The pulsejet is of both fundamental interest due to the complex interactions between the fluid mechanics, acoustics, and chemical kinetics, as well as practical interest for low-cost, scalable, high thrust-to-weight ratio propulsion devices. Although various designs have been proposed since the first Schmidt tube, the basic design of a pulsejet remains essentially the same. In the hobby-scale pulsejet, the exit is flared and anecdotal evidence suggests that this flare aids in starting the engine. In this paper, the dynamics of the vortex ring generated at the exit of the pulsejet is studied computationally. The role of the exit flare in starting the combustion process as well as its effect on thrust are investigated. A new dimensionless parameter, the ratio of the exit plane of the flare to the cross-sectional area of the pulsejet tailpipe, AR, is introduced. The obtained results indicate that for two different fuel flow rates, maximum thrust occurs when AR value is around two, which is 1.14 times larger than that of the hobby-scale pulsejet. A secondary vortex is observed when AR is larger than the critical value of 2, and as AR continues to increase, the origination point of the secondary vortex moves gradually inside of the flare. The appearance of the secondary vortex has a negative impact on thrust. Circulation calculations reveal that the geometry with the maximum thrust is characterized by the maximum vortex ring circulation in each operating cycle.