Hydrodynamic modeling of planing catamarans with symmetric hulls Ghazi S. Bari, Konstantin I. Matveev n School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164 À2920, USA article info Article history: Received 1 October 2015 Accepted 31 January 2016 Keywords: High-speed catamarans Planing hull hydrodynamics Potential flow theory Numerical modeling abstract Despite rising popularity of planing catamarans, numerical methods for predicting their hydrodynamics are rather scarce and incomplete. The hydrodynamic interaction between hulls planing parallel to each other is known to become significant when spacing between hulls is sufficiently small. In the present study, a potential-flow method of hydrodynamic sources is applied for modeling steady hydrodynamic characteristics of twin-hull setups. Parametric calculations are carried out for symmetric hulls in variable speed regimes at different spacings, hull aspect ratio, and deadrise angles. Results are presented for the lift coefficient and center of pressure, and some illustrations are given for the water surface elevations. The lift coefficient is found to increase with smaller spacings and higher aspect ratios at moderate and high Froude numbers. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction Boats moving at high speeds operate in the planing mode when the hydrodynamic lift on their hulls overcomes the hydrostatic lift. To improve lateral stability of such boats and to increase available deck space, twin-hull arrangements are often implemented (Fig. 1). The hydrodynamic interaction between hulls operating in a proximity to each other can be significant and needs to be accounted for at the design stage. The hydrodynamic character- istics of catamaran hulls are often quite different from those of typical monohulls. As discussed by Faltinsen (2005), if the diver- gent waves generated by one hull impinge on and become reflected by the other hull, then the wave field generated by a multi-hull vessel cannot be a simple superposition of wave fields produced by each hull. This happens if the hulls are sufficiently close to each other; and as a consequence, the complex wave pattern in the central region will have strong influence on the hull hydrodynamics. Over the last several decades planing catamarans have gained popularity for commercial, recreational and military purposes, yet there is a relatively limited body of literature on the subject of planing multi-hulls. Savitsky and Dingee (1954) tested flat plates planing in parallel at different spacings and very high Froude numbers and found that the lift increases as the hulls become closer to each other. Liu and Wang (1979) also conducted a test series with planing catamarans and suggested a modification to the empirical correlation for a single-hull lift (Savitsky, 1964) that accounts for the presence of another hull. Dubrovsky and Lyakhovitsky (2001) briefly described extensive studies conducted in Russia on high-speed multi-hulls and discussed performance- enhancing means, such as hydrofoils and interceptors. Morabito (2011) reviewed some of the archival and recent findings for planing catamarans, noting that the lift correction for a hull in the catamaran arrangement is usually below 5% (relative to the single hull lift) when the spacing between hulls exceeds two of the hull beams. Several CFD-type analyses of specific high-speed multi- hulls can be also found in the literature (e.g., Zhou, 2003; Kan- dasamy et al., 2011; Yousefi et al., 2014). The main objectives (and novelties) of this paper are to apply a computationally efficient potential-flow method for evaluating hydrodynamics of planing catamarans and to present numerical results for the lift coefficient and the center of pressure of cata- marans in a range of geometrical parameters and speed regimes. Only prismatic symmetric hulls with hard chines are considered here, as illustrated in Fig. 1. The current numerical model is based on the linearized three-dimensional method of hydrodynamic singularities of a source type that was previously developed and applied for hydrodynamic modeling of single planing hulls in early planing regimes (Matveev and Ockfen, 2009; Matveev, 2014a), when both hydrostatic and hydrodynamic lift components are important. It can be noted that the present method belongs to a family of boundary elements methods, and a number of publica- tions exist on the subject of BEMs applied for single-hull hydro- dynamics. For example, Doctors (1974) and Wang and Day (2007) utilized a distribution of pressure elements over planing surfaces, while Lai and Troesch (1996) and Benedict et al. (2001) applied vortex-lattice methods. A detailed review of modeling techniques for planing hulls has been recently given by Yousefi et al. (2013). Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering http://dx.doi.org/10.1016/j.oceaneng.2016.01.035 0029-8018/& 2016 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ1 509 335 1327; fax: þ1 509 335 4662. E-mail address: matveev@wsu.edu (K.I. Matveev). Ocean Engineering 115 (2016) 60–66