Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
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Shock layer — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The density ratio and the nose pressure coefficient, against Mach number. Two quantities across a normal shock, on a logarithmic Mach axis. Both approach limits that depend on γ and on nothing else: six for the density ratio and 1.8394 for the pressure coefficient at the stagnation point. By Mach five the second is within three per cent of its limit and by Mach twenty within a tenth of a per cent. Above that the flow round a blunt body has stopped depending on how fast it is going and started depending on what the gas is.

    A shock that lies on the body

    Above about Mach eight the flow round a blunt body stops depending on how fast it is going. The density ratio, the nose pressure coefficient and the shock standoff all reach limits set by γ alone — and going from a perfect gas to a dissociating one halves the standoff.

    part 1 · compressible
  2. Behind a strong shock the layer is an exact rotational flow, squeezed into a tenth of the shock's radius. Streamlines of the constant-density shock layer between a spherical shock (radius 1) and a sphere at density ratio ε = 0.167, from the solution ψ = sin²χ(ar⁴ + br² + c/r): the body sits at 0.8944 of the shock's radius, a standoff of 0.118 body radii. The gas enters along the shock, turns, and runs round the body in a layer whose vorticity over r sin χ is the same everywhere.

    The shock layer is Hill's vortex, and it heats the nose a tenth harder than Newton says

    Behind a strong bow shock the gas is squeezed six-fold or more and turned round the nose in a thin layer, and if its density is taken as constant there the layer has an exact solution: the same family of rotational flows as Hill's spherical vortex, fitted to the shock's three conditions. It stands off further than a mass balance says, and its gas accelerates away from the stagnation point a fifth faster than Newton's pressure law implies. Since a nose's heating goes as the square root of that acceleration, the layer heats the nose about ten per cent harder than the estimate every first calculation of re-entry uses.

    part 2 · compressible

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