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基于不可压Navier-Stokes方程, 采用计算流体力学方法, 数值模拟与分析了层流圆管潜射流在密度均匀黏性流体中的演化机理及其表现特征, 定量研究了蘑菇形涡结构无量纲射流长度L*、螺旋型涡环半径R*及其包络外形长度d*等几 何特征参数随无量纲时间t*的变化规律. 数值结果表明, 蘑菇形涡结构的形成与演化过程可分为三个不同的阶段: 启动阶段、发展阶段和衰退阶段. 在启动阶段, L*和d*随t* 线性变化, 而R*则近似为一个常数; 在发展阶段, 蘑菇形涡结构的演化具有自相似性, L*, R*和d*与t*1/2均为同一正比关系, 而且雷诺数和无量纲射流时间不影响该正比关系; 在衰退阶段, L* 和R* 正比于t*1/5, 而d*则近似为一个常数. 此外, 还对蘑菇形涡结构二次回流点、 动量源作用中心及其几何中心的速度变化规律、垂向涡量分布特征和 涡量-流函数关系进行了分析.A numerical investigation on the evolution mechanism and characteristics of the submerged laminar round jet in a viscous homogenous fluid is conducted by using the computational fluid dynamics method based on the incompressible Navier-Stokes equation. Three non-dimensional parameters for the mushroom-like vortex structure, including the length of the jet L*, the radius of the mushroom-like vortex R* and the length of vortex circulation d*, are introduced and the variation characteristics of these parameters with the non-dimensional time t* are quantitatively analyzed. Results show that there exist three distinct stages in the formation and evolution procedures of the mushroom-like vortex structure, including the starting, developing and decaying stages. In the starting stage, L* and d* increase linearly with t*, while R* approximately remains to be a constant; in the developing stage, a considerable self-similarity is confirmed, and L*, R*, d* display the same proportional relationship to t*1/2 regardless of the variations of Reynolds number and injection duration; in the decaying stage, L* and R*are approximately proportional to t*1/5, while d* nearly levels off as a constant. Moreover, velocity characteristics at the secondary backflow point and the momentum and geometry centers, the distribution features of the vertical vorticity, as well as the vorticity-stream function relationship are analyzed for the mushroom-like vortex structure.
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Keywords:
- submerged round jet /
- mushroom-like vortex /
- evolution mechanism
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[2] Fedorov K N, Ginsburg A I 1989 Mesoscale/Synoptic Coherent structures in Geophysical Turbulence 50 1
[3] Van Heijst G J F, Clercx H J H 2009 Annu. Rev. Fluid Mech. 41 143
[4] Meunier P, Spedding G R 2006 J. Fluid Mech. 552 229
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[22] McNaughton K J, Sincair C G 1966 J. Fluid Mech. 25 367
[23] Gill A E 1965 J. Fluid Mech. 14 557
[24] Schneider W 1985 J. Fluid Mech. 154 91
[25] Petrov P A 1973 Fluid Dynamics 8 190
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[29] Qu Y P, Chen S Y, Wang X P, Teng S G 2008 Journal of Engineering Thermophysics 29 957 [曲延鹏, 陈颂英, 王小鹏, 腾书格 2008 工程热物理学报 29 957]
[30] Zhao P H, Ye T H, Zhu H M, Chen J, Chen Y L 2012 Journal of Engineering Thermophysics 33 529 [赵平辉, 叶桃红, 朱昊明, 陈靖, 陈义良 2012 工程热物理学报 33 529]
[31] Du C, Xu M Y, Mi J C 2010 Acta Phys. Sin. 59 6331 (in Chinese) [杜诚, 徐敏义, 米建春 2010 物理学报 59 6331]
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[33] Lee J H W, Chu V H 2003 Turbulent Jets and Plumes: A Lagrangian Approach (Dordrecht: Kluwer Academic Publisher) p6
[34] Schlichting H 1979 Boundary Layer Theory (7th Edn.) (New York: McGraw-Hill) 230
[35] Antonio R, Antonio L S 2002 Phys. Fluids 14 1821
[36] Beckers M, Clercx H J H,vanHeijst G J F 2002 Phys. Fluids 14 704
[37] Meleshko V V, van Heijst G J F 1994 J. Fluid Mech. 272 157
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[1] Ivanov A Y, Ginsburg A I 2002 Proc. Indan Acad. Sci. (Earth Planet. Sci.) 111 281
[2] Fedorov K N, Ginsburg A I 1989 Mesoscale/Synoptic Coherent structures in Geophysical Turbulence 50 1
[3] Van Heijst G J F, Clercx H J H 2009 Annu. Rev. Fluid Mech. 41 143
[4] Meunier P, Spedding G R 2006 J. Fluid Mech. 552 229
[5] Wei G, Dai S Q 2006 Advances in Mechanics 36 111 (in Chinese) [魏岗, 戴世强 2006 力学进展 36 111]
[6] Abramovich S, Solan A 1973 J. Fluid Mech. 59 791
[7] Sozou G, Pickering W M 1977J. Fluid Mech. 80 673
[8] Sozou G 1979 J. Fluid Mech. 91 541
[9] Fan Q L, Wang X L, Zhang H Q, Guo Y C, Lin W Y 2002 Advances in Mechanics 32 109 (in Chinese) [范全林, 王希麟, 张会强, 郭印诚, 林文漪 2002 力学进展 32 109]
[10] Yule A J 1978 J. Fluid Mech. 89 413
[11] Tso J, Hussain F 1989 J. Fluid Mech. 203 425
[12] Fiedler H E 1988 Progress in Aerospace Science 25 231
[13] Sous D, Bonneton N, Sommeria J 2004 Phys. Fluids 16 2886
[14] Sous D, Bonneton N, Sommeria J 2005 European Journal of Mechanics B/Fluids 24 19
[15] Praud O, Fincham A M 2005 J. Fluid Mech. 544 1
[16] Meunier P, Diamessis P J, Spedding G R 2006 Phys. Fluids 18 1
[17] Chen K, You Y X, Hu T Q, Zhu M H, Wang X Q 2011 Acta Phys. Sin. 60 024702 (in Chinese) [陈科, 尤云祥, 胡天群, 朱敏慧, 王小青 2011 物理学报 60 024702]
[18] Danaila I, Dusek J, Anselmet F 1997 Phys. Fluids 9 3323
[19] O'Neil P, Soria J, Honnery D 2004 Exp. Fluids 36 473
[20] Kwon S J, Seo I W 2005 Exp. Fluids 38 801
[21] Reynolds A J 1962 J. Fluid Mech. 14 552
[22] McNaughton K J, Sincair C G 1966 J. Fluid Mech. 25 367
[23] Gill A E 1965 J. Fluid Mech. 14 557
[24] Schneider W 1985 J. Fluid Mech. 154 91
[25] Petrov P A 1973 Fluid Dynamics 8 190
[26] Chen Y, Li D H, E X Q 1991 Acta Mechanica Sinica 23 721 (in Chinese) [陈远, 李东辉, 鄂学金 1991 力学学报 23 721]
[27] Afanasyev Y D, Korabel V N 2004 J. Fluid Mech. 16 3850
[28] Voropayev S I, Afanasyev Y D, Korabel V N, Filippov I A 2003 Phys. Fluids 15 3420
[29] Qu Y P, Chen S Y, Wang X P, Teng S G 2008 Journal of Engineering Thermophysics 29 957 [曲延鹏, 陈颂英, 王小鹏, 腾书格 2008 工程热物理学报 29 957]
[30] Zhao P H, Ye T H, Zhu H M, Chen J, Chen Y L 2012 Journal of Engineering Thermophysics 33 529 [赵平辉, 叶桃红, 朱昊明, 陈靖, 陈义良 2012 工程热物理学报 33 529]
[31] Du C, Xu M Y, Mi J C 2010 Acta Phys. Sin. 59 6331 (in Chinese) [杜诚, 徐敏义, 米建春 2010 物理学报 59 6331]
[32] Durst F, Ray S, Unsal B, Bayoumi O A 2005 J. Fluids Eng. 127 1154
[33] Lee J H W, Chu V H 2003 Turbulent Jets and Plumes: A Lagrangian Approach (Dordrecht: Kluwer Academic Publisher) p6
[34] Schlichting H 1979 Boundary Layer Theory (7th Edn.) (New York: McGraw-Hill) 230
[35] Antonio R, Antonio L S 2002 Phys. Fluids 14 1821
[36] Beckers M, Clercx H J H,vanHeijst G J F 2002 Phys. Fluids 14 704
[37] Meleshko V V, van Heijst G J F 1994 J. Fluid Mech. 272 157
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