Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow
Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow
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DOI：
10.1098/rspa.1972.0040
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发表时间：
1972-03
期刊：
影响因子：
--
通讯作者：
W. Gill;R. Sankarasubramanian
中科院分区：
文献类型：
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作者：
W. Gill;R. Sankarasubramanian
分析了来自连续源的材料的不稳定分散，该连续源在管的入口处的横截面上不均匀地分布，其中流体呈随时间变化的层流。当对流扩散方程中的系数是时间的函数时，叠加积分被开发用于从瞬时源的解中获得由时间变量连续源产生的非稳态浓度分布的解。当系数与时间无关时，这可以简化为传统的叠加积分。数值结果是针对稳定层流中稳定连续源的特殊情况获得的。提出了一种非常好的平均浓度近似值，可以大大减少计算量。针对由于管入口处的不均匀阶跃变化而导致的材料分散的稳态问题，对入口区域进行了边界层分析，并对下游区域进行了正交函数展开。稳态正交函数展开解与本方法相当。边界层解在非常接近管入口处非常有用，因为在该处很难从其他方法获得数值结果。
Unsteady dispersion of material from a continuous source which is non-uniformly distributed over the cross-section at the inlet of a tube in which fluid is in time-dependent laminar flow, is analysed. A superposition integral is developed for use in obtaining solutions for the unsteady concentration distribution created by time variable continuous sources from the solution for instantaneous sources when the coefficients in the convective diffusion equation are functions of time. This reduces to the conventional superposition integral when the coefficients are time-independent. Numerical results are obtained for the special case of a steady continuous source in steady laminar flow. A very good approximation to the mean concentration which considerably reduces the computational labour is proposed. For the steady-state problem of dispersion of material due to a non-uniform step change at the inlet of the tube, a boundary-layer analysis is presented for the inlet region and an orthogonal function expansion is developed for the downstream region. The steady-state orthogonal function expansion solution compares well with the present method. The boundary-layer solution is useful very close to the tube entrance where it is difficult to obtain numerical results from the other methods.