Tile Gap Heat Soak-Back (2D)

Reentry Heat Pulse

Peak heat flux 30 W/cm²

Insulation thickness 5.0 cm

Insulation conductivity 0.048 W/m·K

Coating emissivity 0.85

Gap heating boost 60%

Mission Clock

Phase

Heating (ascent heat pulse)

Mission time

0:00

Heat flux (tile center)

0 W/cm²

Surface — tile center

22 °C

Surface — gap

22 °C

Backface — tile center

22 °C

Backface — gap

22 °C

Spanwise ΔT (backface)

0.0 °C

Penetration depth

0.0 cm

How it works

Real tile TPS is not laid down as one seamless shell — it is thousands of individual tiles separated by narrow gaps (filled with a compliant "gap filler" strip). Where the boundary-layer flow crosses a gap or a small forward-facing step, it can locally reattach and transition, driving noticeably higher heating into that strip than the flat tile faces around it — a well-documented aerothermal effect called gap/step heating that real TPS designs have to size for, not just the nominal flat-plate flux.

This simulator solves the 2D transient heat-conduction equation over a cross-section spanning half a tile out to the neighbouring gap (symmetry planes at both edges), instead of the 1D through-thickness-only slab:

∂T/∂t = α · (∂²T/∂x² + ∂²T/∂y²),   α = k / (ρ·c_p)
x = depth into the tile (surface → backface)
y = spanwise position (tile center → gap centerline)

Surface (x=0, radiative equilibrium, y-dependent flux):
  q"(t,y) − ε·σ·(Ts⁴ − T∞⁴) = −k·∂T/∂x
  q"(t,y) = q"(t) · [1 + boost · exp(−(y−y_gap)²/2σ²)]

Backface (x=L, coupled to airframe):  k·∂T/∂x = h·(Tback − Tcabin)
Both spanwise edges (y=0, y=y_gap): zero-flux symmetry planes

Set gap heating boost to 0% and this model collapses exactly onto the plain 1D soak-back result — every column runs identically, because nothing is driving heat sideways. Raise it and the gap column runs visibly hotter at the surface immediately, and — after the heat has had time to diffuse sideways through the insulation — the backface temperature under the gap measurably outruns the backface under the tile center, even though both sit under the exact same nominal flux rating. That spanwise ΔT is the quantity a 2D model can show and a 1D slab fundamentally cannot.

Peak heat flux — the nominal (tile-center) aeroheating rate at the trajectory's hottest point.
Insulation thickness / conductivity — governs how much of the pulse reaches the structure at all, in both directions now: straight through and diffused in from the gap.
Gap heating boost — how much hotter the gap runs relative to the tile face, expressed as a fraction of the nominal flux (real gap-heating augmentation factors are trajectory- and geometry-dependent; this control lets you see how sensitive backface soak-back is to that factor).
Thermal penetration depth ≈ √(α·t) — how far the heat wave has diffused into the tile in the through-thickness direction.

Cold → hot (cross-section)

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Tile Gap Heat Soak-Back Simulator (2D)