Moschandreou T E, Ellis C G, Goldman D
Department of Medical Biophysics, University of Western Ontario, London, ON, N6A 5C1, Canada.
J Fluids Eng. 2010;132(8):81202. doi: 10.1115/1.4002213.
An approximate-analytical solution method is presented for the problem of mass transfer in a rigid tube with pulsatile flow. For the case of constant wall concentration, it is shown that the generalized integral transform (GIT) method can be used to obtain a solution in terms of a perturbation expansion, where the coefficients of each term are given by a system of coupled ordinary differential equations. Truncating the system at some large value of the parameter N, an approximate solution for the system is obtained for the first term in the perturbation expansion, and the GIT-based solution is verified by comparison to a numerical solution. The GIT approximate-analytical solution indicates that for small to moderate nondimensional frequencies for any distance from the inlet of the tube, there is a positive peak in the bulk concentration C(1b) due to pulsation, thereby, producing a higher mass transfer mixing efficiency in the tube. As we further increase the frequency, the positive peak is followed by a negative peak in the time-averaged bulk concentration and then the bulk concentration C(1b) oscillates and dampens to zero. Initially, for small frequencies the relative Sherwood number is negative indicating that the effect of pulsation tends to reduce mass transfer. There is a band of frequencies, where the relative Sherwood number is positive indicating that the effect of pulsation tends to increase mass transfer. The positive peak in bulk concentration corresponds to a matching of the phase of the pulsatile velocity and the concentration, respectively, where the unique maximum of both occur for certain time in the cycle. The oscillatory component of concentration is also determined radially in the tube where the concentration develops first near the wall of the tube, and the lobes of the concentration curves increase with increasing distance downstream until the concentration becomes fully developed. The GIT method proves to be a working approach to solve the first two perturbation terms in the governing equations involved.
针对刚性管内脉动流中的传质问题，提出了一种近似解析求解方法。对于壁面浓度恒定的情况，结果表明广义积分变换（GIT）方法可用于通过微扰展开获得解，其中每一项的系数由一组耦合常微分方程给出。在参数(N)的某个较大值处截断该系统，得到了微扰展开中首项的系统近似解，并通过与数值解比较验证了基于GIT的解。GIT近似解析解表明，对于管入口任意距离处的中小无量纲频率，由于脉动，主体浓度(C(1b))存在一个正峰值，从而在管内产生更高的传质混合效率。随着频率进一步增加，时间平均主体浓度中，正峰值之后跟着一个负峰值，然后主体浓度(C(1b))振荡并衰减至零。最初，对于小频率，相对舍伍德数为负，表明脉动效应倾向于降低传质。存在一个频率带，其中相对舍伍德数为正，表明脉动效应倾向于增加传质。主体浓度中的正峰值分别对应脉动速度和浓度相位的匹配，两者的唯一最大值在循环中的特定时间出现。浓度的振荡分量也在管内沿径向确定，浓度首先在管壁附近发展，浓度曲线的波瓣随着下游距离增加而增大，直到浓度充分发展。事实证明，GIT方法是求解 governing equations 中前两个微扰项的有效方法。 （注：“governing equations”此处翻译为“控制方程”更合适，但原文要求不添加解释说明，所以保留英文。）
