|Wiwin Sulistyawati||Faculty of Engineering, Universitas Pembangunan Nasional Veteran Jakarta, Jl. RS Fatmawati Raya, Pondok Labu, Jakarta Selatan, 12450, Indonesia|
|Purwo Joko Suranto||Faculty of Engineering, Universitas Pembangunan Nasional Veteran Jakarta, Jl. RS Fatmawati Raya, Pondok Labu, Jakarta Selatan, 12450, Indonesia|
In general, evaluation of ship hydrodynamic efficiency could be produced by an energy-efficient and concentrated cost function. An optimization method with the representation of hull geometry is one of the preliminary design steps that are most appropriate for evaluating hydrodynamic performance. This work presents a comparison of two numerical methods for optimizing the shape of the hull concerning the minimization of total ship resistance in calm water conditions. The optimization method uses a theoretical approach based on Michell's integral and Rankine source methods. The discussion of the two methods emphasizes the comparison of wave resistance, total resistance, wave profiles, and wave contour. The optimized hull form comparison of total resistance between Michell's integral and Rankine source methods decreased by 3.79% and 4.0%, respectively. Comparing wave resistance with decreases by 5.52% based on Michell's integral method and 13.33% by the Rankine source method, the wave profiles generated by these two methods present a fair amount of compatibility. The wave contour illustrates a reasonably straightforward agreement on the optimal hull but are dissimilar on the initial hull.
Optimization; Michell's integral; Rankine source method; Resistance; Series 60; Wave contour; Wave profiles
The fundamentals of ship hydrodynamics are to obtain a design with minimum resistance following a specified speed and displacement. Total resistance is of the utmost importance for the ship, directly affecting speed, power requirements, and fuel consumption. The hydrodynamic performance of the ship can be enhanced by reducing friction and pressure resistance. Several recent techniques have been carried out to achieve reduced drag on ships, i.e., improvements to the hull structure (Ibrahim et al., 2018), micro bubble injection (Sindagi et al., 2018; Zhang et al., 2019), and optimization techniques (Park et al., 2015; Samuel et al., 2015; Choi 2015; Lu et al., 2016; Lu et al., 2019). The hull's geometric optimization is considered a relatively reliable and appropriate method of evaluating ship hydrodynamics. Objective functions, design variables, and limits to obtain optimal hydrodynamic efficiency concerning drag components and vessel performance, such as stability and seakeeping, are considered primary objective functions. It has supported computational optimization that has developed into a practical and fast design technique that automatically generates an optimal hull design to reduce drag. Fast-repetitive processes and reduced cost functions are the designer's choice for using this technique.
The advancement of Computational Fluid Dynamics (CFD) has expanded the domain of hydrodynamic problems effectively in viscous flow solving, domain decomposition, turbulence solver, and physical details of the phenomenon's flow field. The development of CFD computing technology has proven to be useful for evaluating the hydrodynamic performance of ships to produce an optimum hull and attempts to obtain a drag reduction (Yanuar et al., 2017; Wang and Yao, 2018; Zhang et al., 2019; Yanuar et al., 2020). The Rankine source method and Reynolds Averaged Navier Stokes (RANS) based viscous flow methods are potential flow panel methods that were developed in several studies with quite advanced techniques. The Rankine source method is considered fast, efficient, and highly precise in potential flow theory, e.g., Rankine source method with the optimization algorithm Nonlinear Programming Method (NLP) in monohull (Zhang and Zhang, 2015) and multihull optimization (Von Graefe et al., 2013; Von Graefe et al., 2015). The Michell integral method or thin ship theory is considered a more straightforward and faster CFD method (Tuck and Lazauskas, 1998). Several studies (Yanuar and Sulistyawati, 2018; Sulistyawati et al., 2020a; Sulistyawati et al., 2020b; Sulistyawati et al., 2020c) used Michell theory to investigate the hydrodynamic characteristics of pentamarans and compared them with experiments. Any deviations from the Michell integral method were deemed necessary for development. A boundary layer correction for potential flow or the tangency correction of the wave resistance oscillation problem at a small Froude number, Fr, in Michell's theory was delivered by (Baši? et al., 2018). However, these numerical results still require verification with experimental studies to test their validity.
This study represents a method of ship hull form optimization with the Michell integral. The hull is defined by inputting data with a grid offset setting into 21 stations and 21 water lines, a genetic algorithm in multi-objective optimizations to approximate the optimized hull with a minimum wave and total resistance in calm water. Two simple tools based on Michell's theory were quite applicable for investigating resistance performance and optimization (Sulistyawati et al., 2020b; Sulistyawati et al., 2020c). The results were compared with the Rankine source method (Zhang and Zhang, 2015). The Godzilla optimization tool (Lazauskas, 1996) and Flotilla (Lazauskas, 1999) were used for the optimization of the resistance components and contour of the wave elevation.
Conforming to this study's purpose, which investigated the comparison of Michell's integral theory and the Rankine source method, several analyses were carried out on the total resistance, wave resistance, wave profile, and its contours. The optimal model produced by the two methods showed good graphical conformity even with significant differences. Unfortunately, the research of (Zhang and Zhang, 2015) were not carried out at a higher speed, Fr > 0.32. In contrast, the approach with the Michell integral method was deficient at low speeds. Theoretically, the Michell integral method linearizes the shape of the hull and free surface conditions. The form factor approach is perhaps less precise, and the friction factor dominates at low speed. It is, therefore, very likely that this is the reason for a considerable discrepancy between the two methods. The Rankine source method considers the nonlinear on the actual free surface and nonlinear hull surface conditions.
Improvements in the complicated numerical Michell integral should consider the tool's viscous and nonlinear effects, which is needed to obtain more accurate results. Computation between the optimization of these two methods showed differences in the resistance component, wave profile, and contour. It is necessary to review the subsequent analysis of water conditions and the towing experiment at a higher speed.
This research was ?nancially supported by funding internal research of UPN Veteran Jakarta on RIKNAS 2020 following KEP. REKTOR No. 346/ UN61.0/HK.02/2020. The authors also thank Dr. Leo Lazaukas at the University of Adelaide for solution tools based on the Michell integral method.
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