Multi-holdups in co-current stratified flow in inclined tubes A. Ullmann, M. Zamir, S. Gat, N. Brauner * Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Received 3 October 2002; received in revised form 17 July 2003 Abstract Maps of the multi-holdup regions in co-current and countercurrent flows are presented in terms of the controlling non-dimensional parameters. These maps clearly demonstrate the symmetrical relationship between upward and downward co-current inclined flows. The feasibility of obtaining multi-holdups in co- current up flow is validated experimentally using oil–water system. The multiple holdups are shown to be associated with hysteresis phenomenon. The introduction of the multi-holdup regions on flow-pattern maps of various gas–liquid and liquid–liquid systems, indicates that these regions correspond to operational conditions where stratified flow was experimentally observed. The significance of multi-holdups phenomena to transition from stratified flow to other bounding flow patterns is discussed. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Co-current; Holdup; Inclined; Multiple; Stratified 1. Introduction Despite the extensive efforts and the numerous theoretical and experimental investigations into co-current stratified flows in pipes, the issue of multiple holdups attracted a rather limited at- tention. Taitel and Dukler (1976, 1986) two-fluid model is widely used as a predictive tool for stratified gas–liquid flows. Baker and Gravestock (1987) and Baker et al. (1988) first pointed out that this model can predict non-unique values of the holdup for given phases flow rates in upward inclined flows. This issue was the subject of a theoretical investigation by Landman (1991). He showed that the multiple holdups in upward stratified flow are not an artifact of the two-fluid model. Similar behavior is predicted by the exact solution for laminar flows in upward inclined square ducts. International Journal of Multiphase Flow 29 (2003) 1565–1581 www.elsevier.com/locate/ijmulflow * Corresponding author. Tel.: +972-3-640-8127; fax: +972-3-640-7334. E-mail address: brauner@eng.tau.ac.il (N. Brauner). 0301-9322/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0301-9322(03)00143-5