在涵道螺旋桨的设计过程中，由于涵道与螺旋桨之间相互干扰问题的复杂性，桨盘处的诱导速度难以确定，导
致涵道螺旋桨的设计难度相比孤立螺旋桨显著增大。本文建立了涵道螺旋桨的动量理论模型，推导了涵道螺旋桨的桨盘
推力占总推力的比值k与桨盘处诱导速度的对应关系，并基于计算流体力学（CFD）仿真分析揭示了悬停和前飞状态下k
值的变化规律。对于给定的涵道构型，相关规律具体表现为：在悬停状态下，k值几乎不随螺旋桨转速变化，基本保持
为常数；而在前飞状态下，该比值随螺旋桨转速的改变而呈现非线性变化，且不同来流风速下的变化规律不同。进一步
分析发现k值与涵道螺旋桨的推力系数之间存在线性关系，且该线性关系与来流风速无关，这十分有利于建立关于k值的
工程模型。以上研究丰富了对涵道螺旋桨的理论认知，并对涵道螺旋桨设计具有实用价值。
The design of ducted propellers is much more challenging than that of isolated propellers, as the complexity of the
interference between the duct and the propeller makes it difficult to determine the induced velocity at the propeller. In the present
study, the momentum theoretical model of ducted propellers is established, and the ratio of the propeller thrust to the total thrust of
ducted propellers, denoted as k, is analyzed, obtaining its relationship with the induced velocity at the propeller. Further more, the
variation law of k under hovering and forward flight states is revealed by numerical analysis based on computational fluid dynamics
(CFD) simulations. For a given duct configuration, the following variation law of k is found: in the hovering state, k hardly varies
with the change of the propeller's rotational speed; In the forward flight state, k exhibits a nonlinear variation with the change of the
propeller's rotational speed, and the variation law differs under different inflow velocities. Further analysis reveals a linear relationship between the k values and the thrust coefficient of the ducted propeller. The linear relationship is independent of the incoming
wind velocity, which is very beneficial for establishing an engineering model about the value of k. The present study enriches the
theoretical understandings about ducted propellers and has potential application values for the ducted propeller design.
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