Francis Turbine Runner Cascade (2D Unrolled Blade Row)

This 2D companion to the 3D Francis turbine simulator keeps the same real machine and the same Euler turbine equation, but computes it independently through a different, classic turbomachinery technique: unrolling the curved runner rim into a straight linear cascade of blades. Instead of two static velocity-triangle arrows recomputed each frame, water parcels here are integrated forward in time through the cascade in the blade-fixed relative frame, so their paths visibly bend according to the local blade speed and swirl velocity at every point between inlet and outlet. Crucially, the entry mismatch between the flow's relative angle and the blade's fixed leading edge — the incidence angle — is not just reported as a number: it is converted into a genuine shock-loss head that subtracts from the ideal Euler head before shaft power is computed, so running off the shockless design point now visibly costs power and efficiency, not just a warning color. Adjust guide-vane angle, runner speed and net head to find the one combination where the parcels enter the cascade dead straight.