Hydrodynamic performance of a Magnus anti-rolling device at zero and low ship speeds

Highlights

• The hydrodynamic performance of a Magnus anti-rolling device is studied.

• The performance is assessed at zero and low ship speeds by large eddy simulation.

• The swinging rotating cylinder is considered under different motion conditions.

• The effect of the hull on the hydrodynamic performance is disregarded.

• The results of this study contribute to the development of ship seakeeping strategies.

Abstract

Excellent seakeeping performance is the basis of safe ship operation. An anti-rolling device employing swinging rotating cylinders based on the Magnus effect can provide anti-rolling measures at any ship speed. In this study, the operating principle of a Magnus anti-rolling device was examined by studying its hydrodynamic performance using large eddy simulation method. A dimensionless parameter—the rotation to swing ratio (i.e., the ratio of the rotational speed to the swing speed of the cylinder)—was proposed for use in the hydrodynamic analysis. The changes in lift-drag characteristics and wake-flow field of the Magnus anti-rolling device were observed at zero and low ship speeds according to the swing angle, angular velocity, and rotation to swing ratio. The influence of the relative incoming flow velocity on the hydrodynamic characteristics of the Magnus anti-rolling device, when swinging upstream and downstream, was also studied at a low ship speed. The results show that an optimal rotation to swing ratio can be obtained at zero speed, and that the differential swing method can provide a large and consistent lift at low speeds. This analysis of the hydrodynamic characteristics of the Magnus anti-rolling device contributes to the study of ship seakeeping strategies.

Introduction

Owing to the influence of wind, waves, and currents, seagoing ships are constantly subjected to movement with six degrees of freedom (Su et al., 2020b). The impact of rolling motion on the safety, comfort, and operational stability of ships is particularly important given their slender structures. Therefore, the seakeeping performance of ships must be improved using anti-rolling methods. In addition to profile optimisation, the use of active or passive anti-rolling devices offers an effective method to restrain the rolling motion of ships. Commonly used anti-rolling devices mainly include bilge keels (Kristiansen et al., 2014; Yasukawa et al., 2018), anti-rolling tanks (Gu et al., 2015), anti-rolling fins (Mao et al., 2019; Wang et al., 2009, 2016; Taylan, 2007), and gyro stabilisers (Takeuchi et al., 2011; Talha et al., 2017). Traditional anti-rolling devices possess several limitations, specifically: a) large installation space requirements, which limit the loading volume; b) sensitivity to ship speed, which limits applications to certain speeds; and c) high costs, which limit widespread usage.

In this study, a ship anti-rolling device based on the Magnus effect was evaluated owing to its small installation space requirements, suitability at all speeds, and low cost. The anti-rolling principle of this device is as follows. When subjected to an incoming flow, the flow velocities at the upper and lower surfaces of a rotating cylinder generate a speed difference owing to the cylinder rotation. According to Bernoulli's principle, the upper and lower surfaces of the rotating cylinder therefore experience different pressures, resulting in a lift force on the cylinder in the direction perpendicular to the incoming flow. By changing the rotational direction and speed of rotation of the cylinder, the direction and magnitude of the lift can be adjusted to offset the rolling motion of the ship, thereby achieving stability (Isiam and Raghavan, 2006; Kang, 2006; Mittal and Kumar, 2003; Padrino and Joseph, 2006). When the flow velocity is zero, the cylinder must swing to generate the relative incoming flow. Under these conditions, the magnitude of the resulting lift force is related to the cylinder swing speed, swing angle, and rotational speed. The direction of the lift force depends on the rotational direction of the cylinder as well as the swing direction.

The Magnus effect has been applied to prevent ship rolling since the early 1970s. However, it has not been extensively developed owing to the constraints of the structure, waterproofness, difficulty of automatic control, and other technologies. A ship can achieve a considerable anti-rolling effect at zero speed using swing control. The Magnus anti-rolling device has a simple structure and requires only a small cabin capacity for installation. Furthermore, the device can be retracted into the ship cabin when not needed, reducing hull resistance. The low costs of fabrication, installation, and maintenance, as well as the potential for providing all-speed anti-rolling effects, could lead to widespread application of Magnus anti-rolling devices (Dallinga and Papuc, 2008). With advances in electromechanical sealing and automation technologies, extensive research on Magnus anti-rolling devices were conducted. RotorSwing (the Netherlands) was the first company to design and manufacture a retractable Magnus anti-rolling device (Liang et al., 2017). In 2009, Quantum (US) launched the MAGLift™ rotor stabiliser, which employs an electro-hydraulic servo system in the swing system of a Magnus anti-rolling device to improve its output performance substantially.

The hydrodynamic analysis of the swinging rotating cylinder is crucial for the efficient design of the Magnus anti-rolling device. As the cylinder rotates while swinging around one end, the flow field near the cylinder becomes quite complicated. Accurate simulation of this field is crucial when analysing the hydrodynamic characteristics of the device. Computational fluid dynamics (CFD) simulations have been widely used to study the flow around rotating cylinders; the simulation of turbulence is crucial in this application. Researchers have accordingly developed various turbulence models for use in engineering applications. However, turbulence models based on the Reynolds-averaged Navier–Stokes equations reflect only the time-averaging effect and ignore the minute details of the turbulence motion, making these models unsuitable for simulation of complex and fine turbulence structures such as flow separation and the Kármán vortex street (Kim et al., 2016; Wang et al., 2017). In recent times, rapid progress in computing has facilitated the realisation of detached eddy simulation, large eddy simulation (LES), and direct numerical simulation models. These methods provide effective analytical tools for flow field simulations with a high Reynolds number (Re).

The LES method has been widely used to simulate flows with a high Re. Mobini and Niazi (2014) adopted LES to perform a numerical simulation of unsteady turbulent flows around a rotating cylinder. They observed that with an increase in the spin ratio (i.e., the ratio of the cylinder rotational speed to the incoming flow speed) or a decrease in Re, both the front stagnation and top separation points dislocate upwards along the cylinder, resulting in a decrease in the average drag and an increase in the average lift. They also noted the size of the rear vortex of the cylinder to increase with increasing Re. Karabelas et al. (2012) studied a rotating cylinder with an Re of 1.4 × 10⁵, observing that the LES enables a high level of accuracy in flow simulations with a large Re. Rodriguez et al. (2017) studied the impact of surface roughness on the flow around a cylinder from subcritical up to transcritical values of Re using LES. Wu et al. (2020) used LES to study the influence of the spacing ratio and stagger angle on the flow around two stationary staggered cylinders by applying the subcritical Re.

Several studies have been reported wherein numerical simulations and theoretical calculations were performed to investigate the influence of the Re and spin ratio on the flow around a rotating cylinder. The Magnus anti-rolling device has been successfully applied to full-scale ships. Nevertheless, few studies have been conducted on the hydrodynamic performance of a swinging rotating cylinder to quantify the anti-rolling effect of such a device. The hydrodynamic performance of a ship anti-rolling device based on the Magnus effect was investigated in this study via numerical simulations. The hydrodynamic characteristics of a swinging rotating cylinder were investigated at zero and low speeds. The influences of the swing angle, angular velocity, and rotation to swing ratio on the hydrodynamic performance of the swinging rotating cylinder at zero flow velocity were analysed based on the flow field variations around the cylinder. The lift and drag performances of a swinging rotating cylinder were then compared under different relative incoming flow velocities, swing angles, angular velocities, and rotation to swing ratios at low speeds. The lift, drag, and flow field changes were analysed when the cylinder swung downstream and upstream.

The remainder of this paper is organised as follows: Section 2 introduces the numerical model and approach adopted in this study, Section 3 presents an analysis of the numerical results, and Section 4 summarises the findings and provides suggestions for future research.