To minimize the energy consumption of contra-rotating propellers (CRPs), the optimal matched rotational speeds of the forward propeller (FP) and rear propeller (RP) of CRP are investigated based on the potential-based panel method. The optimal matching problem of a set of CRP405 is investigated. The open-water hydrodynamic performances of CRP405 with the FP and RP having the same rotational speed are calculated and the method is validated. The hydrodynamic characteristics of CRP405 with changing FP and RP rotational speeds are investigated. The cubic spline interpolation method is used to determine the equal thrust line at which CRP405 generates the target thrust while keeping the inflow velocity constant. A series of equal thrust points on the equal thrust line is selected for the analysis of the delivered power. The rotational speeds of the FP and RP corresponding to the minimal delivered power are the optimal matched rotational speeds of CRP405. The optimal matching calculations are carried out at different inflow velocities. The results show that, under the condition of a low inflow velocity, properly increasing the rotational speed of the FP and decreasing the rotational speed of the RP are the most direct and efficient ways to reduce the energy consumption and avoid the negative effect of the net torque of the CRP on the transverse stability.
