**1. Introduction**

One of the major barriers to energy-efficient shipping is hull roughness, which is caused by various factors including mechanical causes, chemical and electrochemical processes (i.e., corrosion), and the colonisation of biofouling [1,2]. The associated economic and environmental problems include the added ship resistance and increased fuel consumption and CO2 emissions, as well as the cost for the hull maintenance. From a naval architect or a ship owner's point of view, a proper life cycle assessment is needed to improve the profitability of the ship. In other words, the economic penalties associated with the increased fuel consumption and/or the speed loss of ships should be accurately predicted and compared with the costs associated with the antifouling activities.

Accordingly, there have been investigations and studies to predict the impact of hull roughness on ship performance. The similarity law scaling procedure proposed by Granville [3,4] has been preferred by many researchers, e.g., [5–9], owing to its merits including the computational cost-effectiveness and the robustness for arbitrary ship lengths and speeds [10]. However, Granville's method is still limited by the flat plate simplification, which disregards the 3D effects, e.g., form resistance [11].

On the other hand, a Computational Fluid Dynamics (CFD) approach has been routinely employed in the field of naval architecture and ocean engineering owing to the merits that CFD can overcome the difficulties of nonlinear problems in theoretical studies while it is more cost-efficient compared to physical experiments [12–15]. Furthermore, the afore-mentioned shortcomings of Granville's method can be avoided using CFD. In CFD

**Citation:** Song, S.; Demirel, Y.K.; De Marco Muscat-Fenech, C.; Sant, T.; Villa, D.; Tezdogan, T.; Incecik, A. Investigating the Effect of Heterogeneous Hull Roughness on Ship Resistance Using CFD. *J. Mar. Sci. Eng.* **2021**, *9*, 202. https:// doi.org/10.3390/jmse9020202

Academic Editor: Dong-Sheng Jeng

Received: 28 January 2021 Accepted: 10 February 2021 Published: 16 February 2021

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simulations, the 3D effects can be considered and thus the ship resistance predictions can be more accurate. Furthermore, the CFD method is not only limited to ship hulls, but it can be applied for an arbitrary object in fluid. Accordingly, the CFD method has been used for investigating the roughness effect on ship resistance, e.g., [16–18], propeller performance, e.g., [19,20], and ship self-propulsion performance, e.g., [21,22], as well as the tidal turbine performance, e.g., [23].

Recently, Song et al. [24,25] validated Granville's method and the CFD method by comparing the predictions against a ship model test with a rough surface.

However, the majority of the studies have treated the hull surfaces as uniformly rough, while the real ships' surfaces are not uniform due to the heterogeneous biofouling accumulation on the hull. The simplification of treating the surfaces as uniformly rough can introduce inaccuracies in predicting the added resistance, as claimed by Demirel et al. [26].

Recently, Song et al. [27] conducted towing tests using a Wigley hull model with various hull roughness conditions including homogeneous conditions (i.e., smooth and full-rough) and heterogeneous conditions (i.e., <sup>1</sup> <sup>4</sup> -bow-rough, <sup>1</sup> <sup>4</sup> -aft-rough, <sup>1</sup> <sup>2</sup> -bow-rough and <sup>1</sup> <sup>2</sup> -aft-rough) by applying sand-grit on the hull surface systematically. Owing to the symmetric shape of the Wigley hull, the total resistance with the bow and aft-rough conditions could be compared to each other with the same rough surface areas. The result showed that the bow-rough conditions (i.e., <sup>1</sup> <sup>4</sup> -bow-rough and <sup>1</sup> <sup>2</sup> -bow-rough) showed larger added resistance than the aft-rough conditions (i.e., <sup>1</sup> <sup>4</sup> -aft-rough and <sup>1</sup> <sup>2</sup> -aft-rough). This finding suggests that the hull roughness in the forward part of the hull is more significant than other parts in terms of added resistance. This finding is attributed to the higher local skin friction near the leading edge, which is found either on smooth or rough surfaces. Song et al. [26] suggest that this higher local skin friction near the leading edge results in a higher roughness Reynolds number and thus a more significant roughness effect acts at the forward part of the hull. However, the study could not confirm the underlying cause since the local skin friction on the hull was not determined whilst measuring the total drag of the model.

On the other hand, there have been recent studies modelling the heterogeneous hull roughness in CFD simulations. Östman et al. [28] conducted CFD simulations of a full-scale tanker to investigate the potential in a low-cost approach for ship resistance reduction with selective applications of different quality coatings. In the CFD simulations, a high-quality coating (low roughness) surface was applied on the regions where high skin friction is concentrated, while the rest of the hull was modelled with a low-quality coating (high roughness). The result showed that the low-cost approach can reduce the ship resistance compared to the case when the low-quality coating is applied on the entire hull. Vargas et al. [29] investigated the impact of homogeneous and heterogeneous roughness distributions using CFD. A full-scale combatant was modelled with divided hull sections to evaluate different hull roughness scenarios. The result showed that the increase in the local skin friction due to hull roughness is highest at the bow, followed by sides, flat bottom, stern and transom, suggesting the benefits of partial hull cleaning. However, while these studies showed that the CFD simulations can be used to model the heterogenous hull roughness, their results were not validated against experimental data. Therefore, there is a need for a dedicated validation study to demonstrate the validity of the CFD approaches for predicting the effects of heterogeneous hull roughness.

The aim of the present study is, therefore, to fill this research gap by conducting CFD simulations to predict the effect of heterogeneous hull roughness on ship resistance and also performing a validation study by comparing the results with experimental data. In addition, the CFD simulations enable us to examine the local skin friction and roughness Reynolds number on the hull, and thus the locally varying flow regime over the heterogeneous hull roughness can be examined.

In this study, CFD simulations of the Wigley hull were developed with different hull roughness conditions using the modified wall-function approach with the roughness function model of the sand-grain surface, which were determined from previous

studies [24,25]. The CFD simulations of the Wigley hull model were performed with different hull conditions. The predicted total resistance coefficients for the various hull conditions were compared with the experimental data [27] for validation purposes. Finally, the local skin friction and the roughness Reynolds number distribution on the hull surfaces were correlated with the findings of the effect of heterogeneous roughness.
