CHEN Wei-qi, WANG Bao-shou, YAN Kai, LU Hai-yan. Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1130-1140. doi: 10.3879/j.issn.1000-0887.2013.11.002
 Citation: CHEN Wei-qi, WANG Bao-shou, YAN Kai, LU Hai-yan. Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1130-1140.

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

##### doi: 10.3879/j.issn.1000-0887.2013.11.002
• Rev Recd Date: 2013-06-25
• Publish Date: 2013-11-15
• 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.
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