The influence of swirl on the reattachment length in an abrupt axisymmetric expansion

Abstract

This paper presents a theoretical study on the influence of swirl on the reattachment length in an abrupt axisymmetric expansion. A scale analysis of the equations of motion reveals that this reattachment length decreases with increasing swirl. Moreover, it seems to suggest that there may be a singularity in the non-swirling sudden expansion flow, which disappears with increasing swirl beyond a critical value. This singularity is a possible explanation for the scatter of the data found in the literature at zero swirl. For the swirling flow, an analytical expression for the reattachment length is derived based on similarities found in experimental data between swirling and non-swirling flows. This expression shows that the reattachment length is a function of the swirl number and the expansion ratio and, to some extend, of the reattachment length at zero swirl. It is found that the local swirl number of the detaching streamline S D is a better parameter to characterise the reattachment length than the momentum flux averaged swirl number S. The theoretical model is validated based on values for the reattachment length found in the literature for expansion ratios h = R 2/ R 1 ranging from 1.5 to 2, Reynolds numbers Re from 10,000 to 100,000 and swirl numbers S from 0 to 1.23. Comparison with experiments shows a good agreement between the model and experimental data.