恒定与变速线性楔形体入水过渡阶段的水动力公式
Formulations of Hydrodynamic Force in the Transition Stage of the Water Entry of Linear Wedges with Constant and Varying Speeds
AI总结：
针对水上飞机着水、船体砰击相关理论对二维入水模型的需求，本文数值研究了恒速与变速线性楔形体入水过渡阶段，推导了两类撞击下的水动力公式，提出了适用于5°-70°底升角的砰击与过渡阶段通用水动力表达式。
摘要：
目前，针对应用于水上飞机起飞与着水的2.5维（2.5D）方法，以及应用于船体砰击的切片理论或2D+t理论，人们对开发包含砰击阶段与过渡阶段的二维（2D）入水模型的需求日益增长。受此驱动，本文在假设流体不可压缩、无粘、重力与表面张力效应可忽略且流动无旋的前提下，对恒定与变速线性楔形体入水的过渡阶段开展了数值研究。对于恒速撞击，通过将砰击阶段的力最大值与定常超空泡流动结果的差值进行标度，发现了过渡阶段不同底升角下力衰减的相似性。结合过渡阶段力衰减的相似性与砰击阶段力的线性增长结果，推导得到了水动力的计算公式。对于变速撞击，过渡阶段中由加速度效应引起的水动力通过附加质量系数进行建模，该系数较砰击阶段的附加质量系数平均提升27.13%。最后，本文提出了同时适用于砰击阶段与过渡阶段的水动力通用表达式，该表达式在底升角5°至70°的范围内，对恒速与变速撞击均具有良好的预测效果。
英文摘要：
There is an increasing need to develop a two-dimensional (2D) water entry model including the slamming and transition stages for the 2.5-dimensional (2.5D) method being used on the take-off and water landing of seaplanes, and for the strip theory or 2D+t theory being used on the hull slamming. Motivated by that, this paper numerically studies the transition stage of the water entry of a linear wedge with constant and varying speeds, with assumptions that the fluid is incompressible, inviscid and with negligible effects of gravity and surface tension, and the flow is irrotational. For the constant speed impact, the similitude of the declining forces of different deadrise angles in the transition stage are found by scaling the difference between the maximum values in the slamming stage and the results of steady supercavitating flow. The formulation of the hydrodynamic force is conducted based on the similitude of the declining forces in the transition stage together with the linear increasing results in the slamming stage. For the varying speed impact, the hydrodynamic force caused by the acceleration effect in the transition stage is formulated by an added mass coefficient with an averaged increase of 27.13% compared with that of slamming stage. Finally, a general expression of the hydrodynamic forces in both the slamming and transition stages is thus proposed and has good predictions in the ranges of deadrise angles from 5 deg to 70 deg for both the constant and varying speed impacts.
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