A Study on the Effect of Estimation Accuracy of Hydrodynamic Derivatives and the Interaction Coefficient on the Prediction of Ship Maneuvering motion
Atsushi ISHIBASHI (Tokyo University of Mercantile Marine, Japan)
Hiroaki KOBAYASHI (Tokyo University of Mercantile Marine, Japan)
Abstract: MMG model proposed by Japanese researchers is well known. The special features of MMG model are to separate the hydrodynamics force among the hull, rudder, propeller and their interaction. However, the expression and prediction procedures on forces and interaction are different from each institute. When the experiments using same model ship are carried out by different institutes and there are some differences on the contents of experiments, analyzing procedures and prediction methods of interactions. Some difference in results may happen among institutes. In this paper, the difference in the hydrodynamic force and in predicted ship's maneuvering motion caused by the different procedure mentioned above are discussed using proposed experimental results of Esso Osaka. The hydrodynamic derivatives can have difference as a result of experimental condition, analysis procedures and mathematical models. Therefore, it is not meaningful to carry out the direct comparison of the hydrodynamic derivative proposed by each institutes using the different mathematical model. So, we can compare the unified values by coherent converting way concerning the contents of experimental condition and analyzing procedure. As a results, it is possible that the hydrodynamic forces was compared. It is obvious that there is no big difference in the estimated result of hydrodynamic force using the hydrodynamic derivative proposed by each institutes. The differences in predicted maneuvering motion due to interaction forces are discussed from viewpoint of estimated flow velocity at propeller, rudder position and interaction between hull and rudder. As a result, it is obvious that the change of wake fraction due to maneuvering motion has an important factor on propeller and rudder forces and on predicted maneuvering motions.
23th ITTC pointed out the following tasks for Esso Osaka Specialist Committee in order to present benchmark data of Esso Osaka.
a) Reduce the scatter in existing data either by eliminating suspect data sets, or by stimulating new, benchmark quality experiments.
b) Compare propeller and rudder forces and propeller-hull-rudder interactions.
c) Carry out a systematic series of simulations using one reference mathematical model (e.g. MMG with fixed propeller and rudder forces and interactions) using available sets of hull damping coefficients (linear and non-linear).
d) Compare the results of these systematic simulations with available track data; and particularly the full-scale trials data.
After discussing the reasons of scatter in data, it has been found out that the reasons of scatter exist in experimental conditions, analysing procedure and mathematical model and etc.. Therefore, Esso Osaka Specialist Committee intends to propose benchmark data based on specific experimental condition and specific analysing procedure. Especially, the predictions on ship maneuvering motion are discussed by applying two kinds of mathematical models that are MMG model and Whole Ship model. In this paper, the discussions on the reasons of scatter are explained based on MMG model. This is may be one part of report of Esso Osaka specialist committee. It is shown that the reasons of scatter exist in many phases and the difference of mathematical model cause the difference of prediction on maneuvering motion.
2. MATHEMATICAL MODEL
2.1 Basic Equation of Motion
The mathematical model used in this study is shown below.
The origin of maneuvering motion is at the center of gravity of the ship.
The origin of hydrodynamic force is at the midship section on the centerline of the ship.
m: mass of a ship, IZZ: moment of inertia of yawing, X,Y and N are hydrodynamic forces and moment acting on midship. XG represents the location of C.G. in x-axis direction from the midship.
These hydrodynamic forces and moments can be divided into the following components.
Where subscript H,P and R refer to hull, propeller and rudder respectively.
The lateral force and moment induced by the propeller is not a large value generally, and it is difficult to separate it. Therefore usually expressed as YHP and NHP.
2.2 Hydrodynamic forces and moment acting on the hull
Hydrodynamic forces and yaw moments acting on the hull are as follows:
2.3 Hydrodynamic forces induced by Propeller
The hydrodynamic forces induced by the propeller are expressed as below:
XP = (1-t)T=ρD4Pn2(1-t)KT (4)
KT = a1+a2J+a3J2 (5)
UP = u(1-WP) (7)
where t: thrust deduction factor, n: propeller revolution. DP: Propeller diameter, J: propeller advance constant, a1, a2 and a3: constant for propeller open characteristics
On wake ratio 1-wp, various estimation formulas are proposed. Mathematical models for a 6.0m model and a 2.5m model, which were used in this study, are as follows:
1 - wP - 1 - wP0(JP) + kw1(β - 1'Pr') + kw2(β - 1'Pr')21 (8a)
1 - wP0(JP) = awo + aw1JP + aw2J2P (9)
1 - wP = (1 - wP0) + τ|v'+x'Pr'| + C'P(v'+x'Pr')2 (8b)
2.4 Hydrodynamic Force and Yaw Moment Induced by Rudder
The hydrodynamic forces induced by rudder are described below, in terms of rudder normal force FN, rudder angle δ, and rudder to hull interaction coefficients tR, aH, XH:
XR = - (1 - tR)FNsinδ (10a)
YR = - (1 + aH)FNcosδ (10b)
NR = - (xR + aHxH)FNcosδ (10c)
The following relations applies for rudder normal force FN, using effective rudder inflow velocity UR and effective rudder inflow angle αR.
On effective rudder inflow velocity UR and effective rudder inflow angle αR, various estimation formulas are proposed. Mathematical models for 6.0m model and 2.5m model, which were used in this study, are as follows:
where, η = DP/H, k = kx/ε, ε = 1 - wR/1 - wP
1 - WR = 1 - wRo + kw1(β - l'Pr') + kw2(β - l'Pr')2 (14)
wRo = 1 - ε(1 - wPO) (15)
αR = δ + δR (17a)
VR = γ(v' + lR'r') (16b)
αR = (δ-δ0) + tan-1(VR/uR) (17b)