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沃茨年龄分布（steady-state generalized Danckwerts age distribution）被推广至非稳态工况中。针对研究者在海德堡风洞（Heidelberg Aeolotron）内开展气水热交换研究所采用的三种不同风速，计算结果显示：该分布在初始阶段呈现尖锐峰值，但随过程时长增加逐渐平缓，呈现钟形分布特征；达到稳态分布轮廓所需的时长与风速呈显著反比关系。随着风速升高，年龄分布的宽度显著收窄，偏度（skewness）降低，峰值则进一步升高。平均涡旋更新时间最初随过程时长呈线性增长，随后渐近趋近于最终稳态值，且该稳态值随风速升高大幅降低。假设气相传质阻力可忽略不计，利用该分布分析气体向大体积液体的瞬态吸收过程，针对三种不同风速，我们估算得到了25℃下水中氧气吸收过程的气体吸收系数与溶解气体传递系数。在非稳态工况下，这两个系数呈现相反的变化趋势，表明流体表面单元内溶解气体的积累量有所提升，尤其在吸收初始阶段更为显著。但随着趋近稳态，这两个传质系数逐渐趋于一致。针对20℃下一氧化二氮-水体系的稳态传质系数或传递速度，本研究的理论预测值与海德堡风洞内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%。