In response to a request, I researched how the Apollo spacecraft windows were built, and did a oversimplified steady-state thermal model “by hand” to evaluate how the outer pane of fused silica fared during entry. This model assumed the middle of the pane was isothermal at a full equilibrium soakout, balancing the applied entry convective heating, with conduction into the supporting structure. Plasma radiation was not considered. This was a simple serial thermal resistance model, with the supporting structure a constant-temperature heat sink. It was done as a single-point steady-state analysis, at the max heating point for an Apollo capsule returning from low Earth orbit.
This is by no means an accurate model! To do this correctly requires not only a 2-D (or
preferably 3-D) finite element heat transfer model, but also one done with time as a
variable, and with the applied heating
rate also variable over that time! Such
is not something I can do “by hand”,
even assisted by a spreadsheet. The
process is fundamentally transient,
while my analysis is steady-state.
My estimate is thus an over-estimate of the achieved
center-of-pane temperature. That is why
the same basic outer window pane design actually survived a direct entry at
nearly escape speed, coming back from the
moon. However, I did also investigate the trend of pane
temperature for the higher convective heating rates associated with attached
flow, instead of the separated wake zone
where these Apollo windows were actually located. The results show the extra heating to be
catastrophic.
The entry conditions I analyzed are given in Figure 1. This was done with the rough-estimated entry
analysis given in Reference 1. The
associated rule-of-thumb effective plasma temperature is 6370 K.
Figure 1 – Apollo Entry Conditions From Low Earth Orbit
The window pane geometry and associated assumptions are
given in Figure 2. This is for
only the outer pane of a 3-pane window design used on the Apollo capsule. That design is described in Reference 2. I initially tried a 10-inch by 10-inch
pane, but that design proved infeasibly
hot. I did not get feasible pane soak
temperatures until I shrank the design to 4-inch by 4-inch size. Therefore,
smaller exposed window size is a critical variable.
The 2-part silicone adhesive between the fused silica pane
and the supporting structure is presumed to be bonded only on the structure
side, and is just in intimate contact (under
compression pressure) on the window pane side.
I did not get feasible pane soak temperatures until I reduced the
silicone thickness to 0.020 inches from the initial 0.080 inches. Thus a smaller temperature drop achieved
across the mechanical pane retention seal is another critical design variable.
Figure 2 – Outer Pane Modeling Geometry and Assumptions
The oversimplified thermal resistance model is illustrated
in Figure 3, along with the
results I got for the feasible case that became baseline. I used a couple of worksheets in a
spreadsheet to carry out this analysis.
One worksheet converted units to a common basis, and calculated the necessary cross section
areas through which the heat had to flow,
and the lengths down these resistances that it flowed. The other worksheet ran the actual
steady-state thermal resistance model.
The thermal resistance model took the form of a user-input
heat flow (heat flux times pane area) through the thermal resistances of the
edges of the isothermal pane, and the
thin areas of adhesive on both sides of the pane, to a constant temperature heat sink of the
supporting metal structure. The details
of how the parts bolt together and what the other 2 panes are, are irrelevant to this oversimplified result.
That heat flow through each thermal resistance produces a
steady-state temperature drop across each resistance. Adding those drops to the sink temperature is
thus a steady-state estimate of the temperature near the center of the window
pane, and also on the pane side of the
adhesive.
Note that I did this in Watt-cm-degree K units, instead of the Watt-meter-degree K units that
are “SI” metric. This was done merely
for convenience, since the applied heat
flux numbers are more conveniently measured in Watts per square cm units.
The baseline worksheet images are given in Figure 4.
Figure 3 – Oversimplified Steady-State Thermal Resistance
Model and Baseline Results
Figure 4 – Images of the Spreadsheet Worksheets Used For the
Baseline Case
I accumulated results in the thermal model worksheet for the
baseline wake zone heating case, plus
two higher heating rate cases that correspond to attached flow scrubbing the
window surface, just remote from the
stagnation point. Those results are
given in Figure 5. These heat
fluxes are factor 2 to 3 below that for the stagnation point, while the leeside separation wake zone heat
flux is factor 10 below stagnation.
I reported temperatures in degrees C instead of K, just for convenience. Note that the 316 C failure temperature for
the silicone is actually 600 F, a
well-accepted estimate for that kind of material.
As for the fused silica pane, that material is amorphous silica, which is actually a supercooled liquid of
enormous viscosity. It has no actual
“meltpoint”, only a max service
temperature (1100 C), above which it
increasingly softens (meaning its viscosity falls ever faster), ending in a “liquidus temperature” (1715
C), at which the material flows fast
enough under gravity for humans to easily perceive.
Note that the baseline case is barely feasible for a window
in a separated wake zone, while the 2
higher-heating cases corresponding to attached flow are catastrophically higher
in temperature! Not only that, but the silicone adhesive also overheats for
the 2 attached flow cases, while it is
well within its capability for a window in a wake zone. Thus,
locating exposed windows in a separated wake zone is utterly critical, unless they are to be covered during entry by
suitable heat shielding materials!
Figure 5 – Results Obtained for the Baseline Case and 2
Higher-Heating Cases
Conclusions
#1. Do not use these numbers for design purposes! They must be replaced with 3-D finite element
analyses that are time-dependent. The
numbers given here merely identify critical considerations.
#2. It is utterly crucial that any exposed windows be
located in a separated-flow wake zone somewhere on the leeside of the
spacecraft. Windows not located in a
separation zone are infeasible for survival.
#3. It is imperative that any exposed window panels be small
in dimension. The heat to be managed is
proportional to pane dimension squared,
while the thermal conductances depend linearly on pane dimension, being proportional to area, but inversely proportional to conduction path
length.
#4. The temperature drop across the gasket or sealant layer
between outer pane and its supporting structure for any exposed window, needs to be as minimal as possible, in turn requiring that layer to be quite thin.
This applies to gaskets as well as
sealant adhesives.
Final Remarks Applicable to Any Entering Spacecraft
Designs
#1. Regarding SpaceX’s “Starship” crewed versions: be
sure the proposed window locations actually reside in a reliably-separated wake
zone, or else you must cover those
windows with some sort of shield during entry.
There is reason to believe an attached jet flow might run part-way down
the leeside dorsal surface, especially
at very high angles of attack. Such
happened with NASA’s Space Shuttle, as described
in Reference 3. Changes to the
Shuttle’s nose shape had no influence on that flow field.
#2. The warning in item 1 applies to all other
spacecraft designs featuring windows that are exposed during entry. These must be located in reliable
separated flow zones.
References
#1. G. W. Johnson,
“Back of the Envelope” Entry Model,
published 14 July 2012, on
http://exrocketman.blogspot.com.
#2. O. E. Pigg and S. P. Weiss, Apollo Experience Report – Spacecraft
Structural Windows, NASA TN D 7439, September 1973.
#3. G. W. Johnson,
Evaluations of the SpaceX Starship/Superheavy, published 15 May 2021 on
http://exrocketman.blogspot.com.
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