# SWIRL ATOMIZER FLOW: CLASSICAL INVISCID THEORY REVISITED

**Andrew J. Yule**

Spray Research Group (SRG), Insititute of Materials Research (IMR), School of Computing, Science and Engineering, University of Salford, Manchester, UK; Thermofluids Division, Department of Mechanical Engineering, UMIST

**J. J. Chinn**

Atomization and Sprays Research Group, UMIST, Manchester, UK

## Abstract

The, much quoted, classical theory for swirl atomizer performance requires the discharge coefficient and spray
angle to be dependent only upon a dimensionless group K = A_{i}/{(d_{s}−d_{i})d_{o}}. Observed deviations from the ideal theory have been assumed, in the past, to be caused by "real effects", such as viscosity and surface tension. Additional corrections have been proffered, in particular, using the ratio d_{s}/d_{o}. The authors note that dimensional analysis shows that inviscid atomizer performance cannot depend only upon one group, K, and that an additional group should be specified. Classical inviscid analysis results in a dependency only upon K due to simplifications used to obtain relationships for the air-core diameter. Hitherto inviscid analysis has discharge coefficient CD based on a sole equation, dependent upon at least two independent variables. The dependence is then simplified to K as single independent group under the assumption that the air-core radius will adjust for maximum
discharge and a differentiation, of the expression, was then undertaken. These simplifications were used because
of the failure to apply a further conservation equation to the flow: The conservation of axial momentum. This
conservation equation has been applied by the authors and a new inviscid solution has been derived showing
atomizer performance to depend upon both K and the additional group d_{s}/d_{o}. The results of this analysis are compared with "old" classical theory and experimental results. The theory provides a sounder basis for the performance analysis and design of pressure swirl atomizers and forms a foundation for making enhancements,
such as viscous boundary effects.