Computational study of Newtonian laminar annular horizontal displacement flows with rotating inner cylinder

We computationally study the effects of inner cylinder rotation on the laminar displacement flow of two Newtonian fluids along a horizontal eccentric annulus. This flow arises in primary cementing operations in the oil and gas industry, used to seal wells and prevent leakage. We investigate how the rotational motion of the inner cylinder influences the displacement, affecting the interplay of viscosity and density differences, as well as eccentricity. We first simulate a series of experiments recently performed, in order to validate the computational approach. We then study the effects of the rotating inner cylinder in more detail. The rotation shears the fluid in the narrow annular gap and also drags fluid around the annulus, typically resulting in helical streamlines and a spiral pattern of the concentration. Over short timescales, the rotation tends to increase dispersion, but the redistribution of the fluids around the annulus can then improve the overall displacement, i.e., reducing slumping effects due to buoyancy. We also observe a new patterning instability at the inner cylinder, which was not visible in the previous experiments. This instability arises from destabilization of the wall film of displaced fluid, which forms naturally on the walls of the annular gap. We have studied the dimensional parameter space where this instability occurs. Strong buoyancy can suppress the instability, and a threshold value of dimensionless rotation velocity is required for onset of the instability.