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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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[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
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[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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[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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