  We study the problem of mixing between core and annular flow in a pipe,
examining the effect of a swirling core flow. Such flows are important across a
range of applications, including jet pumps, combustion chambers and aerospace
engineering. Previous studies show that swirl can increase shear layer growth
rates and, in the case of confining walls, reduce flow separation. However, the
effect of swirl on pressure loss in a confined flow is uncertain. To address
this, we develop a simplified model that approximates the axial flow profile as
a linear shear layer separating uniform-velocity core and annular streams. The
azimuthal flow profile is approximated as a solid body rotation within the core
region, and a parabolic mixing profile within the shear layer. This model shows
good agreement with computational turbulence modelling, whilst its simplicity
and low computational cost make it ideal for benchmark predictions and design
purposes. Using this model, we confirm that a swirling core is useful for
increasing shear layer growth rates, but find that it is detrimental to
pressure recovery. This has important implications for the design of diffusers
that incorporate swirling flows. We use the model to describe the slow
recirculation region that can form along the pipe axis for sufficiently large
swirl, by approximating it as a stagnant zone with zero velocity. The criteria
for the development of such a region are established in terms of the pipe
expansion angle and inflow velocity profile.
