This paper describes recent works of practical applications of vortex element methods in the field of fluid machinery, carried by the authors’ group, explaining the mathematical basis of the method based on the Biot-Savart law. It is pointed as one of the most attractive features of the vortex method that the numerical simulation using the method is considered to be a new and simple technique of large eddy simulation, because they consist of simple algorithm based on physics of flow and it provides a completely grid-free Lagrangian calculation. As typical results of virtual operation of fluid machinery, the internal flow of a mixed-flow pump stage, unsteady flows through a wind turbine, and behaviors of submerged vortex in a pump sump are explained.

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