The 3D version renders a duct and animates particles along it. This 2D version instead plots the same Rayleigh-flow state equations on a genuine thermodynamic temperature–entropy (T–s) diagram — the textbook way engineers actually analyse constant-area heat addition, and a representation that has no 3D analogue at all:
T/T* = M²(γ+1)² / (1+γM²)²
p/p* = (γ+1) / (1+γM²)
(s−s*)/R = γ/(γ−1)·ln(T/T*) − ln(p/p*)
Sweeping M from far-subsonic to far-supersonic traces a single closed Rayleigh line in T–s space. Both branches meet at one point — Mach 1 — which is also the curve's entropy maximum (verified numerically: ds/dM changes sign exactly at M=1, both approaching from above and below). That single fact is thermal choking: heat addition always pushes the state point toward higher entropy, so a supersonic inflow can only climb the upper branch toward that peak, never past it. Push heat addition past 100% of the duct's capacity and the state point cannot leave the peak — it pins at M=1, exactly matching the 3D version's "thermal choking / inlet unstart" behaviour, but shown here as a literal geometric limit of the curve rather than a scripted event.
- Top panel — a 2D duct cross-section: colour = local static temperature, dot spacing/speed = local flow Mach number, both read pointwise off the same Rayleigh profile as the readouts.
- Bottom panel — the T–s diagram itself: the grey curve is the full Rayleigh line (γ=1.3), the cyan dot is your inlet state, the amber dot is the exit state after this duct's heat addition, and the arc between them is the actual path the flow's thermodynamic state takes through the combustor.
- When choked, the exit dot sits exactly on the curve's apex — there is nowhere further to go without violating entropy.