The effect of inner swirl on confined co-axial flow

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.