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.本研究将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）推广至非稳态工况。针对研究人员在海德堡艾奥洛特龙风洞（Heidelberg Aeolotron）中开展气-水热交换实验所用的三种不同风速工况，计算结果显示：该分布在初始阶段呈现尖锐峰值，但随过程时间推移会逐渐平缓并呈现钟形特征；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，偏度降低，峰值则相应增大。平均涡旋更新时间在初始阶段随过程时间呈线性增长，随后渐近趋近于最终稳态值，且该稳态值随风速升高而显著降低。基于该分布分析气体向大体积液体的瞬态吸收过程，假设气相传质阻力可忽略不计，针对三种不同风速工况，我们估算了25℃下氧气在水中吸收时的气体吸收系数与溶解气体传递系数。在非稳态工况下，这两个传递系数表现出相反的变化趋势，表明表面微元内的溶解气体累积量更高，尤其在吸收初始阶段。但随着趋近稳态，这两个传质系数会逐渐趋于一致。针对20℃下一氧化二氮-水体系的稳态传质系数或传递速度，本研究得到的理论预测值与在海德堡艾奥洛特龙风洞（Heidelberg Aeolotron）中测得的部分实验数据吻合度较好，预测平均绝对误差为18.1%。