基于SPH法的二维矩形液舱晃荡研究

A study of 2D liquid sloshing in rectangle tanks based on SPH method

液体晃荡是一种复杂的流体运动现象,自由液面的存在使得该现象具有很强的非线性和随机性。针对二维矩形液舱在不同振幅水平激励下的纵荡问题,应用SPH法对其进行了数值研究。首先计算了小振幅激励下的纵荡,计算结果分别与线性理论解、文献VOF法结果及文献SPH法结果作了比较分析,以验证所建数值模型的合理性;然后计算了液舱在大振幅水平激励下的纵荡,着重分析了不同振幅下液体晃荡的速度向量图、液面波动时程、压强波动时程、动量波动时程以及波动的频谱图,并将计算所得液面波动结果与小振幅激励下的液面波动结果作了比较。分析结果表明,在大振幅水平激励下,液面波动的波峰值较小振幅下的结果有较为明显的增大,而波谷值则无过大的变化,总体波动幅值比小振幅下的结果大;随着激励幅值的增大,液面波动幅值呈现明显增大的趋势,压强的整体波动幅值也呈增大趋势,动量波动的均值亦有明显增大;波动能量随着激励幅值的增大而增大并向第一阶频率区域集中。SPH法对处理液体大幅晃荡这种具有自由表面大变形的问题有十分优越的特性。

Liquid sloshing is a very complex liquid phenomenon and has strong non-linearity and rando- micity because of the existance of free surface. Numerical study of sloshing under level force with different swing in 2D rectangle tank is made by SPH. Sloshing under small swing force is calculated firstly, and to validate the rationality of the numerical model, its result is compared with the results calculated by linearity theory, VOF, and other SPH method. Next, sloshing under big swing force is simulated, and some results, including the distributing of velocity, pressure and general momentum elevation histo- ry, surface wave elevation history and its frequency charts, are analyzed carefully. Besides, the surface wave elevation history is compared between big swing force and small swing force. Analysis results show that, firstly, the peak value of surface waves elevation history under big swing force is more bigger than that under small swing force, but both trough values have no outstanding difference, and the gen- eral fluctuate swing under big swing force is bigger than that under small swing force; secondly, along with the accretion of the swing, the values of surface wave elevation history, the pressure course, the average of momentum fluctuate, and the energy of sloshing, all have a trend of evidently increase; third- ly, the energy of sloshing is closing to the first frequency area along with the increase of the swing; last- ly, SPH method has great superiority in dealing with the problem of big swing liquid sloshing with free surface.