The three-dimensional (3D) transient computational fluid dynamic (CFD) method was proposed to predict rotordynamic coefficients for annular gas seals. This transient CFD method uses unsteady Reynolds-Averaged Navier–Stokes (RANS) solution technique and mesh deformation theory, which requires a rotor whirling model as the rotor excitation signal to solve the transient leakage flow field in seal and obtain the transient fluid response forces on the rotor surface. A fully partitioned pocket damper seal (FPDS) was taken as the test object to validate the present numerical method. Comparisons were made between experimental data and rotordynamic coefficient predictions using the three variations of the single-frequency and multiple-frequency rotor whirling models: (1) one-dimensional whirling model, (2) circular orbit whirling model, and (3) elliptical orbit whirling model. The numerical results show that the rotordynamic coefficients predicted by the present CFD method and six different rotor whirling models all agree well with the experiment data, and nearly coincide for all rotor whirling models. The proposed transient CFD method can be used to perform a reasonably accurate prediction of the frequency-dependent rotordynamic coefficients for annular gas seals based on any one of the present six rotor whirling models, as long as ensuring the combination of these whirling model parameters captures the small perturbation theory. The rotor whirling parameters such as whirling orbit, amplitude, and frequency number are important in predicting rotor whirling motion and fluid response forces, but have almost no effect on the computed rotordynamic coefficients. The benefit of the multiple-frequency rotor whirling models is the ability to calculate accurate rotordynamic coefficients of annular gas seals in a wide frequency range with a simulation time on the order of one-tenth the cost of the single-frequency whirling models.