Ocean Engineering 92 (2014) 267-284
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Ocean Engineering
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / o c e a n e n g
Rudder effectiveness correction for scale model ship testing
Michio Ueno *, Yoshiaki Tsukada, Yasushi Kitagawa
National Maritime Research Institute, 6-38-1 Shinkawa, Mitaka, Tokyo 181-0004 Japan
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A R T I C L E I N F O
Artide history:
Received 14 November 2013 Accepted 20 October 2014 Available online 10 November 2014
Keywords:
Manoeuvrability Scale effect
Free-running model test Skin friction correction Rudder normal force
Effective inflow velocity to rudder
A B S T R A C T
The authors propose an idea of rudder effectiveness correction for free-running manoeuvring tests using scale models. The idea aims to realize the full-scale-equivalent manoeuvring motion with scale models using the auxiliary thruster that the authors developed. The auxiliary thruster can generate time varying forward force needed for the rudder effectiveness correction. The auxiliary thrust is represented by the force required for the skin friction correction multiplied by the newly defined rudder effectiveness correction factor. The propulsive performance of the model and full-scale ships in steady straight running determines a value of the factor. Theoretical calculations using the modular mathematical model applied to a container ship and a tanker clarify characteristics of the factor. The tank tests and numerical simulations confirm the feasibility of the idea.
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
The difference of Reynolds number between model and f u l l -scale ships violates the similarity of resistance, propeller load, and, therefore, rudder force i n free-running model tests. This is the reason w h y the manoeuvring motion of free-running model ships is not similar to full-scale ships'.
Followings are among numerous reports on the model-ship correlation in manoeuvrability. Kawano et al. (1963) carried out full and model scale manoeuvring tests and discussed the f u l l -scale equivalent rudder area of model ships. They reported the full-scale equivalent rudder area for model ships is around 70% the geometrically similar rudder. Yumuro (1975) pointed out based on a theoretical calculation the rudder force of mode ship w i t h skin friction correction (SFC) is around 70% the estimated value of f u l l -scale ship. He noted SFC in captive model tests modified model ships rudder effectiveness but significant difference still remains between model and full-scale ships. He proposed captive model tests w i t h such propeller rate as made the rudder effectiveness similar to the full-scale ship, though he did not indicate how to settle such propeller rate. These reports above imply the similarity of rudder effectiveness is neither at the model ship self-propulsion point (MSPP) nor at the ship self-propulsion point (SSPP). I n general, the propeller rate at MSPP is higher than at SSPP because of the relatively larger resistance i n model scale than in f u l l scale.
* Corresponding author. Tel.: -1-81 422 41 3060; fax: +81 422 41 3053.
E-mail address: ueno@nmri.go.jp (M. Ueno).
http://dx.doi.0rg/lO.lOl6/j.oceaneng.2Oi4.lO.OO6 0029-8018/© 2014 Elsevier Ltd. All rights reserved.
Researchers had tried to realize the similar manoeuvring motion to full-scale ships' using scale models. Fujii (1960) used an air-propeller generating auxiliary thrust to make the model ship propeller rate similar to the full-scale ship's, based on the Froude's similarity law, and studied the rudder torque. He states he placed the air-propeller at the pivoting point without describ-ing any reason. The authors deduce the reason is to avoid producing the lateral force due to lateral inflow velocity to the air propeller because the unnecessary lateral force could result i n dissimilar manoeuvring motion. The pivoting point is the point on the centerline where the lateral velocity component is zero. Since the pivoting point does not stay at a fixed point but moves during unsteady motion, the method using air-propeller is effective only in steady turning, but not in general manoeuvring motion. Bindel (1966) summarized SFC on captive and free-running model tests w i t h the air-screw, stating SFC makes the turning radius larger, the speed decrease and d r i f t angle smaller, but no significant differ-ence in the directional stability. Oltmann et al. (1980) investigated the propeller load effect on manoeuvrability w i t h the aid of the computerized planar motion carriage (Grim et al., 1976) that was able to provide a free-running model ship w i t h prescribed con-stant force during tracking the model. They compared full-scale ship data w i t h the numerical simulations results of several different model propeller loads. They stated the easiest way to compensate for the scale effect i n manoeuvrability is to choose the propeller rate which best generates the corresponding rudder inflow velocity of the full-scale. They, anyway, could not reach any concrete proposal how to settle the propeller rate. Crane et al. (1989) state the model propeller slip ratio should be identical to the full-scale ship propeller slip ratio and this can be fulfilled by an
268 M. Ueno et al. / Ocean Engineering 92 (2014) 267-284
air propeller providing part of the thrust. They point out the air force can be measured and dynamically changed as a function of measured model speed to improve results, but do not discuss on the lateral force of the aitTpropeller. Kobayashi et al. (2000) developed an air-jet mechanism placed at the aft end of a model ship for providing w i t h additional forward force. The mechanism should not generate the unnecessary lateral force, but a relatively large air cylinder on a carriage tracking a model ship is indis-pensable. They carried out free-running model tests in which the airjet system was applied and compared the test results w i t h f u l l -scale trial data. Although the air-jet force seems not to have been controlled depending on instantaneous model ship speed but to be kept constant, they stated the free-running model test w i t h SFC is suitable for predicting full-scale manoeuvring motion. Son et al. (2010) developed a towing device consisting of a servo motor on a tracking carriage and wire connected to a load cell placed at the center of gravity of the model ship. The device can provide a free-running model ship w i t h additional longitudinal force. Kajita et al. (1975) carried out a free-running model test using several differ-ent scale models w i t h rudders of differdiffer-ent areas. The test results clarified the smaller models are the more stable their directional stability becomes. They compared the rudder normal force of these models based on the mathematical model and demonstrated the large scale models w i t h reduced rudder area had showed similar manoeuvrability to the full-scale ship. In spite of all these efforts described above, there is no standardized or generally accepted free-running model test procedure to realize full-scale equivalent manoeuvring motion yet.
Above examples on the free-running test procedure, apart from Kajita et al. (1975), shows different types and different uses of the auxiliary thrusters. Especially, an auxiliary thruster capable of providing a model ship w i t h forward force depending on the instantaneous model ship speed without unnecessary lateral force is not familiar even today. This, the authors consider, implies neither a practical mechanism to generate the auxiliary thrust nor a method to use the mechanism is established yet except an example of Son et al. (2010) for SFC. As for the mechanism, Tsukada et al. (2013) developed a prototype of duct fan type auxiliary thruster (DFAT) being able to control its thrust and adjust the propeller load to designated time varying values depending on any measured data without generating the unnecessary lateral force. The prototype consists of a duct fan, a load cell measuring the auxiliary thrust, and a PC. The PC controls the auxiliary thrust of the duct fan depending on measured model ship speed. They demonstrated how the prototype works well by showing the tank test data w i t h and without the speed dependent SFC, comparing also w i t h theoretical calculations. The mechanism is compact enough to be loaded totally onboard i f necessary and, the authors believe, can be a promising experimental tool to find a method for the objective, how to realize full-scale equivalent manoeuvring motion w i t h scale model ships.
In this report the authors propose an idea of rudder effective-ness correction (REC) as an application of the DFAT to realize the full-scale equivalent manoeuvring motion using scale models. REC controls the auxiliary thrust to ensure the similarity of rudder normal force between model and full-scale ships approximately. REC factor, introduced here, characterizes the auxiliary thrust for REC. The authors assembled a new DFAT for practical use. Free-running model test using scale models of a container ship and a tanker w i t h DFAT examine how REC works on the manoeuvrabil-ity. The authors add a term representing the effect of the auxiliary thrust into a modular mathematical model to look into the effect of REC theoretically and also to confirm whether or not the tank test was carried out as desired. Comparisons of the tank test data of model ships w i t h REC, theoretical calculation for model ships w i t h REC, and theoretical calculation for corresponding full-scale
ships clarify how well REC works to compensate for the scale effect on manoeuvrability.
2. Rudder effectiveness correction
2.1. Basic idea
Since the origin of manoeuvring motion is the rudder force, the rudder normal force should be primarily responsible for the similarity of manoeuvring motion between model and full-scale ships. The basic idea of rudder effectiveness correction is to make the ruder normal force of model ships similar to full-scale ones using the auxiliary thruster.
Suppose the geometrically similar rudder angle and constant propeller rate by ignoring the effect of propeller torque variation on the propeller rate. Then, what we can do i n the free-running test using geometrically similar scale models w i t h the auxiliary thruster are to choose the constant propeller rate and to control the auxiliary thrust during manoeuvring motion.
Let us consider a model ship in steady straight running. The longitudinal equilibrium equation taldng into account the auxili-ary thrust is written as follows.
O-t)T+TA-RT = 0 (1)
T, t, and Rj- stand for the propeller thrust, the thrust deduction factor, and the total resistance, respectively. stands for the auxiliary thrust. Since RT is constant at a speed satisfying the Froude's similarity law, TA determines T and, therefore, the propeller rate being constant through the tank test.
Accordingly, the basic idea comes down to the problem how to designate the auxiliary thrust i n a steady straight running condi-tion and how to control it during the manoeuvring mocondi-tion to follow so as to have the similar rudder normal force to the f u l l -scale ship i n the model test.
2.2. Definition of REC factor, fREC
In the discussion concerning the auxiliary thrust the force required for SFC can be a unit of measurement. Let us introduce first the auxiliaiy thrust factor /TA, defined i n the following equation.
TA =fTATs?c (2) TsFc is the auxiliary thrust required for SFC, defined by the
following formula.
TsK =^Smul {(1 +k)(C,om - Cms) - ACp} (3)
Subscripts m and s represent the values of model and full-scale ships, respectively, p, S, and u stand for the density of water, the wetted surface area, and the longitudinal component of ship speed, respectively, k stands for the form factor. Cpo and ACp stand for the friction resistance coefficient of a corresponding plate and the roughness allowance, respectively. Cpo is a function of Reynolds number, Rn (Saunders et al., 1957) and ACp a function of a full-scale ship length (ITTC performance committee, 1978). TSFC is, therefore, a function of the longitudinal ship speed and full-scale ship length.
SFC makes the propeller rate at SSPP. Note that SFC, in spite of its literature, never corrects the skin friction but makes the model ship propeller load equal to the full-scale ship, where the propeller rate is at SSPP. The following equation defines the propeller load r.
M. Ueno et al. / Ocean Engineering 92 (20U) 267-284 269
According to the basic idea of malting the ruder normal force of model ships similar to full-scale ones using the auxiliary thruster, the authors introduce REC factor, /REC, defined as follows.
ƒ REC = JT, (5)
Fjv' Stands for the non-dimensional rudder normal force defined, for example using the ship length, L, draft, d, and ship speed, V, as follows.
(6) (p/2)LdV^
/REC is the factor to define the auxiliary thrust realizing the
similarity of rudder normal force.
2.3. Approximation of/REC
Let us look into how the structure of rudder normal force is. One o f modular mathematical model (Kose et al„ 1981) describes the rudder normal force as follows.
--^Ma^l Sin an (7)
AR, fa and p stand for the rudder area, the l i f t coefficient slope, and the density of water, respectively. UR and OR represent the effective inflow velocity and the effective inflow angle to rudder, respec-tively. The longitudinal and lateral components of effective inflow velocity to rudder, UR and VR, define them as follows.
(8)
aR = ö-tan' (9)
S i n Eq. (9) is a rudder angle.
Following equations (Kose et a l , 1981) elaborate UR and VR.
UR = e(1-w)U:
= e ( l -w)u n 1 + K L 1
( l - w ) ^ 1 + ( 1 - 1 1 ) (10) (11) VR = VRp-rR(v+rlR)
u and 1 -w stand for the longitudinal ship speed and the wake coefficient at propeller position, respectively. KT is the thrust coefflcient, one of the propeller open characteristics, defined as follows.
as follows.
^ = / < p S (14) UR
kp is a constant and s stands for the propeller slip ratio defined as
follows. s = l -( l - w ) u
nP
(15) P is a propeller pitch.
It is obvious that the scale effect of UR is mainly due to r and 1 - w, assuming the insignificant scale effect of e and K. VRP should have the scale effect because of a function of the propeller slip ratio, but the effect is trivial in nature. Suppose the scale effect of YR and IR are small, though they are not clearly known, then the scale effect on VR is indirect through the resultant ship motion represented by v and r.
Although Fjv consists of a lot of parameters as shown i n Eqs. (7) (through 15), is considered a function of UR and VR. Comparing UR and I^R, quantitatively, UR dominates VR since UR represents mostly the velocity of propeller race. Therefore, the above discussion allows us to approximate the REC factor, instead of Eq. (5), by the following equation.
/ R E c = / r / i k = Hs (16)
Note that although a concrete figure o f / R E C needs a mathema-tical model of rudder normal force, the idea o f / R E C itself does not rely on a specific mathematical model as long as the model embodies the basic idea of REC. Then, any one of other rational mathematical models, such as presented by Yoshimura and Nomoto (1978) or Hirano (1980) for example, can replace Eqs. (7) (through 11), and Eq. (15).
2.4. /REC i'i steady straight running
/REC i n a steady straight running defines the auxiliary thrust i n
that condition and corresponding propeller rate that is to be kept constant through the free-running test. Since v is negligible and r is zero in steady straight running, Eq. (16) is a good approximate of the original definition, Eq. (5).
Let us examine what characteristics/REC has by calculating/REC of a container ship, KCS (Stern and Agdrup, 2008), and a tanker, KVLCCl (Stern and Agdrup, 2008). Figs. 1 and 2 are the body plans and profiles. Table 1 lists the principal dimensions and coefficients needed for calculation for /REC. Model scale and length between perpendiculars of the container ship are 1/75.5 and 3.046 m, and
K7 =
pn^D"
(12)
D and n stand for the propeller diameter and rate, respectively. KT is a function of the propeller advance ratio/, defined as follows.
J = ( l - w ) u
nD
(13)
In Eq. (10), 1) is the ratio of propeller diameter to the rudder height, a geometrical parameter e is the ratio o f wake coefficient at the rudder position to that at the propeller position, K is the coefficient concerning velocity increase ratio of propeller race. In Eq. (11), V and r are the lateral ship speed and yaw rate. YR stands for the flow straightening coefficient. IR stands for the hydrodynamic lever representing the yaw rate effect on lateral inflow velocity to rudder. VRP stands for a component of lateral inflow velocity to rudder induced by the propeller revolution i n straight running. Kose et al. (1981) assumed the ratio of VRP to UR
Fig. 1. Body plan and profile of container ship.
270 M. Ueno et al. / Ocean Engineering 92 (20M) 267-284 Table 1
Principal dimensions and coefficients of container ship and tanker in model and full scales.
Item
Container ship Tanker
Item Full-scale Model Full-scale Model
Scale ratio 1 1/75.5 1 1/110.0
Length between p'.s, L (m) 230.00 3.046 320.00 2.909
Breadth (m) 32.20 0.426 58.00 0.527
Draft, d (m) 10.80 0.143 20.80 0.189
Propeller diameter, D (m) 7.90 0.105 9.86 0.090
Propeller pitch ratio, PjD 0.997 0.997 0.721 0.721
Rudder height (m) 9.90 0.131 15.81 0.144
Rudder movable area, An (m^) 45.28 0.007943 112.26 0.009278
Wetted surface area, S (m^) 9645 1.692 27320 2.258
Metacentric height, GM (m) 1.28 0.017 12.10 0.110
Design speed, Vo (knot) 24.0 2.762 15.5 1.478
Design speed, VQ (m/s) 12.35 1.421 7.97 0.760
Froude number, F„, (Design) 0.260 0.260 0.142 0.142
Reynolds number, R„, (Design) 2.39E-H09 3.80E+06 2.15E-(-09 1.94E-(-05
Form factor, 1 + k 1.100 1.100 1.185 1.185
C. plate friction resist, coeff., Cpo 1.38E-03 3.58E-03 1.40E-03 4.08E-03
Cw -Fn curve Oth coeff., Ccwo 0.0039 0.0039 -0.0015 -0.0015
Cvv -Fn curve 1st coeff., Covi -0.1109 -0.1109 0.0550 0.0550
Cw -F„ curve 2nd coeff., Ccw2 1.1438 1.1438 -0.7373 -0.7373
Cw -Fn curve 3rd coeff., Ccw3 -4.9802 -4.9802 4.3380 4.3380
Cw -Fn curve 4th coeff., Ccw4 78310 78310 -9.2452 -9.2452
Wave making resist, coeff., Cw 6.40E-04 6.40E-04 1.06E-04 1.06E-04
Roughness allowance, ACp 2.71 E-04 0 1.76E-04 0
Total resistance coeff., Cj 2.43E-03 4.57E-03 1.40E-03 4.94E-03
Wake coefficient, 1 - w 0.704 0.645 0.708 0.594
Thrust deduction coefficient, l - t 0.793 0.793 0.818 0.818
Wake coefficient ratio, e 0.956 0.956 0.999 0.999
Prop, race factor, K 0.633 0.633 0.562 0.562
Kr -J curve Oth coefL Ciao 0.5375 0.5387 0.2935 0.293
KT -J curve 1st coeff. -0.4666 -0.4666 -0.2748 -0.2748
KT -J curve 2nd coeff. CKT: -0.0408 -0.0408 -0.1389 -0.1389
those of the tanker are 1/110.0 and 2.909 m, respectively. 1 -i-k and wave maldng resistance coefficient Cw, both assumed to have no scale effect, for the container ship are f r o m Kume et al. (2000) and Ukon et al. (2002). Those for the tanker are f r o m Kim et al. (1999) and unpublished tank test data of the National Maritime Research Institute. Polynomial coefficients Ccwo etc. listed i n Table 1 tell Cw as a function of Froude number F„. Cw is a constituent of the total resistance coefficient Cj shown as below.
CT = (1 -f- fe)CFO(i?„) + Cw(F„) + ACp (17)
The roughness allowance ACp is estimated for full-scale ships in accordance w i t h the ITTC procedures (ITTC performance committee, 1978). 1 - w , l - t , e, K, and polynomial coefficients Qnt) etc. of KT as a function o f / are f r o m Yoshimura et al. (2008) for the both model ships. 1 - w and characteristics of KT of full-scale ships are esdmated i n accordance w i t h the ITTC procedures (ITTC performance committee, 1978), while no scale effect is assumed for 1 - 1 , e, and K. Since the scale effect on KT is not significant, the scale effect on 1 - w , Cpo, and resulting CT should have dominant effects o n / R E O
Fig. 3 shows the effect of/TA on UR/U, nj{VjL), T, and s, comparing w i t h those of full scale ships i n steady straight running at designated ship speed. The c o n d i t i o n / M = 0 . 0 represents ordinary free-running model tests w i t h o u t the auxiliary thruster where the propeller operates at MSPP.
UR/U of model ships become equivalent to full-scale ships at
/r/i=0.644 for the container ship and at ƒ « = 0 . 5 6 6 for the tanker, where Eq. (16) defines the/REC values ensuring REC. Resultant/REC of the container ship and the tanker are 0.644 and 0.566, respectively.
njiyjL) of model ships become equal to full-scale ships at larger
value, but still less than 1.0, o f / ^ than / R E C where the similarity of propeller rate of revolution is attained as Fujii (1960) did using the air propeller At this point öf/pA the apparent or hull advance ratio of model ships defined by the following equation are equal to f u l l -scale ships.
T of model ships is identical, as intended, to full-scale ships at /T/I=1.0, where the pfopeller load is equivalent as Kobayashi et al.
(2000) did using the air-jet system and Son et al. (2010) did using the wire-servo system. This point of / T ^ ensures SFC and the propeller operates at SSPP.
s of model ships is equal to full-scale ships at larger value than 1.0. Crane et al. (1989) stated the equality of s is particularly important for the free-running model test to attain using the air propeller. At this point of /r^ the model ship / is equal to the f u l l -scale ship and, therefore, the model ship KT is nearly equal to the full-scale ship since the scale effect of KT is small.
Above discussion reveals the auxiliary thrust necessary for REC is the smallest comparing w i t h the n-equivalent point, the SFC or SSPP point, and s-equivalent point. A l l the methodologies to use auxiliary thruster so far makes the rudder effectiveness of model ships too weak since UR/U of model ships at those points are smaller than full-scale ships. This fact seems to endorse partly the traditional qualitative belief that the faster propeller race and the slower wake flow of model ships would cancel out their scale effects each other, The quantitative discussion above, however, reveals the cancellation is not balanced.
Fig. 4 shows the effect of Fn and scale ratio o n / R E C respectively.
M. Ueno et al. / Ocean Engineering 92 (2014) 267-284 2 7 1
Container ship Tanker (Fn =0.260,i„,/X^=1/75.5) (Fn =0.142, i„,/L^ =1/110.) 1.0
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2 . 0
AA / T A
• M o d e l — = Full-scale
Fig. 3. Effect of auxiliary thrust factor /TA on the longitudinal component of effective inflow velocity to propeller, propeller revolution, propeller load, and propeller slip ratio.
1.0
0.0
Con ainer ihip
LJl : ^ = i / 75:5 0.0 0.2 Fn 0.4 0.0 1.0 0.0 1 ' r • 2oritain< irshiip " 1 ' 1 1 i 1 1 0.260 TaiJcer i i^„=Ö.142 0 100 200 300 0 200 400 Scale ratio, Z j / L m Scale ratio, LsILm
Fig. 4. Effect of Froude number and scale ratio on the rudder effectiveness correction factor/REO
is mainly attributed to the increase of wave-making resistance at higher F„. The effect of scale ratio is almost negligible for wide range of scale models.
2.5. /REC i'n manoeuvring motion
/REC defined in steady straight running does not necessarily
satisfy Eq. (16) i n manoeuvring motion because r and 1 - w , i f not more, i n Eq. (10) varies as manoeuvring motion grows (Kose et al., 1981). Moreover, as v and r grows the approximation of Eq. (16) deteriorates i n principle since VR grows, though the authors believe Eq. (16) is still effective in manoeuvring motion. These are the reasons w h y / R E C should vary during manoeuvring modon. Fulfillment of Eq. (16) i n every time step of manoeuvring motion, however, might require not only the dme varying/REC but also the dme varying n w h i c h should lead a complicated control.
On the other hand, however, the role of TA becomes less important i n manoeuvring modon because TSFC decreases as ti decreases while r increases significantly due to both the decrease of u and the increase of T along w i t h the decrease of / This fact suggests the detailed control of /REC lose its significance i n manoeuvring modon w i t h much decreased speed.
Based on the above discussion and considering the practical applicadon of REC to ordinary free-running model tests w i t h constant n, the authors do not control /REC but hold it a constant value through the whole range of manoeuvring motion.
Note that the basic idea of REC does not take into consideration direcdy the scale effect due to the stall and aeration phenomena of flow around mdder, though the similarity of effective inflow velocity to rudder might compensate for these phenomena to some extent.
3. Tank test
3.1. Test program
The authors carried out a free-running model ship test to confirm what effects REC has i n the model ship manoeuvrability. Table 2
Test program and measurement items of free-running model test.
Item Description
Condition No correction (NC)
Rudder effectiveness correction (REC) Skin friction correction (SFC)
Test Turning
Reversed spiral
Zig-zag (10/10 deg., 20/20 deg.) Measurement Ship position and speed
Yaw (Heading) angle and rate Propeller thrust and revolution Auxiliary thrust and lateral force Rudder angle and rudder normal force Surge, sway, and heave accelerations Roll and pitch angles and rates
Table 3
Specifications of the duct fan type auxiliary thruster.
Item Small Medium Large Note
Duct length (m) 0.047 0.072 0.082
Duct length, overall (m) 0.100 0.125 0.145 Inc. motor Fan diameter (m) 0.055 0.069 0.0792
Duct diameter (m) 0.070 0.090 0.102 External
Blade number 7 5 5
Mass (kg) 0.115 0.190 0.280 Inc. motor Rate of revolution (rps) 617 633 650 Rated max. Thrust(N) 5.10 11.28 19.61 Rated max. Power source (V, DC) 11.1 14.8 22.2
272 M. Ueno et al. / Ocean Engineenng 92 (2014) 267-284
Model ships are the container ship and tanker mentioned i n the previous section of which dimensions are in Table 1. The model ships have studs to stimulate the turbulent flow at S.S. 9.5 and the bulbous bow sections. s
The test site is the Actual Sea Model Basin (Tanizawa et al., 2010) i n the National Maritime Research Institute, Japan. The basin, 80 m long, 40 m wide, and 4.5 m deep, has a carriage system consisting of a main carriage, a sub-carriage suspended f r o m the main carriage, and a turntable on the sub-carriage. The carriage tracks a free-running model ship using a CCD camera and measures a point above the center of gravity and bow direction of a model ship using data of the carriage motion and the camera image analysis combined. Thin cables to supply power and to communicate signals, and four wires to clamp the model ship on acceleration and deceleration connect the model ship to the carriage. They do not interfere w i t h the model ship motion during measurement because they are loosened enough and the carriage tracks the model ship closely enough. Miyazaki et al. (2011) reported the uncertainty analysis of free-running model ship test and Ueno et al. (2013) confirmed high repeatability of the free-running model test at the basin.
Model ship conditions are three, the ordinary free-running model ship test w i t h no correction (NC), that w i t h REC and w i t h SFC as shown i n Table 2. The test program includes turning, reversed spiral, and zig-zag tests. Table 2 also shows the
Duct fan and motor Load cell Load cell amp. Control PC (Tracking carriage) K - 1 a ÜCCCD camera) Motor controller o O
(Free-ruiming model ship)
Fig. 5. Signal path and structure of the duct fan type auxiliary thruster in free-running test using a tracking carriage.
u,x,X
Fig. 7. Coordinate system.
Table 4
Hydrodynamic derivatives of container ship and tanker obtained by captive model tests.
Item Containers. Tanker
-0.0549 -0.035 -0.1084 -0.2166 -0.012 0.0145 -0.0417 0.749 y 0.2252 0.2996 Vr'-m,' 0.0398 0.052 1.7179 1.4537 V>/Ir' -0.4832 0.2132 0.8341 03858 Yrrr' -0.005 0.0143 N/ 0.1111 0.141 Nr' -0.0465 -0.048 Npnil 0.1752 -0.0194 Nm' -0.6168 -0.2767 0.0512 -0.0588 Nrrr' -0.0387 -0.0134 an 0.361 0386 XH' -0.436 -0.425 l - t « 0.742 0.755 k' -0.755 -0.662 kp -0.051 -0.0366 1.0 ^ 0.8 iy 0.6 " j
::2
^ 0.0Contamer ship (Model) + Exp. — A p p r o x . -0.8 -0.4 0 0.4 0.8
Fig. 8. Wake coefficient, 1-w, of container ship model in manoeuvring motion.
A. 1.0 I 0.8 ^ 0.6 I 0.2 ^ 0.0 Tanker(Model) _ + Exp. A p p r o x . -0.8 0.8
Fig. 6. Duct fan type auxiliary thruster with medium size duct fan on tanker model.
-0.4 0 0.4 /9-^pV-'(deg.)
M. Ueno et al. / Ocean Engineering 92 (2014) 267-284 2 7 3 0,3 Q 2 Container s h i p ( M o d e n j JJ; -20 O 20
W(deg.)
40Fig. 10. Lateral component of effective inflow velocity to propeller of container ship model in manoeuvring motion.
-20 0 20 40
Fig. 11. Lateral component of effective inflow velocity to propeller of tanker model in manoeuvring motion.
measurement items. The objective of measuring lateral force of DFAT is only for confirming DFAT not generating unnecessary lateral force but thrust. The propeller revolution was kept con-stant, so the test neglects the engine response to the change of propeller load.
3.2. Auxiliary thruster
The authors, thinking of the achievement of their prototype (Tsukada et al., 2013), assembled a practical DFAT for the tank test. Three duct fans are ready for various types and sizes of model ship, of which specifications are i n Table 3. Fig, 5 illustrates the signal path and structure of the DFAT employed i n a free-running test using a tracking carriage. The load cell on which the duct fan is mounted for measuring the auxiliary thrust is smaller than that of the prototype. The PC calculates the command signal to the duct fan using Eqs. (2) and (3), or w i t h respect to any other rule i f necessary, w i t h feedback data of the measured auxiliary thrust and the longitudinal component of model ship speed.
Since the whole system is compact enough, DFAT is applicable to a free-running test not using a tracking carriage by placing the load cell amplifier and the control PC onboard. In such a case
Container ship (Steady tum)
(Calculation) (Experiment)
I
I P , 0.00 -40 -20 0 20 40-40 -20 0 20 40Rudder angle (deg) Rudder angle (deg.)
Model(NC) Model(NC) Model(REC) - e - Model(REC) Model(SFC) • • • Full-scale Fig. - A - Model(SFC)
12. steady turning characteristics of container ship.
1.0 0.5 0.0 -0.5 -1.0 1.0 0.8 0.6 0.4 0.2 0.0 25
Tanker (Steady tum)
(Calculation) (Experiment) ' • - -l
^ T
-' 1i 11
. i 1. ' r 1 " (''~ r • * - H - r - i 1 ' -1 ' -20 0 20 40-40 Rudder angle (deg)Model(NC) Model(REC) = Model(SFC) • • • Full-scale
Fig. 13. steady turning characteristics of tanker.
mi
-20 0 20 40 Rudder angle (deg.)Model(NC) —e—Model(REC)
274 M. Ueno et al. / Ocean Engineering 92 (2014) 267-284
different means must provide- the onboard PC w i t h data of the longitudinal component of model ship speed.
Fig. 6 is a photograph of the onboard part of auxiliary thruster for the tanker model of which duct fan is the medium size i n Table 3. The container ship model used the large size duct fan because i t runs at higher speed and needs larger auxiliary thrust than the tanker model.
In the model test, are 0.0,/REC, and 1.0 for NC, REC, and SFC conditions, respectively. Corresponding propeller rate of revolu-tions in the tank test are 16.97, 15.13, and 13,97 rps for the container ship, 17.17,14.25, and 11.33 rps for the tanker, both for NC, REC, and SFC conditions, respectively./REC values are 0.644 for the container ship and 0.566 for the tanker.
REC results, w i t h the numerical simulation for the full-scale ship and to see to what extent the model test w i t h REC approximates the full-scale ship performance since no full-scale ship data are available.
4.1. Mathematical model
Fig. 7 is a coordinate system i n which the origin is located on the intersection of midship section and center plane. The equa-tions of motion (Kose et al., 1981; Yoshimura et al., 2008) for the numerical simulation are as follows.
4. Numerical simulation
The basic objectives of numerical simulation are to confirm whether or not the model test results are reasonable, and whether or not the mathematical model is effective to estimate the test results. So the numerical simulations are for NC, REC, and SFC conditions, corresponding to the model test conditions. The primary objective is to compare the model test results, especially
• m(u-vr) = X m ( v + u r ) = y Izzi-^N-XcY
(18)
Dots above variables represent the time derivatives, m and stand for the mass and the moment of inertia of a ship. X, Y, and N stand for the longitudinal and lateral forces, and yaw moment, respectively. XG is the longitudinal coordinate of center of gravity.
, , . Container ship (Steady tum)
(Calculation) (Experiment) in" Ö 0.004 0.000 1 L ) j -- 2 -- 1 0 1 2 3 Rudder angle (deg) Model(NC) Model(REC) Model(SFC) • • • Full-scale
- 2 - 1 0 1 2 3 Rudder angle (deg.) -•K- ModelCNC) -e—Model(REC) Model(SFC)
I
I
Ö ^ ^ (Calculation)Tanker (Steady tum)
(Experiment) -0.3 1.0 0.9 0.8 0.7 0.6 10 5 0 -5 -10 0,010 0.005 0.000 -0.005 -0.010 0.04 0.03 0.02 0.01 0.00 0.02 0.01 0.00 1
L w
1 , 1L w
ir ! M i 1 1 5< \_ ' ' I i ' ' I - 4 - 2 0 2 Rudder angle (deg)Model(NC) =—Model(REC)
Model(SFC) • • • Full-scale
4 -6 -4 -2 0 2 4 6 Rudder angle (deg.) - ^ - Model(NC)
-Model(REC) Model(SFC)
Fig. 14. Steady turning characteristics of container ship (Small rudder angle region enlarged).
Fig. 15. Steady turning characteristics of tanker (Small rudder angle region enlarged).
JM, Ueno et al. / Ocean Engineering 92 (2014) 267-284 275 X, y, and N are written as follows.
' X=-m,ü +Xo(u) +XppP^ + (Xflr-my)pr +Xrrr^+Xp/!pp^+pD'^n^(1-t)KT+TA-(1--tR)FNsin5 Y=-myV+Yp/]+(Yr-m,)r+YpppP\
+ YpürP'r+YprrPr-^ + Ym-r'' - (1 + aH)FNCos5
N = - J J + Npfi + Nrr + Npppfi^+NpprP^r + NprrPr^ + Nrar^ -{XR + aHXH)Fi^cos5
(19)
Note that X includes TA. For model ship simulations, Eq. (2) defines TA where fjA is 0.0,/REC, or 1.0 corresponding to model ship conditions. For full-scale ship simulation TA is zero though the scale effects are taken into consideration for other derivatives, rrix, iriy, and Jzz stand for the longitudinal and lateral added masses and the added moment of inertia of a ship, respectively. XR is the longitudinal coordinate of rudder Eqs. (7) (through 15) represent
FN i n Eq. (19). /? is the d r i f t angle defined as follows.
^ = s m - ' ( - ^ ) (20)
I
SB1
(Calculation) Container ship ( S T B 3 5 ° h m i ) (Experiment) — — fc51
— -- Y/ ^ - — — -"1' 1 * . \ V — — — t j1
1ÏÏ
1 1ÏÏ
1J1
/ / 1 11
-1 180 90 0 -90 -180 1.0 0.5 4 YIL 5-1 3 4 7/X 5 5444-1 ( 5444-1 5444-1 ' "1 " 1 \ " \ \ 1 i i M i l l ; 1 I 1 " 1 r 1 i J _ J. - i J L M i IU M i l l -1 .J._I_L-I i l l ' : : p j L j , . " i _ j ' 1 I 1 1 1 1 i: : r F F i -I -I -I 0.0 20 15 10 5 0 -5 0.10 1 r ' 1 r 1 ^ / ~ 1 1 L I • 1 LJ _ 1 1 1 . I_J-:J„_ _ 1 1 1 1 1 1 r 1 1 1 r ' 1 r 1 ^ / ~ 1 1 L I • " i _ t i r " 1 ' _J J . J L -0__LL_-
1 , 1 _ _ 1 r ' 1 r 1 ^ / ~ 1 1 L I • Zl.- L-U -\ '\ 1-- i -r >_|
-1-
—-
--
1 1 ' 1 . _ L 1 1 11
1 1 T ' T 1 "1" 1 1 1 1 " \ ' \ ' \-1 -1 -1
: - ] ^
1
1-
1
1 , 1 1 -1 11
1
L i ?T
I."\ 1
1 1 1
: - ] ^
1
1-1
-1 11
r
1
J i1
1 1-~n~
11
n
1
-/ I1 1 1
1
1
r
1
J i1
1 1-~n~
11
n
1
-1
11
i
1 11
11
1
11
1
11
.J_-L-J _L. _ I _ L I _ l_ 11-.Il „ L i .l_L. 1 1 1 !_" , I !
1 1 1 i -_2!ii„.f-j_ 0 5 10 l5t(Vo/L) 0 5 10 15<()?o/i) — - M o d e l ( N C ) Model(REC) Model(SFC) • • • F u l l - s c a l e2 7 6 M. Ueno et al. / Ocean Engineering 92 (2014) 267-284
Xo, being equal to -RT in Eq. (1), stands for the resistance,
written as follows.
Xo = - | S U 2 C T (21)
CT is defined by Eq. (17) and, then, Xo is a function of u.
Other coefficients i n Eq. (19) not mentioned above are hydro-dynamic derivatives and interaction coefficients treated i n the following subsection.
4.2. Hydrodynamic derivatives
Table 4 lists the hydrodynamic derivatives and interaction coefficients obtained by the captive model test carried out at MSPP (Yoshimura et al., 2008; Ueno et al., 2009).
The effects of manoeuvring motion, and r', on 1 - w of the model ships are as shown in Figs. 8 and 9 where Xp is non-dimensional x-coordinate, XpjL, and f is non-non-dimensional yaw rate defined by the following equation.
(22)
The numerical simulation takes into account the effects of manoeuvring motion on 1 - w and Vn by approximating data by lines i n Figs. 8 and 9. The same procedure (ITTC performance committee, 1978) as i n the steady straight running estimates 1 - w of the full-scale ships in manoeuvring motion, which means multiplying the same ratios as in the steady straight running to obtain the full-scale values in manoeuvring motion.
(Calculation) Tanker ( S T B 3 5 ° h i m )
i
L l .
i1 /
, \ [ <• ^1 _
> i \
^ i
L - -1
i j r• 1
\ V \ ^ ;r
t 11
1 -1 0 3 YJLA 180 7 L I _ L T 1.0 1 ^ 0.5 0.0 1.2 0.8 ^ 0.4 0.0 20 ê 10 ^ 0C
0-15 ^ 0.10 in 0.05 0.00 I I I ) 1 "1 ! 1 ! " i " —1"
i 1 1 - H - h h--
,_-
. J 1-
, . j , m i - I i l l -_J_. 1 " 1 AJ 1 1 J i l l 1 1 1 1 M 11
1 1 1 1 i r r r r 1 1_
1
J " M l - l J - . 1 1 1 J J J n _iTrr
M T I1
n
1 r r 1 M M 1 1i j f i l
11 rim M M M 1 1i j f i l
1 ! L 1 1 \'\'\ r _ U _ L L 1 1 1 _ L J f i ! 1 1 1 1 1 1 L 1 1 \'\'\ r _ U _ L L 1 1 1 _ L / " ! 1 ! 1 1 : 1 I I I ! 1 ( 11 i
1 1 i 1 (Experiment)1
1 , _ 1
s i J 1 It1 ^
\
1 \ > 1 \_ i
1 1 1 . 1 '~ 1/ if
INI
' // /1 '
f - ! -1 0 3 YIL 4 -!f(Y;aw) . M i l ! : j M - ! . . I t _ M . . M . 7 M^ _ ( i g a l l e r ) r r 1 ! 1 i 1 1 L* — • — • — » ^ \ „ 1 i 1 1 -- 1 LJ-^1 ; _i 1 „ 1 i 1 1 -at • ••••»>•• 1 ~ 1 1fi
r L.L j 1 1 1 - 1 1 tT e l : -
' 1 1i
1- 1 ¬!
r 1 1 1 ' T i l l 1 I 1 1 M M _ . M M 1 . 1 M J . 1 1 1 1 M M " M M" r r i T
_ M J _ L . J J . J _ . L 1!i_r
M M- i | ' ' T
_ M J _ L . J J . J _ . L 1!i_r
M Mli
M - - 1 r r i -M -M 1 M M M 1 1 ^ v r r r " M M M M M M ^ -M M I I I IH +
1 1 1 _ y \ i ! ! 1 1 ! 1 1 1 J I M ' 1 1 1 1 i > 1 0 5 1015
^(^7^)
0 5 10 IS t{VolL)- — M o d e l ( N C ) Model(REC) Model(SFC) • • • Full-scale Fig. 17. Trajectory and time iiistory of starboard 35° turning of tanker.
M, üeno et al. / Ocean Engineering 92 (2014) 267-284 211
Although the generai expression of VR is Eq. (11), the numerical simulation takes into account the effects of manoeuvring motion as shown i n the lines approximating VR/V data i n Figs. 1 0 and 11. No scale effect is taken into consideration on VR/V.
The scale effect on XQ is due to Cpo and ACp, functions of Reynolds number and ship length, respectively.
Propeller rate of revolutions i n the numerical simulations are 1 6 . 9 7 , 1 5 . 0 8 , and 13.88 rps for the container ship, 17.33,14.66, and
12.14 rps for the tanker, both for NC, REC, and SFC conditions,
respectively. Propeller rate of revolutions of full-scale ships are estimated as 1.655 and 1.235 rps for the container ship and tanker, respectively.
Note that the captive model test of the container ship was carried out at 1.100 m/s and MSPP, while the free-running model test and corresponding numerical simulation are at 1.421 m/s. Another difference for the container ship model is the metacentric height, GM; in the roll-free captive model test GM was 0.097 m while here i n the free-running test 0.017 m, shown in Table 1, though the numerical simulation does not take into account the roll motion. The captive test for the tanker model was also at MSPP. The model ship speed and GM of the tanker model are same i n the captive and free-running model tests. However, the tanker model including the model propeller used i n the captive model test and those i n the free-running model test are not identical. Although their scale and specification including the propeller diameter, pitch, blade number, expanded area, etc. are same, only their manufac-turers are different. This difference might result i n the recognizable
Container ship (Calculation) (Experiment) 0
I
~a3I
~i512.0
8.0
4.0
0.0
• P O R T 3 5 ° t a m • S T B 3 5 ° h t mFig. 18. Advance and Tactical diameter and time to those points of container ship.
difference of propeller rate of revolution between the numerical simulation and the experiment of the tanker model. These differ-ences mentioned above might be sources of uncertainty for the comparison of numerical simulation and the free-running model test. The authors, however, consider the differences are not crucial and cannot prevent the discussion on the numerical simulation and the tank test data from the viewpoint of the validation of REC.
5. Discussion on REC
5.J. Steady turning ciiaracteristics
Figs. 1 2 and 13 are non-dimensional yaw rate, f , speed ratio, VjVo, d r i f t angle, dimensional rudder normal force, F^', non-dimensional propeller thrust and auxiliary thrust of DFAT, T and TA i n steady turning of the container ship and tanker, respectively. T and T / are defined as follows.
T,r^ ( 2 3 )
(p/2)LdV'
Numerical simulations seem to explain the experimental results well for the both container ship and tanker. The difference among NC, REC, and SFC is not significant both in the calculation and the tank test except V/VQ, T and TA'. The difference o f r and T /
8 i
Tanker
(Calculation) (Experiment)
4.0
3.0
2.0
1.0
0.0
mm
fi
• PORT35°tum • STB35° tum
Fig. 19. Advance and Tactical diameter and time to those points of tanker.278 M. Ueno et al. / Ocean Engineering 92 (2014) 267-284
among three model ship conditions are designated ones. V/Vo is largest i n SFC and smallest in NC. The difference is more recogniz-able for the tanker than the container ship. Full-scale ship speed decrease is around between REC and SFC.
Although the difference among NC, REC, and SFC is not clear in Figs. 12 and 13, i t becomes significant when these figures are looked into closely. Figs. 14 and 15 are enlarged figures of Figs. 12 and 13 for the small rudder angle range. The experimental data indicate clearly, for the both ships, the unsteady loops become wider i n the order of NC, REC, and SFC. The difference o f v a l u e and corresponding UR/U for the three conditions as shown in Fig. 3 tells these are due to the difference of rudder effectiveness.
As mentioned i n 2.4, the role of becomes less important in large manoeuvring motion region as shown i n Figs. 12 and 13. On the other hand, the magnified Figs. 14 and 15 for small rudder angle range corroborate the importance of TA control around steady straight running condition. The discrepancy between the numerical simulation and the experiment of tanker might be attributed to the reason mentioned in 4.2.
The numerical simulations of tanker explain well the experi-mental data as long as qualitative point of view. The Full-scale ship numerical simulation is close to that of REC. However, the numerical simulation of the container ship does not show distinct unsteady loop while the experiment shows. This discrepancy is mainly attributed to the difference of GIVI between captive model test for the hydrodynamic derivatives and the free-running test, mentioned in 4.2. Miyazaki et al. (2013) indicated the smaller GM is the more unstable the directional stability tends to. Hydrody-namic derivatives in Table 4 might not be suitable enough for simulating the experimental smaller GM condition.
5.2. 35° turning
Figs. 16 and 17 show trajectories and time histories of starboard (STB) 35° turn of the container ship and the tanker, respectively. Both the numerical simulation and experiment indicate distinct differences among NC, REC, and SFC conditions. Although some quantitative discrepancies are, the numerical simulations agree
Table 5
IMO manoeuvrability indices of container ship. Container ship Calculation
IVlodel (NC) Model (REC) Model (SFC) Full-scale Experiment Model (NC) Model (REC) Model (SFC) Advance (L) in 35° turn PORT 3.17 STB 3.27 Tactical diameter (L) In 35° turn
PORT 3.25 STB 3.42 Ini. turn, ability (i) in 10°/10°Z
PORT 1.64 STB 1.67 1st ov. angle (deg.) in 10°/10°2
PORT 7.7 STB 6.9 2nd ov. angle (deg.) in 10°/10°Z
PORT 9.3 STB 12.3 1st ov. angle (deg.) in 20°/20°Z
PORT 15.9 STB 13.5 3.39 3.50 3.49 3.67 1.78 1.81 8.0 6.6 10.8 13.1 16.0 14.5 3.54 3.65 3.66 3.86 1.88 1.91 8.2 7.4 11.5 14.6 16.2 14.5 3.40 3.51 3.51 3.70 1.78 1.81 8.1 6.6 10.3 13.5 16.8 14.3 3.06 3.12 3.06 3.05 1.67 1.58 9.6 9.5 13.5 15.0 16.2 15.4 3.16 3.32 3.28 3.28 1.7S 1.70 10.9 10.3 15.5 17.5 16.1 15.4 3.37 3.32 3.37 3.54 1.85 1.79 13.2 11.7 16.4 20.8 16.8 15.6 Table 6
IMO manoeuvrability indices of tanker.
Tanker Calculation Experiment
Model Model Model Full-scale Model Model Model
(NC) (REC) (SFC) (NC) (REC) (SFC)
Advance (L) in 35° turn
PORT 3.00 3.27 3.56 3.29 2.78 2.98 3.17
STB 3.10 3.39 3.70 3.41 2.86 3.07 3.45
Tactical diameter (L) in 35° turn
PORT 2.96 3.23 3.53 3.31 2.90 3.02 3.35
STB 3.09 3.39 3.70 3.46 3.06 3.37 3.59
Ini. turn, ability (L) in 10°/10°Z
PORT 1.62 1.80 2.01 1.80 1.83 2.05 2.29
STB 1.68 1.86 2.07 1.87 1.77 2.04 2.31
1st ov angle (deg.) in 10°/10''Z
PORT 9.7 11.5 14.8 11.4 8.6 11.6 25.9
STB 6.7 7.9 9.8 8.1 7.9 9.9 14.8
2nd ov. angle (deg.) in 10°/10°Z
PORT 12.1 15.5 21.8 16.1 14.1 17.3
-STB 19.6 26.8 38.8 27.6 17.1 26.1 39.8
1st ov. angle (deg.) in 20°/20°Z
PORT 16.9 19.1 23.1 19.8 13.2 14.4 17.3
(Calculation)
M. Ueno et al. / Ocean Engineering 92 (2014) 267-284
Container ship ( S T B 1 0 7 1 0 ° Z ) (E^p.^ment)
279 t5 10 X/L 20 0 -20 -40 0.4 0.2 0.0 -0.2 -0.4 1.2 0.8 0.4 ^•^ *« 1 ZD— ! 1 t v r , J _ 1 . 1 " J5(S.U d d e r ) _ a w ) . z r i - 1 1
^ i
én
! 1 ! \ 1 1 ' 1 H i r T 1 ' 1" 1 1 " 1 i 1 L _ ' 1 J 1 1 1 - _ i \ ' '"^1 _ , l _ -1 A-1 1 1 r 1 1—I J , — 1 1 1 1 1 1' — 1 1 1 1 1 1 ---— — — " ] -1 1 1 — — inJ
in 0.00 0.02 0.04 0.02 + 1r s
1' 1
1 . 1 . L _ 1 ; L J ' r \ -1 " "1 " L -1 1 n -j 1 - - l i - . - - . . j . — I » * •v
i
i
>«!•-• 0.00 0.01 - £ 2 3 = : ^ 0.00 1 1 •1
1
i
1 , ' ' ' 7 % =i
1i
11
-'
\ \ 1 l_r
/ r
L L L 1 L t iT / 1 .— r 1 " L T 1 j _ -, —1
0 2 4 6 8 K' V i ) 12 0 2 4 6 8 /(Fo/I,)12— M o d e l ( N C ) Model(REC) Model(SFC) • • • Full-scale Fig. 20. Trajectory and time iiistory of starboard 10710° zig-zag manoeuvre of container ship.
well w i t h the experimental data. The ship motion and F^' of f u l l -scale ships' simulation agree w i t h those of model ship simulation w i t h REC, which supports the idea of REC. On the other hand, the full-scale simulations of T shows intermediate value between REC and SFC. The reason w h y the full-scale simulation of T does not agree w i t h those of SFC is the difference of wake coefficient between full-scale and model ships i n large manoeuvring motion which leads to different propeller operating conditions.
Figs. 18 and 19 are non-dimensional advance and tactical diameter, and non-dimensional times to reach the points of advance and tactical diameter of both STB and port (PORT) 35° turn, comparing the experimental data w i t h the numerical simu-lation. Non-dimensional values represent the ratio to L for length and to LjVo for time. The values of advance and tactical diameter in Figs. 18 and 19, IMO manoeuvring indices (IMO, 2002), are in Tables 5 and 6. Qualitative and quantitative difference between the container ship and tanker are not significant. As the rudder
effectiveness decrease or JTA increases, the advance and tactical diameter increase and the times to these points become longer, which both the numerical simulation and the experiment support. The numerical simulations correspond w e l l to the experimental data as a whole including asymmetry of port and starboard turnings. The full-scale ship numerical simulations are close to REC numerical simulations for both the container ship and tanker.
5.3. Zig-zag manoeuvre
Figs. 20 and 21 show trajectories and time histories of STB 10°/ 10° zig-zag manoeuvre of the container ship and the tanker, respectively. As seen i n STB 35° turn, both the numerical simula-tion and experiment correspond well and show distinct differ-ences among NC, REC, and SFC. The non-dimensional times to check yaw are among significant differences. The differences among the three conditions are larger in the tanker than i n the
2 8 0 M. Ueno et al. / Ocean Engineenng 92 (2014) 267-284 S i 60 6 0 >n
I
(Calculation) Tanker ( S T B 1 0 7 1 0 ° Z ) (Experiment) -30 -60 0.4 0.2 0.0 -0.2 -0.4 1.2 0.8 0.4 0.0 15 O -15 0.03 0.00 -0.03 0.04 ^ 1 ;-|— 1 1 • 'fii i • 1 « g i g — 1 ' % deler): i < X T 1" 1 1 1--K-
— i "'i' - — U U -1 -1 I ZEZ • 4 - _L-U.L 1 1 1 1 1 1 j j j „.r
1 1 _ L i -1 -1 i " *rrr
1 1 1 T i f— 1 1 1 1 1 _ L i-
1 1 1 1 1 1 T 1 1 1 1 1 r l-.l-L 1 ! 1 LJ L 1 1 !u
n —-
1
1 1 1 ' T T 1 1 "1 i 1 1- JJ.
-
zr
1.1
_L_L._ l l
L .
1 [ L ' f-^^^
1.r
-14-
1 1--
fl "
i-1
1-
. . L L - j 1 . 1 L 1 ll' c i r ^ i — -1*-1 *-1 T 1 1 ' 1 TTJ. 'i I
1X1
I T
0.02 - f - l 0.00 0.02 0.00 1 1. 1
1 T1
i .- t -
0 » > 41
1
' " * r l - t l . , L —...
-• " i " 1 { t ^ : . .
r T T T
' T
" i "
. l i i J - L L _ L L.
•-]---; —-
.-!-!-1 .-!-!-1 1 i 1i
1 1 1 O 4 8 12 tiVo/L) 0 4 8 — M o d e l ( N C ) Model(REC) Model(SFC) 12 t(VJL) • Full-scale Fig. 21. Trajectory and time iiistory of starboard 10710° zig-zag manoeuvre tanker.container ship, of which reason is the tanl<:er is more directionally unstable than the container ship. The simulations of REC agree well w i t h the full-scale simulations except the propeller thrust. The full-scale simulation of propeller thrust agrees well w i t h that of SFC, of which extent is better i n STB 10°/10° zig-zag manoeuvre than in 35° turn because the manoeuvring motion is smaller i n STB 10°/10° zig-zag manoeuvre.
Figs. 22 and 23, trajectories and time histories of STB 20°/20° zig-zag manoeuvre also confirm the qualitative agreement of the numerical simulation w i t h the experiment and also of the f u l l -scale simulations w i t h REC simulations other than of T. Compar-isons of PORT 10°/10° and PORT 20°/20° zig-zag manoeuvres, though omitted i n this report, support the same discussion.
Some discrepancies between the numerical simulations and the experiment are attributed to the facts as follows; the hydrodynamic
derivatives obtained in different ship speed and different GM for the container ship, 1 - w and l - t obtained only at MSPP for the both ships, and the model ship and model propeller are not identical to those used in the captive model tests for the hydrodynamic derivatives. Figs. 24 and 25 show the first and second overshoot angles, !Foai and !Foa2. and non-dimensional first and second time to check yaw, TuKLjVol and TL2KLIV0) o f t h e container ship and the tanker, respectively, including both STB and PORT, and both 10°/ 10° and 20°/20° zig-zag manoeuvres. Fig. 26 defines !Foai, foa2, Tn, and TL2. Although i t might be more reasonable or consistent to define f o a i and lPoa2 measured f r o m the yaw angle at the beginning of Tu and TL2, respectively, the authors follow here the convention of the IMO standards for ship manoeuvrability (IMO, 2002). The tank size limitation did not allow to measure 'Foa2 and TL2 of PORT 10°/10° zig-zag manoeuvre of the tanker
M. Ueno et al. / Ocean Engineering 92 (2014) 267-284 281 Sl ö in (Calculation) Contamer ship ( S T B 2 0 7 2 0 ° Z ) (Experiment) CD Q 0 50 -0.5 1 0.0-8 X/L I - J ':$ (Rudder)
.0.5 r-'-:-^
1.2 h _ 1 1 1 L 1 '1
( • " 1 j 1 l _ ' ; . T • ! r ' I 1 faw) t _ | . _ : —\zz. M ^ / - j . . — 1 — 1 . . . 1 ; -- aiSdêf 1 H- d IL^ 1 ^—- 1 1 -" 1 0.4 0.0 15 O -15 0.04 0.00 -0.04 0.06 0.04 0.02 0.00 0.02 0.00 1 - .1- - 1 1 " 1 1 ' ] . . . . 1 ! ! 1 " 1 " i ' 1 " \ r1
j — 1 f 1 ' ] 1 J 1 1 1 1 f 1 ' ] 1 1 1 1 1)
t - . -1 — "1 1 " 1 1 i 1 1 \ " i 1 1 L L..- X -
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rs J 1 1 1 - i d'ïir
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1
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0 2 4 6 8 t{y^L)\l 0 2 4 6 8 t{y,jL)\l Model(NC) Model(REC) Model(SFC) • • • Full-scale Fig. 22. Trajectory and time history of starboard 20720° zig-zag manoeuvre of container ship.model. Figs. 26 and 27 show the initial turning ability (IMO, 2002) for the container ship and tanker, respectively, where the unit is the ship length L. The initial turning ability is the track length a ship traveled i n 10°/10° zig-zag manoeuvre from the initial steering to the time the heading has changed by 10° from the original heading. The values of f o a i and ¥'oa2 of 10°/10° zig-zag manoeuvre, !Poai of 20°/20° zig-zag manoeuvre, and the initial turning ability, IMO manoeuvring indices, are in Tables 5 and 6.
Ifoai, ! f o a 2 , Tn, Tu, and the initial Uiming ability grow as/M grows
for the bodi ships, which imply the directional instability increase as / M increase, same tendency shown in the steady turning
character-istics mentioned in 5.1. The numerical simulations seem to explain well the characteristics obtained by the experiment such as depen-dency of the rudder angle and its polarity, though some quantitative discrepancies are seen especially in Tn and la of both the container ship and tanker. Full-scale ship numerical simulations are again close
to REC numerical simulations. Although, the REC numerical simula-tions do not necessarily quantitatively correspond to the experimental data well, this fact does not imply the idea of REC is not suitable to realize full-scale-equivalent manoeuvring motion using scale models. Since same land of discrepancies are seen in NC and SFC the discrepancy in REC between the simulation and experiment is mainly attributed to the matiiematical model, hydrodynamic derivatives and coefficients used in the numerical simulation. Therefore, REC experi-ment seems to represent the full-scale-equivalent manoeuvring motion most.
6. Conclusions =
The authors proposed the idea of rudder effectiveness correc-tion, REC, to realize the full-scale equivalent manoeuvring motion
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(Calculation)
M. Ueno et al. / Ocean Engineering 92 (2014) 267-284 Tanker ( S T B 2 0 7 2 0 ° Z ) (Experiment) 1
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1 — i - . 1 _ 1 L . , " 1 1 i * 1 - • _ i * - l t n -— i - . 1 _ 1 L . , " 1 1 i * 1 - • 1 1 " 1 1 1 1 1 1 1 1 { 1 1 1 1 — 1 1 1 1 S"S \1 2 t . t b r " | T " V 1 1 ^ A- j j -1—; ^ 1 ! ! ! . ! 1 ' 1 1 1 1 < < 1 1 —\—!—!— t 1 i O 4 8 12 t{V^L) O 4 8 12 tiy^lD, Model(NC) Model(REC) Model(SFC) • • • Full-scale Fig. 23. Trajectory and time Iiistory of starboard 20720° zig-zag manoeuvre tankerusing free-running scale models. REC aims to make the rudder normal force of a model ship similar to a corresponding full-scale ship approximately using an auxiliary thruster The authors' intro-duced REC factor, /RHC, representing the ratio of the aiutiliary thrust for REC and the thrust required for the skin friction correction.
The calculation using a modular mathematical model clarified characteristics of/REC of the container ship and the tanker models by assuming the similarity of the longitudinal component of effective inflow velocity to rudder to approximate the similarity of rudder normal force. The calculation also clarified n of the model ships w i t h REC is not at MSPP, SSPP, the point of equivalent ] , nor the point of equivalent / H to the full-scale ships Fig. 28.
The authors assembled the duct fan type auxiliary thruster, DFAT, based on their former prototype. The free-running model
test using the scale models of the container ship and the tanker w i t h DFAT examined the idea of REC, where n and /REC are assumed constant. The numerical simulations using modular mathematical model taking into consideration the effects of auxiliary thrust confirmed the tank test data.
Comparisons of the tank test data of the model ships w i t h REC, theoretical calculation for the model ships w i t h REC, and theore-tical calculation for corresponding full-scale ships clarified h o w well REC works to compensate for the scale effect on manoeuvr-ability. Although the application of REC w i t h constant n and /REC is quite simple, these comparisons confirmed that, f r o m a practical point of view, REC using DFAT is a promising way to realize the full-scale equivalent manoeuvring motion using free-running scale models.
!["Un papiro aramaico da El Hibeh del Museo Archeologico di Firenze", Edda Bresciani, "Aegyptus", 39, 1959, fasc. 1-2 : [recenzja]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)