"Swirling multiphase flows are found in a wide range of industrial processes. Such flows are used for separation of flows containing phases of different densities and for devices such as the spinning tensiometer. These flows are challenging to predict computationally, due to the presence of a phase boundary and the large pressure gradient generated by the swirl. In the present work the applicability of the front tracking method to swirling multi-phase flows is demonstrated by studying the evolution of a bubble in spinning tensiometer. Previous studies show that the evolution of a bubble in the spinning drop tensiometer can be used to measure the interfacial tension and other rheological properties. The front tracking method is applied to the spinning tensiometer problem to study several cases and verify the convergence of the solutions. The results are validated with other computational methods, theoretical models and experimental results. The length scales obtained from the front tracking method are in agreement with the corresponding values from experiments and other computational studies. The shape of the end of the elongated bubble obtained from the simulations is found to be similar to that suggested by a theoretical expression from previous studies. The simulations predict that the relaxation of bubble radius is exponential with time, at a rate that is found to be slightly greater than that predicted by the theoretical model."