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With the relative movement of neighboring blade rows,flows in multi-stage turbomachinery are unsteady and periodic in time at the design condition.As an alternative to the widely used time domain time marching method,the harmonic balance (HB) method has been successfully applied to simulate the essentially unsteady flow of multi-stage turbomachinery.By modelling various number of harmonics,the accuracy of this method could be adjusted at different level of computational cost.In this article,accuracy of the harmonic balance method is not only validated against the time domain time marching method,as in most previous works on this topic,but also against the data from an experiment campaign of a two-stage high-pressure turbine where strong tip leakage flow exists.Efficiency of this method is also assessed in detail by adjusting the number of harmonics and comparing with time domain time marching solution results.Results show that the harmonic balance method is a flexible tool with adjustable accuracy for fast-turnaround unsteady flow simulation of multi-stage turbomachinery.Results from this work can provide a guidance in applying the harmonic balance method with balance between accuracy and computational cost.