基于伪弧长移动网格算法的爆炸与冲击多介质问(4)
图3t=0.2时刻Air-helium激波管问题计算结果Fig.3 Calculated results of air-helium shock-tube problem fort=0.2
图4t=0.2时刻冲击波区域局部放大图Fig.4 Partial enlarged detail of shock wave in air-helium shock-tube fort=0.2
图5 体积分数随时间变化曲线图Fig.5 Time changing curves of volume fraction in air-helium shock-tube problem
图6 网格自适应变化图Fig.6 Trajectory of meshes
3.2 二维水下爆炸问题
本算例为二维水下爆炸问题[22-23]。初始条件是将300 g球形梯恩梯(TNT)炸药放置于94.1 m深的水中,炸药半径为r0=3.528 7 cm.对于爆轰产物(l=1)和水(l=2)的状态方程,均采用JWL状态方程(14)式,其参数见表2.
表2 爆轰产物(l=1)和水(l=2)的JWL状态方程参数Tab.2 Material parameters for gaseous explosive(l=1)and water(l=2)modeled by JWL EOSlρ0/(g·cm-3)A1/MPaA2/MPaR1R2γ×.×
计算区域为[0 cm,20 cm]×[0 cm,20 cm],计算网格数为200×200,TNT炸药中心坐标为(10 cm,10 cm),计算初值为
式中:r为到TNT炸药中心的距离,的单位分别为g/cm3、g/cm3、cm/s、cm/s和MPa.同样对PALM算法和MM-PALM算法采用不同的伪弧长自适应函数。PALM算法采用如下控制函数:
MM-PALM算法采用如下控制函数:
图7、图8、图9分别为固定网格算法、PALM算法和MM-PALM算法在t=6.0×10-5s时刻计算结果,图10为t=6.0×10-5s时刻计算网格分布图。从图7、图8、图9和图10中可以得到与3.1节算例相同的结果,即PALM算法与MM-PALM算法的计算网格都在冲击波区域进行加密,计算结果都优于固定网格算法。在爆轰产物与水的交界面处,PALM算法凭借其自适应网格的优点,能够得到优于固定网格算法的界面分辨率,但其精确度仍然较差。而MM-PALM算法不需要在爆轰产物与水的交界面进行网格加密,就能够精确地描述爆轰产物与水的交界面。
图7t=6.0×10-2ms时刻结果图(固定网格算法)Fig.7 Two-dimensional underwater explosive problem fort=6.0×10-2ms(fixed mesh algorithm)
图8t=6.0×10-2ms时刻结果图(PALM算法)Fig.8 Two-dimensional underwater explosive problem fort=6.0×10-2ms(PALM algorithm)
图9t=6.0×10-5s时刻结果图(MM-PALM算法)Fig.9 Two-dimensional underwater explosive problem fort=6.0×10-5s(MM-PALM algorithm)
图10t=6.0×10-5s时刻网格分布图Fig.10 Meshes of two-dimensional underwater explosive problem fort=6.0×10-5s
4 结论
本文针对多介质爆炸与冲击问题提出了NM-PALM算法。该算法是在PALM算法的基础上,在多介质界面单元处加入人工界面压缩技术,实现了多介质爆炸与冲击问题的数值模拟。多介质爆炸与冲击问题采用五方程模型进行建模,利用一般形式的Mie-Grüneisen状态方程表示不同材料。通过一维激波管算例和二维水下爆炸算例可以看出,MM-PALM算法既能够高效精确捕捉冲击波阵面,又可以精确描述多物质间界面。因此,MM-PALM算法可以很好地实现对多介质爆炸与冲击问题的数值模拟。
[1] 王宇新, 陈震, 孙明.多相介质爆炸冲击响应物质点法数值模拟[J].爆炸与冲击, 2008, 28(2): 154-160.
WANG Y X, CHEN Z, SUN of explosion and shock involving multiple materials based on the material point method[J].Explosion and Shock Waves, 2008, 28(2): 154-160.(in Chinese)
[2] KARNI flow calculations by a consistent primitive algorithm[J].Journal of Computational Physics, 1994, 112(1): 31-43.
[3] ABGRALL R.How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach[J].Journal of Computational Physics, 1996, 125(1): 150-160.
[4] UNVERDI S O, TRYGGVASON G.A front-tracking method for viscous, incompressible, multi-fluid flows[J].Journal of Computational Physics, 1992, 100(1): 25-37.
[5] HIRT C W, NICHOLS B D.Volume of fluid(VOF)method for the dynamics of free boundaries[J].Journal of Computational Physics, 1981, 39(1): 201-225.
[6] NOH W F, WOODWARD P.SLIC(simple line interface calculation)[J].Lectures Notes in Physics,1976,59: 330-340.
[7] SCARDOVELLI R, ZALESKI S.Direct numerical simulation of free-surface and interfacial flow[J].Annual Review of Fluid Mechanics, 1999, 31: 567-603.
[8] OSHER S, SETHIAN J A.Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J].Journal of Computational Physics, 1987, 79(1): 12-49.
[9] FEDKIW R P, ASLAM T, MERRIMAN B,et al.A non-oscillatory Eulerian approach to interfaces in multimaterial flows(the ghost fluid method)[J].Journal of Computational Physics, 1999, 152(2): 457-492.
[10] SAUREL R, ABGRALL R.A simple method for compressible multifluid flows[J].SIAM Journal on Scientific Computing, 2012, 21(3): 1115-1145.
[11] LARROUTUROU B.How to preserve the mass fractions positivity when computing compressible multi-component flows[J].Journal of Computational Physics, 1991, 95(1): 59-84.
文章来源:《爆炸与冲击》 网址: http://www.bzycjzz.cn/qikandaodu/2021/0709/1295.html
上一篇:冲击载荷下螺栓预紧力对应力波影响分析
下一篇:三维多物质欧拉界面处理的并行算法研究