[AR] Re: AR Nose Heating (was:. 3D-printed RL-10)
- From: Norman Yarvin <yarvin@xxxxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Thu, 6 Apr 2017 01:18:38 -0400
On Thu, Apr 06, 2017 at 11:44:18AM +1000, Troy Prideaux wrote:
You might be able to BOE the leading surfaces maybe(?) by doing a
temperature conversion of the RMS velocity of the air molecules to
gather a ball park number?
vrms = sqrt(3RT/Mm)
R = molar gas constant = 8.3145
T = Ambient Temperate of the air = 298 Kelvin
Mm = molar mass of the air in kg per mole = ~29 for air
So air molecule vrms = sqrt((3 x 8.3145 x 298) / 29) = ~506 m/s (ie
rocket in ambient temperature in a stationary position)
Rearranging for T at… dunno say Mach 2 which let’s say is 670 m/s so
can we assume the vrms hitting the leading surfaces would be
approx. 506+670 = 1176 m/s ?
So now rearranging:
T = (vrms^2 x Mm) / (R x 3) =
(1176^2 x 29) / (8.3145 x 3) = ~1608 deg K
Converting to say deg C = 1608 -273 = 1335 deg C
Which seems a bit high? Dunno?
That calculation would be appropriate if the air were so thin that it
could be modeled as individual molecules hitting the surface, with no
interactions between those molecules as they approached the surface.
In that case a sharp nose wouldn't help. But really this is in air
that is thick enough that it has to be regarded as a fluid, so sharp
noses do help: they mean that the air (at least most of it) doesn't
slow down much and thus doesn't reach the stagnation temperature.
That is, most of the incoming molecules don't hit the surface: instead
they hit other air molecules which hit still other air molecules which
... which hit air molecules which hit the surface.
There is a thin boundary layer which does slow down quite a lot -- the
usual assumption is that the innermost extreme of the boundary layer,
which touches the rocket, has zero velocity relative to it -- but that
layer is thin enough that it quickly gets cooled. That's one reason
why the tip of the nose cone sees the most heating, and thus is the
part people make out of metal: downstream from it, the boundary layer
has already been cooled. (Another reason, and possibly a more
important one, is that the tip is where the shock wave impinges -- or
perhaps it would be better to say that it is where the shock wave
starts from.)
Other related posts:
