Data from: A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function

The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady-state conditions. For three different wind speeds used by researchers on air-water heat exchange on the Heidelberg Aeolotron, calculations reveal that the distribution has a sharp peak during the initial moments, but flattens out and acquires a bell-shaped character with process time, with the time taken to attain a steady-state profile being a strong and inverse function of wind speed. With rising wind speed, the age distribution narrows significantly, its skewness decreases and its peak becomes larger. The mean eddy renewal time increases linearly with process time initially but approaches a final steady-state value asymptotically, which decreases dramatically with increased wind speed. Using the distribution to analyze the transient absorption of a gas into a large body of liquid, assuming negligible gas-side mass-transfer resistance, estimates are made of the gas-absorption and dissolved-gas transfer coefficients for oxygen absorption in water at 25ºC for the three different wind speeds. Under unsteady-state conditions, these two coefficients show an inverse behavior, indicating a heightened accumulation of dissolved gas in the surface elements, especially during the initial moments of absorption. However, the two mass-transfer coefficients start merging together as steady state is approached. Theoretical predictions of the steady-state mass-transfer coefficient or transfer velocity are in fair agreement (average absolute error of prediction = 18.1%) with some experimental measurements of the same for the nitrous oxide – water system at 20ºC that were made in the Heidelberg Aeolotron.新近推导得到的稳态广义丹克韦茨（Danckwerts）年龄分布已被拓展至非稳态工况范畴。针对研究者在海德堡艾奥洛特龙（Heidelberg Aeolotron）装置上开展气-水热交换实验所采用的三种风速工况，计算结果显示：该分布在初始阶段呈现尖锐峰值，随过程时长增加逐渐平缓并呈现钟形分布特征；达到稳态分布轮廓所需的时间与风速呈显著负相关关系。随着风速升高，年龄分布的宽度显著收窄，偏斜度（skewness）降低，峰值则进一步增大。平均涡旋更新时间（eddy renewal time）初始阶段随过程时长呈线性增长，随后渐近收敛至最终稳态值，且该稳态值随风速升高呈显著下降趋势。借助该分布分析气体向大体积液体的瞬态吸收（transient absorption）过程，假设气相传质阻力（gas-side mass-transfer resistance）可忽略不计，针对25℃下水体中氧气吸收的三种风速工况，分别估算了气体吸收系数与溶解气体传质系数（dissolved-gas transfer coefficients）。非稳态工况下，这两种传质系数呈现相反的变化趋势，表明表面微元内的溶解气体出现显著积累，尤其在吸收初始阶段。但随着系统趋近稳态，这两个传质系数的数值将逐渐趋于一致。针对20℃下氧化亚氮-水体系（nitrous oxide – water system）的稳态传质系数（mass-transfer coefficient）或传质速率（transfer velocity），本研究得到的理论预测值与海德堡艾奥洛特龙装置上开展的部分实验测量结果吻合度较好，预测平均绝对误差为18.1%。