Second International Symposium on Marine Propulsors smp’11, Hamburg, Germany, June 2011 From single to multistage marine propulsor: a fully numerical design approach Stefano Gaggero 1 , Davide Grassi 2 , Stefano Brizzolara 1 1 Marine CFD Group, Department of Naval Architecture, Marine and Electrical Engineering, University of Genova, Italy. 2 ZF Marine Group, Arco di Trento, Italy. ABSTRACT The limitations of classical theories for the design of contrarotating propellers suggest the necessity to develop fully numerical procedures to address designs with different front/rear rotational speed or number of blades, unbalanced distributions of thrust between the propellers and the presence of hub and ducts. The present paper compares the design of a couple of contrarotating propellers carried out by a classical Morgan-Lerbs approach and a fully numerical procedure based on a variational approach (Coney, 1989) for the bounded circulation. Results in terms of circulation distribution, self-induced velocities and blade geometry are presented. Three different analysis tools, a lifting surface, a panel method and a RANS solver are finally applied to analyze the hydrodynamic performance of the generated designs in order to validate the design approach. It will be shown that the propellers designed with the two proposed approaches satisfy the design requirements as confirmed by all the three analysis methods. Moreover it will be stated that the balanced load solution is the more efficient. Keywords Contrarotating propellers, Propeller Design, RANS, Panel Method, Lifting Surface. 1 INTRODUCTION Contra-rotating propellers are widely used since decades in outboard propulsion units for fast-planing craft or in podded drives for fast ships or mega-yachts due to its advantage in terms of overall propulsive efficiency, mechanical balance and shallow draft (an important issue, in particular for pleasure boats). By splitting the thrust and torque between the fore and the aft propeller, the expanded area ratio and the diameter can be reduced, keeping the same cavitation margin, when compared to a classical single propeller solution. However, the potential application of contra-rotating propellers is really wide, being suitable also for large displacement ship in conventional shaft line arrangement. The present paper deals with comparison between two different design approaches and three analysis tools; a set of contra- rotating propellers for podded drives has been designed through a classical lifting-line theory and a fully numerical lifting-line approach. Then the resulting geometries have been analyzed via a lifting-surface code, a panel code and commercial RANS tool in order to compare performances in terms of thrust/torque curves and induced velocities. The classical lifting-line approach is based upon the Morgan-Lerbs theory for calculating optimum blade circulation with some additional features like the numerical treatment of the induced velocities, the possibility to unload the optimum blade circulation at tip and hub radial positions and a fully automated blade geometry optimization for cavitation and strength assessment. While the foregoing method assumes a thrust/torque balance between the front and aft propeller and does not take into account for any hub effects, the fully numerical design approach solve a Lagrange multiplier minimization problem allowing for different load distribution and modelling the presence of the hub. For the analysis, a lifting surface (Grassi & Brizzolara, 2009) and a panel (Gaggero & Brizzolara, 2009) code both developed for single propellers have been modified in order to account for multi-stage propulsor following an iterative approach and solving each propeller as a single one in a wake-adapted condition where the inflow velocity is calculated by solving the other propeller. Moreover, in order to solve both the propellers together, a RANS commercial solver has been used following a quasi-steady and a fully unsteady approach The former RANS solution approach allows for a fast averaged solution of the contra-rotating propeller set, each operating in a time constant inflow wake. In this sense the quasi steady approach is similar to the iterative approach, based on the mean inflow, adopted for the analysis of the contrarotating propellers by the potential flow based methods. On the other hand the RANS fully unsteady solution allows to compute the unsteady effects related to