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Combining Analytical Models and Mesh Morphing Based Optimization Techniques for the Design of Flying Multihulls Appendages Journal of Sailing Technology 2021, volume 6, issue 1, pp. 151 – 172. The Society of Naval Architects and Marine Engineers. Combining Analytical Models and Mesh Morphing Based Optimization Techniques for the Design of Flying Multihulls Appendages Ubaldo Cella University of Rome “Tor Vergata” and Design Methods - Aerospace Engineering, Italy, [email protected]. Corrado Groth University of Rome “Tor Vergata” and RBF Morph, Italy. Stefano Porziani Downloaded from http://onepetro.org/JST/article-pdf/6/01/151/2478351/sname-jst-2021-09.pdf by guest on 24 September 2021 University of Rome “Tor Vergata” and RBF Morph, Italy. Alberto Clarich ESTECO, Italy. Francesco Franchini EnginSoft, Italy. Marco Evangelos Biancolini University of Rome “Tor Vergata” and RBF Morph, Italy. Manuscript received March 15, 2021; revision received May 18, 2021; accepted June 22, 2021. Abstract. The fluid dynamic design of hydrofoils involves most of the typical difficulties of aeronautical wings design with additional complexities related to the design of a device operating in a multiphase environment. For this reason, “high fidelity” analysis solvers should be, in general, adopted also in the preliminary design phase. In the case of modern fast foiling sailing yachts, the appendages accomplish both the task of lifting up the boat and to make possible upwind sailing by contributing balance to the sail side force and the heeling moment. Furthermore, their operative design conditions derive from the global equilibrium of forces and moments acting on the system which might vary in a very wide range of values. The result is a design problem defined by a large number of variables operating in a wide design space. In this scenario, the device performing in all conditions has to be identified as a trade-off among several conflicting requirements. One of the most efficient approaches to such a design challenge is to combine multi-objective optimization strategies with experienced aerodynamic design. This paper presents a numerical optimization procedure suitable for foiling multihulls. As a proof of concept, it reports, as an application, the foils design of an A-Class catamaran. The key point of the method is the combination of opportunely developed analytical models of the hull forces with high fidelity multiphase analyses in both upwind and downwind sailing conditions. The analytical formulations were tuned against a database of multiphase analyses of a reference demihull at several attitudes and displacements. An aspect that significantly contributes to both efficiency and robustness of the method is the approach adopted to the geometric parametrization of the foils which was implemented by a mesh morphing technique based on Radial Basis Functions. Keywords: multiobjective optimization; mesh morphing; Radial Basis Functions; foiling catamarans; aerodynamic design. 151 NOMENCLATURE 퐶푓 Friction drag coefficient 퐶푇 Total hull resistance coefficient 퐶푤 Hull wave drag coefficient 퐷퐻 Bare hull drag [Kg] 퐹푁 Froude number 푮 known values at source points [m] 퐿퐻 Hull side force [Kg] 푁 Number of source points 푷 Constraint matrix 푅푒 Reynolds number 푠 Interpolation function 2 Downloaded from http://onepetro.org/JST/article-pdf/6/01/151/2478351/sname-jst-2021-09.pdf by guest on 24 September 2021 푆퐻 Hull side force reference surface [m ] 2 푆푤푒푡 Hull wet surface [m ] 푼 Interpolation matrix 푉 Boat velocity [m s-1] 푊퐻 Operative displacement [Kg] 풙 Coordinates vector [m] 훽 Leeway angle [rad] 휸 Vector of radial function coefficients 휕퐶 퐿퐻 slope of the hull side force polar curve [rad-1] 휕훽 휼 Vector of polynomial coefficients -3 휌푤 Sea water density [kg m ] 휑 Radial function 6DoF Six Degree of Freedom CAD Computer Aided Engineering CFD Computational Fluid Dynamics RANS Reynolds-averaged Navier-Stokes RBF Radial Basis Functions VOF Volume Of Fluid VPP Velocity Prediction Program 152 1 INTRODUCTION Foiling is the modern term used to describe a sailing condition in which the boat is raised up from the water by lifting surfaces. It is not a new idea. The concept was first introduced, more than 100 years ago, by the Italian engineer, inventor and aeronautical pioneer, Enrico Forlanini. He had been studying the idea since 1898 and in 1905 he tested his first prototype equipped with a ladder system of foils under the hull and a 60 hp engine. During tests, the hydrofoil managed to reach a top speed of 37 knots flying half a metre above the water of Lake Maggiore (Calabrò, 2004). The first known sailing hydrofoil was produced by the Americans Robert Rowe Gilruth and Carl William Price who managed to achieve the same feat, albeit very slowly, under sail in 1938 (Sheahan, 2013). As often occurs for many innovative solutions, however, the efficient exploitation of the potentialities of adopting foils on sailing boats was related to the technological improvements in materials, manufacturing processes and design tools capability. The beginning of the modern era of foiling sailing boats (from the engineering point of view) might be identified with the 34th America's Cup. The foiling solutions developed for the AC72 catamarans stimulated the effort in adopting sophisticated engineering design approaches which had been limited to very high Downloaded from http://onepetro.org/JST/article-pdf/6/01/151/2478351/sname-jst-2021-09.pdf by guest on 24 September 2021 technological environments such as aerospace. This view encouraged competing teams to enter into technical partnerships with companies specialized in aerospace technologies. An example of this synergy was the collaboration between AIRBUS and Oracle team USA for the 35th edition of the America's Cup. Airbus, more recently, has supported the team American Magic in the development of the AC75 for the edition 2021. The solutions adopted in the major classes also gave a strong impulse to the evolution of smaller multihull classes which, furthermore, today can benefit from the availability of engineering services at a cost that begins to be compatible to their market requirements. The literature offers several references to hydrofoils application for fast mono and multi hull crafts (Besnard, et al., 1998; Prastowo, et al., 2016; Kandasamy, et al., 2011). An historical review of their application on several types of fast crafts, together with an experimental report of the advantages in several sailing conditions, is reported in (Migeotte, 2002). Sighard F. Hoerner is historically one of the most important contributors to this topic. His books represent one of the main references for hydrodynamic (Hoerner, et al., 1954) and aerodynamic (Hoerner & Borst, 1975) designers. The literature is, however, not so abundant on problems facing hydrofoil design for sailing boat applications. Reviews of America's Cup case studies (Cassio, 2016) or references to numerical analysis methodologies (Paulin, et al., 2015) are common. Apart from some recent valuable publications as (Graf, et al., 2021; Hagemeister & Flay, 2019), the same cannot be said in the case of foils design methodologies suitable to fast sailing crafts. This paper aspires to contribute to filling this gap. This paper describes a foils design methodology, based on a numerical optimization environment able to evaluate the performance of a flying catamaran when sailing in both upwind and downwind conditions. The analysis of the surface piercing foils in flying configuration is performed by a two- phase CFD simulation. To reduce the computational resources, the foils forces in non-flying configuration are evaluated by a single phase CFD run in which the hull is present only as a small fixed portion of a rounded inviscid surface in the upper domain boundary. The contribution of the floating hull is integrated by opportunely developed analytical models. The foils geometric parametrization was implemented by a cutting-edge mesh morphing technology based on Radial Basis Functions. To demonstrate the capabilities and the potentialities of the methodology, the design of A-Class catamaran foils was selected as a pilot study. The A-Cat test case represents a highly constrained problem that includes most of the typical complexities involved in flying boat appendages design. The work was previously reported in (Biancolini, et al., 2018). What follows integrates the presentation of the methodology with a more detailed description of the analytical formulations developed to model the hull hydrodynamic forces. 153 The A-Class, born in the late 50s, is a small high-tech catamaran that is considered the fastest single-handed racing dinghy in the world. The rules are very simple and mainly constrain the minimum weight (75 Kg), the hulls length (18 ft) and the sail surface (150 ft2). In 2009, when the interest in flying configurations began to rise, new rules were added with the intention of preventing foiling for A-Cats. Given that the concept of hydrofoiling prohibition was ambiguous and difficult to define, an indirect approach was chosen. The idea was to introduce a set of constraints aimed at limiting the surfaces suitable for sustaining the boat so as to make a flying configuration unfavourable compared to a traditional one. The assumption adopted to the adjustment of the rules proved, however, to be conservative and was not able to prevent the development of very favourable flying configurations. Nevertheless, they made the foils dimensioning a complex and strongly constrained design problem that represents a challenging test case for engineering design tools and methodologies. The method here described, adopted for the A-Cat test case, is suitable for any class of flying boats of any dimension. The description of the methodology and the work performed are reported in four sections. First a description of the parameterization strategy adopted, with the relative theoretical recall and setup Downloaded from http://onepetro.org/JST/article-pdf/6/01/151/2478351/sname-jst-2021-09.pdf by guest on 24 September 2021 procedure, is provided. In the following section the A-Cat foils design problem, and its constraints, is introduced.
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