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

Adiabatic wall — where it appears

A surface across which no heat passes, so that it settles at whatever temperature the flow leaves it at. In a fast flow that is not the free stream's but most of the way to the stagnation temperature, and it is the temperature the heat flux to any other wall is driven from.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

What the skin settles at, before anything is done to it. The adiabatic wall temperature against Mach number, in air at 216.7 K, with the stagnation temperature above it. The gap between the two is the recovery factor, which is 0.8417 here and stays there at every Mach number — it is a property of the Prandtl number and not of the speed. At Mach 2 the skin sits at 363 K, at Mach 3 at 545 K, and at Mach 5 at 1128 K, which is past what aluminium will do. Nothing has been burnt and nothing has been rubbed: the air was brought to rest, and this is where its kinetic energy went.

The wall that heats itself

A surface told nothing about its temperature does not settle at the air's. It settles most of the way to the stagnation temperature, and the heat flux is driven from that invented temperature rather than from the free stream's — so a wall hotter than the air can be being heated by it.

compressible · Recovery A skin lags the air by a time its own thickness sets. A skin held at one flight condition, relaxing towards the adiabatic wall temperature. The approach is exponential with a time constant ρc τ / h — 8.37 s at 2 mm, 25.1 s at 6 mm, 50.2 s at 12 mm — so the temperature a steady recovery calculation gives is reached after several minutes rather than at once. The fluid supplies one number to this calculation, the adiabatic wall temperature, and the structure supplies everything else.

The skin that lags the flight

A wall can be told its temperature or told nothing, and both are solved problems. A real skin is told neither. It has heat capacity, so its temperature is a transient whose time constant is its own thickness divided by what the layer delivers — and the number the steady calculation returns is an upper bound a short exposure never collects.

compressible · Recovery Measuring the air temperature in flight is not measuring the air temperature. Three temperatures against Mach number in a stream at 220 K: the free stream itself, the stagnation temperature a perfect probe would read, and what a probe recovering 0.98 of the rise actually reads. At Mach 0.85 the rise is 31.79 K and the probe misses 0.64 K of it. The instrument is a small stagnation region with a thermocouple in it, so it obeys the same recovery arithmetic a wall does — a probe is a wall told nothing about its temperature, made small and put on a stalk, and its recovery factor is a calibration constant rather than a one.

The thermometer that heats itself

A total-temperature probe is a wall told nothing about its temperature, made small and put on a stalk, so it obeys the same recovery arithmetic an aircraft skin does. Its recovery factor is a calibration constant near 0.98 rather than a one — and the static temperature inferred from its reading amplifies that shortfall rather than inheriting it.

compressible · Recovery

Named alongside it

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

Boundary conditionHeat transferMach numberRecovery factorStagnation temperatureAerodynamic heatingCorrelationBoundary layerDissipationEnergy equationHysteresisInitial condition

All concepts