Currently,the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics (CFD) to evaluate the five rotordynamic coefficients.The simulations are based on the traditional quasi-steady method.In this work,an improved quasi-steady method along with the transient method was presented to compute the rotordynamic coefficients of a long seal.By comparisons with experimental data,the shortcomings of quasi-steady methods have been identified.Then,the effects of non-uniform incoming flow on seal dynamic coefficients were studied by transient simulations.Results indicate that the long seal has large cross stiffness k and direct mass M which are not good for rotor stability,while the transient method is more suitable for the long seal for its excellent performance in predicting M.When the incoming flow is non-uniform,the stiffness coefficients vary with the eccentric directions.Based on the rotordynamic coefficients under uniform incoming flow,the linearized fluid force formulas,which can consider the effects of non-uniform incoming flow,have been presented and can well explain the varying-stiffness phenomenon.