Wavespeed and volumetric fraction in core annular ¯ow A.C. Bannwart Department of Energy, University of Campinas, UNICAMP Cx. P. 6122, 13083-970, Campinas, SP, Brazil Received 29 January 1997; received in revised form 16 June 1998 Abstract Kinematic wave theory is used to study the speed of interfacial waves observed in core annular ¯ows of viscous oils with water. The theory provides a method for measuring the volume fraction of the core. The results obtained by this method are in very good agreement with experimental data. The model also con®rms the observation that for oils lighter than water waves move slower than the core in upward ¯ow, faster than the core in downward ¯ow and at the same velocity of the core in horizontal ¯ow. A general correlation for the core fraction in wavy core annular ¯ows at low annulus-to-core viscosity ratio is proposed. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Oil-water ¯ow; Core annular ¯ow; Volumetric concentration; Wavespeed; Slip ratio 1. Introduction In many circumstances when two liquids of dierent viscosities ¯ow together in a pipe, a core annular ¯ow appears with the more viscous ¯uid in the core and the other in the annulus. An important practical application of this ¯ow pattern has been found in the pipeline transportation of heavy oils by using water as lubricant. As in gas±liquid annular ¯ow, the interface in a core annular ¯ow is usually wavy as a result of the complex interactions between the two phases. However the wave pattern in core annular ¯ow is not a chaotic one. Due to the high viscosity of the core, the waves form a single pattern traveling at constant speed and wavelength depending on the ¯ow rates, orientation and ¯uid properties. An interesting recent study on these waves in vertical core annular was made by Bai (1995). A detailed description of his experiment and the dierent ¯ow patterns for up¯ow and down¯ow was presented earlier in the book by Joseph and Renardy (1993). In upward ¯ow of International Journal of Multiphase Flow 24 (1998) 961±974 0301-9322/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S0301-9322(98)00019-6 PERGAMON