Third International Symposium on Marine Propulsors smp’13, Launceston, Tasmania, Australia, May 2013 Hub effect in propeller design and analysis S. Brizzolara 1 , S. Gaggero 2 , D. Grassi 3 1 Visiting Associate Professor, Department of Mechanical Engineering, MIT, Cambridge, USA 2 Department of Naval Architecture (DITEN), Università di Genova, Genova, Italy 3 ZF Marine, Arco di Trento, Italy ABSTRACT The importance of considering hub effects in the design, optimization and verification of marine propellers is discussed in the paper. Different design variants of optimum moderately loaded modern propellers are obtained by means of fully numerical lifting line/surface vortex lattice methods, with and without hub effect. Anti- symmetric vortex images are used to implement the effects of the hub by the vortex lattice codes. Classical parametric lifting surface corrections are also used to correct pitch and camber. Global as well as local (pressure distribution) hydrodynamic properties of the propellers are compared as obtained from a fully numerical lifting surface method, a boundary element method and a finite volume RANS solver, referred to as the closest model of the real flow. The comparison permits to highlight the undesired consequences which a designer should expect if an inadequate or inconsistent hub modeling is used in some part of the propeller design process. Indeed, the best propeller design, in terms of efficiency, thrust matching and shock-free condition on its inner section is found when the hub effect is considered by all the numerical methods used for design. Keywords Marine Propeller Design, Hub Effect, Lifting Line Vortex Lattice, Lifting Surface, Panel Method, RANSE. 1 INTRODUCTION Modern marine propeller design still relies on the lifting line theory, at least in the first design stage when the optimum circulation distribution needs to be selected. Actually the majority of the contemporary design codes are still based on the classical of Eckhardt and Morgan (1955) propeller design method that proposes a good engineering solution to the original problem definition valid for lightly or moderately loaded propellers developed by Lerbs (1952), who completely ignored the presence of the hub. McCormick (1955) first proved that the effect of finite hub radius in the range of 0.2-0.4 times the propeller radius effectively has a non-negligible influence on the optimum circulation distribution, found according to the Betz optimum condition. In his analysis McCormick modeled the effect of an infinitely long cylindrical hub by imposing a zero radial velocity at its radial position, thus permitting to find a non-null circulation that, summing up at the end of the hub cap forms the hub vortex in the propeller wake. This boundary condition at the blade root (hub surface) seems closer to reality than the zero- circulation condition imposed by Tachmindji (1956) and Tachmindji and Milam (1957), considering the evidence from the experiments on model propellers: in fact the hub at least partially does have a wall effect and maintains a finite circulation at the hub, which according McCormick changes with the number of blades, propeller load and advance ratio. Finite circulation at the hub means that each blade releases a trailing vortex at the root section. These trailing vortexes are summing up at the hub trailing edge into a single, stronger hub vortex. This is the physical evidence well highlighted for example by Kerwin (2007). The hub vortex is characterized by a viscous core that prevents the ideal pressure recovery on the stern closure of the hub cap, inducing an additional drag force (effective thrust deduction). Lifting line methods with hub effects must correctly consider this additional drag when optimizing the circulation for optimum propeller efficiency, as first pointed out by Wang (1985), who proposes a simplified method for calculating this added drag. Kerwin and Leopold (1964) were the first to adopt a 2D image vortex method to represent the symmetric flow condition imposed by the cylindrical surface of the hub at the blade position, effectively imposing the same boundary condition of infinitely long cylinder used by McCormick in his analytical method. Sanchez-Caja (1988) presented a higher fidelity lifting line model of a propeller, where hub effects are represented by means of quadrilateral panels distributed on the (cylindrical) hub surface, demonstrating the almost perfect correspondence with the less computationally expensive vortex image method proposed by Kerwin and Leopold (1964). Coney (1989) discusses in a certain detail all these different approximated models, in the end selecting the one proposed by Kerwin and Leopold (1964) for the development of his fully numerical lifting line design code. Also Kimball and Epps (2010) in OpenProp, a 110