This article is a direct follow-on to the updates posted
to “Purported SR-72 Propulsion”,
posted 1 September 2023. As I
have said there, and multiple places and
times elsewhere, if you do not
have a thermal management design concept,
you do not have a feasible hypersonic flight concept! This article attempts to put some bounds on
that problem.
Lateral Skin Study
The following is a simplified equilibrium skin panel surface
temperature estimate for lateral-facing skin panels. These could be on aerosurfaces (wings and
fins), or on the sides of a fuselage
body. I did not consider any conduction
inward or to adjacent panels. I did not
consider any active cooling. There is
convection to the panel, and thermal
re-radiation from it. It soaks out hot
enough to balance the two.
I did this for Mach numbers from subsonic to Mach 7, using standard compressible flow methods and
the high-speed heat transfer models that are based upon it. I used free-stream conditions as the good
approximation that they really are, for
local edge-of-boundary layer conditions.
I did not analyze past Mach 7,
because the fundamental assumptions underlying compressible flow
analysis methods are breaking down, due
to ionization into something that is no longer air as we know it.
I show temperature curves in Figure 1 for air total temperature, boundary layer recovery temperature (the driver for heat transfer to the panel), and equilibrium panel soak temperatures for low and high thermal emissivity. The service temperature limits for a variety of materials are also shown. Figure 2 shows the film coefficient trends vs Mach at 40 kft, for low and high emissivity. Beyond about Mach 3 or 4, these are pretty constant. Data in the same formats for 85 kft are in Figure 3 and 4, and for 130 kft Figures 5 and 6.
Figure 1 – Skin Panel Soak-Out vs Mach at 40 kft
Figure 2 – Film Coefficients vs Mach at 40 kft
Figure 3 – Skin Panel Soak-Out vs Mach at 85 kft
Figure 4 – Film Coefficients vs Mach at 85 kft
Figure 5 – Skin Panel Soak-Out vs Mach at 130 kft
Figure 6 – Film Coefficients vs Mach at 130 kft
Skin Study Correlation:
Recovery temperatures do not change so drastically with
altitude, unlike film coefficients. See Figure 7.
Figure 7 – Replots of Film Coefficient and Soakout vs
Altitude at Mach 5
As the figure shows,
the result is a drastic change in soakout temperatures, driven by drastically lower film coefficients
at extreme altitudes. The recovery
temperatures all fall between 3800 and 4500 F at Mach 7, as shown in Figures 1, 3, and 5 above. This suggests that a single analysis could
establish a representative film coefficient value insensitive to changes in
speed, at Mach 4+ and some altitude, which could be quickly scaled to other
altitudes. Calculating recovery
temperatures at each flight condition is a far easier thing to do. The correlation supporting that shortcut is
given in Figure 8. Doing it that
way is only a ballpark estimate that supports better, more detailed analyses later. But it is useful.
Figure 8 – Correlating High-Speed Film Coefficient vs
Altitude
Leading Edge Stagnation Study
There is a compressible flow-based heat transfer correlation
for stagnation zone heating. It exists
in two forms, determined by a coefficient
on the Nusselt number expression: C =
1.28 for nose tips, and C = 0.95 for
aerosurface leading edges. I looked at
leading edges for this study, so bear in
mind that nose tips will run a little hotter still.
In this Nusselt correlation,
you evaluate boundary layer properties at the total pressure and total
temperature properties behind a normal shock at flight conditions. I used the NACA 1135 tables for this. It also uses a second viscosity evaluated at
the flight conditions. I did this for
Mach 2 to Mach 7, at the same three altitudes
as the skin panel study. The idea was to
balance convective heating against thermal re-radiation, with no conduction or active cooling, as in the skin panel study.
The results at 40 kft are given in Figures 9 and 10. Figure 9 shows trends of total
temperature, and two local stagnation-region
equilibrium temperatures, one at low
emissivity, one at high emissivity. Figure 10 superposes material service
limits on the same curves. The same data
in the same format is given in Figures 11 and 12 at 85 kft, and Figures 13 and 14 at 130 kft.
Figure 9 – Stagnation Region Soakout
Results vs Mach at 40 kft
Figure 10 – Soakout at 40 kft with Service Limits, and a Speed Limit Indicated with Inconel
X-750
Figure 11 – Stagnation Region Soakout Results vs Mach at 85
kft
Figure 12 – Soakout at 85 kft with Service Limits, and a Speed Limit Indicated with Inconel
X-750
Figure 13 – Stagnation Region Soakout Results vs Mach at 130
kft
Figure 14 – Soakout at 130 kft with Service Limits, and a Speed Limit Indicated with Inconel
X-750
In Figures 10,
12, and 14, I have included data for the service
temperature limits and tensile strength at those limits, as part of the figure. Of the metals possibly useful for these high
speed exposures, Inconel X-750 is by far
the strongest, leading to thinner parts
of lower weight. So, I used it as the selection here, for “best” performance. Under the earlier name “Inconel-X”, this was in fact the skin material and
leading edge for the X-15 rocket plane,
which skin was a major load-bearing portion of its airframe.
Even so, the speed
limit for Inconel X-750 in a stagnation zone is only about Mach 4.9 at 40
kft, about Mach 5.2 at 85 kft, and about Mach 5.8 at 130 kft. For lateral skins, this was nearer Mach 6 at 40 kft, Mach 7 at 85 kft, and likely near or above Mach 8 at 130 kft, because the convective heat to be reradiated
is far lower for lateral skins, compared
to stagnation zones.
A good guess says the stagnation limit for Inconel X-750 is about
Mach 5.5 at 100 kft, which neatly
explains why the X-15A-2 with the drop tanks was coated all-over with an
ablative for its flights to Mach 6 and beyond,
despite the indicated survivability of its lateral skins at Mach 7+, near 100 kft.
The craft reached Mach 6.7 at 99,000 feet on flight
188, and suffered shock-impingement
heating damage to the underside of its tail,
to both lateral and stagnation surfaces.
That phenomenon drastically raises the local heating rate, but not the actual gas temperatures, as described in another of my articles on
this site: “Shock Impingement Heating Is
Very Dangerous”, posted 12 June 2017. See also NASA TM-X-1669 ““Flight Experience
With Shock Impingement and Interference Heating on the X-15-2 Research
Airplane”, dated October 1968, and written by Joe D. Watts, at the Flight Research Center, Edwards,
CA. This document is publicly
available over the internet.
Stagnation Study Results:
Use no metals for leading edge stagnation zones that are cooled
only by re-radiation, past about Mach 5.5, and then only above 100 kft. You must instead use ablatives, or apply massive active cooling. See Figure 15.
Figure 15 – Results for Stagnation Zone Equilibrium
Nose tips will run slightly hotter than leading edges
(higher h values at the higher C raise Tsurf),
thereby have a somewhat lower speed limitation than leading edges. The risk with both locations is distortion
and collapse of the parts, as they
weaken rapidly with increasing overheat.
Alloys like Rene 41 and Alloy 188 can take slightly higher
temperatures than Inconel X-750, but are
inherently weaker structurally by around a factor of 2. This is a crucial consideration, because stagnation zones see the highest
positive surface pressures on the airframe. Distorted or failed leading edges lead to
higher drag, loss of lift, and intrusion of hot gas inside the
aerosurface, something to be assiduously
avoided. In general, weaker is thicker, which is heavier.
Lateral Skin Results:
Speed limits versus altitude for Inconel X-750 lateral skins
are about Mach 6 at 40 kft, a bit over
Mach 7 at 85 kft, and likely above Mach
8 at 130 kft. This is complicated by the
risks of shock impingement heating,
which occurrence is complex and difficult to predict, and which can do fatal damage at much lower
speeds nearer only Mach 6. See Figure
16. Bear in mind that the analysis
method is invalid above about Mach 7,
although the prediction is likely still crudely true.
Figure 16 – Results for Lateral Skin Equilibrium
As with stagnation zones,
there are alloys that will go a little hotter, but at far lower strength. This is a crucial consideration, because in monocoque construction, the skins are an integral part of the
airframe structure, bearing much more
than just local surface pressure loads.
Weaker is thicker, which is
heavier.
Remarks About Airbreathers:
Components associated with airbreathers (of any type) were not
studied here. The X-15 was a rocket
plane. The results above apply to both
rocket-powered hypersonic vehicles, and
to hypersonic gliders.
All airbreathers will have some sort of supersonic inlet
capture structures, some sort of
post-capture air ducting that leads to the engine device (whatever it is), and that engine device and its nozzle. The ducting,
engine device, and nozzle might
be either buried inside the airframe, or
exposed as part of the airframe.
Air
Inlet Components
Inlet capture features suffer worse heating effects than leading
edge (or nose tip) stagnation surfaces,
This is because they are heated (unequally) on both outside and inside
surfaces, but can re-radiate to cool
from only the exterior surfaces, with
very localized stagnation soak-out on leading edges that must stay thin and
sharp, in order to function
properly. There is little opportunity
for any conduction-as-cooling, and not
much opportunity for any active cooling.
They must also contain serious internal pressures without shape
distortion.
Buried subsonic inlet ducts will inevitably soak out to essentially
the full air recovery temperature, or
else they must be actively cooled. They cannot re-radiate, being buried inside the airframe. They must be externally insulated to protect
the rest of the airframe and its contents.
Exposed inlet ducts are unlikely in hypersonic designs, as too much airframe drag gets added. However,
these are also internally heated,
and can only re-radiate to cool from that portion of the outside
surfaces not inside a fairing or facing the fuselage. They will still tend to approach air recovery
temperature soak-out, although not as
closely as buried ducts.
Combustor
and Nozzle Components
Buried or exposed combustors eventually soak out to something
in between the external and internal recovery temperatures, and will likely need active cooling. The buried combustor will take a longer time
to equilibriate, because it starts off
exposed to low airframe internal temperatures,
with a relatively low thermal conductivity for the free convection or
insulated interfaces between it and the skin.
But it will soak out very hot!
An exposed combustor can re-radiate directly to the
surroundings, while the buried combustor
cannot (while the airframe skin can), so
the exposed combustor may possibly equilibriate a little cooler than the buried
combustor. But neither has a cold “sink”
to dump heat into. They both get very
hot!
The same applies to propulsion nozzle structures, whether buried or not.
Turbomachinery
As for turbomachinery (compressors and turbines), these must be isolated completely from hot
intake airflow above about Mach 3 to 3.5.
Beyond that speed, the very
intake air temperature exceeds the turbine inlet temperature limits of almost
any conceivable design. The main flying
examples of these speed limitations were the XB-70 (Mach 3.0), the SR-71 (Mach 3.2), and the Mig-25 (Mach 3.5).
(Subsonic-Combustion)
Ramjet
Ramjet can fly faster than turbine, before hitting overheat speed limits. Flight tested but not fielded as
operational, the ASALM-PTV test vehicle
was designed to cruise steady state at Mach 4 and 80 kft, followed by an average Mach 5 terminal dive
onto its target. It did so successfully
in flight test.
In one test of ASALM-PTV,
an assembly error led to a throttle runaway incident, with the vehicle accelerating to fuel
exhaustion at Mach 6 at low altitude (near 20 kft). It suffered airframe overheat damage, but actually survived the short transient
flight and was recovered after it crashed.
If designed for it,
ramjet could conceivably be made to work steady-state at Mach 6, or even a bit faster, perhaps.
The internal air duct and combustor/nozzle will require active cooling
for a long flight. The inlet cowl lip
surfaces will likely need to be made of a really high-melting metal, like tungsten or columbium, so that they remain both sharp and thin, without distorting.
Supersonic-Combustion
Ramjet (Scramjet)
Scramjet can fly faster still than ramjet, but faces similar overheat risks for its
inlet capture and supersonic isolator duct,
and its combustor and nozzle structures.
These get ridiculously difficult to design for, as speeds increase beyond Mach 7. The same can be said for airframe stagnation
surfaces and lateral skins. Short
transients and ablative materials make such flight possible, but those are neither reusable, nor are they long-range.
Altitude
Limits
The problem with all airbreathers, of any type whatsoever, is the “service ceiling” effect. These devices produce an altitude-dependent
characteristic trend of thrust versus speed,
with lower thrust levels in the thinner air at higher altitudes. Roughly speaking, thrust is proportional to the ambient
atmospheric pressure at altitude. So is
drag. But weight does not vary with
altitude, only with time as fuel burns
off.
The vehicle requires enough lift to offset the perpendicular
component of its weight, as it tries to
fly up an ascending path. It also
requires enough thrust to offset the sum of drag and the pathwise component of
its weight. See Figure 17.
Figure 17 – Why There Is an Altitude Limit for Airbreathers
There is an altitude at which there is insufficient thrust
to overcome drag and the weight component,
regardless of any wings that might solve the lift problem. Above that altitude, it cannot even fly level steady-state, at all.
As a rule-of-thumb at speeds in the Mach 5 to 7 range, that’s around 130 kft, almost no matter what sort of airbreather you
might design.
Remarks on Active Cooling
This can be done reusably with a dedicated liquid
coolant, or it can be done
regeneratively with the fuel. For rocket
systems, the oxidizers are not generally
very good coolant materials, while the
fuels generally are. Either way, the coolant may not be allowed to boil inside
the cooling passages, because that leads
to vapor lock and a stoppage of coolant flow.
That in turn requires you to operate your coolant passages at very high
pressures to avoid boiling, which costs
weight, and power to run.
However, even if you
deliberately allow boiling, that reduces
heat transfer capacity of the coolant,
because the gas density is so much lower than the liquid density, for all known coolant materials. This is really a per unit volume problem, rather than a per unit mass problem, because the passage sizes are pretty much
fixed.
Final Remarks
What I have done here is bound the problem for
rocket-propelled vehicles, or gliders, that fly hypersonically. I did this in terms of steady-state
equilibrium surface temperatures, for
lateral skins, and for stagnation zones
on nose tips and aerosurface leading edges.
I have provided some discussions, but no numbers, for the airbreathing propulsion components
that might be applied to hypersonic vehicles.
Those are worse to thermally-manage than stagnation zones.
I have commented upon the “service ceiling” effect that
applies to any airbreather of any kind at all.
This is related to the narrow flight corridor to orbit, that resulted from the X-15 program. See also “About Hypersonic Vehicles”, posted 1 June 2022, on this site.
Plots of that corridor are in that article.
And I have commented upon the difficulties faced by any
actively-cooled designs.
Note:
This article has been included in the catalog article, under the topics “aerothermo” and “ramjet”. That article is “Lists of Some Articles by
Topic Area”, posted 21 October
2021. The fastest way to reach it is to
use the navigation tool on the left side of this page. To use it,
you need the article posting date,
and its title, so in
general, jot that stuff down. Click on the year, then on the month, then on the title if more than one item was
posted that month. Simple as that.
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