Update
23 March 2024:
For the readers of this and other similar articles about ramjet
propulsion, be aware that GW’s ramjet
book is finally available as a self-published item. Its title is “A Practical Guide to Ramjet
Propulsion”. Right now, contact GW at gwj5886@gmail.com to buy your copy.
He will, upon receipt of payment by surface mail or Western
Union (or similar), manually email the
book to you as pdf files. This will take
place as 9 emails, each with 3 files
attached, for a total of 27 files (1 for
the up-front stuff, 1 each for 22
chapters, and 1 each for 4
appendices). The base price is
$100, to which $6.25 of Texas sales tax
must be added, for an invoice total of
$106.25.
This
procedure will get replaced with a secure automated web site, that can take credit cards, and automatically send the book as
files. However, that option is not yet available. Watch this space for the announcement when it
is.
GW is working
on a second edition. No projections yet
for when that will become available.
--------------
In November 1993, I
gave a paper on the title topic at the JANNAF (Joint Army Navy Nasa Air Force) meeting
held at the Naval Postgraduate School in Monterrey, California.
It was an unclassified paper given at a classified session at that
meeting. It raised quite a stir.
The topic of this paper was threefold:
(1) documenting the engineering design analysis model for a
gas generator-fed ramjet with an unchoked gas generator, that was capable of evaluating multiple
influences, to include variable throat
area,
(2) experimental ground tests that verified the engineering
design analysis model, and
(3) mission predictions evaluating this “unchoked throttle”
in a gas generator-fed ramjet propulsion system for an AMRAAM missile, plus variable drag as candidate means to
improve the throttling control.
This was work I did at what was then Rocketdyne/Hercules in
McGregor, Texas, ably assisted by Venton A. Kocurek. Unfortunately, my friend and colleague Venton is now
deceased, but he was a listed author on
the paper that I presented. That paper
is Ref. 1.
I literally photographed the figures in my hard copy of the
original presentation, to produce most
of the figures presented herein. There
was no other readily-available way to digitize them.
Background
In most gas generator-fed ramjet designs, the gas generator is a solid propellant
device that is fuel-rich in formulation,
with a choked exit, meaning the
flow is sonic at the minimum area of that exit.
For more details, see Refs. 2, 3, and
4.
These designs may be fixed flow, or flow to a fixed delivery history set by
the propellant grain design, or else
they can be reliably throttled by varying the choked area of the sonic exit, per Ref. 5. As it turned out, attempting to vary the propellant effective
burn rate by means of mechanically-extracted wires proved to be unreliable in
test. That concept was tested at another
contractor. The variable-area
valve, in the form of a pintle
valve, was invented at
Rocketdyne/Hercules. I played a key role
in that.
The alternative throttle approach described here is to
let the gas generator exit run unchoked,
so that the ramjet engine chamber pressure essentially drives the propellant
burn rate inside the gas generator chamber. If the solid propellant ballistic
characteristics and generator exit design are correct, this can approximate constant fuel/air ratio
control quite well, regardless of the absolute
level of the engine airflow. This has
distinct advantages for systems that must fly from low to high altitudes, and it does this with no moving parts or
control systems. Fuel regulation is
limited, but inherent to the design.
This technique was demonstrated by the French in flight test
(see Ref. 6), but was not pursued
by them, as they did not have fuel
propellants of the required ballistic characteristics (namely burn rate
exponents near unity). We did have
appropriate propellants at Rocketdyne/Hercules,
and I pursued this into extensive testing, on company independent research and
development (IR&D) funds, in full
scale engine hardware, using short-burn
gas generators based on convenient lab motor hardware.
After the JANNAF paper,
we continued testing of various fuel propellants in the
unchoked-generator hardware set on IR&D.
We found it to be a safer test method for experimental propellants than
the usual choked generator, because the unchoked
generator is essentially a “strand bomb” at only the limited engine
pressure. Many such fuel candidates were
tested this way, including a
highly-metallized boron formulation, and
a completely non-metallized “clean fuel” that met NATO min smoke criteria.
The generator effluent stream is the fuel to be burned with
air in the ramjet chamber just downstream.
This offers the potential of the far-higher specific impulse of the
airbreathing ramjet, while
simultaneously offering the “wooden round” simplicity and reliability of the
solid. Given some sort of fuel rate control
to the right fuel/air ratio, this
potential can be achieved across a variety of missions.
Fixed and fixed-delivery designs suffer when flying to high
altitudes. Choked-throttle designs offer
some altitude capability at the cost of propellant load displaced by the volume
of the throttle. The unchoked-throttle
approach offers high altitude capability without any fuel volume displacement
by a throttle valve. However, it is not an arbitrary-command throttle
technique, which the choked throttle
valve is.
There is a very strong effect of both fuel propellant
formulation and ramjet chamber flameholding flowfield geometry, upon achieved combustion efficiencies, as described in Ref. 7. For the IR&D effort, I used single center port fuel injection into
an asymmetric twin inlet geometry. If
choked, the port was small. If unchoked,
the port was large. Results are
thus comparable for both choked and unchoked tests, despite the slightly non-optimal injection geometry. The heavyweight lab motor as a short-burn gas
generator was very convenient, and I was
often able to use the full size flight-like combustors twice, before refurbishment! (The IR&D tests included testing
experimental insulations, too.)
Engineering Design Analysis of Unchoked Generators
The simplest design analysis model makes generator fuel flow
proportional to ramjet chamber pressure raised to the fuel propellant’s burn
rate exponent. This model includes the
assumptions that (1) burning surface is a constant, that (2) there are no soak temperature
effects upon burn rate, and that (3) changes
in ramjet chamber pressure do not affect the speed in the injection port. Those are generally bad assumptions, as all of these are first-order effects.
The next simplest model makes the fuel propellant burn rate
proportional to ramjet chamber pressure raised to the fuel propellant burn rate
exponent, but allows a variable burning
surface. This still neglects soak
temperature and port speed effects. Both
of those are first order effects.
The model presented in the JANNAF paper, which I devised, avoids these difficulties. It only presumes a convergent-only
approach to the min port area.
Further, the ramjet pressure is
the actual forward-dome static pressure where the fuel jet enters, not some other measure of ramjet chamber
pressure. This matches the subsonic jet
condition that jet pressure equals surrounding pressure. See Fig. 1.
It does not presume constant speed through the port, nor does it presume anything about the fuel
propellant burning surface or propellant grain temperature soak-out effects
upon burn rate. It even includes the
effects of generator chamber c* velocity,
which reflects gas generator flame temperature and (effective) gas properties. This model even includes transient c*
efficiency effects.
There are 3 things to worry about: (1) the propellant grain flow rate, (2) the port flow rate, and (3) other relevant relationships. The “other relevant relationships” are how
you tie together the propellant grain and subsonic port models. Each is detailed here, resulting in a final expression for fuel flow
rate as a function of ramjet chamber forward dome pressure.
Figure 1 – Image of Presentation Chart Showing the Situation
to be Modeled
Propellant
grain flow rate
The propellant grain flow rate wf is a function
of gas generator expulsion efficiency ηexp, burning surface S, propellant density ρ, and the power law describing burn rate versus
chamber pressure r = a PGn. That relationship is normally expressed as wf
= ρ
ηexp S a PGn. The factor “a” in the burning rate law
is also a function of the propellant soak-out temperature.
If we let G = ρ ηexp S, and we let e = (PG/P3)n
= (1 + 0.5*(γ
– 1)*Mp2)exp where exp = n γ/(γ –
1), and where Mp is the port
Mach number and γ the specific heat ratio of the gas generator effluent
stream, then we have wf = G a
e P3n. Note that “a”
scales as fT = exp[σp(T – Tref)]
to model grain soak-out temperature T:
a-at-T = a-at-Tref * fT. Tref is usually taken to be 77 F =
25 C, and fuel-rich propellant σp
usually falls in the 0.2%/F = 0.002/F range,
sometimes a bit higher. (Fully
oxidized σP
is usually about half that value.)
Port
flow rate
The port flow rate into the ramjet combustor is wf
= ρP
VP Ap, where ρP
and VP are the density and velocity at the minimum port area AP, and the Mach number Mp in that
port is subsonic, which also implies Pjet
= P3. We presume that ideal
gas compressible flow considerations apply at specific heat ratio γ, for the density vs pressure and
temperature, and also for the
speed-of-sound. Speed-of-sound is for the
velocity versus Mach number relationship.
The empirical characteristic velocity c* includes both
achieved chamber temperature and effective chamber gas properties, and there is a time-dependent scaling factor
on c* that is denoted by η*, which can model
the start-up effects of low free volume and cold surfaces. The empirical steady-state c* is best
determined from motor tests at various pressures, and is modeled as another power law c* = K PGm. For fuel-rich propellants, m usually falls in the 0.01 to 0.10
range, larger than for fully-oxidized.
Thus, including the start-up
effects, c* = η* K PGm.
Now, we let d be a
particular Mach number function as d = (1/Mp)*(1 + 0.5*(γ –
1)*Mp2)exp,
where exp = m γ / (γ – 1) – 0.5.
And, we let B = gc {[(γ +
1)/2]exp}0.5 where exp = (γ + 1)/(γ – 1). Under these definitions, the port massflow expression becomes wf
= [P3(1-m) Ap B]/[η* K d]. See
the third consideration for more definitions.
Other
relevant relationships
The normal power law for propellant burn rate is r = a PGn. Be aware that when plotting burn rate r
versus chamber pressure PG on a log-log plot, the slope of the line is the exponent n. There may be different values of n (and
therefore “a”) that apply in different regimes of PG. Be aware that “a” also scales by fT very nonlinearly with grain soak-out
temperature, as already indicated.
From theory, the
characteristic c* velocity is a function of achieved chamber temperature TG
and gas properties. The usual equation
is c* = {[gc RP TG / γ][0.5*(γ + 1)]exp}0.5,
where exp = (γ + 1)/(γ – 1). RP is the gas constant Runiv/MW. This is normally applied to choked nozzles as
wf = PG CD At gc /
c*. But with an appropriate port Mach
number function (d as described above),
it can be used for unchoked ports.
For a subsonic jet issuing from the fuel port, the static pressure in the jet Pjet
must equal the surrounding static pressure P3. Thus Pjet = P3. The d function then gets you from PG
to Pjet which is P3.
We now define flow function f to be the product of flow
function e from the grain massflow, and
flow function d from the port massflow.
Thus f = de = (1/Mp)*(1 + 0.5*(γ – 1)*Mp2)exp, where exp = (n + m) γ / (γ – 1) – 0.5. We also define factor H to be H = a K, at any given soak-out temperature. That is how the grain and port models are
tied together.
Overall
Unchoked Flow Rate Relationship
Combining the information from these three sources, the overall port flow function is
G H f η* = P3(1-n-m) AP B
which determines MP via f from any given
value of P3. G, H, AP, and B are constants for any given
mission, as are n and m. Finding MP from f is a
transcendental (or numerical interpolation) solution. Once MP is known, e can be found, and the grain flow equation yields wf
for any value of P3:
wf = G a e P3n
The overall propulsion balance of wf versus P3
in an actual engine is iterative, since
the value of P3 depends upon both the value of the captured airflow, and the delivered fuel flow (as well as the
air total temperature). But for
ground test approximation purposes, the
iterative balance need not be calculated,
since test airflow is fixed by intent.
For that, one plots combustor
fuel flow rates versus calculated P3 values at the test total
temperature, parametric upon inputs for
air flow rate and mixture ratio. Then
one calculates fuel flow out of the generator as a function of assumed P3
values, parametric upon burning surface
and soak temperature (if applicable).
These are superposed on the same plot.
Any proper ramjet cycle code can be used to compute a map of
fuel flow rate wf versus P3 for a given value of air total
temperature Tt2, parametric
upon both air flow wa and fuel/air ratio (or equivalence ratio φ), as shown in Fig. 2. This creates a sort of carpet-plot map.
Figure 2 – Image of Presentation Chart Showing Superposed
Ramjet Map and Generator Flow Lines
These gas generator relationships as described herein can
define fuel flow rate versus the same P3 values as are listed for
the ramjet map, without any iteration to
balance P3 in the ramjet engine.
At any given airflow (and air temperature), where the engine and gas generator wf
curves cross, is where the system will
equilibriate. You just
interpolate the P3 and mixture ratio values expected for the test. Mixture
ratio is an output, not an input, in this scenario. The figure shows that, as well. This presentation approach is something I
devised. It worked rather well.
What is important here is the shape and slope of the
generator fuel flow rate curves versus P3. If the propellant burn rate exponent is exactly
unity, these will be straight lines versus
P3. THAT is exactly-constant
fuel/air ratio operation, which is
exactly constant-φ operation,
regardless of the airflow (and air temperature). A high burn rate exponent very near unity
(above or below!) will therefore approximate constant fuel/air ratio control
quite closely. A low fuel propellant
exponent will not, and fuel/air ratio
will thus vary as airflow varies.
Stability
The first thing I did with this model was to check the sensitivities
of the equilibrium point mixture ratio to changes in various design
parameters. I looked at the effects of
burn rate, port area size, and inlet air total temperature, and plotted these at two different values of
design port Mach number. The design
point was 9.2 lbm/sec air at 800 R, with
an equivalence ratio near 1, meaning
stoichiometric. Results are given in Fig.
3. This is a plot of equivalence
ratio versus percent change in each parameter.
There is a plot at the low port Mach number, and another at the higher port Mach
number.
Figure 3 – Image of Presentation Chart Showing Sensitivity
of Equivalence Ratio to Various Parameters
The influence of burn rate is very strong indeed, as evidenced by the very large slopes on the
plots associated with it. Burning
surface, though not plotted, would have a similar large effect. The product of burn rate coefficient and
burning surface area is in the G factor of the model.
Air total temperature has a much weaker effect, reflected in its modest slope. This is true for both the lower and higher
port Mach numbers.
The design port area has a small effect (low slope) at the
lower port Mach number, but a much more
pronounced effect (steeper slope) at the higher port Mach number. At first glance that would seem to suggest
that a variable port area mechanism might be used to compensate for soak-out
changes to burn rate, and also to
compensate for burning surface variations as the propellant web burns. All that would be required to make this
possible, is designing to a high
subsonic port Mach number instead of a very low subsonic port Mach number.
As seductive as that notion was, due diligence required that I verify motor
stability. Choked motors are notoriously
unstable if burn rate exponent approaches unity too closely. For the unchoked generator, we want a burn rate exponent very close to
unity, or even somewhat greater than
unity.
For a conventional choked motor, the chamber pressure PG drives
both grain massflow, and massflow
through the nozzle. You simply plot the
massflow versus pressure curves for the grain and the nozzle onto the same
plot. Where the curves cross is the
operating point. The slope of the
nozzle massflow curve needs to be greater than that of the grain massflow curve, at that operating point, in order for the motor to be stable.
In that stable case, an
upward excursion in pressure takes the choked motor to a point where the nozzle
massflow is larger than the grain massflow.
That acts to drain the chamber and reduce its pressure back toward
equilibrium. A similar argument prevails
for a downward excursion in pressure:
the grain massflow is larger than the nozzle massflow. That acts to fill the chamber and raise its
pressure back toward equilibrium. THAT
is the choked motor stability argument in a nutshell.
For the unchoked port,
both pressures PG and P3 are important, but the backpressure P3 actually
drives the system, since their ratio is
determined by the port Mach number MP. The most direct analog to the choked motor
stability plot is the grain massflow and port massflow versus P3. The same slope ratio consideration
applies for stability: the slope of the
port massflow curve needs to exceed the grain massflow curve at the design
point where the curves cross.
Because the ratio of the two pressures is controlled by the
value of MP, an alternative
format for the stability plot is grain and port massflows plotted versus MP
instead. Because I wanted to investigate
whether a low or high value of subsonic MP can be used safely, that format was selected here.
The propellant used for this investigation was LPH-258, an early version of a choked-generator throttling
fuel, of which some mixes showed a lower
exponent in the very low pressure range,
a higher exponent in an intermediate range, and a lower exponent in the high range of
pressures. This particular mix tested as
having an exponent greater than unity in that intermediate range.
Plots of grain and port massflow versus MP were
made for the low range of pressures and the intermediate range, where it was anticipated that unchoked test
articles might be operated. The
breakpoint between those pressure ranges was at PG = 65 psia for
this mix of propellant. Those plots are
given in Fig. 4.
On the left hand plot,
where exponent is less than unity,
the slope of the nozzle massflow is larger than the slope of the grain
massflow at the indicated operating point where the curves cross, where port Mach number is roughly MP
= 0.7. This indicates stable operation
with this propellant is feasible at higher subsonic MP, when operating in the low range of P3
and PG.
On the right hand plot,
where the exponent is greater than unity, there are actually two curve crossings, indicating two candidate operating
points, one near MP =
0.7, the other nearer MP =
0.95. The nozzle curve slope is greater
than the grain massflow curve at the lower MP, but the reverse is true at the upper MP! That upper point is unstable, and is so close to choking, that the generator could easily and
spontaneously choke and explode! The
stable lower point is just not that far away from the upper unstable
point. A sufficient disturbance (like a sudden
P3 drop for any reason) could drive the motor to the instable condition, whereupon it might explode.
Figure 4 – Image of the Presentation Chart Showing Unchoked
Stability Plots For 2 Regimes of Exponent
The lessons here were rather clear. First, you want lower values of subsonic MP, most especially when the exponent is near or
exceeds unity. Second, to maximize the stability margin at that
lower stable operating point, you need
to design for very low values of MP indeed, closer to 0.1 than 0.5. Third, that low MP design choice makes
modulating AP unattractive for compensating burn rate, soak-out,
or burning surface variations, precisely
because the sensitivity to that variable is going to be so low.
Short-Burn Full-Scale Ground Tests
The test hardware is shown in Fig. 5, along with some data on the first four successful
live-burn tests conducted in it. The gas
generator was a standard 6-inch heavyweight lab motor with one or two
cartridge-loaded internal burning propellant grains. The inlet and combustor rig was
full-scale, flight-like hardware
borrowed from the contract VFDR (variable-flow ducted rocket, being a choked, valve-controlled gas generator-fed ramjet) program, and insulated on IR&D.
The lab motor is coupled to the combustor with a custom
adapter forward dome that was fabricated on IR&D. It was detail-designed by my friend and
colleague Jerry Lammert. The big
injector tube in the figure was only used once, on the very first test, which resulted in a “no-burn” (airbreathing
ignition failure) in the ramjet. After
that, the big injector tube was deleted
from the test rig.
The direct-connect test facility at Rocketdyne/Hercules by
this date had 20 lbm/sec airflow capability at up to 1660 R total
temperature. It used two 10 lbm/sec
lines that used pebble bed heaters, one capable
of 1210 R, the other capable of 1660
R. These tests were run at open-air
nozzle conditions, although the facility
had high altitude capability by means of a supersonic diffuser plus a steam
ejector.
Figure 5 – Image of the Presentation Chart Showing Test
Hardware and Initial Tests to be Run
Venton Kocurek was still a fairly recent hire at that
time, and I “broke him in” on ramjet
work planning for these tests and reducing the data afterward. Plus,
we did some of the “dirty-fingernails” test article assembly and
post-test disassembly work together.
The very first test run in this configuration was a no-burn
run with a propellant designated LPH-563A.
However, even though no ramjet
combustion was obtained, we did
demonstrate that the fuel flow followed the airflow variations in this unchoked
generator mode. That data is given in Fig.
6.
The left panel shows plots versus time for the pressure at
the air metering venturi, and the combustor
P3 response. The right panel
shows the traces versus time for combustor P3 and generator PG. It is quite clear that the fuel tracked the
air, in a fair approximation to constant
fuel/air ratio.
The no-burn on that very first test was attributed to the
fuel injector. The proof: after its deletion, we never had any trouble again, lighting the ramjet combustor, with any of the fuels tested.
Figure 6 – Image of the Presentation Chart Showing Unchoked
Fuel Control in a No-Burn Test
Subsequent to the 4 live-fire tests presented at the JANNAF
meeting, a series of experimental fuels
was tested in this same hardware set, as
full-scale, short-burn tests. Some of those were unchoked with graphite
nozzle inserts of very large diameter and internal-burning grains, others were choked with graphite insert
nozzles of very small diameter and end-burning grains. All were simple single-port dome injection on
centerline, which while not “tuned up” for
max performance, performed well enough
to see the correct trends among the experimental propellants.
Flight Predictions
I had Venton Kocurek modify an Air Force-supplied trajectory
program called ZTRAJ to correctly model the unchoked generator option. He was more of an expert at computer programs
than I was, and he was aware of my
full-blown unchoked analysis, which made
him the perfect choice. This was a large
effort that took some time, but Venton
did an outstanding job.
We did not use the full-blown, full-capability unchoked generator analytical
model for this. Instead, we used the intermediate model described
above, that essentially just makes fuel
flow a power function of P3,
using n as the exponent.
But, we added correction factors
for modeling variations in burning surface,
and for modeling the effects of soak-out temperature upon burn
rate. The actual changes to the code
were more complex than just that notion,
as is illustrated in Fig. 7.
Figure 7 – Image of the Presentation Chart Showing the
Modifications to the ZTRAJ Code
We already had the ZTRAJ computer model for the throttled
ducted rocket ramjet, here designated
TDR. We had the data for the fixed-flow
ducted rocket ramjet, designated
FFDR, and so we easily set up a computer
model of it. I sized an unchoked
generator propulsion scheme for these same basic missile models, termed “backpressure rate control” or BRC. My as-sized BRC is shown in Fig. 8. The as-sized TDR and FFDR are shown in Fig.
9. A comparison of sizepoint data
among the 3 designs is given in Fig. 10.
All three were sized using the same low-percentage boron fuel, thus entirely removing fuel characteristics
as a variable, from the fuel management
and performance comparison.
These vehicles size quite differently, because of their quite-different propulsion
characteristics. The FFDR sizes at cold
takeover, cold-soaked, where it runs the leanest. It has to meet Air Force-specified thrust
margins, at a min takeover speed
supplied by the integral (nozzleless) booster.
It has to meet an inlet pressure margin specification at sizing. At warmer conditions, it has more-than-minimum thrust margin, and runs richer in mixture. This enrichment reduces its takeover thrust
margin again, when soaked out hot, because it runs over-rich, which in turn reduces performance once again.
The TDR sizes at the hot takeover conditions, soaked out hot. It has to meet min thrust margin requirements
soaked out hot, and also an inlet
pressure margin. It exceeds thrust
requirements at colder conditions,
because its mixture ratio is under full control with the throttle valve
system.
The BRC was sized at its shock-on-lip Mach number, hot soaked on a hot day, at max tolerable mixture. Thrust margin was maximized at this
condition. For all 3 propulsion systems, inlet size was constant, only the ramjet throat area A5 was
revised to match-up the engine balance in the sizing.
Figure 8 – Image of the Presentation Chart Showing the
As-Sized BRC Missile
Figure 9 – Image of the Presentation Chart Showing the
As-Sized TDR and FFDR Missiles
Figure 10 – Image of the Presentation Chart Showing
Sizepoint Data Variations for All 3 Missiles
There are 4 plots in Figure 10. Upper left is thrust margin versus soak-out
temperature at min takeover speed.
Lower left is equivalence ratio vs soak temperature. Equivalence ratio is a measure of mixture
strength: 1 is stoichiometric, greater than 1 is fuel-rich, less than 1 is lean. Upper right is inlet pressure margin data
versus soak temperature. These need to
stay positive, and they do. Lower right is a normalized specific impulse
versus soakout. These data were
normalized to stay unclassified, and
probably need to remain so for ITAR (international traffic in arms regulation) reasons.
The BRC generally falls intermediate in min takeover performance values between
the TDR and the FFDR.
The missions chosen for evaluation were co-altitude head-on
engagements, with the launch aircraft
and the target both flying at Mach 0.9.
Standard day conditions were presumed.
Upon seeing the launch, the
target turns 180 degrees and accelerates rapidly at thrust/weight = 1 to Mach
1.5 as an attempt to get away,
converting the engagement to a tail chase. This was evaluated at 20,000 feet with the
target making his turn at 9 gees, and at
40,000 feet with the target making his turn at 4 gees in the thinner air.
Missile engagement limitations were intercept Mach 2.26 at
33 gees at 20,000 feet, and intercept
Mach 2.60 at 18 gees at 40,000 feet in the thinner air. To be a hit,
miss distance had to be no more than 10 feet. See Fig. 11.
These computer simulations were run with our modified ZTRAJ
code, by Venton Kocurek under my
guidance. The code already had fuel
control options to model the FFDR and the TDR.
By adding the BRC to it, we could
do this comparative study.
What results are of interest are F-pole versus launch
range, and intercept Mach versus launch
range, plotted for several different
launch ranges (each launch range its own computer run). End of mission could be propulsion limited
(out-of-propellant and coasting down) or time-limited (battery life for the
guidance). Launch range is self explanatory, being the horizontal separation distance between
the two aircraft when the missile is launched.
F-pole is the slant range between launch aircraft and target at the time
the missile intercepts the target. It is related to something called an “F-pole
turn” by the combat pilots.
The TDR, BRC, and FFDR missiles (as I sized them) were
evaluated on these missions. The Air
Force asked us to include some dive brake “drag flippers” on the BRC, to determine if drag modulation might be a
better way to help manage the fuel supply in the BRC. These brakes would “trigger” at a set speed, to keep the vehicle flying slower, thus hopefully conserving fuel. The Air Force suggested that we use a 3500
feet per second trigger speed. Initial
runs were made using that suggested trigger speed.
Figure 11 – Image of the Presentation Chart Showing the Two
Missions Used For Evaluation
Results for the two altitudes in terms of F-pole versus
launch range are given in Fig. 12.
Results for intercept Mach versus launch range are given in Fig. 13. These results were normalized to avoid
classification, and probably should
remain normalized because of ITAR.
At the low altitude,
there was little difference in the F-pole performance versus launch
range among all the configurations. The
TDR did the best, the BRC
intermediate, and the FFDR the least. Drag flippers on the BRC made very little
difference, as the missile just barely
reached the trigger speed.
The story at the high altitude was similar, except that there was a significant shortfall
of F-pole performance of the FFDR relative to the TDR. The BRC was intermediate, but very nearly as good as the TDR. Here, the
drag flipper trigger speed was never reached by the BRC missiles at all, so there is no difference traceable to it.
Figure 12 – Image of the Presentation Chart Showing F-Pole
Results
For the intercept Mach versus launch range results, the story is still quite similar. The spread between TDR and FFDR is almost
zero at the lower altitude, but
considerable at the high altitude.
At the low altitude, the BRC does a little worse than the
FFDR, but only just a little. The drag flippers made very little
difference, with the drag flipper BRC
very slightly worse than the plain BRC.
At the high altitude,
the BRC configurations both did almost as well as the TDR, and much better than the FFDR. The drag flippers made no difference, not being triggered at all on this
mission.
Figure 13 – Image of the Presentation Chart Showing
Intercept Mach Results
At this point, we
re-ran only the BRC, with and without
the drag flippers, on only the 40,000
foot mission. The only change was
lowering the drag flipper trigger speed to 3100 ft/sec, so that they would trigger over a more significant
portion of the mission.
The results of this revision are given in Fig. 14. This shows only intercept Mach versus launch
range, and that for only the two BRC
configurations.
There is a significant difference between the plain BRC and
the BRC with the drag flippers. The
plain BRC simply does far better. It has
higher intercept speeds at longer launch ranges.
Apparently, the fuel
that might have been saved by slowing down,
instead gets eaten-up overcoming the extra drag, and then some. Therefore,
drag modulation is just not very attractive as a means to improve the
fuel regulation in the BRC propulsion scheme.
We already know the BRC design responds weakly to port area
modulation, because stability margins
demand very low port Mach numbers at very large port diameters.
It would appear that designs featuring as low a propellant
burn rate sensitivity σP as possible, and as neutral a surface-web trace as
possible, is the best route for further
development of BRC propulsion.
These results were communicated to the Air Force before the
JANNAF presentation was made.
Figure 14 – Image of the Presentation Chart Showing
Intercept Mach at Higher Altitude and Lower Trigger Speed
Final Remarks
Further tests of experimental fuel propellants were made in
this short-burn test hardware, but not
in time for the JANNAF presentation.
These tests are well-described in Refs. 4 and 7, including some color photography from those
tests, plus there was a propellant
“shoot-off” on the contract VFDR program.
The two low-percentage boron fuels reported in the JANNAF presentation
were part of that “shoot-off”, along
with a high-metal boron-titanium propellant,
and a non-metallized “clean fuel” that met NATO min smoke criteria, despite being oxidized with ammonium
perchlorate. I developed both of those
very rapidly on IR&D, using these
short-burn test methods and hardware. The contract “shootoff” verified that all four
of those IR&D fuels were every bit as good as the two contract fuel
propellants.
The problem of achieving low propellant burn rate
temperature sensitivity had been addressed earlier on IR&D, and on the contract VFDR programs, with something called the “strand augmented
end burner” (SAEB). Those gas generators
on the contract programs were end burners,
fitted with a throttle valve. The
SAEB version used LPH-563A fuel rich matrix propellant, with a fully-oxidized strand propellant using
the same binder system. The plain end
burner used LPH-453 propellant, which
had been developed from the much earlier LPH-258 formulation that I tested
unchoked on IR&D.
By fitting such grains with fully-oxidized propellant
strands that had burn rates always higher than the majority fuel-rich matrix
propellant, we divorced the burn rate
ballistics from the fuel effluent characteristics that we needed. The strands had half or less the temperature
sensitivity of the matrix fuel propellant.
That allowed more of the valve area turndown to address fuel rate
turndown for high altitude, instead of
compensating for temperature sensitivity. See Fig. 15 for an image of the SAEB.
Figure 15 – The End-Burning Dual-Propellant SAEB Design
Designs like the FFDR could feature either end-burning or
internal-burning grain designs, using
high intrinsic burn rates in the end-burners, and low intrinsic burn rates in the
internal-burners, just all at high
chamber pressures. The end burners have
slightly-higher cross-sectional loadings.
There is no propellant displacement by a throttle valve or its
interstage in the FFDR.
The BRC featured internal-burning grain designs using high intrinsic
burn rates, just at very low chamber
pressures where the actual burn rate is low.
To solve the propellant burn rate temperature sensitivity issue, we needed a similar two-propellant solution
for the internal-burning designs.
On IR&D, I had my
friend and colleague W. Ted Brooks develop a model for such a device. He named it the “circumferentially-augmented
radial burner” (CARB). Ted Brooks (now
deceased) was my mentor in internal ballistics when I was a young
engineer, and he wrote the NASA
monograph on internal ballistics (Ref. 8).
I believe the CARB would have worked very well, but we never got to test it. See Fig. 16 for an image of the CARB
design.
Figure 16 – The Internal-Burning Dual-Propellant CARB Grain
Design
All of these gas generator designs use case-bonded grain
technology, but must survive cold soak
to -65 F without cracking the propellant or peeling its bond away from the
case. End-burning designs are the worst
offenders in this respect, but some high
cross sectional-loading internal burners also suffer. Solid elastomer internal case insulation is
just not compliant enough to do that job.
At Rocketdyne/Hercules, we
invented something called the stress-relieving liner that was compliant enough
to serve this function successfully. See
Fig. 17.
Figure 17 – The Stress-Relieving Liner Design That Supports
End-Burners and Other Designs
As an aside,
the integral booster shown above for the 3 configurations analyzed above
was a “nozzleless booster”. This used a
two-propellant overcast to minimize the losses otherwise inherent in a
nozzleless booster rocket, which ejects
no booster nozzle assembly or debris.
That design and those propellants were developed on IR&D and went to
the contract VFDR program for validation,
and they became the baseline.
That concept is illustrated in Fig. 18.
Figure 18 – The Dual-Cast Nozzleless Booster Concept
Right after the subject JANNAF presentation described here, the plant closure announcement was made. The following November (1994), I was laid off in the first wave of layoffs, being most closely associated with new
product IR&D work, not ongoing
contract work. That ended my career in
aerospace defense work, there being a
massive industry contraction underway, after
the fall of the Soviet Union.
The plant finally closed for good within another year (by late
1995). The sad tale of what happened to
the incredible gas generator-fed ramjet (and nozzleless booster) technologies
that we had, is covered by refs. 4, 5, and
7. All of that was lost! If the US military wants a ramjet missile of
AMRAAM class today, then they have to
buy the “Meteor” from the Europeans. It’s
a TDR type of gas generator-fed ramjet,
very similar to what we had.
Their valve geometry is a bit different,
but it is the same basic notion.
References
Most (but not all) of these references are articles posted
elsewhere on this site. The others can
be located by an internet search,
excepting possibly this particular JANNAF presentation (ref. 1), which is why I wrote this article. There is a catalogue of some related articles
that may be relevant, in Ref. 9.
To quickly find any of the articles on this site, you need the date and title to use in the
navigation tool, left side of this
page. Click first on the year, then the month, then on the title if need be (if multiple
articles were posted in that month).
Clicking on any figure in an article lets you see all the figures
enlarged. Top right is an X-out feature
that takes you right back to the article.
#1. Gary W. Johnson and Venton A. Kocurek, “Evaluation of Unchoked Generator Ducted
Rocket Ramjets”, paper given at the 1993
JANNAF meeting held at the Naval Postgraduate School, Monterrey,
CA, given November 17, 1993.
#2. Gary W. Johnson,
“Primer On Ramjets”, article
posted on http://exrocketman.blogspot.com, 10 December 2016.
#3. Gary W. Johnson,
“Ramjet Cycle Analyses”, article
posted on http://exrocketman.blogspot.com, 21 December 2012.
#4. Gary W. Johnson,
“The Ramjet I Worked On The Most”,
article posted on http://exrocketman.blogspot.com, 2 August 2021.
#5. Gary W.
Johnson, “Use of the Choked Pintle Valve
for a Solid Propellant Gas Generator Throttle”,
article posted on http://exrocketman.blogspot.com, 1 October 2021.
#6. Propulsion and Energetics Panel Working Group 22, “Experimental and Analytical Methods for the
Determination of Connected-Pipe Ramjet and Ducted Rocket Internal Performance”, AGARD Advisory Report 323, July 1994.
#7. Gary W.
Johnson, “Ramjet Flameholding”, article posted on http://exrocketman.blogspot.com, 3 March 2020.
#8. W. Ted Brooks, “Solid Propellant Grain Design and Internal
Ballistics”, NASA SP-8076, March 1972.
#9. G. W.
Johnson, “Lists of Some Articles By
Topic Area”, article posted on http://exrocketman.blogspot.com, 21 October 2021.
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