flxed a can be observed both i n the measurements and i n the calculations. Fig. 10, which agree quite well, whereeis Eq. (18) overes-timates the resistance by about 10%, Fig. 11. For all but the small attack angles, the resistance is mostly the induced resistance, which occurs only i n 3D flow and is independent from viscosity. Computed CM,O.25 functions show small deviations from the measurements for Ar=1.0 and 2.0, Fig. 12, while for Ar=S.O up to 25% error are observed at a = 16°. Doubling the number of cells around the rudder for ^4^=3.0 gave no substantial improvement. The reason why Ar=3.0 has a large CM,O.25 error is not clear. The stall effect influences the moment quite substantially: after stall the transverse rudder force acts farther aft than before stall. Eq. (19) gives fair predictions for ^4^=1.0 and 3.0, but is i n error by about 20% for ^^=2.0, Fig. 13.
6.2 Reynolds N u m b e r Effects
To demonstrate the influence of the Reynolds number, the flow around a rudder is computed
at Rn = 1.82 • 10^ and Rn = 1.82 • 10^. The rudder has the proflle shape N A C A 0015, Ar = 3.0
and Tr = 0.45. Figs. 14, 16, and 18 show the computed functions C L ( Q ! ) , Coia) and
CM,O.25(O!)-No mcEisurements are available at Rn — 1-82 • 10^, but Whicker and Fehlner have tested this rudder at Rn = 1.82 • 10^ and Rn = 2.70 • 10^.
The experiments indicate that l i f t , drag, and moment differ noticeably between these two
Rn only near the stall angle. The same is observed i n the numerical computations: A t larger Rn, the computation gives larger stall angles than the meeisurements, Fig. 14. Again the
computed CL values agree well w i t h the measurements, whereas Eq. (17), which does not give the stall angle, shows a fair agreement of CL before stall. Fig. 15. The numerical computations predict CD better than Eq. (18) which over-predicts CD beyond a > 15°, Fig. 16 and 17. But the CM,O.25 measurements agree weh w i t h Eq. (19) while the computational results give larger errors (about 50%) at larger a. Figs. 18 and 19.
6.3 Profile Shape Effects for Constant M a x i m u m Thickness
Thieme (1963) measured forces and moments aX Rn = 0.78-10^ for rudders w i t h taper ratio
1.0 and aspect ratio 1.0. Numerical calculations are performed here for the rudder shapes: NACA 0025 and IfS 62TR25. Additionally, a corresponding one w i t h the profile shape HSVA MP73-25 designed by Brix (1993) is also computed. Figs. 20, 22, and 24 show the experimental results and computed curves C£,(a), CD{O) and 6 * ^ 0 . 2 5 ( « ) •
For NACA 0025 the computed and measured CL agree well for 0° < a < 10°, whereas computed values are about 8% larger than the measured ones for a > 10°, Fig. 20. The measured CL,max and agtall of NACA 0025 are 4% and 9% larger than the computed values, respectively. Eq. (17) gives excellent agreement with the measurements before the measured
1.6 1.4 1.2 1.0 CL 0.8 0.6 0.4 0.2 0.0 1 ! 1 /I \jC \ • \ 1 1 .. j . _ . ( T • E x p . C o m p . r=1 O r=2 • r=3 •
-/ -/
— — A A - A E x p . C o m p . r=1 O r=2 • r=3 •-/ -/
— — 1 i 1 10 15 20 25 30 35 40 45 50Fig. 8: CL of rudders with different Ar
( N A C A 0015,r^=0.45,iï„ = 1.82 • 10«) 1.6 1.4 1.2 1.0 CL 0.8 0.6 0.4 0.2 O.Oi ^ / / /
/
/
/ / / / M ~ 0 A / • / / A/ / i • < •*
• 7 ^ hi - A A A E x p . ( r=1 o r=2 • r=3 • !^omp • 7 ^ hi E x p . ( r=1 o r=2 • r=3 • • 7 ^ hi i 10 15 20 25 30 35 40 45 50 OFig. 9: CL of rudders with different Ar
( N A C A 0015,r^=0.45,i?„ = 1.82 • 10«):
com-putations according to Eq. (17)
0.8 0.2 O.Oi E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • 0 5 10 15 20 25 30 35 40 45 50
Fig. 10: Gu of rudders with different Ar
( N A C A 0015,T^=0.45,iï„ = 1.82 • 10«) 1.2 1.0 0.8 CD 0.6 0.4 0.2 O.OI 1 ! ! E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • E x p . C o m p . Ar=1 O Ar=2 • Ar=3 • / / ( / 0 / / ( / 0
//
O -O 0 5 10 15 20 25 30 35 40 45 50 a(°)Fig. 11: Cj5 of rudders with different Ar
( N A C A 0015,T^=0.45,i?„ = 1.82 • 10"):
com-putations according to Eq. (18)
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 V P — — V P — —
•
E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • ••
E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • i 3 \ i b ! i 3 \ 0 5 10 15 20 25 30 35 40 45 50 a(°)Fig. 12: CM,0.25 of rudders with different Ar
( N A C A 0015,T,=0.45,E„ = 1.82 • 10") 0.10 0.05 0.00 CM,0.25 -0.05 -0.10 -0.15 -0.20 1 I 1 1 1 -e-""-" j . . . / - I j J o O N s 1
•
O Q E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • ••
O Q E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • i E x p . C o m p . Ar=1 o . Ar=2 • Ar=3 • i D 1 i i D 1 5 10 15 20 25 30 35 40 45 50 OFig. 13: CMfi.25 of rudders with different Ar
( N A C A 0015,Tr=0.45,ü„ = 1.82 • 10"):
com-putations according to Eq. (19)
stall angle, Fig. 21.
For the profile IfS 62TR25 the computed CL agrees well w i t h the measured one up to a = 30°, whereas the measured CL,max and agtaii are 12% and 17% larger, respectively, than the computed values. I n Eq. (17) the section shape is not considered; thus the about 20% larger CL values compared to profile NACA 0025 are not reproduced by this formula, Fig. 21. The computations for the rudder with profile HSVA MP73-25 show that this rudder produces about 8% more CL than that w i t h the NACA 0025 profile, i.e. about the same l i f t as the IfS 62TR25 profile below stall. But HSVA MP73-25 has a larger a^tall than both the NACA 0025 and IfS 62TR25 profile. The l i f t increase compared to the NACA 0025 profile is smaller (about 8%) i n 3D flow than i n 2D flow (about 20%), see Chau (1997) for 2D results, but both computations show the same tendency of the CL{a) curves.
The computed CD is about 5% larger than the measured one for both NACA 0025 and IfS 62TR25 proflles, Fig. 22. The C£)(o;) curve of HSVA MP73-25 is between the two other profiles. The computed CD of HSVA MP73-25 and IfS 62TR25 is 12% and 25%, respectively, larger than that of NACA 0025 for large attack angles, while at small a HSVA MP73-25 does not differ substantially from N A C A 0025 w i t h respect to C D . Equation (18), which does not take into account the profile shape, seems to be a compromise between CD values measured for NACA 0025 and IfS 62TR25, Fig. 23.
The computed CMfi.25 of N A C A 0025 and IfS 62TR25 agree weh w i t h the corresponding measurements. Fig. 24. The profile HSVA MP73-25 produces a moment intermediate between that of the profiles N A C A 0025 and IfS 62TR25. Eq. (19) approximates CMfi.2b{a) well for small a and the NACA 0025 profile, but i t produces large errors at larger a > 25° and for the IfS 62TR2 profile. Fig. 25.
7. Conclusion
The three-dimensional rudder flow calculations reproduced the well-known fact that a large aspect ratio gives a large l i f t slope dCLjda, small astaii and small drag for a given l i f t . However, no substantial CD difference exists among different aspect ratios at the same rudder angle. Not well known is the result that larger aspect ratios give somewhat smaller values
CL,max-Raising the Reynolds number increases astaii and CL,max', thus i n ships CL,max may be substantially larger than the values measured i n wind tunnel experiments.
To investigate the influence of profile shape on the rudder characteristics i n 3D flow, three rudders w i t h profiles NACA 0025, IfS 62TR25 and HSVA MP73-25 were compared. IfS 62TR25 and HSVA MP73-25 offer about the same l i f t slope dCL/da which is larger than that of NACA 0025.
The computed results appear accurate enough for various practical applications, especially for optimizing the shape of the rudder. The simple formulae proposed by Söding give fair agreement w i t h the measurements below the stall angle, but they neglect the influence of Reynolds number, profile shape, taper ratio and profile thickness which can be studied by the present method - especially the infiuence of these parameters on CL,max and
agtaii-Here only rudders i n a uniform inflow field were studied. I n practice the ship hull and the propeller have a strong influence on the inflow to the rudder and, thus, on its performance. Rudders absorb some of the rotational energy of the propeller wake, thus increasing the ship's propulsive efficiency.
0.10 0.05 0.00 CM,0.25 -0.05 -0.10 -0.15 1 1
8
8 i
1 \ E x p . • Rn=1.82.10S O Rn=2.70.10S • C o m p . Rn=1.82-10^ Rn=1.82-10^ O \ E x p . • Rn=1.82.10S O Rn=2.70.10S • C o m p . Rn=1.82-10^ Rn=1.82-10^ 1 ^ — 10 15an
20 25 30Fig. 18 CM,O.25 of rudders at different Rn (NACA 0015, Ar=3, Tr=0A5)
0.10 0.05 0.00, CM,0.25 -0.05 -0.10 -0.15 -fl -J O E x p . Rn=1.82-108 O Rn=2.70.10S • O E x p . Rn=1.82-108 O Rn=2.70.10S • . 10 15 a(°) 20 25 30
Fig. 19: CM,O.25 of rudders at different i?„ (NACA 0015, Ar=3, Tr=0.45): computations according to Eq. (19)
O
an
Fig. 20: CL of rudders witfi different sections Fig. 21: CL of rudders witfi different sections
{Ar=1.0, Tr = 1.0, Rn = 0.78 • 10") ( ^ = 1 . 0 , T,.=1.0, Rn = 0.78 • 10"):
computa-tions according to Eq. (17)
— I 1 1 J 1 \ 1 1 i l.mM E x p . C o m p . N A C A O H S V A IfS • — J 1 \ 1 1 i l.mM E x p . C o m p . N A C A O H S V A IfS • — < 9 E x p . C o m p . N A C A O H S V A IfS • — A o A o { 1 / > 1 ¥ ^ j 1
an
Fig. 22: CD of rudders with different sections (Ar=1.0, r,=1.0, Rn = 0.78 • 10") 1.2 1.0 0.8 CD 0.6 0.4 0.2 0.0 i 1 1 ! ' E x p . C o m p . N A C A O H S V A IfS • — E x p . C o m p . N A C A O H S V A IfS • — f E x p . C o m p . N A C A O H S V A IfS • — A i c o A i c o / c f " •-< 3 1 * \ 1 t
an
Fig. 23: Co of rudders with different sections
{Ar^l.O, Tr=1.0, Rn = 0.78 • 10"):
computa-tions according to Eq. (18)
1 1 1 1 1 N ' s \ » \ )
\
O E x p . C o m p . N A C A O H S V A IfS •\
O E x p . C o m p . N A C A O H S V A IfS • 1• ^\
\ O h E x p . C o m p . N A C A O H S V A IfS • 0 5 10 15 20 25 30 35 40 45 50 55an
Fig. 24: CM,O.25 of rudders with different
sec-tions {Ar = 1.0, Tr = 1.0, Rn = 0.78 • 10") 0.05 -0.05 CM,0.25 -0.10 -0.15 -0.20 -0.25 ) c f-W—1 i c 4 C < • •)., O E x p . C o m p . N A C A O H S V A •" IfS • — < • •)., O E x p . C o m p . N A C A O H S V A •" IfS • — "1 r < o h E x p . C o m p . N A C A O H S V A •" IfS • — i 1 i i 0 5 10 15 20 25 30 35 40 45 50 55
an
Fig. 25: CM,O.25 of rudders with different sec-tions {Ar=1.0, Tr=1.0, Rn = 0.78 • 10"): com-putations according to Eq. (19)
References
BRIX, J.E. (1993), Manoeuvring Technical Manual, Seehafen Verlag, Hamburg
CHAU, S.W. (1997), Numerical investigation of free-stream rudder characteristics using a multi-block
finite volume method, IfS Report 580, Univ. Hamburg
LAUNDER, B.E.; SPLADING D.B. (1974), The numerical computation of turbulent flows. Computer Methods in Appl. Mech. and Eng., Vol. 3
PATANKAR, S.V. (1980), Numerical heat transfer and fluid flow. Hemisphere Publ. Corp., London PERIC, M. (1985), A finite volume method for the prediction of three-dimensional fluid flow in complex
ducts, Ph.D. Thesis, University of London
RHIE, C M . ; CHOW, W.L. (1983), Numerical study of the turbulent flow past an airfoil with trailing
edge separation, AIAA J. 21/11
SÖDING, H. (1993), Rudders, fundamental hydrodynamic aspects, in BRIX (1993)
STONE, H.L. (1968), Iterative solution of implicit approximation of multidimensional partial equations, SIAM J. of Num. Analysis 5
SUZUKI, H.; TODA, Y.; SUZUKI, T. (1994), Computation of viscous flow around a rudder behind a
propeller - Laminar flow around a flat plate rudder in propeller slipstream, 6th Int. Conf. Num. Ship
Hydrodyn., Iowa
SWANSON, R.S.; TOLL, T.A. (1943), Jet-boundary corrections for reflection-plane models in
rectan-gular wind tunnels, NACA Report 770
TAMASHIMA, M.; MATSUI, S.; YANG, J.; MORI, K.; YAMAZAKI, R. (1993), The method for
predicting the performance of propeller-rudder system with rudder angle and its application to the rudder design. Trans. West-Japan Soc. Naval Arch. 86
THIEME, H. (1963), Zur Formgebung von Schiffsrudern, Jahrbuch der STG, Band 56, Springer Verlag VINOKUR, M.(1983), On one-dimensional stretching functions to finite-difference calculations, J. Comp. Physics 50
WHICKER, L.F.; FEHLNER, L.F. (1958), Free-stream characteristics of a family of low-aspect-ratio,
all-movable control surfaces for application to ship design, David Taylor Model Basin 93
Model Experiments w i t h Surface Piercing Propellers^
Wojciech Miller, Ship Design and Research Centre (CTO) J a n Szantyr, Inst, of Fluid Flow Machinery^
1. Introduction
Surface piercing propellers (SPP) are established for many years now as propulsors for high speed racing boats and small sport craft. They are designed for this application by trial and error with f u l l scale prototypes until the required performance is obtained. The accumulated practical experience with these propellers has highlighted several specific problems which must be considered i n design of boats and ships propelled by SPP, namely:
- lack of reliable methods for computational design and performance prediction of SPP - lack of data on interaction effects i n multi-propulsor configurations
- high level of hydrodynamic transverse forces affecting boat t r i m and steering character-istics
- highly variable hydrodynamic loading of blades, leading to vibration and fatigue problems Despite these problems, there is a widely accepted opinion, supported by successful f u l l scale prototypes, Allison (1981), that SPPs may constitute a viable propulsion option for high speed craft, reaching efHciency even exceeding that of waterjets at speeds over 50 knots. This high efficiency results from lack of appendages typical for classical propellers, complete emergence of loss-producing hub, and production of thrust by tips of blades only, where thrust/torque ratio is the highest.
To fill the gap i n available knowledge, a special research project i n the Institute of Fluid Flow Machinery developed design and analysis procedures, supported by experiments, to sup-ply the necessary qualitative and quantitative information. The experiments, conducted i n the Gdansk Model Basin (CTO) are described i n this paper.
2. Surface piercing propeller models
SPPs were designed for a 280 tons patrol boat having design speed of 35 knots. Originally classical cavitating propellers and waterjet propulsors were envisaged for this boat. SPP con-stituted a third propulsion option. Because of large diameter, a twin screw configuration of SPPs was planned, i n contrast to triple waterjets and triple cavitating propellers.
A five-bladed controllable pitch SPP was designed manually, using data of Olofsson (1996),
Rose and Kruppa (1991). This propeller has a special blade geometry, resembling that of
supercavitating propellers. Fig. I .
3. P r o g r a m of experiments
The program of experiments was inspired by Olofsson (1996) and Rains (1981). The ex-periments were conducted i n the model basin at atmospheric pressure. Full ventilation of blades was expected at the design condition and influence of cavitation number on the hydro-dynamic characteristics i n this situation is negligible, Olofsson (1996). The experiments were videotaped. The maximum attainable carriage speed and propeller dynamometer parameters limited the scope of experiments to the lower region of what is usually regarded as 'high speed'.
The experiments were arranged i n four series:
Series I measured thrust and torque of a single isolated propeller w i t h zero inclination and yaw for a deeply immersed propeller. Then for immersions h/D=0.3 and h / D = 0 . 4 thrust and
^Research funded by the Pohsh Scientific Research Committee grant no. 9T12C 025 11 ^J. Fiszera 14, PL 80952 Gdansk, Poland
I
Fig. 1. Geometry of propeller model
torque were measured w i t h zero yaw angle and 6.6° shaft inclination.
Series I I measured thrust, torque and transverse forces on a single propeller for immersion h/D=0.3 and h / D = 0 . 4 for shaft inchnation angle 6.5° and yaw angles 5°, 0°, and - 5 ° .
Series I I I measured thrust, torque, transverse forces on the shaft and two unsteady bending moments on a single blade in the twin screw configuration (inward turning propellers) for shaft inclination 6.6°, for immersions h/D=0.3 and h / D = 0 . 4 and for shaft yaw 5°, 0°, and —5°. Altogether this series consisted of 6 operating conditions.
Series I V was analogical to Series I I I , but this time the direction of rotation was outward and shaft yaw was varied (5°, 0°, - 5 ° ) together w i t h shaft inclination (6.6°, 12°) and propeller immersion (h/D=0.3 and h / D = 0 . 4 ) . This series consisted of 12 operating conditions.
4. Presentation of the results
Fig. 2 shows the definition of operational parameters of the SPP which have been var-ied during the experiments. Selected results of measurements are presented i n the following diagrams.
Fig. 3 shows the open water characteristics of the SPPs for four different immersions: f u l l immersion, h / D = 0 . 3 , h / D = 0 . 4 and h/D=0.5. The maximum efficiency of fully immersed propeller is much lower than that of partially immersed propellers. On the other hand the deepest partial immersion h/D=0.5 produces the highest efficiency.
Fig. 4 presents the open water characteristics of the single right turning SPP at h/D=0.3 for shaft yaw angles 5°, 0°, - 5 ° . The yaw angle does not affect propeller efficiency, but any non-zero yaw of the shaft results in increased propeller loading.
Fig. 5 is analogical to Fig. 4, but this time the propeller immersion is h/D=0.4. Again, the shaft yaw angle does not affect propeller efficiency, but this time the effect of yaw on propeller loading is rather mixed. Negative yaw, i.e. i n the direction of propeller rotation, produces higher propeller loading, while positive yaw does not affect the loading.
Fig. 6 refers to the twin screw system tested at immersion h/D=0.4, shaft yaw angle 5° and
Fig. 2. Definition of tiie operating parameters of tlie SPPs
shaft inchnation 6.6° and i t presents the effect of direction of propeller rotation on the open water characteristics and on the transverse forces. Inward rotation results i n slightly higher propeller loading and higher horizontal transverse force. The vertical transverse force fluctuates strongly and changes its direction with advance coefficient. This may lead to problems w i t h keeping boat t r i m at changing speed.
Fig. 7 is analogical for shaft yaw angle 0°. There is almost no visible effect of the direction of rotation on the open water characteristics and on transverse forces.
Fig. 8 is analogical for shaft yaw angle —5°. Here the outward direction of rotation produces higher propeller loading, especially at higher advance coefficients. Again, the direction of rotation does not infiuence propeller efficiency. The direction of rotation may change sign of the vertical transverse force at high advance coefficient. This should be taken into account in the design analysis of the boat t r i m .
Fig. 9 refers to the twin screw system. I t shows the influence of shaft inclination on the open water characteristics and on the transverse forces. The tested system operates w i t h outward rotation at shaft yaw angle 0° and at immersion h/D=0.3. Increasing shaft inclination from 6.6° to 12° increases slightly the propeller loading without affecting the propeller efficiency. Similarly, the transverse forces are almost unaffected.
Fig. 10 is analogical to Fig. 9, but for the twin screw system immersed to h / D = 0 . 4 . The consequences of changing the shaft inclination here are similar as for propeller immersion h/D=0.3.
Fig. 11 shows the influence of the shaft yaw angle on the unsteady bending moments on a single blade of the propeller operating at advance coefficient J=0.779, immersion h/D=0.3 and shaft inchnation 12°. The variation of the bending moments w i t h blade position is relatively smooth at the yaw angle 0°, while increasing this angle in both directions generates high amplitude and high frequency secondary fluctuations of both measured quantities.
Fig. 12 presents the influence of the shaft inclination angle on the unsteady bending mo-ments on a single SPP blade at advance coefficient J=0.779, immersion h / D = 0 . 4 and shaft yaw angle 0°. A n increase i n shaft inclination increases slightly amplitudes of both bending moments without changing the character of their variation w i t h the blade position.
5. Conclusions
The maximum efficiency of SPPs obtained in the experiments was lower than for corre-sponding classical propellers; SPP would perform better for truly high speeds, unattainable i n the present model basin.
The values of transverse hydrodynamic forces are high i n both directions and they definitely must be taken into account in the design of the boat.
The horizontal transverse force may be employed for increasing propelling force by a few % through applying proper combination of shaft yaw and direction of rotation i n the twin screw configuration.
The time variation of hydrodynamic loading on a blade may be surprisingly smooth in some cases and quite complicated, w i t h high amplitude secondary fluctuations in other cases; this suggests the existence of complicated, highly unsteady flow phenomena accompanying the operation of SPP.
The observed picture of flow around an operating SPP is so disorderly and highly unsteady that i t is difficult to imagine a theoretical model taking into account all meaningful physical phenomena; any effective computational design or analysis method for SPP would have to include decisive empirical corrections developed on the basis of experiments similar to these described above.
References
ALLISON, J.L. (1978), Propellers for high speed craft, Marine Technology 15/4, pp.335-380
OLOFSSON, N . (1996), Force and flow characteristics of a partially submerged propeller, PhD thesis, Chalmers Univ. of Technology, Gothenburg
RAINS, D.A. (1981), Semi-submerged propellers for monohull displacement ships, SNAME Propellers'81, pp.15-40
ROSE, J.C; KRUPPA, C.F.L. (1991), Methodical series model tests results, FAST'91, Trondheim, Vol.2, pp.1129-1145
KT 0.4¬ 0.3-0.2H 0.1 WKQ 0.8-0.6 0.4 0.2-1 OOO 0.6 0.5 0.4 0.3 0.2 0.1 4»
r
0.5 1.0 J 0.5 1.0 J 0.5 1.0 JFig.3: Open-water cliaracteristics of SPP for four immersions; • f u l l , o h/D = 0.3, -|- h/D = 0.4,
* h/D = 0.5 KT 0.08¬ 0.06-0.04H 0.02 * o IOKQ 0.20-0.15 0.10 0.05-1 0.2 0.4 0.6 0.8 J 0.6 0.5 0.4 0.3 0.2 0.1 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J Fig.4: Infiuence of the shaft yaw angle /3 on the SPP open-water characteristics for relative immersion h/D = 0.3; • /3 = - 5 ° , o /3 = 0°, /3 = + 5 ° KT 0.08 ^ 0.06 0.04 0.02 H lOi^Q 0.20-0.15 0.10 0.05 n T~ 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J V 0.6 0.5 0.4 0.3¬ 0.2¬ 0.1 0.2 0.4 0.6 0.8 J Fig.5: Influence of the shaft yaw angle (3 on the SPP open-water characteristics for relative immersion h/D = 0.4; • f3 = - 5 ° , o /? = 0°, /? = + 5 °
KT 0.08-0.06 0.04 0.02 0.2 0.4 0.6 0.8 J Kfy' 0.02-1 0.01 WKQ 0.20-0.15 O.IOH 0.05¬ 0.01-V 0.6^ 0.5 0.4 0.3 0.2 0.1 0.2 0.4 0.6 0.8 J ^ r 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J
Fig.6: The effect of direction of rotation on the open-water characteristics and transverse forces of the twin-screw system at h/D = 0.4, j3 = 5°, a = 6.6°; • inward, o outward
KT 0.08¬ 0.06-1 0.04¬ 0.02-K f y 0.02¬ 0.01-• 8%. IOKQ 0.20 H *« 0.15H ° 0.10 0.05 - i r 0.6 0.5 0.4 0.3 0.2 0.1 0.2 0.4 0.6 0.8 J n r ê o 0.2 0.4 0.6 0.8 J ~ 1 1 1 ~ 0.2 0.4 0.6 0.8 J 0.01-0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J
Fig.7: The effect of direction of rotation on the open-water characteristics and transverse forces of the twin-screw system at h/D = 0.4, ^ = 0°, a = 6.6°; • inward, o outward
KT 0.08¬ 0.06¬ 0.04¬ 0.02-K f y 0.02¬ 0.01-O 0.01-O 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J WKQ 0.20¬ 0.15¬ 0.10¬ 0.05-1 0.01-O O 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J 0.6¬ 0.5¬ 0.4 0.3-] 0.2 O.H 0.2 0.4 0.6 0.8 J
Fig.8: The effect of direction of rotation on the open-water characteristics and transverse forces of the twin-screw system at h/D = 0.4, /3 =-5°, a = 6.6°; • inward, o outward
KT 0.08H 0.06 0.04 0.02 0 * 0 9 S 0.2 0.4 0.6 0.8 J K f y 0.02¬ 0.01-I 0.2 0.4 0.6 0.8 J WKQ 0.20-0.15 0.10 0.05 o g • O n 1 r 0.2 0.4 0.6 0.8 J K -0.01 O O n r 0.2 0.4 0.6 0.8 J 0.6 0.5 0.4-1 0.3 0.2 0.1 0.2 0.4 0.6 0.8 J
Fig.9: The effect of shaft inclination on the open-water characteristics and transverse forces of the twin-screw system rotating outward at h/D = 0.3, ;9 = 0°; • a = 6.6°, o a = 12°
KT 0.08¬ 0.06¬ 0.04¬ 0.02-K f y 0.02 0.01 0.2 0.4 0.6 0.8 J IOKQ 0.20-0.15 0.10-1 0.05-K f . 0.01-8 : • . 0.6 0.5 0.4 0.3 0.2 0.1 -] r 9 • 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J 0.2 0.4 0.6 0.8 J ~ i r ~ 0.2 0.4 0.6 0.8 J
Fig. 10: Tlie effect of shaft inchnation on the open-water characteristics and transverse forces of the twin-screw system rotating outward at h/D = 0.4, /3 = 0°; • a = 6.6°, o a = 12°
90° 180°
F i g . l l : The influence of the shaft yaw angle /3 on the unsteady bending moments on the blade of SPP at J = 0.779, h/D = 0.3, a = 12°; average hydrodynamic moments mt and rriq [Nm] over blade position [deg]; • ^ = 5 ° , o ^ = 0°,-h/Ö =-5°
Fig. 12: The influence of the shaft inclination angle a on the unsteady bending moments on the blade of SPP at J = 0.779, h/D = 0.3, /? = 0°; average hydrodynamic moments mt and mq [Nm] over blade position [deg]; • a = 6.6°, o a = 12°
Memory-Based Learning Approach to Selection of Basis Ship
in Conceptual Design
Dongkon Lee, K y u n g - H o Lee, Korea Research Inst, of Ships and Ocean Eng.^ Jaeho K a n g , K w a n g - R y e l R y u , Pusan National University^
1. Introduction
The design of a new ship follows the owner's order which usually specifies the type, the required deadweight D W T and the design speed. The designer then selects from the database of previous ship designs the reference ships of the same type with similar D W T and speed. The most similar among these reference ships is selected as a basis ship. The designer determines the major parameters of a new ship's principal particulars Lpp, B, D, T and CB- The designer considers the tendency of these parameters to differ among the reference ships, depending on their varying D W T and speed.
This paper presents a method of applying a memory-based learning (MBL) technique to automatic building of an indexing scheme to access reference ships from a database during the conceptual design stage of a ship. We developed an M B L method that can build an effective indexing scheme for retrieving good reference ships from an existing database. For learning, we used bulk-carrier data of past designs w i t h the record of reference history showing the ref-erence ships used for designing each ship. Empirical results show that the indexing scheme generated by M B L outperforms those by other learning methods such as decision-tree learning.
Schwabacher et al. (1994) showed a decision-tree learning method to be effective for deriving an
indexing scheme for yacht design. However, the decision tree sometimes misses an important condition and thus recommends inappropriate reference ships, seemingly because the learning algorithm attempts to minimize the size of the derived tree too severely for making it noise tolerant.
2. Correlation between the design parameters
Fig. I shows the correlation between Lpp and D W T of bulk carriers. The ships are clustered into many groups of similar sizes where some of the ships i n the same group are close to each other, but the boundaries between different groups are not always clear. Reference ships for designing a new ship of given requirements may have to be selected first by identifying the group the new ship should belong to, and then by selecting those ships w i t h design require-ments similar to those of the new ship. Although Fig. I shows that Lpp increases w i t h D W T , there are some irregularities and exceptions due to the owner's additional requirements and other factors such as the ship's navigation route and voyage condition. Moreover, the rate of
Lpp change w i t h D W T differs from group to group. Therefore, we need a learning method that
can capture not just the global tendency, but the local tendency as well.
3. Indexing scheme by learning algorithm 3.1. Memory-based learning for refer-ence ships
Since M B L algorithms just save training instances in memory and the inductive process actually takes place at the time a test instance is given, they are often called lazy learning algorithms. I n contrast, the eager learning algorithms such as neural networks and decision tree learning algorithms try to induce the best classification rules or hypotheses at the time of training. Aha (1997), Friedman et al. (1996). One generally known strength of lazy learning over eager learning is that the lazy learning can derive solutions that are more sensitive to the
^Shipbuilding System Dept., POB 101, Yusung-Ku, Teajeon 305-600, Korea, dklee@mailgw.kimm.re.kr ^Dept. Computer Eng., San 30 Jangjeon-Dong, Kumjeong-Ku, Pusan 609-735, Korea
context of a given problem, because i t can reflect the local tendency or case-specific character-istics as well as the global tendency or average charactercharacter-istics, Atekson et al. (1997), Friedman
et al. (1996).
Most lazy learning systems use nearest neighbor (NN) algorithms. Cover and Hart (1967), for finding past cases similar to a given problem, Stanfill et al. (1986), Aha (1991), Cost
and Salzberg (1993), Atekson et al. (1997). I n this paper, we retrieve reference ships for a
new design by using an N N algorithm. The reference ships to be retrieved are those of the previously designed ships that satisfy the requirements of a new ship most closely. Unlike most other NN algorithms which are usually used for identifying a single most similar case to a given instance, our N N algorithm should retrieve multiple reference ships similar to a given new ship. Moreover, i t should be able to recommend the most similar one as a basis ship.
DWT(ton)
Fig. I : Correlation between Lpp and D W T Fig. 2: A n M B L approach to reference of bulk carriers ship selection
Fig. 2 shows how M B L can be used for selecting the reference ships, given a new ship of specified speed and D W T requirement. Ships of past design are designated by the a;'s and each of them is enclosed by a boundary that represents the range within which the ship is worth referencing. A new ship of specified speed and D W T is shown in the figure as a point indicated by an arrow. For a new ship gi, xi becomes a reference ship. For q2, both X2 and are worth referencing, while the one closer to q2 under a certain similarity measure becomes the basis ship. For the ship gs, there is no reference ship available because none of the previous ships is similar to this one at all. The range of reference for X4^ is sensitive to speed, and i n general the boundaries for the ships are not necessarily in regular or symmetric shapes. The two important tasks of our learning algorithm are to determine the range of reference for each ship and to provide a way to measure the degree of similarity between two given ships.
3.2. Calculation of similarity metric between design and target ship
We calculate the similarity between a previous ship x and a new ship q by the following similarity function:
S{x,q) = J { s i { x , q ) ( I )
where Si is the kernel function, Atekson et al. (1997) to compute the similarity of the two ships in terms of the i - t h design requirement (either speed or D W T i n this problem). S and Sj have values in the range from 0 to 1. So they can be considered as the probabilities measuring the likelihood of a ship being referred to by another. By doing so, we can easily determine w i t h a uniform measure whether a ship is qualified as a reference ship; i n this research the ships w i t h the similarity values of 0.5 or higher are always qualified. W i t h the usual distance measure of most N N algorithms, however, it is not easy to set a uniform threshold value for reference ship qualification. Multiplication is used i n this function instead of summation because the two ships should not be considered similar when the similarity of the two ships i n any one of the
design requirements is not liigli enougli. E.g., iiowever similar the speeds of the two ships are, one cannot refer to the other i f the D W T difference between the two exceeds a certain limit.
Various functions can be used for Sj, Fig. 3. The step function takes the value 1 when di < 9 and the value 0 otherwise, di is the difference of the i-th design requirement of the two ships
X and g, and Ö is a certain threshold value. When the step function is used for Sj, the range
of reference is determined by the threshold value 6 and the similarity is represented simply by binary values 1 and 0. Under this scheme, we cannot tell how much a ship is worth referencing and thus we have no way to select a basis ship among the retrieved reference ships. To provide a notion of degree of similarity, we need a function having a slope nearby the threshold value. The sigmoid function is such a function that we decided to use as the kernel function Sj i n this research. The threshold value 6 for the sigmoid function is determined such that Sj becomes 0.5 at e.
A n advantage of using the sigmoid kernel function comes from the fact that the slope change does not affect the threshold. Fig. 3(b). The threshold corresponds to the range of reference and the slope to the mechanism of providing the degree of similarity, and these two are to be learned for each ship for later reference. Since the threshold and the slope of the sigmoid function can be adjusted independently of each other, the learning algorithm can search for their values much more easily.
0
Ö rf/ e d, e d, (a-1) step function (a-2) sigmoid function (b) sigmoid functions w i t h varying
slopes at a fixed threshold. Fig. 3: Candidate functions for Si
The similarity metric that we need for reference ship retrieval is asymmetric, Ricci and
Avesani (1995). E.g., a previous ship w i t h the D W T w may be worth referencing when the
D W T of a new ship to be designed is w -|- a, but not when it is t« - a. Therefore, for both the speed and the D W T the threshold and the slope in both directions should be learned separately.
I n the equations regarding the similarity metric, the kernel function Sj which computes the similarity of x and q i n terms of the i - t h design requirement is expressed as a sigmoid function of the difference di of the i - t h design requirement of x and g, the threshold 0^;, and the slope
Si{x,q) = K{di{x,q),9:ci,kx,) (2) 1 + e('i+0)/k xii) _ q{i) > 0
~ 1
e'i ff x^^ - g(^) < 0 (4) I r.^. i i a;(^) - g « > 0 . . . ^ ^ ^ " l e ff x « - g W < 0Eqs. (4) and (5) tell us that the values for the threshold and the slope are different i n the positive and the negative directions due to the asymmetry, where a;^') and g^*^ are the i-th requirement of the ships x and q, respectively.
3.3. Determination of the threshold and slope
Building an indexing scheme for reference ship selection is completed by assigning appro-priate sigmoid kernel functions to each ship of previous designs. I n our problem, there must be four sigmoid functions for each ship: two for the speed and two for the D W T . Two different sigmoid functions are required for each of the speed and D W T because the ranges of reference and the degrees of similarity i n the positive and the negative directions may be different. Since each sigmoid function is completely determined by fixing the threshold and the slope values, there are eight such values that should be determined for each ship. Given a record of reference history, what we want is to find the optimal threshold and slope values for each of the design requirements ( D W T , speed) that minimize the following error Ex for a given ship x:
(
Ex= J2(^Ex{x,Xj)-S{x,Xj)Y (6) \ i /
SEX{X, X j ) is the value of similarity between x and Xj given from the examples i n the record of reference history, and S{x,Xj) is the similarity value computation based on Eqs. (1) - (5), with the threshold and slope values gissigned to certain initial values at the beginning. The goal of learning from the examples i n the record of reference history is to search for optimal values for the thresholds and slopes which minimize Ex- We tried several heuristic search methods for this optimization and found that genetic algorithms gave the best result.
4. Application to design environment
We used 122 bulk carrier data designed from 1974 to 1995 with the record of reference history, of which the earliest 100 ships were used for training and the remaining 22 for testing. We compared the performance of M B L w i t h those of a simple heuristic, a decision-tree learning, and a neural network. The design requirements are the D W T and the speed. Designing a new ship of certain requirements, i n the conceptual design stage, involves determination of the major parameters which are Lpp, B, D, and T . A good conceptual design derived from the reference ships promises efficiency and quality of the whole design process. Therefore, we tried to evaluate different learning methods by deriving an initial design by performing linear regression on the reference ships recommended by each method, and compared the results w i t h the real test ship data.
Table I compares the correctness (% of correct reference ships retrieved) and the complete-ness (% of reference ships actually retrieved among all the reference ships) of the reference ships retrieved by different methods. DWT(5%) and DWT(10%) i n the table respectively rep-resent the simple heuristics by which all the ships within 5% and 10% differences of the D W T value of the target ship are retrieved as reference ships. These heuristics are tried because the D W T is considered the most important among all the design requirements. As more ships are retrieved and thus the completeness becomes higher, the proportion of the correct reference ships among those retrieved gets smaller (low correctness), because more irrelevant ships tend to be selected. The result of decision-tree learning by the C4.5 program, Quinlan (1993), ex-hibits low correctness although its completeness is high. We found that the reason for this low correctness is that a few rules derived by C4.5 were missing the most important feature D W T from its condition part, apparently as a result of attempting to derive a minimal decision tree. The learning strategy of C4.5 to minimize the decision tree is generally good for capturing a global tendency o f t h e training data i n noisy environments. As argued i n section 2, our problem prefers a method which can capture a local tendency as weh as the global tendency. We can
see i n tlie table that the result by M B L reveals the highest correctness w i t h reasonably com-promised completeness. I n our experiment, a ship is qualified as a reference ship i f the ship's similarity to the new ship computed by our similarity function is greater than or equal to 0.5. C4.5 cannot rank the reference ships but our M B L can, thus only the M B L can recommend a basis ship among the retrieved reference ships.
Table I : Comparison of correctness and completeness of various methods. Method Correctness Completeness
DWT(5%) 55.2% 58.0%
DWT(10%) 39.9% 99.2% Decision Tree 49.8% 100.0%
M B L 81.8% 75.6%
Table I I compares the quafities o f t h e initial designs (where Lpp, B, D, and T are determined) derived by performing linear regressions on the reference ships retrieved by various methods. The first row shows the result by regressing on all the ships w i t h respect to the D W T . The neural network on the second row is an exception; instead of a hnear regression, the parameter values are derived by directly training the neural network on each of the parameters. The row DWT(5%) means that all the ships within 5% difference of the D W T value of the target ship are used for regression. For the rows 'decision tree' and ' M B L ' , the reference ships retrieved by each method are used for regression. The last row shows the result of the regression on the actual reference ships obtained from the record of reference history. M B L consistently provides the values with the lowest average errors for each of all the parameters.
Table I I : Average errors of major parameter values derived by various methods. Method Lpp{m) B{m) D{m) T ( m ) A l l Ships 6.75 0.70 0.50 0.59 Neural Network 3.04 0.59 0.21 0.17 DWT(5%) 6.41 0.79 0.34 0.21 Decision Tree 1.81 0.31 0.27 0.32 M B L 1.51 0.31 0.11 0.10 Ships i n the record 0.14 0.05 0.09 0.10
5. Conclusion
A memory-based learning technique can be effectively applied to indexing of reference ships for the conceptual design of a new ship. The similarity metric we proposed i n this paper is based on the concept of joint probability of independent events rather than the concept of summation of distances of each features, as is usually found in most other nearest neighbor algorithms. Our similarity metric can easily represent cases where a ship cannot refer to an-other due to the difference i n a single feature exceeding a certain limit, despite the similarities in most of the other features. The probabilistic nature of our similarity metric also allows us to easily determine whether a ship should qualify as a reference ship; e.g., a ship of similarity greater than or equal to 0.5 qualifies. The kernel function we used is a sigmoid function to take advantage of the fact that the threshold and the slope can be controlled independently of each other, and thus the learning algorithm can search for the optimal values more efficiently. One rather distinctive aspect of our application is that our similarity metric should be asymmetric due to the nature of referencing i n the conceptual ship design. The asymmetry causes more parameters to appear i n learning, thus increasing the search complexity, although relatively few training examples were available. However, empirical results still showed that the indexing
scheme generated by our memory-based learning technique outperformed those of other learn-ing methods includlearn-ing C4.5 and neural networks.
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