Maneuverability is an important hydrodynamic performance of a ship, and should be taken into account during the ship design stage. The present study of Computational Fluid Dynamic (CFD) calculations aims to offer a numerical tool for maneuvering prediction with high accuracy. The virtual captive model tests for a model scale KCS container ship are conducted using unsteady Reynolds-averaged Navier–Stokes (RANS) computation to obtain the full set of linear and nonlinear hydrodynamic derivatives in the 3rd-order Abkowitz model. The numerical uncertainty analysis is carried out for the pure sway and yaw–drift tests to verify the numerical accuracy. It is concluded that the lower order Fourier coefficients are preferred in the computation of the hydrodynamic derivatives. Moreover, part of the computed hydrodynamic forces and moments are compared with the available captive model test data, and good agreement is obtained. By substituting the computed hydrodynamic derivatives into the mathematical model, the standard turning and zigzag maneuvers are predicted. By comparing the predicted maneuvering results with the available experimental data and the prediction results by others, it is demonstrated that acceptable prediction accuracy can be achieved with the present method, which shows the effectiveness of the present method in predicting ship maneuverability.


1.1 Background of the Study
Maneuverability is an important hydrodynamic performance of a ship. The International Maritime Organization (IMO) has promulgated the Standards for Ship Maneuverability (IMO, 2002) to ensure the safety of navigation. To assess ship maneuverability at the design stage, reliable methods for predicting ship maneuverability are required. The Maneuvering Committee of the International Towing Tank Conference (ITTC, 2008) and the Workshop on Verification and Validation of Ship Maneuvering Simulation Methods (SIMMAN, 2008, 2014) collected and sorted all methods for prediction of ship maneuverability in practical applications. In general, maneuverability predictions using Free Running Model Tests (FRMT) such as zigzag and turning circle tests are believed to be most close to the reality.
At the Ship Maneuvering Simulation Methods (SIMMAN) workshops, many organizations such as Maritime Research Institute Netherlands (MARIN) provided Free Running Model Tests data for the standard ship models KVLCC1 & 2, KCS and DTMB 5415 (Quadvlieg, 2017). Besides, the system-based prediction method, which uses the mathematical model of maneuvering motion with the hydrodynamic coefficients obtained from empirical formulae (EMP) (Kijima, et al., 1990; Sutulo&Guedes, 2014; Tran, et al., 2013; Zhang &Zou, 2011), is widely applied. Among the methods for determining the hydrodynamic coefficients, the captive model test method is regarded as the most reliable one, which includes an oblique towing test, rudder force test, planar motion mechanism (PMM) test, and Circular motion test (CMT), etc.
The advantage of the captive model test is that it can obtain all the linear and nonlinear hydrodynamic coefficients in the mathematical model. However, it also has some drawbacks, such as the fact that specific test facilities are required, and it is not convenient for the evaluation and optimization of ship maneuverability at the design stage. With the rapid development of computer techniques and the Computational Fluid Dynamics (CFD) method, these methods have been successfully applied in naval architecture (Zhang, Zhang, Tezdogan, Xu, & Lai, 2018), especially in the investigation of ship maneuverability (Stern et al., 2013; Sun, Su, Wang, & Hu, 2016).
There are two types of Computational Fluid Dynamics (CFD) application in maneuvering predictions. One is the direct numerical simulation of standard maneuvers in the full time domain with steering rudder(s) and rotating propeller(s) (Dubbiosoet al., 2016; Wang, Zou, & Wan, 2017). However, the requirement of huge computational resources and the heavy computational burden limit its practical application. Another Computational Fluid Dynamics (CFD) application is more practical. It first determines the maneuvering hydrodynamic forces by conducting virtual captive model tests, i.e. simulating the captive model tests with a Reynolds-averaged Navier–Stokes (RANS)- based solver, and then predicts the standard maneuvers using the mathematical models with the obtained hydrodynamic coefficients.
Two classic types of mathematical models – the Abkowitz model (Abkowitz, 1964) and the Maneuvering Modeling Group (MMG) model (Yasukawa & Yoshimura, 2015) – for predicting ship maneuverability are generally adopted. More and more researchers are trying to use Computational Fluid Dynamics (CFD) methods for predicting the hydrodynamic derivatives. Otzen and Simonsen (2014) and Simonsen, Otzen, Klimt, Larsen, and Stern (2012), identified a reduced test matrix to be applied for PMM simulations, and standard maneuvers were conducted for the appended KCS ship model by using the Abkowitz model. Sakamoto, Carrica, and Stern (2012) conducted unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of static and dynamic PMM tests for an un-appended surface combatant model 5415. Sung, Park, and Jun (2015) developed an easy procedure of virtual captive model tests to obtain the linear and nonlinear hydrodynamic derivatives for un-appended Kriso Container Ship (KCS) and KVLCC1 & 2. He et al. (2016) computed the linear hydrodynamic derivatives of the KVLCC2 ship model by numerically simulating pure sway and pure yaw tests and performed the standard free running maneuvers using Maneuvering Modeling Group (MMG) mathematical model.

1.2 Statement of problem
Regarding the environmental concern and increase of fuel price, optimizing the fuel consumption is nowadays an important issue in all industries. In ship industry one way to decrease the fuel consumption is improving the propulsion system of the ship which results in higher propulsive efficiency. One of the options to reach this aim is evaluation of different locations of the rudder in order to improve the propulsive efficiency. It would be time consuming and not cost effective to make a model of every rudder location. Computational fluid dynamic is a good solution for this problem, because you can easily do several cost effective test in a proper amount of time. Different rudder positions can be modelled and simulated in order to improve and optimize the design by trying to increase the propulsion efficiency and at the same time decreasing the side effects such as cavitation and loss in maneuverability.

1.3 Aim and objectives of the study
The main aim of this research is to study the maneuverability characteristics of the Twin Propeller/Twin Rudder Experimental Kriso Container Ship (KCS). In order to achieve the aim, the following specific objectives were formulated to guide the study. They include;
To numerically simulate a series of captive model with the propeller operating at a certain ship propulsion point
To verify static constant forces or moments as well dynamic verification of time series for forces and moments affecting the maneuverability characteristics of a ship’s propeller
To compare results for the static rudder and rudder–drift operation at different rudder angles and captive speeds and how it affects the maneuverability characteristics of a ship’s propeller