经典瑞利-泰勒不稳定性界面变形演化的改进型薄层模型
|
摘要
激光惯性约束聚变(ICF)内爆靶丸通常采用多壳层组合结构设计,各壳层界面的流体力学不稳定性影响内爆加速和聚变点火,是ICF十分关心的问题.本文建立了描述任意Atwood数、任意初始界面分布Rayleigh-Taylor(RT)不稳定性界面变形及非线性演化的薄层模型.通过分析薄层中流体微团的受力,得到了运动微分方程组,并在二维情况进行数值求解.在线性阶段,薄层模型描述的界面演变规律与模拟结果符合很好;在非线性阶段,薄层模型可以描述至"蘑菇"形结构,与数值模拟的结果很接近.目前薄层的RT不稳定性非线性解析理论研究仅限于弱非线性阶段,本工作发展的薄层解析理论能很好地研究薄层非线性"气泡-尖钉"发展过程.
The thin shell(layer) configuration is adopted in inertial-confinement fusion(ICF) implosions. The weakly nonlinear deformation of the thin shell significantly influences the performances of implosion acceleration and fusion ignition, which is an important issue for the study of ICF physics. Based on the thin layer model of Ott(Ott E 1972 Phys. Rev. Lett. 291429), an improved thin layer model is proposed to describe the deformation and nonlinear evolution of the perturbed interface induced by the Rayleigh-Taylor instability(RTI). Differential equations describing motion are obtained by analyzing the forces of fluid elements(i.e., Newton's second law), which are then solved by numerical method. Then the position of the perturbed interface with an initial perturbation can be obtained. The linear growth rate obtained from our thin layer approximation agrees with that from the classical RTI. For fixed Atwood number(wave number),the total amplitudes of the bubble and spike obtained from the improved thin layer model agree with those from the three-order weakly nonlinear model. In addition, we compare the deformation and evolution of the layer from our model with results of the numerical simulation. In the linear regime, the amplitudes of the bubble and spike obtained from our model agree with those from the numerical simulation. And the evolution of the perturbed interface obtained from the improved thin layer model is consistent with that from the numerical simulation. In the nonlinear regime, the evolution trends of the total amplitude of the bubble and spike for both the improved thin layer model and numerical results are the same. However, the amplitude of the bubble is obviously greater than that of the spike in the later stage of the perturbation. This is because of some shortcomings in the improved thin layer model. The first shortcoming is that ignoring the dynamical pressure in the pressure difference. In fact, the shear velocity of the fluids plays an important role in the nonlinear regime of the perturbation. The second shortcoming is that the surface area of the upper interface equals the lower interface in the whole perturbation process of the present model. Thus, the present model can be used to describe the nonlinear evolution of the perturbed interface before the mushroom structure. Finally, it is worth noting that the improved thin layer model can be used to describe the deformation and nonlinear evolution of a thin layer for arbitrary Atwood number with a perturbation of large initial amplitude and arbitrary distribution. The initial perturbations of the triangular and rectangular waves are also discussed.
The thin shell(layer) configuration is adopted in inertial-confinement fusion(ICF) implosions. The weakly nonlinear deformation of the thin shell significantly influences the performances of implosion acceleration and fusion ignition, which is an important issue for the study of ICF physics. Based on the thin layer model of Ott(Ott E 1972 Phys. Rev. Lett. 291429), an improved thin layer model is proposed to describe the deformation and nonlinear evolution of the perturbed interface induced by the Rayleigh-Taylor instability(RTI). Differential equations describing motion are obtained by analyzing the forces of fluid elements(i.e., Newton's second law), which are then solved by numerical method. Then the position of the perturbed interface with an initial perturbation can be obtained. The linear growth rate obtained from our thin layer approximation agrees with that from the classical RTI. For fixed Atwood number(wave number),the total amplitudes of the bubble and spike obtained from the improved thin layer model agree with those from the three-order weakly nonlinear model. In addition, we compare the deformation and evolution of the layer from our model with results of the numerical simulation. In the linear regime, the amplitudes of the bubble and spike obtained from our model agree with those from the numerical simulation. And the evolution of the perturbed interface obtained from the improved thin layer model is consistent with that from the numerical simulation. In the nonlinear regime, the evolution trends of the total amplitude of the bubble and spike for both the improved thin layer model and numerical results are the same. However, the amplitude of the bubble is obviously greater than that of the spike in the later stage of the perturbation. This is because of some shortcomings in the improved thin layer model. The first shortcoming is that ignoring the dynamical pressure in the pressure difference. In fact, the shear velocity of the fluids plays an important role in the nonlinear regime of the perturbation. The second shortcoming is that the surface area of the upper interface equals the lower interface in the whole perturbation process of the present model. Thus, the present model can be used to describe the nonlinear evolution of the perturbed interface before the mushroom structure. Finally, it is worth noting that the improved thin layer model can be used to describe the deformation and nonlinear evolution of a thin layer for arbitrary Atwood number with a perturbation of large initial amplitude and arbitrary distribution. The initial perturbations of the triangular and rectangular waves are also discussed.
引文
[1]Wang J H 1994 Nonstationary Flow and Shock for TwoDimensional(Beijing:Science Press)p10(in Chinese)[王继海1994二维非定常流和激波(北京:科学出版社)第10页]
[2]Rayleigh L 1893 Proc.R.Math.Soc.14 170
[3]Taylor G I 1950 Proc.R.Soc.London:Ser.A 201 192
[4]Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability(London:Oxford University Press)pp429–514
[5]Nuckolls J H,Wood J,Thiessen A,Zimmerman G 1972Nature 239 139
[6]Lindl J D,Amendt P,Berger R L,Glendinning S G,Glenzer S H,Haan S W,Kauffman R L,Landen O L,Suter L J 2004 Phys.Plasmas 11 339
[7]Atzeni S,Meyer-ter-Vehn J 2004 The physics of Inertial Fusion:Beam Plasma Interaction,Hydrodynamics,Hot Dense Matter(Oxford:Oxford University Press)
[8]He X T,Zhang W Y 2007 Eur.Phys.J.D 44 227
[9]Remington B A,Drake R P,Ryutov D D 2006 Rev.Mod.Phys.78 755
[10]Remington B A,Arnett D,Drake R P,Takabe H 1999Science 284 1488
[11]Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Science2001 Frontiers in High Density Physics(Washington,DC:Academic Press)
[12]Vlemmings W H T,Diamond P J,Imai H 2006 Nature440 58
[13]Wang L F,Ye W H,Li Y J 2010 Phys.Plasmas 17052305
[14]Liu W H,Wang L F,Ye W H,He X T 2012 Phys.Plasmas 19 042705
[15]Wang L F,Wu J F,Fan Z F,Ye W H,He X T,Zhang W Y,Dai Z S,Gu J F,Xue C 2012 Phys.Plasmas 19112706
[16]Wang L F,Ye W H,Sheng Z M,Don W S,Li Y J,He X T 2010 Phys.Plasmas 17 122706
[17]Ye W H,Wang L F,He X T 2010 Phys.Plasmas 17122704
[18]Wang L F,Ye W H,He X T,Zhang W Y,Sheng Z M,Yu M Y 2012 Phys.Plasmas 19 100701
[19]Wang L F,Ye W H,Wu J F,Liu J,Zhang W Y,He X T 2016 Phys.Plasmas 23 052713
[20]Wang L F,Ye W H,Wu J F,Liu J,Zhang W Y,He X T 2016 Phys.Plasmas 23 122702
[21]Wang L F,Ye W H,He X T,Wu J F,Fan Z F,Xue C,Guo H Y,Miao W Y,Yuan Y T,Dong J Q,Jia G,Zhang J,Li Y J,Liu J,Wang M,Ding Y K,Zhang W Y 2017 Sci.China:Phys.Mech.Astron.60 055201
[22]Zhang W Y,Ye W H,Wu J F,Miao W Y,Fan Z F,Wang L F,Gu J F,Dai Z S,Cao Z Y,Xu X W,Yuan Y T,Kang D G,Li Y S,Yu X J,Liu C L,Xue C,Zheng W D,Wang M,Pei W B,Zhu S P,Jiang S E,Liu S Y,Ding Y K,He X T 2014 Sci.Sin.:Phys.Mech.Astron.44 1(in Chinese)[张维岩,叶文华,吴俊峰,缪文勇,范征锋,王立锋,谷建法,戴振生,曹柱荣,徐小文,袁永腾,康洞国,李永升,郁晓瑾,刘长礼,薛创,郑无敌,王敏,裴文兵,朱少平,江少恩,刘慎业,丁永坤,贺贤土2014中国科学:物理学力学天文学44 1]
[23]Reipurth B,Bally J 2001 Annu.Rev.Astron.Astrophys.39 403
[24]Jacobs J W,Catton I 1988 J.Fluid Mech.187 353
[25]Kull H J 1991 Phys.Rep.206 197
[26]Sanz J 1994 Phys.Rev.Lett.73 2700
[27]Garnier J,Raviart P A,Cherfils-Clérouin C,Masse L2003 Phys.Rev.Lett.90 185003
[28]Haan S W 1991 Phys.Fluids B 3 2349
[29]Youngs D L 1984 Physica D 12 32
[30]Zhang Y,Drake R P,Glimm J 2007 Phys.Plasmas 14062703
[31]Jacobs J W,Catton I 1988 J.Fluid Mech.187 329
[32]Waddell J T,Niederhaus C E,Jacobs J W 2001 Phys.Fluids 13 1263
[33]Wilkinson J P,Jacobs J W 2007 Phys.Fluids 19 124102
[34]Olson D H,Jacobs J W 2009 Phys.Fluids 21 034103
[35]Wang L F,Ye W H,Li Y J 2010 Chin.Phys.Lett.27025203
[36]Wang L F,Wu J F,Ye W H,Zhang W Y,He X T 2013Phys.Plasmas 20 042708
[37]Davies R M,Taylor G I 1950 Proc.Roy.Soc.A 200 375
[38]Layzer D 1955 Astrophys.J.122 1
[39]Zhang Q 1998 Phys.Rev.Lett.81 3391
[40]Goncharov V N 2002 Phys.Rev.Lett.88 134502
[41]Sohn S 2003 Phys.Rev.E 67 026301
[42]Abarzhi S I,Nishihara K,Glimm J 2003 Phys.Lett.A317 470
[43]Mikaelian K O 2003 Phys.Rev.E 67 026319
[44]Tao Y S,Wang L F,Ye W H,Zhang G C,Zhang J C,Li Y J 2012 Acta Phys.Sin.61 075207(in Chinese)[陶烨晟,王立锋,叶文华,张广财,张建成,李英骏2012物理学报61 075207]
[45]Ott E 1972 Phys.Rev.Lett.29 1429
[46]Manheimer W,Colombant D,Ott E 1984 Phys.Fluids27 2164
[47]Colombant D,Manheimer W,Ott E 1984 Phys.Rev.Lett.53 446
[48]Wang L F,Guo H Y,Wu J F,Ye W H,Liu J,Zhang W Y,He X T 2014 Phys.Plasmas 21 122710
[2]Rayleigh L 1893 Proc.R.Math.Soc.14 170
[3]Taylor G I 1950 Proc.R.Soc.London:Ser.A 201 192
[4]Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability(London:Oxford University Press)pp429–514
[5]Nuckolls J H,Wood J,Thiessen A,Zimmerman G 1972Nature 239 139
[6]Lindl J D,Amendt P,Berger R L,Glendinning S G,Glenzer S H,Haan S W,Kauffman R L,Landen O L,Suter L J 2004 Phys.Plasmas 11 339
[7]Atzeni S,Meyer-ter-Vehn J 2004 The physics of Inertial Fusion:Beam Plasma Interaction,Hydrodynamics,Hot Dense Matter(Oxford:Oxford University Press)
[8]He X T,Zhang W Y 2007 Eur.Phys.J.D 44 227
[9]Remington B A,Drake R P,Ryutov D D 2006 Rev.Mod.Phys.78 755
[10]Remington B A,Arnett D,Drake R P,Takabe H 1999Science 284 1488
[11]Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Science2001 Frontiers in High Density Physics(Washington,DC:Academic Press)
[12]Vlemmings W H T,Diamond P J,Imai H 2006 Nature440 58
[13]Wang L F,Ye W H,Li Y J 2010 Phys.Plasmas 17052305
[14]Liu W H,Wang L F,Ye W H,He X T 2012 Phys.Plasmas 19 042705
[15]Wang L F,Wu J F,Fan Z F,Ye W H,He X T,Zhang W Y,Dai Z S,Gu J F,Xue C 2012 Phys.Plasmas 19112706
[16]Wang L F,Ye W H,Sheng Z M,Don W S,Li Y J,He X T 2010 Phys.Plasmas 17 122706
[17]Ye W H,Wang L F,He X T 2010 Phys.Plasmas 17122704
[18]Wang L F,Ye W H,He X T,Zhang W Y,Sheng Z M,Yu M Y 2012 Phys.Plasmas 19 100701
[19]Wang L F,Ye W H,Wu J F,Liu J,Zhang W Y,He X T 2016 Phys.Plasmas 23 052713
[20]Wang L F,Ye W H,Wu J F,Liu J,Zhang W Y,He X T 2016 Phys.Plasmas 23 122702
[21]Wang L F,Ye W H,He X T,Wu J F,Fan Z F,Xue C,Guo H Y,Miao W Y,Yuan Y T,Dong J Q,Jia G,Zhang J,Li Y J,Liu J,Wang M,Ding Y K,Zhang W Y 2017 Sci.China:Phys.Mech.Astron.60 055201
[22]Zhang W Y,Ye W H,Wu J F,Miao W Y,Fan Z F,Wang L F,Gu J F,Dai Z S,Cao Z Y,Xu X W,Yuan Y T,Kang D G,Li Y S,Yu X J,Liu C L,Xue C,Zheng W D,Wang M,Pei W B,Zhu S P,Jiang S E,Liu S Y,Ding Y K,He X T 2014 Sci.Sin.:Phys.Mech.Astron.44 1(in Chinese)[张维岩,叶文华,吴俊峰,缪文勇,范征锋,王立锋,谷建法,戴振生,曹柱荣,徐小文,袁永腾,康洞国,李永升,郁晓瑾,刘长礼,薛创,郑无敌,王敏,裴文兵,朱少平,江少恩,刘慎业,丁永坤,贺贤土2014中国科学:物理学力学天文学44 1]
[23]Reipurth B,Bally J 2001 Annu.Rev.Astron.Astrophys.39 403
[24]Jacobs J W,Catton I 1988 J.Fluid Mech.187 353
[25]Kull H J 1991 Phys.Rep.206 197
[26]Sanz J 1994 Phys.Rev.Lett.73 2700
[27]Garnier J,Raviart P A,Cherfils-Clérouin C,Masse L2003 Phys.Rev.Lett.90 185003
[28]Haan S W 1991 Phys.Fluids B 3 2349
[29]Youngs D L 1984 Physica D 12 32
[30]Zhang Y,Drake R P,Glimm J 2007 Phys.Plasmas 14062703
[31]Jacobs J W,Catton I 1988 J.Fluid Mech.187 329
[32]Waddell J T,Niederhaus C E,Jacobs J W 2001 Phys.Fluids 13 1263
[33]Wilkinson J P,Jacobs J W 2007 Phys.Fluids 19 124102
[34]Olson D H,Jacobs J W 2009 Phys.Fluids 21 034103
[35]Wang L F,Ye W H,Li Y J 2010 Chin.Phys.Lett.27025203
[36]Wang L F,Wu J F,Ye W H,Zhang W Y,He X T 2013Phys.Plasmas 20 042708
[37]Davies R M,Taylor G I 1950 Proc.Roy.Soc.A 200 375
[38]Layzer D 1955 Astrophys.J.122 1
[39]Zhang Q 1998 Phys.Rev.Lett.81 3391
[40]Goncharov V N 2002 Phys.Rev.Lett.88 134502
[41]Sohn S 2003 Phys.Rev.E 67 026301
[42]Abarzhi S I,Nishihara K,Glimm J 2003 Phys.Lett.A317 470
[43]Mikaelian K O 2003 Phys.Rev.E 67 026319
[44]Tao Y S,Wang L F,Ye W H,Zhang G C,Zhang J C,Li Y J 2012 Acta Phys.Sin.61 075207(in Chinese)[陶烨晟,王立锋,叶文华,张广财,张建成,李英骏2012物理学报61 075207]
[45]Ott E 1972 Phys.Rev.Lett.29 1429
[46]Manheimer W,Colombant D,Ott E 1984 Phys.Fluids27 2164
[47]Colombant D,Manheimer W,Ott E 1984 Phys.Rev.Lett.53 446
[48]Wang L F,Guo H Y,Wu J F,Ye W H,Liu J,Zhang W Y,He X T 2014 Phys.Plasmas 21 122710