Characterization of interfacial waves in horizontal core-annular flow

In this work, we characterize interfacial waves in horizontal core annular flow (CAF) of fuel-oil and water. Experimental studies on CAF were performed in an acrylic pipe of 15.5mm internal diameter, and the time evolution of the oil-water interface shape was recorded with a high speed camera for a range of different flow-rates of oil ($Q_o$) and water ($Q_w$). The power spectrum of the interface shape shows a range of notable features. First, there is negligible energy in wavenumbers larger than $2\pi/a$, where $a$ is the thickness of the annulus. Second, for high $Q_o/Q_w$, there is no single dominant wavelength, as the flow in the confined annulus does not allow formation of a preferred mode. Third, for lower $Q_o/Q_w$, a dominant mode arises at a wavenumber of $2\pi/a$. We also observe that the power spectrum of the interface shape depends weakly on $Q_w$, and strongly on $Q_o$, perhaps because the net shear rate in the annulus appears to depend weakly on $Q_w$ as well. We also attempt to build a general empirical model for CAF by relating the interfacial stress (calculated via the mean pressure gradient) to the flow rate in the annulus, the annular thickness and the core velocity.