Turbine Setting Height and Cavitation

What is modelled

Water leaves the runner of a reaction turbine at a pressure below the surrounding atmosphere, because the runner sits above the tailwater and the water is still moving. If that pressure drops to the vapour pressure, bubbles form and collapse against the blades (cavitation), which pits the metal. The higher the site, the less atmosphere pushes; the warmer the water, the easier it boils; and a faster, higher specific speed runner needs more margin.

Equations

• Atmospheric head Ha = patm(altitude) / ρg, vapour head Hv = pv(T) / ρg.
• Specific speed ns = N √P / H5/4; critical number σc = 7.54×10−5 ns1.41 (empirical).
• Plant number σ = (Ha − Hv − Hs) / H; cavitation when σ < σc.
• Highest safe setting Hs,max = Ha − Hv − σc H.

Checks run in the page

• Standard atmosphere and water vapour pressure against tables.
• Specific speed unchanged by affinity-law scaling.
• The setting limit found by bisection against the closed form.
• Diffuser pressure recovery by numerical integration of the Bernoulli equation.

Honest simplifications

The critical number comes from a single empirical correlation for Francis runners, so real plants use model tests; the turbine efficiency is fixed at 92 %, the draft tube recovery at 85 %, the outlet speed is a fixed fraction of the spouting speed, and neither the unsteady vortex rope nor the effect of the operating point on the runner are modelled. The bubble animation is only a picture of the deficit.

• Press High site, warm water: the safe runner height drops by several metres.
• Press Cavitating and watch the bubbles appear in the draft tube.
• Press Low head, submerged runner: a low head and a slow runner need almost no margin, so the runner may even sit below the tailwater with room to spare.