Mixing and spreading in stratified flow
Mixing and spreading in stratified flow
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DOI：
10.1063/1.2427089
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发表时间：
2007-01-01
影响因子：
4.6
通讯作者：
Carrera, Jesus
中科院分区：
文献类型：
--
作者：
Dentz, Marco;Carrera, Jesus
G. I. Taylor [Proc. R. Soc.伦敦，Ser. A 219，186（1953）]通过恒定的泰勒分散系数，在渐近长时间内量化了通过管的流动中的增强的溶质混合，这提供了溶质浓度的渐近分散动力学和演化的良好表示。然而，在preasymptomatic时间，使用的常数泰勒色散系数不便于忠实地表示实际的混合或扩散，这是控制因素的化学反应速率。空间变化流场中的输运通常表现出非Fickian或异常行为，这反映在有效弥散随时间演变的事实上。在这里，我们研究和量化的机制，导致增强溶质混合在空间非均匀流场使用“本地”空间矩，即，传输绿色函数的矩。在这样的局部矩公式的基础上，我们定义了有效弥散系数来表征有效的前渐近溶质扩散和混合。我们将这些概念的有效运输的一般分层流的特征，并说明他们在一个二维通道的特殊情况下的运输。我们研究有效的混合和传播在preasymptomatic时间的有效色散系数的显式解析表达式，以及通过数值随机游走模拟。我们发现，垂直平均浓度分布包含的物理混合和扩散过程中发生的preasymptomatic时间的信息很少。这导致我们定义一个替代的平均，有效浓度，其演变的特点是有效的分散系数，主要反映平均有效的溶质混合，而不是纯粹的对流扩散的初始溶质分布。
G. I. Taylor [Proc. R. Soc. London, Ser. A 219, 186 (1953)] quantified enhanced solute mixing in the flow through a tube at asymptotically long times by the constant Taylor dispersion coefficient, which provides a good representation of both the asymptotic dispersion dynamics and evolution of the solute concentration. At preasymptotic times, however, the use of the constant Taylor dispersion coefficient does not facilitate a faithful representation of either the actual mixing or spreading, which are controlling factors for chemical reaction rates. Transport in spatially varying flow fields often displays non-Fickian or anomalous behavior, which is reflected by the fact that effective dispersion evolves in time. Here we study and quantify the mechanisms leading to enhanced solute mixing in spatially nonhomogeneous flow fields using "local" spatial moments, i.e., moments of the transport Green function. On the basis of such a local moment formulation, we define effective dispersion coefficients to characterize effective preasymptotic solute spreading and mixing. We apply these concepts to the characterization of effective transport in general stratified flows, and illustrate them for the particular case of transport in a two-dimensional channel. We study effective mixing and spreading at preasymptotic times in terms of explicit analytical expressions for the effective dispersion coefficients as well as by numerical random walk simulations. We find that the vertically averaged concentration profiles contain little information on the physical mixing and spreading processes occurring at preasymptotic times. This leads us to define an alternative average, effective concentration, whose evolution is characterized by the effective dispersion coefficient and which reflects mainly the average effective solute mixing rather than purely advective spreading of the initial solute distribution.