Characterization of interfacial waves and pressure drop in horizontal oil-water core-annular flows

We study the transportation of highly viscous furnace-oil in a horizontal pipe as core-annular flow (CAF) using experiments. Pressure drop and high-speed images of the fully developed CAF are recorded for a wide range of flow rate combinations. The height profiles (with respect to the centerline of the pipe) of the upper and lower interfaces of the core are obtained using a high-speed camera and image analysis. Time series of the interface height are used to calculate the average holdup of the oil phase, speed of the interface, and the power spectra of the interface profile. We find that the ratio of the effective velocity of the annular fluid to the core velocity, $α$⁠, shows a large scatter. Using the average value of this ratio (⁠$α=0.74$⁠) yields a good estimate of the measured holdup for the whole range of flow rate ratios, mainly due to the low sensitivity of the holdup ratio to the velocity ratio. Dimensional analysis implies that, if the thickness of the annular fluid is much smaller than the pipe radius, then, for the given range of parameters in our experiments, the non-dimensional interface shape, as well as the non-dimensional wall shear stress, can depend only on the shear Reynolds number and the velocity ratio. Our experimental data show that, for both lower and upper interfaces, the normalized power spectrum of the interface height has a strong dependence on the shear Reynolds number. Specifically, for low shear Reynolds numbers, interfacial modes with large wavelengths dominate, while, for large shear Reynolds numbers, interfacial modes with small wavelengths dominate. Normalized variance of the interface height is higher at lower shear Reynolds numbers and tends to a constant with increasing shear Reynolds number. Surprisingly, our experimental data also show that the effective wall shear stress is, to a large extent, proportional to the square of the core velocity. Using the implied scalings for the holdup ratio and wall shear stress, we can derive an expression for the pressure drop across the pipe in terms of the flow rates, which agrees well with our experimental measurements.