The windmilling imbalance condition occurs after engine shut-down due to fan blade loss, but the engine continues to rotate under aerodynamic forces. This condition can induce undesirable structural excitation throughout the engine and airframe. Especially in the progression of larger high-bypass-ratio fans with fewer blades with larger chords, the excitation is considerably greater and is directly determined by the fan rotational speed. The aim of this study is to explore the windmilling flow through damaged fan rotor numerically according to the zero-torque characteristic, and to develop a prediction method of the windmilling rotational speed of damaged fans. An idealized span-damaged type is introduced to examine the effect of blade-to-blade flow interaction on the rotational speed of fans with various degrees of damage. In full-annulus simulations, whenever the damage of a single blade reaches 35%, the positive torque of the damaged blade reaches its maximum value, and the fan rotational speed instead reaches a new minimum. The results also show that the radial flow profiles at the rotor outlet are independent of airflow and can be determined using only the geometry of the damaged fan. This indicates the self-similar nature of the intra-stage flow. According to numerical results, a speed similarity coefficient of damaged fan is identified, and the dynamic pressure at the damaged fan outlet is the appropriate scale for the stagnation pressure loss across the rotor. Further, the engine is regarded as a finite number of variable cross-section frictional ducts, which facilitates the construction of a total stagnation pressure-loss model, allowing the windmilling airflow for any flight Mach number to be obtained. Finally, this study proposes a mathematical model to predict the windmilling rotational speed using the damaged fan speed similarity coefficient and the one-dimensional windmilling airflow function. The model can be applied to the early stages of high-bypass turbofan development and can be used to evaluate the safety characteristics during engine windmilling operations.

风车不平衡情况发生在发动机因风扇叶片丢失而关闭后，但发动机在空气动力的作用下继续旋转。这种情况会在整个发动机和机身中引起不良的结构激励。尤其是在叶片较少、弦长较大的较大型高涵道比风扇的发展过程中，激励相当大，并且直接由风扇转速决定. 本研究的目的是根据零转矩特性对损坏风扇转子的风车流动进行数值研究，并开发一种损坏风扇风车转速的预测方法。引入了一种理想化的跨度损坏类型，以检查叶片间流动相互作用对具有不同损坏程度的风扇转速的影响。在全环空模拟中，每当单个叶片损坏达到35%时，损坏叶片的正扭矩达到最大值，风扇转速反而达到新的最小值。结果还表明，转子出口处的径向流动剖面与气流无关，并且可以仅使用损坏风扇的几何形状来确定。这表明阶段内流动的自相似性质。转子上的停滞压力损失。进一步，将发动机看成有限数量的变截面摩擦管道，便于构建全停滞压损模型，从而可以得到任意飞行马赫数下的风车气流。最后，本研究提出了一种利用受损风扇转速相似系数和一维风车气流函数预测风车转速的数学模型。该模型可应用于高旁通比涡扇发动机开发的早期阶段，并可用于评估发动机风车运行期间的安全特性。