Immiscible displacement flows in axially rotating pipes

Abstract

We experimentally study buoyant immiscible displacement flows in an axially rotating pipe, with varying flow parameters, such as the mean imposed flow velocity, density difference, pipe rotation speed, and pipe inclination angle. Via employing image processing and ultrasound Doppler velocimetry techniques, we analyze key flow features, including displacement regimes, interfacial instabilities, interfacial front velocities, and velocity and concentration fields. We find that immiscible displacement flows are distinguished by the emergence of one or two heavy fluid fronts, particularly depending on the rotation speed. Furthermore, our dimensional analysis reveals that the displacement flow is governed by four dimensionless parameters, including the Reynolds, densimetric Froude (or Archimedes), and Rossby numbers, as well as the pipe inclination angle. Using these dimensionless groups, we succeed in categorizing the main flow regimes as efficient and inefficient displacements. Moreover, we classify the interfacial regimes as stable, intermittently unstable, kinks, and separating interfacial patterns. Our analysis shows that the interfacial instabilities observed are indeed characterized by the Kelvin–Helmholtz instability. Our analysis of the velocity fields suggests remarkable differences between displacements in stationary and rotating pipes, especially in terms of the absence and presence of a countercurrent flow, respectively. Finally, our assessment of concentration fields using a Fourier transform approach provides a preliminary fundamental understanding of the characteristics of concentration waves and their corresponding amplitudes.