The use of pressure swirl injectors in wall-guided spark ignition direct-injection engines has emerged as a potential solution to decrease the specific fuel consumption of conventional port fuel injection systems. A major hurdle in the use of these injectors is that the spray characteristics, like the cone angle and drop sizes, are sensitive to the operating conditions, especially when the fuel undergoes a phase-change process inside the nozzle. This phase-change process, when driven by thermal effects, is known as flash boiling. A precise control of this mechanism can be used to achieve a well-atomized spray with higher cone angles and smaller drop sizes. However, such control is extremely difficult considering the highly transient nature of the phase-change process. An accurate modeling of flash boiling is critical if these injectors are used in practice. As this phenomenon is mainly driven by interphase heat transfer and has a time scale that is comparable to the flow-through times in the system, a finite-rate model should be employed for these simulations. In this work, the homogeneous relaxation model was used to conduct transient, three-dimensional simulations of a pressure swirl injector. The working fluid used in the calculations is n-hexane and all its thermophysical properties are obtained from NIST databases. The geometry includes the inlet swirl ports, the swirl chamber, the injector nozzle and the combustion chamber. A parametric study under four different operating conditions has been conducted and qualitative comparisons with experiments are presented.