Multi-frequential harmonic balance approach for the computation of unsteadiness in multi-stage turbomachines

In turbomachines, the relative motion of fixed and rotating blades gives rise to deterministic unsteady interactions at frequencies termed BPFs (Blade Passing Frequencies). In a multi-stage turbomachine, a row sandwiched between two other rows is submitted to (at least) two BPFs, hence the need for methods able to capture these unsteady effects. Initially developed for single frequency problems, harmonic methods have been extended to account for multiple frequencies. Applied to turbomachines, these methods allows to capture unsteady phenomena of the flow field with a cost four seventy cheaper compared to classical unsteady methods. Mots clefs : Harmonic Balance ; Turbomachines ; Row interactions