Numerical parametric study of medium sized container ship squat

https://doi.org/10.1016/j.apor.2021.102563Get rights and content

Highlights

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    CFD computation of self-propelled container ship squat in shallow water.

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    Validation of CFD simulations against benchmark experiment data.

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    Systematic investigation into the impact of varying principal particulars on squat.

Abstract

A numerical investigation has been undertaken to study the impact of varying a container ship's principal particulars on squat in shallow water. Initially, a statistical review of the principal particulars of commonly operating container ships is discussed and used to determine the range for length-to-beam ratio (L/B), beam-to-draft ratio (B/T) and block coefficient (CB) to be analysed systematically. Unsteady RANS CFD simulations are adopted to predict the squat of a self-propelled S175 container ship where the approach is successfully verifed and validated against benchmark experimental data. The same methodology is adapted to a KCS hull as a representation of modern container ships and systematic parametric transformations are conducted to study the effect of varying L/B, B/T and CB on squat. The results show that sinkage and trim are inversely related to L/B while sinkage is independent of B/T, but trim is inversely related to B/T. Sinkage is also found to be independent of CB whereas trim magnitude becomes increasingly stern down when CB increases due to the nature of the parametric transformations in this study. It is identified in this study that the relative position of the LCB to the LCF is responsible for the change in trim direction. Most empirical predictions show similar trends for varying L/B and B/T but contradicting trends are observed for varying CB.

Introduction

In the competitive nature of the container shipping industry, economies of scale is a fundamental tactic which can help reap substantial cost savings by introducing larger container ships that have lower unit costs. The substantial cost savings contribute to considerable decrease in maritime transport cost which in turn facilitates trade (Merk, 2018). Consequently, the increase in container ship size has accelerated and this growth can be seen in Fig. 1. This trend has continuously brought challenges to operate larger container ships in relatively shallow approach channels and ports due to the accentuated squat phenomenon in such conditions. Apart from increasing in size, container ship hullform have changed noticeably over the years, including more pronounced bulbous bows, stern bulbs and transom sterns(Gourlay et al., 2015). Even container ships designed within the same generation can have markedly different parameters which are dictated by different priorities and compromises made for many conflicting requirements in the design spiral (Papanikolaou, 2014). Some past studies suggest that subtle changes in hullform can alter squat behaviour (Uliczka and Wezel, 2005). Therefore, it is beneficial to understand the influence of hull principal particulars on squat in shallow water. A reliable CFD numerical investigation can play a vital role to predict squat and avoid grounding accidents, while larger container ships are maneourving into approach channels at different tidal conditions.

Ship squat has been investigated extensively where pioneering investiations were presented by Constantine (1960) regarding the different squat behaviour in open water for subcritical (Frh < 1), critical (Frh = 1) and supercritical (Frh > 1) vessel speeds. A slender-body theory for squat estimation in laterally unrestricted shallow water was developed by Tuck (1966). The work of Tuck (1966) then became the foundation for the development of various other prediction methods such as the work of Beck et al. (1974); Naghdi and Rubin (1984); Cong and Hsiung (1991).

Furthermore, model scale experiments were widely used to aid the study of ship squat, most of which were then used to develop semi-empirical formulae. For example, a semi-empirical prediction technique for full form ships was developed by Dand and Ferguson (1973), whereas Fuehrer and Römisch (1977) presented an empirical formula which accounted for varying cross section parameters of the canal. Empirical corrections for the propulsion effect on bulk carriers were derived by Duffy and Renilson (2000). Similarly, Delefortrie et al. (2010) empirically developed a mathematical model for the effects of muddy bottom and propeller action.

In addition, numerical methods have quickly become favoured in ship squat studies as computation power improves. Potential flow methods have been applied by Yao and Zou (2010); Zhang et al. (2015) to investigate the shallow water hydrodynamics where promising results were obtained for subcritical and supercritical flow but not for trans-critical flow due to neglection of non-linear effects. Jachowski (2008) demonstrated early use of Computational Fluid Dynamics (CFD) for squat prediction where non-linear and viscous effects can be accounted for in laterally unrestricted shallow water. Various other CFD studies have been conducted recently such as investigation of container ships advancing through different canals (Elsherbiny et al., 2020), the study of muddy layer effect on ship resistance and squat (Kaidi et al., 2020) as well as scale effect in squat (Kok et al., 2020c).

Throughout the studies, it is well agreed that bulk carriers tend to trim by the bow when squatting. However, the squat behaviour of container ships is not as well understood as different container ship hull forms may trim either by the bow or stern (Gourlay et al., 2015). Initial suggestions that the block coefficient determines the trim (Barrass, 1979) proved otherwise as Uliczka and Wezel (2005) pointed out that the trim depends on hull form details and, vessels with the same block coefficient but a subtly different hull form may exhibit different trim direction.

Given that subtle changes to hullform can cause substantial difference in squat and that the container ship hull design parameters can vary significantly, it is beneficial to understand the effect of manipulating certain design variables on squat. Currently, there are no literature discussing the sensitivity of squat to ship design parameters particularly that of a modern container ship hullform. Thus, this paper aims to investigate the influence of modern container ship principal particulars on squat by means of unsteady Reynolds Averaged Navier-Stokes (URANS) simulations.

The ensuing section presents the deviation in parameters for a sample of medium sized, currently operating container ships (to be used as a reference for the range for each principal particulars) followed by discussion regarding the hull forms and set-ups used in the study. The structure of this paper is such that discussions of the numerical modelling method as well as the verification and validation process are based on a model test of a self-propelled S175 container ship. Upon successful verification and validation, the same method is adapted to the KRISO Container Ship (KCS) hull form which serves as a representation of modern container ships. A systematic parametric investigation of the KCS hull is then conducted to investigate the main objective of this study; the effects of each principal particular on squat. The cause for change in trim direction is discussed. Comparisons with empirical predictions are also presented.

Section snippets

Statistics of container ship principal particulars

Sample data of 85 different container ships visiting/departing an Australian port courtesy of OMC International (2018) is used to study the range of parameters of currently operating container ships. Statistics of these ships are provided in Table 1. These container ships are considered medium sized (no ultra large crude carriers involved) and have an average length of 268m with displacement of approximately 75,000 tonnes. A plot of the parametric ratios of these ships are shown in Fig. 2. The

Hull form and set-up

As mentioned, two hullforms are used in the present study; the S175 for verification and validation purposes followed by the KCS as the parent hullform for the ensuing systematic parametric study. The S175 is a well-documented benchmark hullform used in various studies but it is a relatively dated design as discussed by Gourlay et al. (2015). On the contrary, the KCS is one of the very few publicly available benchmark hull form that is considered modern. Although it should still be acknowledged

Governing equations

In this investigation, the commercial CFD software STAR-CCM+ is used to conduct the computations where the incompressible RANS equation is resolved using the finite volume method of discretisation. The free surface effect (air and water phases) is accounted for by implementation of the Volume of Fluid (VOF) method. According to Rusche (2002), the governing equations for two phase incompressible flow are given as:∇·u=0∂ρu∂t+∇·[ρuu]=−∇p*−g·x∇ρ+∇·[μ∇u+ρτ]+σTκγ∇γτ=2ρμtS−23kI

In the above equations, u

Verification and validation

In this study, the verification and validation procedure was conducted based on the triplets method presented by Wilson et al. (2001); Stern et al. (2001). However, only the grid spacing uncertainty (UG), and time step uncertainty (UT), were considered whereas iterative uncertainty (UI), was neglected as the iterative uncertainty for ship motion response simulations in Star-CCM+ URANS solver is less than 0.2% for seakeeping applications (Tezdogan et al., 2015). Hence, the total numerical

Parametric study

Upon verified and validated the numerical method, further systematic studies of the effect of parametric variations can be conducted. The computation domain for this study is similar to the previous set-up with the exception that the KCS hullform is used instead and the waterway is laterally unrestricted. In order to ensure that the lateral boundaries are sufficiently far away from the vessel, the distance of the side walls are placed greater than the influence width (yinfl), as derived by

Results

The following section will firstly discuss the results in terms of the effect of varying L/B ad B/T. This is followed by the effect of varying CB and a discussion regarding the factors affecting trim direction in this study. Finally, a brief comparison between various empirical predictions against the CFD results are examined.

Conclusions

A systematic numerical investigation has been undertaken to study the effect of parametric hull variations on container ship squat. In this study, the statistics of the principal particulars of currently operating container ships surveyed by OMC International (2018) were studied and used as the range to be investigated.

Prior to the main investigation, a URANS simulation is modelled based on a self-propelled model scale S175 squat experiment in the AMC Towing Tank for verification and validation

CRediT authorship contribution statement

Zhen Kok: Formal analysis, Investigation, Writing - original draft. Jonathan Duffy: Supervision, Conceptualization, Writing - review & editing. Shuhong Chai: Supervision, Writing - review & editing. Yuting Jin: Methodology, Visualization, Writing - review & editing. Mohammadreza Javanmardi: Resources, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors acknowledge the funding and resources provided by NCMEH Australian Maritime College, University of Tasmania and the Tasmanian Partnership for Advanced Computing for the HPC for performing the computations. The geometry model of the S175 used for the URANS simulation is derived from 3D scanning of the existing 1:70 scale model in AMC towing tank courtesy of the Defence Science and Technology Organisation and the AMC Underwater Collision Research Facility. The authors would also like

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