Experiments are carried out on a laboratory-scale annular combustor with liquid heptane to examine the effects of swirlers on azimuthal instabilities. Five types of swirlers varying in swirl numbers and pressure drops are considered. These swirlers can be broadly categorized into two groups, lower-swirl, and higher-swirl groups, based on their swirl numbers. Results reveal that none of the swirlers in the lower-swirl category exhibit instability in the operating region considered, whereas the higher-swirl units feature strong azimuthal instabilities. Among the higher-swirl group, a higher pressure drop swirler is associated with a broader instability map. This shows that the transition to instability mainly depends on the swirl number through its effect on flame structure and pressure drop adds to further variations. An attempt is made to interpret the occurrence of instabilities by making use of flame describing functions (FDFs) measured in a single-injector combustor. The observed instability behavior is tentatively interpreted using an instability analysis in which the injector and upstream plenum are represented by an impedance that shifts the instability band. The unstable behavior is then linked to the relative position of the FDF phase with respect to the instability band in the expected azimuthal mode frequency range. The phase and gain of the FDF notably depend on the swirl number, and it is possible to distinguish, for the present configuration, a category of low swirl number injectors inducing stable operation and another category of high swirl number units leading to oscillations.