液-液並行流動中非線性界面波及捲波之研究

The Experimental Study of Nonlinear Interfacial Waves and Roll Waves in Cocurret Liquid-Liquid Flows

郭介元(Chieh-Yuan Kuo)

指導教授 ： 蘇淵源

國立臺北科技大學/工程學院/化學工程研究所/碩士(2007年)

摘要

本研究是以高黏度矽油/24.8wt%鹽水兩種流體配對，在分別提高個別流體的流量下，並行流進寬厚比28:1之方形溝槽，所產生不穩定的界面波動，使用高速攝影機搭配影像擷取與軟體進行分析。其中我們運用高階頻譜、以及線性理論分析針對流動系統計算波時間成長速率，並以Gaster Transformation轉換的波空間成長速率與實驗所得數據比較。本研究於低流量範圍操作下，隨矽油流量改變，波行為屬線性理論可描述之長波系統。當接近擾動波成長相當小的情形時，我們調高鹽水流量，分析系統波的行為，發現頻率介於0.98Hz ~ 1.50Hz範圍內有最不穩定的界面模式。首先藉由bicoherence量測顯示overtones與fundamental之間的交互作用將能量從fundamental傳至first overtone。當fundamental達臨界振幅時，激起ㄧ個subharmonic mode並隨fundamental能量減弱而成長。藉由bicoherence的量測其間的能量傳遞，同時利用cross spectrum估算波速並取得之間相差的關係，驗證其存在的共振效應。其次主要波與sidebands之間交互作用所形成的低頻波，隨下游距離緩慢地成長。我們也利用線性理論分析預測低頻模式的成長速率，並與氣-液流動系統來比較，證明在本研究的液-液系統觀察相似捲波的形成。

關鍵字

界面波 ； 高階頻譜 ； 非線性 ； 次簡諧波 ； 捲波

並列摘要

In this study, we utilize a high-speed camera grabber with the help of data processing techniques to perform the stability analysis of liquid-liquid concurrent flow by varying flow rates of both fluids through a coextrusion die followed by a rectangular flow channel with an aspect ratio 28:1. A cross spectrum is performed to determine the wave speed and the wavelength of each harmonic of interfacial waves, thus the temporal growth rate can be evaluated by linear stability theory. The theoretical spatial growth rate is then obtained by Gaster Transformation and compared with the experimental observations. In order to examine the nonlinear behavior of downstream interfacial waves, induced by a substantial increase in brine flow rate, the high-order spectral analysis is utilized. It is shown that the most unstable interface mode, which has frequencies of 0.98Hz ~ 1.50Hz, grows initially-followed immediately by the first overtone. Measurements of the bicoherence spectrum indicate that the overtone and fundamental are coherent in phase, which suggests that energy transfer from the fundamental to the first overtone. When the fundamental has reached a critical amplitude, a subharmonic mode can be excited and grows at the expense of the fundamental. Sidebands to the main peak may also occur. These sidebands can involve interactions with low-frequency modes and thereby transfer energy to frequency much below the fundamental. In addition, the growth rate of low-frequency modes predicted by linear stability theory is compared with that obtained in gas-liquid concurrent flow system and it is demonstrated that the low-frequency mode, evolving into roll waves downstream, observed in our liquid-liquid flow system is similar to that in the gas-liquid one.

並列關鍵字

interfacial waves ； higher-order spectrum ； nonlinear instability ； subharmonics ； roll waves

參考文獻

1. Russell, T. W. F., Hodgson, G. W. and Govier, G. W., “Horizontal Pipeline Flow of Mixtures of Oil and Water,” The Canadian Journal of Chemical Engineering, Vol. 37, pp. 9-17 (1959).

2. Charles, M. E. and Lilleleht, L. U., “Co-current Stratified Laminar Flow of Two Immiscible Liquids in a Rectangular Conduit,” The Canadian Journal of Chemical Engineering, Vol. 43, pp. 110-116 (1965).

3. Han, C. D. and Shetty, R., “Studies on Multilayer Film Coextrusion Ⅱ.Interfacial Instability in Flat Film Coextrusion,” Polymer Engineering and Science, vol. 18, , pp. 180-186 (1978).

4. Han, C. D., Kim, Y. J. and Chin, H. B., “Rheological Investigation of Interfacial Instability in Two-Layer Flat-Film Coextrusion,” Polymer Engineering Reviews, vol. 4, pp. 178-200 (1984).

5. Schrenk, W. J., Bradley, N. L., Alfrey, T. and Maack, H., “Interfacial Flow Instability in Multilayer Coextrusion,” Polymer Engineering and Science, vol. 18, pp. 620-623 (1978).