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The design of a single, uniform inflow operating propeller is quite a straightforward process. Traditionally, in fact, this problem has been solved and is, still, widely solved following the pioneering work by Lerbs: a lifting line with a vortical trailing wake substitutes each blade of the propeller and, via influence functions, the best circulation distribution that satisfy the thrust
constraint with the higher efficiency is selected. Some lifting surfaces corrections could be applied and the optimum geometry can be designed on the light of robustness and cavitating criteria.
This classical approach is, unfortunately, unable to treat, in a rigorous way, complex configuration. First of all the propeller hub cannot be included, in the original procedure by Lerbs, except adopting some empirical corrections of the optimum circulation. In the same way,configurations like ducted propellers or multi stage propulsors pose some important tasks for the design procedure.
A more general design code, based on a fully numerical approach, is presented. Build as a Lagrange multipliers minimization problem, the proposed design code represents an efficient way to design propellers overtaking all the limitations of the original Lerbs' approach. The fully numerical algorithm allows to design a propeller whose optimal circulation is, directly,  influenced by the presence of the hub and, for instance, of a duct.
In the paper the numerical design strategy will be addressed, highlighting the capabilities to treat complex configurations. Afterwards the design of single and ducted propellers, Panel and RANSE methods will be applied in order to validate the design procedure.
In particular openFOAM will be employed to assess the accuracy of the design approach and the results from the panel method, with special attention on the pressure distribution of the duct and the related risk of cavitation.