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A New Method For Resistance and Propulsion Prediction of Ship Performance in Shallow Water
Practical Design of Ships and Other Floating Structures You-Sheng Wu, Wei-ChengCui and Guo-Jun Zhou (Eds) 9 2001 Elsevier Science Ltd. All rights reserved
509
A NEW METHOD FOR RESISTANCE AND PROPULSION PREDICTION OF SHIP PERFORMANCE IN SHALLOW WATER T. Jiang European Development Centre for Inland and Coastal Navigation D-47057 Duisburg, Germany
ABSTRACT To improve the resistance and propulsion prediction of ships in shallow water, model tests were performed with an inland ship-model and a container ship-model at different water-depths in the Shallow Water Towing Tank Duisburg (VBD). After an introduction of an effective ship speed, defined by the mean sinkage which combines the blockage effect near the ship and the effective deptheffect under the ship, a new method is proposed for resistance and propulsion prediction of the ship performance in shallow water. For the subject two ships in the subcritical speed range and in a not too extremely shallow water, it has been found that the total resistance could be considered as a unit function of the effective speed and independent of the water depth. Furthermore, at a ship selfpropulsion point corresponding to the effective speed, it has been shown that the delivered power at propeller could be considered as a unit function of the blockage speed. Since the mean sinkage can be accurately calculated by means of the potential theory, for instance using an extended shallow-water approximation, this new method could impact the resistance and propulsion prediction of the ship performance in shallow water. KEYWORDS Resistance and propulsion prediction, Ship performance, Shallow water, Effective speed.
1 INTRODUCTION For designing new ships, resistance and propulsion predictions are a central task not only for a towing tank but also at a design company. For ships sailing in shallow water, the corresponding predictions at different water depths are an additional part of the contract. Depending on the individual requirements two methods are commonly in use. For a ship which mainly operates in deep water, e.g. a seagoing ship, empirical formulae and diagrams are often applied to predict the increased resistance and the additional power demand. For a ship which mainly operates in shallow water at different depths, e.g. an inland ship, the more expensive, additional model tests can be performed at the water-depths interested. In the empirical approximation of the above problem, the basic consideration is to correct or to include the boundary effects caused by the water bottom and channel walls. Physically, this is equivalent to the
510 different blockage correction caused by ships moving in a towing tank and in an operating area considered. A large number of theoretical and experimental investigations has been devoted to this problem. As documented by Gross and Watanabe (1972), there are two methods for correcting these boundary effects. One is to correct the resistance and the other to correct the speed. These two methods are combined in the so-called Schlichting's hypothesis (1934). According to his hypothesis the wave resistance is the same at the same wave length corresponding to different speeds in deep and shallow water and the viscous resistance is the same at the same speed relative to the water at different waterdepths. The speed change due to the blockage effect can be empirically estimated either by using the simple control parameter defined by Schlichting (1934) without correcting the wall effects or by using a control parameter based on the hydraulic radius given by Landweber (1939), which is also applicable for a real shape of the channel section. The speed change at each parameter value can be either read in the corresponding diagrams or calculated from the empirical formulae, e.g. Lackenby (1963). For narrow channels, like many small towing tanks, the mean flow theory based on the one-dimensional continuity and Bernoulli's equation has been widely used. These tow equations lead to a mean flow over the whole channel section. The mean flow change near the ship's surface can then be obtained by means of an empirical factor, e.g. Emerson (1959) using a constant value independent of the speed and Kim (1963) using a factor depending on speed and block coefficient. The present study focuses on a physically reasonable and practically applicable method for resistance and propulsion prediction of ships in shallow water at a subcritical speed. After analyzing the resistance characteristics at different water-depths, a new method is proposed for predicting the total resistance which can be considered as a unit function of the effective speed defined by the mean sinkage. Accordingly, the propulsion tests will be conducted at a ship self-propulsion point corresponding to the effective speed. It can be shown that the delivered power at propeller seams to be a unit function of the blockage speed. In comparison to the earlier empirical approximation, the new method includes one additional information, namely the mean sinkage, which is an individual quantity depending both on the ship geometry and speed as well as on the geometry configuration of the operating area. Since the mean sinkage can be accurately calculated by means of the potential theory, for instance using an extended shallow-water approximation, this new method could impact the resistance and propulsion prediction of the ship performance in shallow water.
2 RESISTANCE P E R F O R M A N C E The experiments reported here were conducted in the main towing tank (200 m x 9.81 m x 1.2 m) of the Duisburg Shallow Water Towing Tank (VBD). Its water depth can be adjusted to any value between 0-1.2 meter. Two ships were chosen for model tests. One is an inland-ship with a ducted propeller and its model of scale 14 has a length at the load waterline 7.857 m, a beam 0.818 m, a draft 0.214 m and a wetted surface 9.059 m 2 , see the body plan in Fig. 1. More details could be found in the work of Lochte-Holtgreven et al.(2001). The other is a typical containership model with a conventional single screw. It has a length-beam ratio 6.08 and a beam-draft ratio 2.9. The model has a draft 0.255 m and a wetted surface 4.0 m 2.
I
Figure 1: Body plan of the subject inland ship
511 For the inland ship the water depth was adjusted to ratios of the water depth to the draft h/T=l.5, 2.0, and 3.0 and for the subject container ship to h/T=2.0, 2.6, and 4.0. The resistance tests were conducted by free trim and sinkage. The measured total resistance and sinkage for the inland ship model are plotted in Fig. 2 as a function of the towing speed, e.g. the speed over ground. The towing speeds were all at the depth-Froude numbers F,h < 0.7. In this subcritical speed range, the sinkage and the total resistance monotonously increase with the increased towing speed at the same water depth and with the decreased water depth at the same towing speed. 40
-] ,
30!
.
[/]. "3 0 =. ---I--h/'r=2.0--'i/ + h/]'=1.5 _ ., 9;
,,?
/
10
_4,..~
0
....
0.5
-
60 5o
2o-1',
0.0
70 ~'
~ F - - h
/1
l
/ l I
* .=-d
--z ,_..
,1o
]
30
- - e - - h/T=3.0 - - i - - h/T=2.0 + h/'r=1.5
9
[ 11 =
.
-
20 -- pIPl . . t r 'i
0-
1.0
1.5
0.0
0.5
v=[m/s]
1.0
1.5
v=Im/s]
Figure 2: Characteristics of sinkage and measured resistance of the subject inland ship model 3 ANALYSIS METHOD 3.1 Introduction o f a Mean Effective Speed Based on the Mean Sinkage
Referring to the definition of an effective depth-Froude number given by Graft (1963), a mean effective speed VEbased on the mean sinkage z~, is introduced here Ve=
2
+2gz r
--~-) = V
2gzv
(1-
z v)
(1)
/1
where g denotes the acceleration due to gravity and V the ship speed. This effective velocity combines the blockage effect near the ship and the effective depth-eftect under the ship. The former is important for the viscous effect and the latter for the wave effect. According to Horn (1932), the mean deformation of the water surface under the ship can be assumed to be equal to the mean sinkage z v . Therefore, the mean near-ship water-velocity relative to the ship can be obtained by means of Bernoulli's equation: vs = ~/Vz + 2 g zv
(2)
For a measured sinkage zv. the velocity VB defined by equation (2) combines both potential and viscous effects. Since the viscous effect on the mean sinkage is negligible small, the velocity V~can be called as a blockage speed near the ship. It implies that the blockage velocity can be estimated by means of potential calculations. However, the viscous effects on the ship are more associated with the blockage speed, since the local friction is a function of the local velocity relative to the ship's surface, not necessarily of the ship speed over the ground. 3.2 Model Resistance as a Function o f the Effective Speed
Now by re-construction of the total resistance measured at different water-depths as a function of the effective speed, Fig. 3 and 4 show that the model resistance of the subject inland ship and the container ship, respectively, is almost a unit function of the effective velocity and independent of the water-
512 depths tested. The novel result leads to a new hypothesis for the total resistance of ships in shallow water: For a ship moving at a subcritical speed and in not extremely shallow water, the total resistance could be considered as a unit function o f the effective velocity and independent o f the water depth. For the two subject ships tested, this hypothesis holds for a speed F,h ---0.7 and a water depth h/T > 1.5. If this hypothesis could be systematically validated for other ships, it would substantially impact the resistance prediction of ships in shallow water. 70
I
60
h/T=2.0
_
,~
,o "
z
= :
"
h/T=1.5
50
I
40 -
30 "
--
30
_~t'
h/T=4.0 h/T=2.6 hFr=20
+
/
/
z 9
20
-~
_
20 "
~
/
lO
0 . . . . ~'I' ll'A~ 0.0
r
o
0.5
1.0
1.5
20
0.5
o.o
1.0
VEM[rrVs]
1.5
2.0
2.5
VE• [m/s]
Figure. 3: Total model resistance as a function of the effective speed for the subject inland ship
Figure 4: Total model resistance as a function of the effective speed for the subject container ship
3.3 Unit Form-Factor Based on the Effective Speed The uniform total model resistance should also lead to a unit form-factor, if the model speed VM for the identification of the form factor is replaced by the effective speed V ~ . The well-known HughesProhaska formula reads now CrM~ - (m+k)~ + y. F,~ (3) CFOME CFOME here the model resistance is normalized by p / 2 . S M 9V ~ instead of by p / 2 . S M 9V~. The Froude number F.E and Reynolds number R.~M for the ITTC friction line refer also to the effective speed. The resulting form factor should be thus called as an effective form-factor. 2.5
-
2.5 I
_ 20
0
.,~
_ 2'
,* /,,," -
nu
'.
1.5
/o
2.0_0.0
r
h/T=2.0 - - 0 - - h/T=1.5
0.2
0.3
0.4
0.5
1.5
i~~ ~ : ~ = - - - -
1
1.0
-
9 ~ @ " ,,...,-II
h/T=3.0
~
0.1
h/T=2.0 h/T=1.5
+
/ -==.9149
9
~ , J ~e~
0.0
= h/T=:3.0
=
i !e.e-e"
0
-
p
1.o0.6
Fn4/C~ou
(a) Conventional evaluation based on the
0.0
0.1
0.2
0.3
0.4
0.5
0.6
FnE41C~oEM
(b) New evaluation based on the effective towing speed speed Figure 5: Hughes-Prohaska form-factor at different water depths for the inland ship
513 4 RESISTANCE PREDICTION Considering the special feature of the model resistance as a unit function of the effective speed, the conventional prediction of the ship resistance by means of the common form-factor method can be demonstrated as follows: 9 Estimating the model wave resistance Re (V~:M) as a function of the effective speed VEM
R ~ ( V F ~ ) = RrM(VEM)-R~7~(V~)= RrM(VF~)-(I+k)ECFoEM ~PJu "SM . V ~
(4)
with the ITTC friction line CFOEM = 0.075/(1og R,F~-2) 2 for a Reynolds number corresponding
VEM 9L M/v M ;
to the effective speed at model scale R,EM = 9
Evaluating the ship speed Vs = VM ~
9
Predicting the ship resistance at the corresponding water-depth tested Rrs(Vs)=Rvs(VEs)+Rws(VEs)=[(I+k)ECFoEs +CA]~pSV~s +p/pMR~7,423
as well as the effective speed VEs = VF~ "f-2; (5)
with the ITTC friction line CFo~s = 0.075/(1og R,Es-2) 2 and for the effective Reynolds number at 9
the full scale R,,Es = VEs L s/v s ; Predicting the ship resistance at the water-depth h/T=Prediction from the available model test h/T=Test:
[RTs(Vs)]hlT=PredictJo n
--[Rvs(VEs)]h/T=PredicOo n 4" RwshlT=Test(VESihlT=PredietJon) (6) = [(l+k>~.CFoEs.~P.S.V~]wr=pr~,~on + p/pM[Rga,tL=V=t'A 3 According to the prediction mentioned above, the measured resistance at h/T=3.0, 2.0 and 1.5, see the full-filled symbols in Fig. 6, was directly converted to its full scale value via equation (5) and then compared with those predicted by means of the model test at the water depth h~=3.0 via equation (6), where the measured sinkage at h~=2.0 and 1.5 was used to determine the corresponding effective speed. As shown in Fig. 6, the agreement is generally acceptable. Similar agreement was also found at different scales for the same inland ship, see Lochte-Holtgreven et al.(2001). However, it was shown in their work, there is a disagreement for the extremely shallow water at h ~ = 1.2. Generally speaking, the proposed method is only valid for a subcritical speed F,h < 0.7 and in a not too extremely shallow water. 150
-
I
= --
120
Z
!
I
h/'l'=3.0 hfr=2.0 h f r = 2 . 0 Prediction hfr=1.5 h/T=1.5 Prediction
1 O
,4" .,"-
_(,",I /
~o
=v i
0
2
4
6
8
10
12
14
16
18
20
22
Vs[krrgh]
Figure 6: Comparison of the predicted ship-resistance via equation (5) with those from the direct conversion via equation (6) for the subject inland ship The excellent agreement for h/T=l.5 in Fig. 6 demonstrates the quality of the proposed method for predicting the ship resistance in shallow water. More importantly, it implies that the model tests at h/T= 1.5 could be entirely saved if the corresponding sinkage is realistically approximated, for instance by empirical formulae for ships moving at a narrow channel and by numerical calculations based on the potential theory. Fig. 7. compares the predictions based on the measured sinkages and the empirical estimations by Emerson (1959). Fig. 8 compares the predictions based on the measured
514
sinkages and the numerical calculations by Jiang (2000) using an approximation based on the extended shallow-water theory. For the geometry configuration of the VBD towing tank the agreement is equally remarkable for both sinkage estimations. However, since the numerical estimation can be applied for general shallow water cases, the combination of the proposed prediction method with the well-established shallow-water approximation could be a new method for the resistance prediction of ships in shallow water. 15o -
1
I
I
I
I
1
Prediction . - - - - t - - h / T = 2 . 0 b a s e d on m e a s u r e d - - - o - - h / ' r = 2 . 0 b a s e d on e s t i m a t e d
12o - .
sinkage sinkage h / T = 1 . 5 b a s e d on m e a s u r e d sinkage h / ' l = 1 . 5 b a s e d on estimated sinkage
+ z
E
~r ~r
iw,,,,,,,~iJ,, ~ 4 ~
,-
~~ . . . . . _ o . - - - ~ " ~ 0
2
4
6
8
10
12
14
16
18
20
22
Vs[km/h]
Figure 7: Comparison of the predicted ship-resistance using measured and empirically estimated sinkage 150
-
~
_
12o
-
,._., z
9o
.
I
h/T=2.0 - - . t 3 - - hFl'=2.0 ----4,-- h / T = 1 . 5 h/T=1.5
I
!
Prediction based based based based
on on on on
1 measured calculated measured calculated
1 sinkage sinkage sinkage sinkage
,./.,
6o 30 0 0
2
4
6
8
10
12
14
16
18
20
22
Vs[km/h]
Figure 8: Comparison of the predicted ship-resistance using measured and calculated sinkage 5 PROPULSION PERFORMANCE
Since the propulsion tests can be conducted by means of the so-called English method, in principle the self-propulsion point at any considered propeller loading can be found. For a ship in shallow water, the ship self-propulsion point should correspond a towing force defined by
FoL-(VM ) = (CFoEM -- CFoES -CA) ~ PM S• V~M (7) where C A is an empirical model-ship correction allowance. The delivered propeller-power at the ship self-propulsion point defined above is plotted in Fig. 9 versus the effective speed for the water depth h/T=4.0, 2.6 and 2.0. For this subject container ship, the delivered power at the same effective speed is slightly higher in deeper water. This means the propulsion features could not be assumed as a unit function of the effective speed. However, if the delivered propller-power at the ship self-propulsion point is plotted now versus the blockage speed defined by equation (2), as shown in Fig. 10, it can be found that the delivered power at propeller can be considered as a unit function of the blockage speed and independent of the water depth. If this would be true, it would lead to a new hypothesis for the propulsion performance: The delivered power at propeller at the ship self-propulsion point corresponding to the effective speed could be considered as a unit function of the blockage speed and independent of the water depth.
515 Physically, the wave effect included in the effective speed is less important or may be not reasonable for the propulsion characteristics behind the ship. However, due to possible errors in the measurements for one specific ship, this hypothesis has to be proved by analyzing measurements of other ships.
,o ~
1
70-
1
60
- - ----e--- h / T = 4 . 0
so
-h/T=2.6 ----0--- h / T = 2 . 0
.T
60
= -
"
so -
40 .
.
.
.
.
.
I'~T=4.0
Vl
+ h/T=2.6 --4F-- h/T=2.0
a!
L
40
30-
30
/
-
_
D_ 20
2o-,
7
10
-
-- I,
'r ~ ' ~
--
9
0
o 0.0
0.5
1.0
1.5
2.0
2.5
VEU[m/s]
Figure 9: Delivered power at propeller as a function of the effective speed
O.O
0.5
1.0
1.5
2.0
2.5
VsM[m/s]
Figure 10: Delivered power at propeller as a function of the blockage speed
6 CONCLUSIONS Based on a novel analysis of model tests for an inland ship-model and a container ship-model at different water-depths conducted in the Shallow Water Towing Tank Duisburg (VBD), a new method is proposed for resistance and propulsion prediction of the ship performance in the subcritical speed range and in a not too extremely shallow water by using an effective and blockage speed defined by the mean sinkage. Whereas the total resistance is found to be a unit function of the effective speed and independent of the water depth, the delivered power at propeller at a ship self-propulsion point corresponding to the effective speed could be considered as a unit function of the blockage speed.
Acknowledgement This work was partially supported by the Ministry of Education and Research (BMBF) of the Federal Republic of Germany. The author is grateful to Mr. Lochte-Holtgreven for conducting the model experiments. References Emerson, A. (1959): Ship Model Size and Tank Boundary Correctioo_ Journal of North East Coast Engineers. Graff, W., Kracht, A. and Weinblum, G. (1964) : Some Extensions ofD.W. Taylor's Standard Series, Transactions of Society of Naval Architects and Marine Engineers, Vol. 72. Gross, A. & Watanabe, K.(1972): On Blockage Correction. Proceedings of the 13th ITTC, Berlin~Hamburg. Horn, F. (1932): Hydrodynamische Probleme des Schiffsantriebs. Editor: G. Kempf und Foerster Jiang, T. (2000): Ship Waves in Shallow Water. Habilitation Thesis, Mercator University Duisburg, Germany. Kim, H.C.(1963): Blockage Correction in a Ship Model Tank. Report of Michigan University No. 04542, Part III. Lackenby, H. (1963): The Effect of Shallow Water on Ship Speed. The Shipbuilder and Marine Engine-Builder. Landweber, L.(1939): Tests of a Model in Restricted Channels. TMB-Report 460. Lochte-Holtgreven, H., List, S. & Jiang, T.(2001): Widerstandsprognose flit Schiffe auf flachem Wasser. VBD-Bericht Nr. 1532. Schlichting, O.(1934): Schiffswiderstand aufbeschraenkter Wassertiefe. 3ahrbuch d. STG, Bd 35.
509
A NEW METHOD FOR RESISTANCE AND PROPULSION PREDICTION OF SHIP PERFORMANCE IN SHALLOW WATER T. Jiang European Development Centre for Inland and Coastal Navigation D-47057 Duisburg, Germany
ABSTRACT To improve the resistance and propulsion prediction of ships in shallow water, model tests were performed with an inland ship-model and a container ship-model at different water-depths in the Shallow Water Towing Tank Duisburg (VBD). After an introduction of an effective ship speed, defined by the mean sinkage which combines the blockage effect near the ship and the effective deptheffect under the ship, a new method is proposed for resistance and propulsion prediction of the ship performance in shallow water. For the subject two ships in the subcritical speed range and in a not too extremely shallow water, it has been found that the total resistance could be considered as a unit function of the effective speed and independent of the water depth. Furthermore, at a ship selfpropulsion point corresponding to the effective speed, it has been shown that the delivered power at propeller could be considered as a unit function of the blockage speed. Since the mean sinkage can be accurately calculated by means of the potential theory, for instance using an extended shallow-water approximation, this new method could impact the resistance and propulsion prediction of the ship performance in shallow water. KEYWORDS Resistance and propulsion prediction, Ship performance, Shallow water, Effective speed.
1 INTRODUCTION For designing new ships, resistance and propulsion predictions are a central task not only for a towing tank but also at a design company. For ships sailing in shallow water, the corresponding predictions at different water depths are an additional part of the contract. Depending on the individual requirements two methods are commonly in use. For a ship which mainly operates in deep water, e.g. a seagoing ship, empirical formulae and diagrams are often applied to predict the increased resistance and the additional power demand. For a ship which mainly operates in shallow water at different depths, e.g. an inland ship, the more expensive, additional model tests can be performed at the water-depths interested. In the empirical approximation of the above problem, the basic consideration is to correct or to include the boundary effects caused by the water bottom and channel walls. Physically, this is equivalent to the
510 different blockage correction caused by ships moving in a towing tank and in an operating area considered. A large number of theoretical and experimental investigations has been devoted to this problem. As documented by Gross and Watanabe (1972), there are two methods for correcting these boundary effects. One is to correct the resistance and the other to correct the speed. These two methods are combined in the so-called Schlichting's hypothesis (1934). According to his hypothesis the wave resistance is the same at the same wave length corresponding to different speeds in deep and shallow water and the viscous resistance is the same at the same speed relative to the water at different waterdepths. The speed change due to the blockage effect can be empirically estimated either by using the simple control parameter defined by Schlichting (1934) without correcting the wall effects or by using a control parameter based on the hydraulic radius given by Landweber (1939), which is also applicable for a real shape of the channel section. The speed change at each parameter value can be either read in the corresponding diagrams or calculated from the empirical formulae, e.g. Lackenby (1963). For narrow channels, like many small towing tanks, the mean flow theory based on the one-dimensional continuity and Bernoulli's equation has been widely used. These tow equations lead to a mean flow over the whole channel section. The mean flow change near the ship's surface can then be obtained by means of an empirical factor, e.g. Emerson (1959) using a constant value independent of the speed and Kim (1963) using a factor depending on speed and block coefficient. The present study focuses on a physically reasonable and practically applicable method for resistance and propulsion prediction of ships in shallow water at a subcritical speed. After analyzing the resistance characteristics at different water-depths, a new method is proposed for predicting the total resistance which can be considered as a unit function of the effective speed defined by the mean sinkage. Accordingly, the propulsion tests will be conducted at a ship self-propulsion point corresponding to the effective speed. It can be shown that the delivered power at propeller seams to be a unit function of the blockage speed. In comparison to the earlier empirical approximation, the new method includes one additional information, namely the mean sinkage, which is an individual quantity depending both on the ship geometry and speed as well as on the geometry configuration of the operating area. Since the mean sinkage can be accurately calculated by means of the potential theory, for instance using an extended shallow-water approximation, this new method could impact the resistance and propulsion prediction of the ship performance in shallow water.
2 RESISTANCE P E R F O R M A N C E The experiments reported here were conducted in the main towing tank (200 m x 9.81 m x 1.2 m) of the Duisburg Shallow Water Towing Tank (VBD). Its water depth can be adjusted to any value between 0-1.2 meter. Two ships were chosen for model tests. One is an inland-ship with a ducted propeller and its model of scale 14 has a length at the load waterline 7.857 m, a beam 0.818 m, a draft 0.214 m and a wetted surface 9.059 m 2 , see the body plan in Fig. 1. More details could be found in the work of Lochte-Holtgreven et al.(2001). The other is a typical containership model with a conventional single screw. It has a length-beam ratio 6.08 and a beam-draft ratio 2.9. The model has a draft 0.255 m and a wetted surface 4.0 m 2.
I
Figure 1: Body plan of the subject inland ship
511 For the inland ship the water depth was adjusted to ratios of the water depth to the draft h/T=l.5, 2.0, and 3.0 and for the subject container ship to h/T=2.0, 2.6, and 4.0. The resistance tests were conducted by free trim and sinkage. The measured total resistance and sinkage for the inland ship model are plotted in Fig. 2 as a function of the towing speed, e.g. the speed over ground. The towing speeds were all at the depth-Froude numbers F,h < 0.7. In this subcritical speed range, the sinkage and the total resistance monotonously increase with the increased towing speed at the same water depth and with the decreased water depth at the same towing speed. 40
-] ,
30!
.
[/]. "3 0 =. ---I--h/'r=2.0--'i/ + h/]'=1.5 _ ., 9;
,,?
/
10
_4,..~
0
....
0.5
-
60 5o
2o-1',
0.0
70 ~'
~ F - - h
/1
l
/ l I
* .=-d
--z ,_..
,1o
]
30
- - e - - h/T=3.0 - - i - - h/T=2.0 + h/'r=1.5
9
[ 11 =
.
-
20 -- pIPl . . t r 'i
0-
1.0
1.5
0.0
0.5
v=[m/s]
1.0
1.5
v=Im/s]
Figure 2: Characteristics of sinkage and measured resistance of the subject inland ship model 3 ANALYSIS METHOD 3.1 Introduction o f a Mean Effective Speed Based on the Mean Sinkage
Referring to the definition of an effective depth-Froude number given by Graft (1963), a mean effective speed VEbased on the mean sinkage z~, is introduced here Ve=
2
+2gz r
--~-) = V
2gzv
(1-
z v)
(1)
/1
where g denotes the acceleration due to gravity and V the ship speed. This effective velocity combines the blockage effect near the ship and the effective depth-eftect under the ship. The former is important for the viscous effect and the latter for the wave effect. According to Horn (1932), the mean deformation of the water surface under the ship can be assumed to be equal to the mean sinkage z v . Therefore, the mean near-ship water-velocity relative to the ship can be obtained by means of Bernoulli's equation: vs = ~/Vz + 2 g zv
(2)
For a measured sinkage zv. the velocity VB defined by equation (2) combines both potential and viscous effects. Since the viscous effect on the mean sinkage is negligible small, the velocity V~can be called as a blockage speed near the ship. It implies that the blockage velocity can be estimated by means of potential calculations. However, the viscous effects on the ship are more associated with the blockage speed, since the local friction is a function of the local velocity relative to the ship's surface, not necessarily of the ship speed over the ground. 3.2 Model Resistance as a Function o f the Effective Speed
Now by re-construction of the total resistance measured at different water-depths as a function of the effective speed, Fig. 3 and 4 show that the model resistance of the subject inland ship and the container ship, respectively, is almost a unit function of the effective velocity and independent of the water-
512 depths tested. The novel result leads to a new hypothesis for the total resistance of ships in shallow water: For a ship moving at a subcritical speed and in not extremely shallow water, the total resistance could be considered as a unit function o f the effective velocity and independent o f the water depth. For the two subject ships tested, this hypothesis holds for a speed F,h ---0.7 and a water depth h/T > 1.5. If this hypothesis could be systematically validated for other ships, it would substantially impact the resistance prediction of ships in shallow water. 70
I
60
h/T=2.0
_
,~
,o "
z
= :
"
h/T=1.5
50
I
40 -
30 "
--
30
_~t'
h/T=4.0 h/T=2.6 hFr=20
+
/
/
z 9
20
-~
_
20 "
~
/
lO
0 . . . . ~'I' ll'A~ 0.0
r
o
0.5
1.0
1.5
20
0.5
o.o
1.0
VEM[rrVs]
1.5
2.0
2.5
VE• [m/s]
Figure. 3: Total model resistance as a function of the effective speed for the subject inland ship
Figure 4: Total model resistance as a function of the effective speed for the subject container ship
3.3 Unit Form-Factor Based on the Effective Speed The uniform total model resistance should also lead to a unit form-factor, if the model speed VM for the identification of the form factor is replaced by the effective speed V ~ . The well-known HughesProhaska formula reads now CrM~ - (m+k)~ + y. F,~ (3) CFOME CFOME here the model resistance is normalized by p / 2 . S M 9V ~ instead of by p / 2 . S M 9V~. The Froude number F.E and Reynolds number R.~M for the ITTC friction line refer also to the effective speed. The resulting form factor should be thus called as an effective form-factor. 2.5
-
2.5 I
_ 20
0
.,~
_ 2'
,* /,,," -
nu
'.
1.5
/o
2.0_0.0
r
h/T=2.0 - - 0 - - h/T=1.5
0.2
0.3
0.4
0.5
1.5
i~~ ~ : ~ = - - - -
1
1.0
-
9 ~ @ " ,,...,-II
h/T=3.0
~
0.1
h/T=2.0 h/T=1.5
+
/ -==.9149
9
~ , J ~e~
0.0
= h/T=:3.0
=
i !e.e-e"
0
-
p
1.o0.6
Fn4/C~ou
(a) Conventional evaluation based on the
0.0
0.1
0.2
0.3
0.4
0.5
0.6
FnE41C~oEM
(b) New evaluation based on the effective towing speed speed Figure 5: Hughes-Prohaska form-factor at different water depths for the inland ship
513 4 RESISTANCE PREDICTION Considering the special feature of the model resistance as a unit function of the effective speed, the conventional prediction of the ship resistance by means of the common form-factor method can be demonstrated as follows: 9 Estimating the model wave resistance Re (V~:M) as a function of the effective speed VEM
R ~ ( V F ~ ) = RrM(VEM)-R~7~(V~)= RrM(VF~)-(I+k)ECFoEM ~PJu "SM . V ~
(4)
with the ITTC friction line CFOEM = 0.075/(1og R,F~-2) 2 for a Reynolds number corresponding
VEM 9L M/v M ;
to the effective speed at model scale R,EM = 9
Evaluating the ship speed Vs = VM ~
9
Predicting the ship resistance at the corresponding water-depth tested Rrs(Vs)=Rvs(VEs)+Rws(VEs)=[(I+k)ECFoEs +CA]~pSV~s +p/pMR~7,423
as well as the effective speed VEs = VF~ "f-2; (5)
with the ITTC friction line CFo~s = 0.075/(1og R,Es-2) 2 and for the effective Reynolds number at 9
the full scale R,,Es = VEs L s/v s ; Predicting the ship resistance at the water-depth h/T=Prediction from the available model test h/T=Test:
[RTs(Vs)]hlT=PredictJo n
--[Rvs(VEs)]h/T=PredicOo n 4" RwshlT=Test(VESihlT=PredietJon) (6) = [(l+k>~.CFoEs.~P.S.V~]wr=pr~,~on + p/pM[Rga,tL=V=t'A 3 According to the prediction mentioned above, the measured resistance at h/T=3.0, 2.0 and 1.5, see the full-filled symbols in Fig. 6, was directly converted to its full scale value via equation (5) and then compared with those predicted by means of the model test at the water depth h~=3.0 via equation (6), where the measured sinkage at h~=2.0 and 1.5 was used to determine the corresponding effective speed. As shown in Fig. 6, the agreement is generally acceptable. Similar agreement was also found at different scales for the same inland ship, see Lochte-Holtgreven et al.(2001). However, it was shown in their work, there is a disagreement for the extremely shallow water at h ~ = 1.2. Generally speaking, the proposed method is only valid for a subcritical speed F,h < 0.7 and in a not too extremely shallow water. 150
-
I
= --
120
Z
!
I
h/'l'=3.0 hfr=2.0 h f r = 2 . 0 Prediction hfr=1.5 h/T=1.5 Prediction
1 O
,4" .,"-
_(,",I /
~o
=v i
0
2
4
6
8
10
12
14
16
18
20
22
Vs[krrgh]
Figure 6: Comparison of the predicted ship-resistance via equation (5) with those from the direct conversion via equation (6) for the subject inland ship The excellent agreement for h/T=l.5 in Fig. 6 demonstrates the quality of the proposed method for predicting the ship resistance in shallow water. More importantly, it implies that the model tests at h/T= 1.5 could be entirely saved if the corresponding sinkage is realistically approximated, for instance by empirical formulae for ships moving at a narrow channel and by numerical calculations based on the potential theory. Fig. 7. compares the predictions based on the measured sinkages and the empirical estimations by Emerson (1959). Fig. 8 compares the predictions based on the measured
514
sinkages and the numerical calculations by Jiang (2000) using an approximation based on the extended shallow-water theory. For the geometry configuration of the VBD towing tank the agreement is equally remarkable for both sinkage estimations. However, since the numerical estimation can be applied for general shallow water cases, the combination of the proposed prediction method with the well-established shallow-water approximation could be a new method for the resistance prediction of ships in shallow water. 15o -
1
I
I
I
I
1
Prediction . - - - - t - - h / T = 2 . 0 b a s e d on m e a s u r e d - - - o - - h / ' r = 2 . 0 b a s e d on e s t i m a t e d
12o - .
sinkage sinkage h / T = 1 . 5 b a s e d on m e a s u r e d sinkage h / ' l = 1 . 5 b a s e d on estimated sinkage
+ z
E
~r ~r
iw,,,,,,,~iJ,, ~ 4 ~
,-
~~ . . . . . _ o . - - - ~ " ~ 0
2
4
6
8
10
12
14
16
18
20
22
Vs[km/h]
Figure 7: Comparison of the predicted ship-resistance using measured and empirically estimated sinkage 150
-
~
_
12o
-
,._., z
9o
.
I
h/T=2.0 - - . t 3 - - hFl'=2.0 ----4,-- h / T = 1 . 5 h/T=1.5
I
!
Prediction based based based based
on on on on
1 measured calculated measured calculated
1 sinkage sinkage sinkage sinkage
,./.,
6o 30 0 0
2
4
6
8
10
12
14
16
18
20
22
Vs[km/h]
Figure 8: Comparison of the predicted ship-resistance using measured and calculated sinkage 5 PROPULSION PERFORMANCE
Since the propulsion tests can be conducted by means of the so-called English method, in principle the self-propulsion point at any considered propeller loading can be found. For a ship in shallow water, the ship self-propulsion point should correspond a towing force defined by
FoL-(VM ) = (CFoEM -- CFoES -CA) ~ PM S• V~M (7) where C A is an empirical model-ship correction allowance. The delivered propeller-power at the ship self-propulsion point defined above is plotted in Fig. 9 versus the effective speed for the water depth h/T=4.0, 2.6 and 2.0. For this subject container ship, the delivered power at the same effective speed is slightly higher in deeper water. This means the propulsion features could not be assumed as a unit function of the effective speed. However, if the delivered propller-power at the ship self-propulsion point is plotted now versus the blockage speed defined by equation (2), as shown in Fig. 10, it can be found that the delivered power at propeller can be considered as a unit function of the blockage speed and independent of the water depth. If this would be true, it would lead to a new hypothesis for the propulsion performance: The delivered power at propeller at the ship self-propulsion point corresponding to the effective speed could be considered as a unit function of the blockage speed and independent of the water depth.
515 Physically, the wave effect included in the effective speed is less important or may be not reasonable for the propulsion characteristics behind the ship. However, due to possible errors in the measurements for one specific ship, this hypothesis has to be proved by analyzing measurements of other ships.
,o ~
1
70-
1
60
- - ----e--- h / T = 4 . 0
so
-h/T=2.6 ----0--- h / T = 2 . 0
.T
60
= -
"
so -
40 .
.
.
.
.
.
I'~T=4.0
Vl
+ h/T=2.6 --4F-- h/T=2.0
a!
L
40
30-
30
/
-
_
D_ 20
2o-,
7
10
-
-- I,
'r ~ ' ~
--
9
0
o 0.0
0.5
1.0
1.5
2.0
2.5
VEU[m/s]
Figure 9: Delivered power at propeller as a function of the effective speed
O.O
0.5
1.0
1.5
2.0
2.5
VsM[m/s]
Figure 10: Delivered power at propeller as a function of the blockage speed
6 CONCLUSIONS Based on a novel analysis of model tests for an inland ship-model and a container ship-model at different water-depths conducted in the Shallow Water Towing Tank Duisburg (VBD), a new method is proposed for resistance and propulsion prediction of the ship performance in the subcritical speed range and in a not too extremely shallow water by using an effective and blockage speed defined by the mean sinkage. Whereas the total resistance is found to be a unit function of the effective speed and independent of the water depth, the delivered power at propeller at a ship self-propulsion point corresponding to the effective speed could be considered as a unit function of the blockage speed.
Acknowledgement This work was partially supported by the Ministry of Education and Research (BMBF) of the Federal Republic of Germany. The author is grateful to Mr. Lochte-Holtgreven for conducting the model experiments. References Emerson, A. (1959): Ship Model Size and Tank Boundary Correctioo_ Journal of North East Coast Engineers. Graff, W., Kracht, A. and Weinblum, G. (1964) : Some Extensions ofD.W. Taylor's Standard Series, Transactions of Society of Naval Architects and Marine Engineers, Vol. 72. Gross, A. & Watanabe, K.(1972): On Blockage Correction. Proceedings of the 13th ITTC, Berlin~Hamburg. Horn, F. (1932): Hydrodynamische Probleme des Schiffsantriebs. Editor: G. Kempf und Foerster Jiang, T. (2000): Ship Waves in Shallow Water. Habilitation Thesis, Mercator University Duisburg, Germany. Kim, H.C.(1963): Blockage Correction in a Ship Model Tank. Report of Michigan University No. 04542, Part III. Lackenby, H. (1963): The Effect of Shallow Water on Ship Speed. The Shipbuilder and Marine Engine-Builder. Landweber, L.(1939): Tests of a Model in Restricted Channels. TMB-Report 460. Lochte-Holtgreven, H., List, S. & Jiang, T.(2001): Widerstandsprognose flit Schiffe auf flachem Wasser. VBD-Bericht Nr. 1532. Schlichting, O.(1934): Schiffswiderstand aufbeschraenkter Wassertiefe. 3ahrbuch d. STG, Bd 35.