Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Cavitation — the series

5 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The stretch of surface that is boiling. The pressure coefficient along both surfaces of a section at 4 degrees, computed from the same potential-flow solution as the other ideal-flow aerofoil figures. The horizontal line is the vapour pressure at a cavitation number of 1: wherever the suction curve is above it, the liquid there has been pulled below its vapour pressure and is boiling at whatever temperature it happens to be. This section cavitates at any σ below 1.428.

    When a body tears the water

    A propeller blade moving fast enough pulls the pressure at its own surface below the vapour pressure of the liquid, and the water boils at whatever temperature it happens to be. Where that happens is decided by an inviscid calculation of the pressure along the blade.

    part 1 · applied
  2. Ninety microseconds, and most of it spent barely moving. The radius of a collapsing cavity against time, both as fractions of their own totals. The bubble spends most of the collapse near its original size and the last few per cent of the radius in the last fraction of a per cent of the time. The total is 91.47 microseconds for a millimetre cavity at one bar, computed by quadrature and agreeing with the closed form in gamma functions to a part in 10⁹.

    The bubble that hammers

    A vapour cavity swept into higher pressure does not deflate. It collapses, in ninety microseconds for a millimetre bubble, and the model that describes the collapse predicts a wall speed that reaches the speed of sound in water at three per cent of the original radius — which is to say it predicts its own failure, and locates it.

    part 2 · applied
  3. A threshold that is a curve, not a pressure. The tension a rectangular pulse has to reach to make a five-micron bubble run away, against how long the pulse lasts. At a tenth of a microsecond it takes forty bar; at a hundred microseconds it takes 1.05, which is within about one per cent of the static threshold. There is no such thing as the cavitation pressure of this bubble on its own.

    A threshold that is also a duration

    The cavitation number treats inception as a pressure: below it the liquid tears, above it does not. A five-micron bubble asked to grow in 0.3 microseconds needs 43 bar of tension and the same bubble given a hundred needs 1.05, because it has to make a journey and not merely respond.

    part 3 · applied
  4. The vapour fraction that would stop a cavity, against temperature. How much vapour a cavity would have to make, as a multiple of the liquid volume it cools, before the cooling had used up the whole driving tension. In cold water it is six hundred and the effect is unreachable; at the boiling point it is below one and the effect is the dominant thing in the problem. Four decades across the range a pump might see, out of a vapour density that rises by a factor of two hundred.

    A cavity that cools the water it came from

    The usual account takes the vapour pressure as a property of the liquid, looked up once. It is a property of the liquid at whatever temperature the cavity has left it — and making vapour costs latent heat, so a cavity suppresses itself. In cold water that is unmeasurable and in liquid hydrogen it is the dominant term.

    part 4 · applied
  5. A travelling bubble's B-factor grows as the square root of its age, and the bubble turns heat-limited when it reaches B*. The vapour a growing bubble has made over the liquid it has cooled, against its age, in water at 80 °C under a tension 10 kPa below the vapour pressure, while inertia limits its growth; the dashed line is B, at which the cooling would use up the whole tension. B is 4.3 at a microsecond and 136 at a millisecond, and meets B = 31.6 at 53.8 µs, when its radius is 0.141 mm.

    A bubble is throttled by its age, and a sheet by its length

    A cavity cools the liquid it boils, and the cooling lowers the vapour pressure it needed. Whether that matters was a question about one number, the B-factor — vapour made over liquid cooled — and no real cavity's was known. Computed, the two kinds a pump has are nothing alike. A travelling bubble cools a thin shell that thins further as it stretches, so its B grows as the square root of its age and reaches the critical value at Brennen's thermal time: a millisecond in water at 60 °C, four microseconds at the boiling point. An attached sheet keeps renewing the liquid it cools, so its B is a few, fixed by its length and speed. In warm water the bubbles are suppressed forty degrees before the sheet.

    part 5 · applied

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