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

Feedback — where it appears

Using a measurement of a system's output to adjust its input, so that the system corrects its own departures. In a flow it can damp an instability the uncontrolled system would grow, but only within limits its delays and gains allow.

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

A frequency set almost entirely by how nearly sonic the flow behind the shock is. The Strouhal number of the loop against the local Mach number behind the shock. The band drawn across it is what is measured on aerofoils in buffet, 0.06 to 0.08, and the arithmetic meets it at a post-shock Mach number of 0.971. Two per cent either side of that number changes the frequency by a third, which is why buffet onset is predicted by correlation rather than by calculation.

A shock that will not stand still

A converged transonic solution puts the shock in a definite place. Over a band of conditions the real one sweeps back and forth across a fifth of the chord at a fixed frequency, and the period is set almost entirely by how nearly sonic the flow just behind it is — a quantity that is small, hard to compute, and multiplies everything.

compressible · Transonic With a small plenum, stall feedback closes the hysteresis loop. The stall amplitude against the throttle as it is closed slowly past the peak and opened again, at B = 0.2, with no stall feedback and with feedback at twice the critical gain; closing solid, opening dashed. Without feedback the cell appears suddenly near γ₀ = 0.6094 and vanishes only at 0.6428, and the loop between the two legs has an area of 0.078. With feedback the cell grows gradually as the throttle closes and shrinks along the same curve as it opens: the area is 0.0014.

A throttle can hold the peak only in a small plenum

A compressor makes its most pressure at the peak of its characteristic, and at the peak it either surges or stalls. A throttle moved by feedback can fight both. Driven by the plenum's pressure it damps surge, with a gain that grows as the square of Greitzer's B; driven by the flow, it cannot. Driven by the stall cell's amplitude it turns the sudden jump into deep stall into a gradual one and closes the hysteresis loop — but only while the plenum is small. Above B of about a third the same feedback turns the jump into a cycle.

applied · Turbomachine

Named alongside it

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

Model limitBifurcationBuffetDynamical systemHysteresisMeasurementOscillationPump characteristicSeparationShock waveSignal speedStability

All concepts