A three-order finite volume method and its applicationto under-expanded jet shock wave structure simulation
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摘要: 以喷管出口欠膨胀射流为研究对象，在Lagrange坐标系下建立欠膨胀射流二维积分形式的流动方程。通过在单元交接面处进行三阶ENO(essentially nonoscillatory)格式插值，构造得到一种适用于求解该方程的三阶ENO有限体积法。采用该格式对一维Sod激波管算例和喷管出口欠膨胀射流进行数值计算。计算结果表明，该方法具有高精度、基本无振荡的特点，能很好地捕捉包含激波、滑移线以及三波交点等复杂流场波系结构。计算得到的波系结构中马赫盘的位置与实验结果吻合很好，相对误差小于1.1%。Abstract: By considering the under-expanded jet flow from nozzle exit, the integral form Euler equations for unsteady compressible flow in the Lagrange coordinates of a moving control volume was developed. By using three-order essentially non-oscillatory (ENO) interpolations at cell interfaces, a three-order ENO finite volume method for the integral form Euler equations was presented. The Sod shock tube case and nozzle outlet under-expanded jet shock wave structures were used to test the proposed scheme. The numerical results demonstrate that the method is accurate and non-oscillatory, and it can capture the wave structures of jet flow fields including shock cell structure, slip lines, jet boundary and the triple point well. Meanwhile, the simulated Mach disk locations in wave structures coincide with the experimentally measured ones, especially the error of the first Mach disk locations in wave structures between the numerical results and the experimental results was less than 1.1%.
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表 1 三阶ENO有限体积法密度误差
Table 1. Density error for third-order ENO finite volume method
网格尺度 L1误差 计算时间/s 收敛精度 0.02 3.03×10-3 0.072 6 0.01 4.09×10-4 0.296 2 2.89 0.005 3.90×10-4 1.102 2 2.96 
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[1] Matsuda T, Umeda Y, Ishii R, et al.Numerical and experimental studies on chocked under-expanded jets[C]//19th AIAA, Fluid Dynamics, Plasma Dynamics, and Lasers Conference.Honolulu, HI, USA, 1987, 7: 87-1378-281. [2] 刘小军, 傅德彬, 牛青林, 等.燃气射流冲击传热特性的数值模拟[J].爆炸与冲击, 2015, 35(2):229-235. http://www.bzycj.cn/CN/abstract/abstract9452.shtmlLiu Xiaojun, Fu Debin, Niu Qinlin, et al.Numerical simulation of heat transfer for exhausted gas jet impinging[J].Explosion and Shock Waves, 2015, 35(2):229-235. http://www.bzycj.cn/CN/abstract/abstract9452.shtml [3] 薛晓春, 余永刚, 张琦.双股燃气射流在充液室内扩展特性的实验研究[J].爆炸与冲击, 2013, 33(5):449-455. doi: 10.3969/j.issn.1001-1455.2013.05.001Xue Xiaochun, Yu Yonggang, Zhang Qi.Experimental study on expansion characteristics of twin combustion-gas jets in liquid filled chamber[J].Explosion and Shock Waves, 2013, 33(5):449-455. doi: 10.3969/j.issn.1001-1455.2013.05.001 [4] Ivan L, Groth C P T.High-order central ENO finite-volume scheme with adaptive mesh refinement[C]//18th AIAA Computational Fluid Dynamics Conference.Miami, Florida, 2007. [5] Luo H, Luo L P, Nourgaliev R, et al.A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids[J].Journal of Computational Physics, 2010, 229(19):6961-6978. doi: 10.1016/j.jcp.2010.05.033 [6] 范进之, 李桦.高精度有限体积法与间断有限元法的比较[J].国防科技大学学报, 2014, 36(5):33-38. http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201405006Fan Jinzhi, Li Hua.Comparison of high-precision finite volume method and discontinuous Galerkin method[J].Journal of National University of Defense Technology, 2014, 36(5):33-38. http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201405006 [7] Harten A, Enquist B, Osher S, et al.Uniformly high order essentially non-oscillatory schemes[J].Journal of Computational Physics, 1987, 71(2):231-303. doi: 10.1016-0021-9991(87)90031-3/ [8] 程晓晗, 封建湖, 聂玉峰.求解双曲守恒方程的WENO型熵相容格式[J].爆炸与冲击, 2014, 34(4):501-507. http://www.bzycj.cn/CN/abstract/abstract8897.shtmlCheng Xiaohan, Feng Jianhu, Nie Yufeng.WENO type entropy consistent scheme for hyperbolic conservation laws[J].Explosion and Shock Waves, 2014, 34(4):501-507. http://www.bzycj.cn/CN/abstract/abstract8897.shtml [9] 徐文灿, 黄振宇.高精度ENO格式在射流数值模拟中的应用[J].空气动力学学报, 2001, 19(4):401-406. doi: 10.3969/j.issn.0258-1825.2001.04.006Xu Wencan, Huang Zhenyu.Flow field calculation with high resolution ENO[J].Acta Aerodynamica Sinica, 2001, 19(4):401-406. doi: 10.3969/j.issn.0258-1825.2001.04.006 [10] 陆霄露, 邓康耀.进排气一维非定常流动的基本无振荡有限体积法的研究[J].内燃机工程, 2013, 34(2):52-61. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QKV20132013060900061050Lu Xiaolu, Deng Kangyao.Study of essentially non-oscillatory finite method for one-dimension unsteady intake and exhaust flows[J].Chinese Internal Combustion Engine Engineering, 2013, 34(2):52-61. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QKV20132013060900061050 [11] Wang Yongjian, Zhao Ning, Wang Donghong, et al.A kind essentially non-oscillatory finite volume scheme in Lagrangian coordinates[J].Journal on Numerical Methods and Computer Application, 2007, 28(4):250-259. [12] 朱孙科, 陈二云, 马大为, 等.燃气自由射流的正格式数值模拟[J].空气动力学报, 2011, 29(3):380-384. http://d.old.wanfangdata.com.cn/Periodical/kqdlxxb201103020Zhu Sunke, Chen Eryun, Ma Dawei, et al.Numerical simulation of gas free jet by positive schemes[J].Acta Aerodynamica Sinica, 2011, 29(3):380-384. http://d.old.wanfangdata.com.cn/Periodical/kqdlxxb201103020 [13] Ruggles A J, Ekoto I W.Experimental investigation of nozzle aspect ratio effects on under-expanded hydrogen jet release characteristics[J].International Journal of Hydrogen Energy, 2014, 39(35):20331-20338. doi: 10.1016/j.ijhydene.2014.04.143 -
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