Francis turbines at part load matrix simulating the gaseous rope

The schematisation of the gaseous rope is the key-point for the prediction of hydraulic fluctuations in a circuit including a Francis turbine. The study hereafter is based upon a well-known linear method : the matrix method. The specificity of the rope simulation is its representation by a pipe characterised by three parameters: length, wave celerity (very low) and a coefficient-connected to the radius variation of the rope with discharge-. Main theoretical consequences of this approach are presented and compared with experimental results.