物体垂直出入水的非定常空泡数学模型

研究了物体从水下向水面高速运动产生的非定常垂直空泡，建立了出水垂直空泡的数学模型，得到了匀速、空泡压力不变条件下的空泡外形、长度、体积随水深变化的解析解，给出了出水通气空泡发展为超空泡的条件．利用类似的方法建立了水平空泡和入水空泡的数学模型，并对3种空泡进行了比较研究．比较研究的结论是，随物体距水面的水深减小，出水空泡体积自身有增大趋势，空泡不容易发生泄气现象．且要保持出水空泡压力不变，空泡内的气体含量就应该增加（可通过人工通气方式）．入水空泡正好相反，随物体入水深度增加，空泡体积自身有收缩的趋势，并挤压空泡内的气体从环境压力较低的空泡尾部喷射而出，导致空泡内的气体含量减少，空泡压力降低．但是当空泡压力低于环境压力后，空泡尾部又将被环境高压所封闭，气体喷射不出来．随着入水深度继续增加，空泡尾部将重复上述过程，形成周期性的喷射 封闭 喷射 封闭的脉动过程，这个脉动喷射过程将在空泡尾部的流体中形成一连串小气泡，并由于空泡内的压力波动而导致空泡形状发生波动现象．

Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities

The unsteady vertical water-entry and water-exit cavities produced by a high-speed body were investigated theoretically, the mathematical models of the water-entry and water-exit cavities were proposed, and the solutions of the cavity shape varying with water depth were derived. Based on the solutions, the cavity length, cavity volume，closure depth of water-entry cavity and the condition for the formation of supercavity were obtained. The results show that the volume of the water-exit cavity increases with the reduction in water depth. Therefore, in order to maintain (or increase) the pressure of the water-exit cavity, more volume of gas injection is required in contrast to horizontal cavity, which also means that it is harder for the water-exit cavity to form supercavity, but simultaneously the advantage is that the water-exit cavity is hard to leak gas due to the increase in its volume. On the contrary, with the increase in water depth, the water-entry cavity has the tendency to shrink its volume, and squeeze gas within the cavity to jet out from the rear end of the cavity, with the gas reduction within cavity due to the gas jet, the pressure of the cavity will decrease, if the pressure falls below the environmental pressure, the rear end of the cavity will be closed by the environmental high-pressure, and thus the gas jet will terminate. As a result, a periodic impulsive process that consists of successive jetting-closure phases will be formed at the rear end of the cavity, resulting in the formation of a series of small bubbles in the wake of the cavity and wavelike fluctuations on the surface of the cavity due to the fluctuations of the pressure within the cavity.