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

Fatigue — where it appears

The weakening of a structure by repeated loading well below the load that would break it at once. Its life is counted in cycles, so the spectrum of an unsteady load, and not only its peak, decides how long a wing or a blade lasts.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

What a downstream blade sees going past. The axial velocity a blade in the second row meets, over one revolution, as it passes through the wakes of thirty upstream blades. Each dip is one wake, and the blade meets all thirty of them every time it goes round.

A row that meets the row before it

A compressor blade is loaded and unloaded thirty times a revolution by geometry it does not have. The forcing sits at the blade count of the row in front of it and at multiples of that, and how far up the harmonics it reaches is decided by how far apart the two rows are.

circulation · Cascade An elliptic wing filters the gust like a round aperture. How much of a gust component with spanwise wavenumber k₂ survives the span average, against κ = k₂b/2, for three weights. A uniform strip is a slit and its filter is sinc², falling as κ⁻² between its zeros. An elliptic loading is a circular aperture and its filter is the Airy pattern (2J₁(κ)/κ)², whose first zero is at 3.83 and whose envelope falls as κ⁻³, but which stays near one to larger κ: the ellipse's weight is narrower, so its filter is wider. A rectangular wing of aspect ratio nine weights the span by its own loading and lies between, with the ellipse's κ⁻³ fall because its loading too goes to zero at the tips as a square root.

A wing averages a gust through its own loading

A finite span averages a turbulent gust and so tames the load it causes, but it does not average uniformly. The reverse-flow theorem says exactly how it weights the span: by the loading the wing makes at a uniform incidence. An elliptic wing therefore filters the gust the way a round aperture diffracts light, passes eight per cent more of its short scales than a uniform strip, and crosses its mean load up to four per cent more often.

circulation · Gust

Named alongside it

The objects these essays reach for when they reach for this one.

SpectrumAveragingCascadeFrequency responseGustIncidenceLifting lineMeasurementMemory kernelModel limitModel validityNoise

All concepts