等热流密度加热垂直下降液膜的研究
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摘要
利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明,模型方程在小到中等Reynolds数下都适用,并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加,展向不稳定性增长率则随着Marangoni数增加而增加,随着Reynolds数增加而减小,流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明,在等热流密度加热条件下,液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构,液膜与气体的换热也因溪流状结构的出现而加强;在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强,液膜会提前破裂;在随机扰动的基础上引入占优势地位的流向最不稳定扰动时,液膜的换热会增强,但不会提前破裂;在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时,换热会加强且液膜会提前破裂。
A three-dimensional regularized model(RM) was used to study vertical falling liquid film on a uniformly heated plate with a constant heat flux.Linear stability analysis shows that RM is applicable from small to moderate Reynolds numbers; streamwise growth rate increases as Reynolds number and Marangoni number increase,and spanwise growth rate increases as Marangoni number increases,but decreases as Reynolds number increases; for streamwise and spanwise growth rates,there exists an unstable interval of disturbance wavenumber.Three-dimensional numerical simulation shows that a random disturbance can give rise to three-dimensional rivulet structures after a sufficient evolution of the film layer,and thus heat transfer between liquid and gas is enhanced; the three-dimensional rivulet structures arise earlier and heat transfer is enhanced as long as a dominant most unstable spanwise disturbance is added to the film besides random disturbance,but the rupture of the liquid film occurs earlier; the heat transfer is enhanced and the liquid film doesn't rupture earlier under the circumstance that only a dominant most unstable streamwise disturbance is added besides random disturbances.
A three-dimensional regularized model(RM) was used to study vertical falling liquid film on a uniformly heated plate with a constant heat flux.Linear stability analysis shows that RM is applicable from small to moderate Reynolds numbers; streamwise growth rate increases as Reynolds number and Marangoni number increase,and spanwise growth rate increases as Marangoni number increases,but decreases as Reynolds number increases; for streamwise and spanwise growth rates,there exists an unstable interval of disturbance wavenumber.Three-dimensional numerical simulation shows that a random disturbance can give rise to three-dimensional rivulet structures after a sufficient evolution of the film layer,and thus heat transfer between liquid and gas is enhanced; the three-dimensional rivulet structures arise earlier and heat transfer is enhanced as long as a dominant most unstable spanwise disturbance is added to the film besides random disturbance,but the rupture of the liquid film occurs earlier; the heat transfer is enhanced and the liquid film doesn't rupture earlier under the circumstance that only a dominant most unstable streamwise disturbance is added besides random disturbances.
引文
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[2] Benney D J.Long waves on liquid films[J].Journal of Mathematics and Physics,1966,45(1):150-155.
[3] Shkadov V Y.Wave -flow theory for a thin viscous liquid layer[J].Fluid Dynamics,1968,3(2):12-15.
[4] Ruyer-Quil C,Manneville P.Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations[J].Physics of Fluids,2002,14(1):170-183.
[5] Ruyer-Quil C,Manneville P.Improved modeling of flows down inclined planes [J].The European Physical Journal B -Condensed Matter and Complex Systems,2000,15(2):357-369.
[6] Ruyer-Quil C,Manneville P.Modeling film flows down inclined planes[J].The European Physical Journal B -Condensed Matter and Complex Systems,1998,6(2):277-292.
[7] Ruyer-Quil C,Scheid B,Kalliadasis S,et al.Thermo -capillary long waves in a liquid film flow.Part 1:Low-dimensional formulation[J].Journal of Fluid Mechanics,2005,538:199-222.
[8] Scheid B,Ruyer-Quil C,Kalliadasis S,et al.Thermocapillary long waves in a liquid film flow.Part 2:Linear stability and nonlinear waves[J].Journal of Fluid Mechanics,2005,538:223-244.
[9] Kalliadasis S,Ruyer-Quil C,Scheid B,et al.Falling Liquid Films[M].London:Springer,2012.
[10] Scheid B.Evolution and Stability of Falling Liquid Films with Thermocapillary Effects[D].Universite Libre de Bruxelles,2004.
[11] Trevelyan P M J,Scheid B,Ruyer-Quil C,et al.Hea-ted falling films[J].Journal of Fluid Mechanics,2007,592:295-334.
[12] Shkadov V Y.Solitary waves in a layer of viscous liquid[J].Fluid Dynamics,1977,12(1):52-55.
[13] Smith M K.The mechanism for the long-wave instability in thin liquid films[J].Journal of Fluid Mechanics,1990,217:469-485.
[14] Goussis D A,Kelly R E.Surface wave and thermo -capillary instabilities in a liquid film flow[J].Journal of Fluid Mechanics,1991,223(2):25-45.
[15] Scheid B,Kalliadasis S,Ruyer-Quil C,et al.Interaction of three -dimensional hydrodynamic and thermocapillary instabilities in film flows[J].Physical Review E,2008,78(6):066311.
[16] Trefethen L N.Spectral Methods in MatLab[M].SIAM,2000.
[17] Nusselt W.Die OberflachenKondensation des wasserdamfes [J].VDI-Zs,1916,4:569-575.(in German)