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.

为了使对向旋转螺旋桨（CRP）的能量消耗最小，基于基于势能的面板方法，研究了CRP的前螺旋桨（FP）和后螺旋桨（RP）的最佳匹配转速。研究了一组CRP405的最佳匹配问题。计算了FP和RP具有相同转速的CRP405的开水水动力性能，并验证了该方法的有效性。研究了FP和RP转速变化时CRP405的水动力特性。三次样条插值法用于确定等推力线，CRP405在该等推力线保持目标流速不变的情况下生成目标推力。选择等推力线上的一系列等推力点来分析所传递的功率。FP和RP的对应于最小输出功率的转速是CRP405的最佳匹配转速。最佳匹配计算是在不同的流速下进行的。结果表明，在低进水速度的情况下，适当提高FP的转速和降低RP的转速是降低能耗，避免电网负面影响的最直接，最有效的方法。 CRP的扭矩对横向稳定性的影响。