激波作用下SF_6气泡界面演化和射流发展的数值模拟
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摘要
数值研究了平面激波冲击氮气环境中SF6气泡界面的Richtmyer-Meshkov不稳定性,重点关注其中的激波聚焦及射流的产生和发展过程。在入射激波马赫数为1.23的情况下,给出了压力、密度、数值纹影和涡量等物理量的演化图像,定量分析了流场中压力最大值、密度最大值、射流速度、环量和斜压力矩随时间的变化关系。计算结果表明,平面激波冲击SF6气泡过程有很强的聚能效应,在气泡内部靠近下游极点处发生激波近似理想聚焦和点爆炸现象,直接导致出现二次波系以及向下游运动的细长射流结构。相比入射激波,二次波系产生斜压力矩和涡量的能力要弱得多。
The Richtmyer-Meshkov instability occurring on a heavy gas(SF6) bubble surrounded by N2 is numerically investigated in the present work.The interface evolution,shock focusing and jet development are emphasized.Numerical schlieren images and distributions of pressure,density and vorticity are exhibited for an incident shock wave of Mach number 1.23.The jet velocity,circulation and baroclinic torque versus time as well as peak values of pressure and density in the flow field are quantitatively analyzed.The results indicate that SF6 gas bubble accelerated by a planar shock wave has a strong cumulative energy effect so that it produces nearly ideal shock focusing and point source explosion phenomenon near the downstream pole within the bubble interface,which directly results in a secondary wave pattern and a slender jet moving in the streamwise direction.Compared with the secondary wave pattern,the incident shock wave brings on more intense baroclinic torque and vorticity.
The Richtmyer-Meshkov instability occurring on a heavy gas(SF6) bubble surrounded by N2 is numerically investigated in the present work.The interface evolution,shock focusing and jet development are emphasized.Numerical schlieren images and distributions of pressure,density and vorticity are exhibited for an incident shock wave of Mach number 1.23.The jet velocity,circulation and baroclinic torque versus time as well as peak values of pressure and density in the flow field are quantitatively analyzed.The results indicate that SF6 gas bubble accelerated by a planar shock wave has a strong cumulative energy effect so that it produces nearly ideal shock focusing and point source explosion phenomenon near the downstream pole within the bubble interface,which directly results in a secondary wave pattern and a slender jet moving in the streamwise direction.Compared with the secondary wave pattern,the incident shock wave brings on more intense baroclinic torque and vorticity.
引文
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[25]Sedov L I.Similarity and Dimensional Methods in Mechanics[M].New York:Academic Press,1959.
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[2]Meshkov E E.Instability of the interface of two gases accelerated by a shock wave[J].Fluid Dyn,1969,4(5):101-104.
[3]Winkler K H A,Chalmers J W,Hodson S W,et al.A numerical laboratory[J].Phys Today,1987,40(10):28-37.
[4]Haas J F,Sturtevant B.Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities[J].JFluid Mech,1987,181:41-76.
[5]Picone J M,Boris J P.Vorticity generation by shock propagation through bubbles in a gas[J].J Fluid Mech,1988,189:23-51.
[6]Quirk J J,Karni S.On the dynamics of a shock-bubble interaction[J].J Fluid Mech,1996,318:129-163.
[7]Cowperthwaite N.The interaction of a plane shock and a dense spherical inhomogeneity[J].Phys D,1989,37(1/2/3):264-269.
[8]Zabusky N J,Zeng S M.Shock cavity implosion morphologies and vortical projectile generation in axisymmetricshock-spherical fast/slow bubble interactions[J].J Fluid Mech,1998,362:327-346.
[9]Giordano J,Burtschell Y.Richtmyer-Meshkov instability induced by shock-bubble interaction:Numerical and ana-lytical studies with experimental validation[J].Phys Fluids,2006,18(3):036102.
[10]Niederhaus J H J,Greenough J A,Oakley J G,et al.A computational parameter study for the three-dimensionalshock-bubble interaction[J].J Fluid Mech,2008,594:85-124.
[11]Ranjan D,Oakley J,Bonazza R.Shock-bubble interactions[J].Annu Rev Fluid Mech,2011,43:117-140.
[12]Li Q B,Fu S,Xu K.A compressible Navier-Stokes flow solver with scalar transport[J].J Comput Phys,2005,204(2):692-714.
[13]Tian B L,Fu D X,Ma Y W.Effects of adiabatic exponent on Richtmyer Meshkov instability[J].Chin Phys Lett,2004,21(9):1770-1772.
[14]Bai J S,Zou L Y,Wang T,et al.Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders[J].Phys Rev E,2010,82:056318.
[15]Yan C L,Sun D J,Yin X Y,et al.Numerical simulations of Richtmyer-Meshkov instability[J].Chinese Journal ofComputation Physics,2001,18(1):27-32.(in Chinese)严长林,孙德军,尹协远,等.Richtmyer-Meshkov不稳定性的数值模拟[J].计算物理,2001,18(1):27-32.
[16]Sun M,Takayama K.Conservative smoothing on an adaptive quadrilateral grid[J].J Comput Phys,1999,150(1):143-180.
[17]Sun M.Numerical and experimental studies of shock wave interaction with bodies[D].Sendai,Japan:Tohoku Uni-versity,1998.
[18]Sun M,Yada K,Jagadeesh G,et al.A study of shock wave interaction with a rotating cylinder[J].Shock Waves,2003,12(6):479-485.
[19]Sun M,Takayama K.A holographic interferometric study of shock wave focusing in a circular reflector[J].ShockWaves,1996,6(6):323-336.
[20]Luo X.Unsteady flows with phase transition[D].Eindhoven,Netherlands:Eindhoven University of Technology,2004.
[21]Luo X,Prast B,van Dongen M E H,et al.On phase transition in compressible flows:Modelling and validation[J].J Fluid Mech,2006,548:403-430.
[22]Fan M R,Zhai Z G,Si T,et al.Numerical simulations of interface with different shape accelerated by aplanar shock[J].Scientia Sinica G,2011,41(7):862-869.(in Chinese)范美如,翟志刚,司廷,等.激波与不同形状界面作用的数值模拟[J].中国科学G辑,2011,41(7):862-869.
[23]Zhai Z,Si T,Luo X,et al.On the evolution of spherical gas interfaces accelerated by aplanar shock wave[J].PhysFluids,2011,23:084104.
[24]Zhai Z G,Si T,Luo X S,et al.On the evolution of SF6spherical gas interface accelerated by planar shock wave[C]//Pro-cedings of the 14th Chinese National Symposium on Shock Waves,Huangshan,2010:371-376.(in Chinese)翟志刚,司廷,罗喜胜,等.平面激波作用下SF6球形界面变形与发展的研究[C]//第14届全国激波与激波管学术会议论文集,黄山,2010:371-376.
[25]Sedov L I.Similarity and Dimensional Methods in Mechanics[M].New York:Academic Press,1959.
[26]Schilling O,Latini M,Don W S.Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability[J].Phys Rev E,2007,76(2):026319.