Some papers on Taylor-Couette flow with axial through flow:

Donnelly, R.J., Fultz, D., "Experiments of the Stability of Spiral Flow Between Rotating Cylinders" Proc. Natl. Acad. Sci. (U.S.) 46 1150-1154 (1960b)

Krueger, E.R., Di Prima, R.C., "The Stability of a Viscous Fluid Between Rotating Cyliders with an Axial Flow", Journal of Fluid Mechanics, 19 528-538 (1964)

Chung, K.C., Astill, K.N., "Hydrodynamics Instability of Viscous Flow Between Rotating Coaxial Cylinders with Fully Developed Axial Flow", Journal of Fluid Mechanics, 81 641-656 (1977)

Gu, Z.H., Fahidy, T.Z., "Visualization of Flow Patterns in Axial Flow Between Horizaontal Coaxial Rotating Cylinders", The Canadian Journal of Chemical Engineering, 63 14-21 (1985)