Hydrofoil Cavitation Inception Speed

Flow Conditions

Foil speed V 12.0 m/s

Angle of attack α 4.0°

Submergence depth h 1.0 m

Water temperature T 20 °C

Cavitation Status

flow attached — no vapor

Cavitation number σ

—

Min pressure coeff. C_p,min

—

Inception speed at this α, h, T

—

How it works

A hydrofoil moving through water speeds the flow up over its curved suction side. By Bernoulli's principle that faster flow means lower local pressure. If the local pressure drops to the water's vapor pressure, the liquid flashes into vapor bubbles — cavitation — well before boiling would occur at rest.

Cavitation number:   σ = (p∞ − pv) / (½ρV²)
Ambient pressure:    p∞ = p_atm + ρgh
Vapor pressure:      pv(T)  (Antoine equation, water)
Inception criterion: σ ≤ −Cp,min  ⇔  p∞ + Cp,min·½ρV² ≤ pv

C_p,min is the lowest pressure coefficient reached on the suction surface, growing sharply with angle of attack as the leading-edge suction peak intensifies:

Cp,min(α) ≈ −(0.42 + 0.09|α| + 0.012α²)

Speed V — raises the dynamic pressure ½ρV² in the denominator of σ, so σ falls and the suction peak drops toward the vapor pressure.
Angle of attack α — steepens the leading-edge suction peak (more negative C_p,min), lowering the inception speed needed.
Depth h — adds hydrostatic head ρgh to p∞; shallow, near-surface running is far more cavitation-prone than deep running.
Temperature T — raises the vapor pressure pv, shrinking the margin (p∞ − pv) and again lowering the inception speed.

Real-world relevance: this is why hydrofoil craft, ship propellers and pump impellers are speed- and depth-limited — once σ drops below −Cp,min, the suction side erupts in vapor, killing lift/thrust and eroding the metal as the bubbles collapse downstream.

High pressure margin Near cavitation onset Vapor bubbles (cavitating)

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