• 作者： Lee, S. J.; Chang, C. Y.; Chiu, C. Y.; Huang, W. H.; Shih, S. M.
• 中文摘要： 型式簡單的液滴內循環週期公式，有助於掌握各不同流線液體的內循環週期(t/sub c/)與流線函數值(ξ)之間的關係，藉以評估內循環對液滴質量傳送的影響。Kronig and Brink (1950)曾導得低雷諾數液滴的內循環週期公式，但其中包含型式複雜的橢圓積分函數，求值不便，較難用於工程設計或推算。本研究嘗試建立型式簡單的內循環週期公式。先經由解析性的衍導獲得液滴表面微分厚度區域內流體的內循環週期(t/sub cs/)，如式(19)。式(19)的t/sub cs/值與Kronig and Brink(1950)者相符，其相對誤差在ξ≦0.1與0.2範圍，僅分別小於3.6與6％; 故對ξ≦0.2範圍，式(19)的解析解應可適用。經由與Kronig and Brink (1950)表列理論值的比對，進一步修正t/sub cs/為可適用液滴全體範圍(0≦ξ≦1)的t/sub cf/，如式(20)；其相對誤差在ξ≧0.01範圍，小於 1.1%。以上二式係以常用函數表示，使得t/sub c/理論數值的求得變得容易，但其函數型式仍不夠簡單。更進一步，直接推求Kronig and Brink (1950)各組理論數值的函數相關性，而得到型式簡單的近似式，如式(21)；對10/sup -6/≦ξ≦1範圍，式(21)的相對誤差小於3.7%。依式(21)顯示：當流線函數值由ξ=1(內循環核心點)降至大約ξ=1/117.5，t/sub c /增為2倍；當由ξ=1降至ξ=10/sup -6/，t/sub c/增為3.9倍。
• 英文摘要： Simple approximate solutions of internal circulation periods (t/sub c/) of liquid in falling droplets for low Reynolds number (N/sub Re/), which are needed for describing the effect of internal circulation of liquid in droplets on the gas absorption rate of liquid drops, were obtained. A simple solution of t/sub c/ for the liquid in the differential shell region near the inside surface of a droplet, denoted as t/sub cs/, was first analytically derived in terms of .xi., where .xi. is the stream function describing the flow motion in the liquid drop. The values of t/sub cs/ (Eq. (19)) agree with those of Kronig and Brink (1950) with relative errors less than 3.6 and 6% for .xi..ltoreq.0.1 and 0.2, respectively. Thus, the theoretical solution of Eq. (19) is valid for .xi..ltoreq. 0. 2. The obtained t/sub cs/ was further modified by simple correlation to extend its applicability to the full range of.xi.(0.ltoreq..xi..ltoreq.1). The relative errors of the modified solutions or the full .xi., denoted as t/sub cf/, were less than 1.1% for.xi..gtoreq.0.01. A simple correlation equation based on the theoretical values of Kronig and Brink (1950) was also made. The relative errors of this correlation equation were less than 3.7% for 10/sup -6/.ltoreq..xi..ltoreq.1. The solutions of this analysis avoid the complexity of the elliptic integral terms encountered in that of Krong and Brink (1950) and thus are much easier to apply and may help in engineering design or estimation. With the simple solutions, one can easily note that t/sub c/ increases twice and 3.9 times as .xi. decreases from .xi.=1 to about 1/117.5 and 10/sup -6/, respectively.
• 中文關鍵字： 液滴內循環; 循環週期; 液滴; 質量傳遞; 吸收
• 英文關鍵字： Internal Circulation; Circulation Period; Liquid Drop; Mass Transfer; Absorption