Simulation of Expansion of High Pressure Bubble under Water in Complex Calculation Region using NGFM in Cartesian Coordinate System
-
摘要: 采用NGFM(New version of Ghost Fluid Method)处理复杂计算域的固壁边界，用RGFM(Real Ghost Fluid Method)求解气-水界面附近网格节点的状态参数，从而在直角坐标系下对复杂计算域的水下高压气泡膨胀问题进行数值模拟。流场控制方程选用Euler方程，用五阶WENO格式离散空间导数项，二阶Runge-Kutta法离散时间导数项；气-水界面追踪使用Level Set方法，对Level Set方程，用五阶HJ-WENO(Hamilton-Jacobi WENO)和三阶Runge-Kutta法求解。将计算结果与任意坐标系下的结果进行对比，验证了NGFM在笛卡尔网格中处理复杂形状固壁边界的可行性。得到了水下流场压力等值线图、高压气泡的演变过程以及特定点处的压力-时间曲线。计算结果表明，高压气泡在固壁反射激波的作用下，膨胀过程受到抑制；强激波在固壁的反射会导致固壁附近出现大范围的空化流动。
-
关键词:
- 高压气泡膨胀 /
- 任意坐标系 /
- 复杂计算域 /
- Level Set方法 /
- Ghost Fluid方法
Abstract: We adopted a new version of ghost fluid method (NGFM) to treat the wall boundary in a complex calculation region in Cartesian coordinate system, and real ghost fluid method (RGFM) to predict the flow states at grid nodes just next to the gas-liquid interface.Flow field was solved by Euler equation with 5th-order WENO spatial discretization and 2nd-order Runge-Kutta (R-K) time discretization.We used the level set method to keep track of gas-liquid interface.Level set function was discretized by 5th-order Hamilton-Jacobi WENO and 3rd-order R-K method.We verified that NGFM was easy to extend and could be applied to treat complex wall boundary in Cartesian grid by comparing with results in arbitrary coordinate system.We carried out pressure contours, the change process of bubble shape and pressure history at some given points.The numerical results demonstrate that the expansion of high pressure bubble is restricted by the reflected shock wave from the wall.It is also shown that the reflection of strong shock wave from wall can lead to extensive cavitation flow. -
图 1 RGFM中气-水界面附近节点赋值示意图(一维模型)
Figure 1. Updating the real and ghost nodes bordering the gas-liquid interface in RGFM (1D)
图 2 NGFM中流-固界面附近节点赋值示意图(一维模型)
Figure 2. Updating the real and ghost nodes next to the liquid-solid interface in NGFM (1D)
图 3 t=0.210 ms时，用NGFM处理固壁边界的数值解和理论解的比较
Figure 3. Comparison of results using NGFM to treat the wall boundary with the theoretical results at t=0.210 ms
图 4 t=0.270 ms时，用NGFM处理固壁边界的数值解和理论解的比较
Figure 4. Comparison of the results using NGFM to treat the wall boundary with the theoretical results at t=0.270 ms
图 6 激波传播和高压气泡变化过程(蓝色虚线表示高压气泡，红色虚线表示空化区域；Δp为相邻压力等值线间的压差)
Figure 6. Shock wave propagation and change process of high pressure bubble (Blue dashed line indicates high pressure bubble, red dashed line indicates cavitation region; Δp indicates the pressure difference between adjacent isolines)
-
[1] Blake J R, Gibson D C. Growth and collapse of a vapour cavity near a free surface[J]. J Fluid Mech, 1981, 111: 123-140. doi: 10.1017/S0022112081002322 [2] Pearson A, Cox E, Blake J R, et al. Bubble interactions near a free surface[J]. Eng Anal Bound Elem, 2004, 28(4): 295-313. doi: 10.1016/S0955-7997(03)00079-1 [3] Liu M B, Liu C R, Lam K Y. A one dimensional mesh free particle formulation for simulating shock waves[J]. Shock Waves, 2003, 13: 201-211. doi: 10.1007/s00193-003-0207-0 [4] Liu M B, Liu C R, Zong Z, et al. Numerical simulation of underwater explosion by SPH[J]. Advan Comput Eng Sci, 2000: 1475-1480. [5] Liu M B, Liu C R, Zong Z, et al. Computer simulation of the high explosive explosion using smoothed particle hydrodynamics methodology[J]. Comput Fluids, 2003, 32(3): 305-322. http://www.sciencedirect.com/science/article/pii/S0045793001001050 [6] Vernon T A. Whipping response of ship hulls from underwater explosion bubble loading, AD-A178096[R]. Nova Scotia: Defence Research Establishment Atlantic Dartmouth, 1986. [7] Zong Z. A hydroplastic analysis of a free-free beam floating on water subjected to an underwater bubble[J]. J Fluid Struct, 2005, 20(3): 359-372. doi: 10.1016/j.jfluidstructs.2004.08.003 [8] Zhang A M, Yang W S, Huang C, et al. Numerical simulation of column charge underwater explosion based on SPH and BEM combination[J]. Comput Fluids, 2013, 71: 169-178. doi: 10.1016/j.compfluid.2012.10.012 [9] Fedkiw R P. Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method[J]. J Comput Phys, 2002, 175(1): 200-224. http://doi.ieeecomputersociety.org/resolve?ref_id=doi:10.1006/jcph.2001.6935&rfr_id=trans/tg/2009/03/ttg2009030493.htm [10] Wang C W, Liu T G, Khoo B C. A real ghost fluid method for the simulation of multimedium compressible flow[J]. J Sci Comput, 2005, 28(1): 278-302. http://dl.acm.org/citation.cfm?id=1122832 [11] Wardlaw A B Jr. Underwater explosion test cases, IHTR-2069[R]. Maryland: Naval Surface Warfare Center Indian Head Division, 1998. [12] Liu T G, Khoo B C, Xie W F. Isentropic one-fluid modelling of unsteady cavitating flow[J]. J Comput Phys, 2004, 201(1): 80-108. http://www.ams.org/mathscinet-getitem?mr=2098854 [13] Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations[J]. J Comput Phys, 1988, 79(1): 12-49. http://www.ams.org/mathscinet-getitem?mr=965860 [14] Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow[J]. J Comput Phys, 1994, 114(1): 146-159. [15] Liu T G, Khoo B C, Yeo K S. Ghost fluid method for strong shock impacting on material interface[J]. J Comput Phys, 2003, 190(2): 651-681. http://www.sciencedirect.com/science/article/pii/S0021999103003012 [16] Adalsteinsson D, Sethian J A. The fast construction of extension velocities in level set methods[J]. J Comput Phys, 1999, 148(1): 2-22. http://www.sciencedirect.com/science/article/pii/s0021999198960909 [17] Shu C W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report[R]. Rhode Island: Brown University, 1997. [18] Jiang G S, Peng D. Weighted ENO schemes for Hamilton Jacobi equations[J]. SIAM J Sci Comput, 2000, 21(6): 2126-2143. doi: 10.1137/S106482759732455X [19] Shu C W, Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes[J]. J Comput Phys, 1988, 77(2): 439-471. [20] 曹乐.利用Level set方法捕捉气、水界面的三维数值研究[D].合肥: 中国科学技术大学, 2009: 20-21.Cao L. Three-dimensional computations on capturing of gas-water interface by level set method[D]. Hefei: University of Science and Technology of China, 2009: 20-21. (in Chinese) -
下载:
点击查看大图
图(7)
计量
- 文章访问数: 6769
- HTML全文浏览量: 2324
- PDF下载量: 255
