基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小. 

ANALYSIS OF UNSTEADY CAVITATION FLOW OVER HYDROFOIL BASED ON DYNAMIC MODE DECOMPOSITION

Cavitation is a special flow phenomenon with strong unsteadiness that often occurs in propeller of ships and underwater vehicles. The occurrence of cavitation often affects the hydrodynamic performance and efficiency of propulsion systems. In order to study the unsteady cavitation flow field structure around hydrofoil, numerical prediction and flow field structure analysis of unsteady cavitation flow around two-dimensional hydrofoil are investigated by using Schnerr-Sauer cavitation model and SST $k$-$\omega $ turbulence model. The validity of the established numerical method is verified by comparing the numerical prediction of cavitation evolution and pressure data with experimental results. The velocity field of the cavitation flow field is analyzed by using Dynamic Mode Decomposition (DMD). The results show that the first-order mode is 0Hz, which represents the average flow field. The second-order mode is about the frequency of cavitation shedding, which reveals the cavities grow and shed periodically at the leading edge of the hydrofoil. The third-order mode has a corresponding frequency about 2 times of the second order mode, which reveals that the fusion behavior of two large-scale vortices behind the hydrofoil. The fourth-order mode has a corresponding frequency about 3 times of the second order mode, which characterizes the fusion behavior of some small-scale eddies in the flow field. Finally, the modal decomposition analysis of the cavitation flow field under different cavitation numbers was carried out. It was found that the vortex structure of the shedding cavities increased with the decrease of the cavitation number, and the second-order mode frequency decreases with decreasing cavitation number.