What Is Flameholding?
Everybody was taught the fire triangle in grade school: put fuel, air, and a source of ignition in the same place at the same time, and you get a fire. When the fuel and air are brought together in a flowing duct, as in a ramjet combustor, there must be not only an initial source of ignition, but also a continuing source of ignition, or the fire immediately blows out.
The reason for this is actually quite simple: most fuels do not spontaneously ignite upon contact with air. Those that do are termed “hypergolic” or “pyrophoric”, and all that need be done with them is get good mixing of the fuel and air to get efficient combustion. Metallic magnesium in vapor form is one of these; the liquids triethyl borane (TEB) and triethyl aluminum (TEA) are two others.
The rest are “non-hypergolic” and generally require a source of ignition to start the combustion, followed by a continuing source of ignition to maintain it. With flow speeds in a ramjet combustor around 1000-1500 ft/sec, and turbulent flame speeds being only 50-100 ft/sec, this source of continuing ignition must be protected from the really extreme wind blast in some way.
The proven method of doing this is to provide a wake zone behind some obstruction or some sharp change in duct area. The flow within that wake zone is a little bit slower than the main flow (both are well subsonic), but more importantly, it recirculates around and around in that wake zone. This is a vortex, or perhaps multiple vortices, in that wake zone.
If that recirculation zone (RZ) vortex (or vortices) has both fresh fuel and fresh air getting entrained within it, and has been ignited, then that vortex (or those vortices) burn continuously without getting blown downstream. The hot gas output from this zone is the fixed-location “pilot flame” that can ignite the fuel-air mixture out in the main flow. And THAT is “flameholding” or “flame stabilization”.
That burning proceeds across the main flow at an angle defined by the ratio of turbulent flame speed to main flow speed. The flame front needs to travel all the way across the main flow before the combustor exit is reached, if the potential of good efficient combustion is to be actually attained.
This sort of RZ-based “flameholder” or “flame stabilizer” is totally unnecessary for a hypergolic fuel. For the hypergolics, the old adage “if it’s mixed, it’s burnt” is quite literally true. For the non-hypergolics, you must have the flame stabilizer in addition to the mixing. See Figure 1.
There is, of course, an exception. If the air stream temperature is hot enough to be above the fuel’s autoignition temperature with air, then the hot air will heat the fuel up upon contact, so that spontaneous combustion of hot mixture then begins, at an effective flame speed limited only by the mixing rate for unmixed streams. This effect obtains mostly because the air outweighs the fuel by far.
If this happens with pre-mixed fuel and air mixture, then you have a massive explosion. It all burns at once. That is the mechanism of detonation in gasoline car engines, and it is why Diesel engines have direct injection of fuel into the cylinders containing already-compressed hot air.
The Known Flame Stabilizer Geometries
The known, well-proven, stabilizer geometries for ramjets are depicted in Figure 2.
The oldest are the blockage-element flameholders at the bottom of the figure. There are basically two types: the V-gutter and the perforated can. The V-gutter stabilizer was used in the ramjet SAM “Bomarc”, and is still used in jet engine afterburner ducts today.
The perforated can stabilizer has two implementations shown in the figure: the regular can, and the inverted can, which was used in the ramjet SAM “Talos”. With direct fuel injection into the can, instead of further upstream, the regular can is the most frequently-used flame stabilizer in all gas turbine engines.
At the top of the figure is the coaxial dump geometry, which has no blockage elements creating wake zones, but instead has a sudden increase in duct area that creates an annular recirculation zone about the entering air stream. It can be used with either a nose inlet, or a chin inlet. This was used in the ramjet test vehicle ASALM-PTV that flew in flight tests, and the AAAM air-to-air missile concept that never flew.
There are multiple possibilities for side-mounted sudden-dump inlets, shown in the middle of the figure. These vary with the number and placement of the inlets. The 4-inlet form was flight-tested in the prototype standoff attack missile ALVRJ, as well as being used in the Russian anti-ship missiles “Sunburn” and “Krypton”.
The Russian SAM SA-6 “Gainful” used a variant of the 4 side inlet geometry, but also used hypergolic magnesium vapor fuel, needing only mixing, no flame stabilizer. This was discussed thoroughly in the “One of Several Ramjets That I Worked On” article.
Liquid vs Solid Fuel Effects
There are liquid-fueled ramjets, solid-fueled ramjets, and solid-propellant gas generator-fed (GG-fed) ramjets.
The liquid-fueled ramjets have a tank from which liquid fuel is pumped or fed to the fuel injectors, which are usually located mostly in the inlet duct or ducts. That fuel is sprayed for good atomization, and then vaporized by the heat in the elevated-temperature inlet air, so that the flameholding and main combustion processes deal only with a one-phase vapor fuel. Such are discussed in this article.
The GG-fed ramjets have instead of a tank of liquid fuel, a fuel-rich solid-propellant gas generator resembling a solid propellant rocket motor. The solid propellant in that gas generator burns, creating a combustible effluent directed into the combustor, usually directly instead of into the inlets. In the combustor, that effluent then mixes and burns with the air in a manner that is superficially the same as what happens in a liquid-fueled ramjet. Such are also discussed in this article.
The solid-fueled ramjets are quite different. The fuel is a hollow chunk of solid combustible material located within the combustor, through which the inlet air stream is directed. All of the fundamental flow and combustion processes are quite distinctly different from the liquid and GG-fed ramjets. It’s not even superficially similar to the other two types of ramjet. Such are NOT discussed in this article.
What is different between the liquid and GG-fed ramjets is the fundamentally two-phase nature of the fuel effluent. In the liquids, the fuel is largely-vaporized by the time it enters the combustor. Any still-unvaporized fuel has a fairly-low heat energy to draw from the surroundings in order to vaporize. That tends to minimize any quenching effects traceable to the presence of liquid fuel reaching the RZ. But if there is significant liquid fuel present in the RZ, then the risk of quench effects is non-trivial.
This would be due to the wrong choice of fuel. For low speed systems (subsonic to about Mach 1.5), vaporization requirements force the choice of high-volatility gasoline. From Mach 1.5 to about 2.5, a medium-volatility wide-cut fuel like JP-4 or Jet-B can be used. Above Mach 2.5, a low-volatility kerosene like JP-5, JP-8, or Jet-A can be used.
In the GG-fed solid, the effluent is largely gaseous and solid fuel species, with significant gaseous and solid/liquid combustion product species. The gaseous fuel is dominated by carbon monoxide, and the solid fuel is dominated by carbon soot.
The real physical differences here are (1) that the soot burns 10-100 times slower with air than the carbon monoxide, and (2) there is a very high energy input needed to heat up soot to its ignition point with air. Thus the presence of large amounts of soot within the flame-stabilizing RZ is a very serious quenching risk, as well as an inherent mismatch of needed time-to-burn relative to time available (local RZ residence time). This has very serious implications for both the RZ flow pattern and for the formulation of the fuel-rich solid GG propellant, as will be discussed below. See Figure 3.
The net effect here is that liquid fuels will flamehold successfully in pretty much any of the geometries depicted in the article, while the GG-fed solids will not. This is precisely because of those wildly-different characteristics between the liquid sprays and the GG effluents.
The only ways around that dilemma (limited feasible flameholding geometries) with the GG-fed solids are (1) to select only a feasible air entry geometry, and then also use it with an appropriate fuel injection geometry, or else (2) one must use a hypergolic gas generator effluent.
Air Entry Flowfields
Perhaps the simplest inlet entry flow field of all is the coaxial dump already shown in Figure 2 above. In it, the entering air stream is a centered free jet spreading gradually into the full combustor cross section.
Experimental results generated in the 1970’s by Tom Curran at WPAFB (the recognized expert in these configurations, and Tom was a personal friend of mine) confirm that the length of the separated zone surrounding that air jet is about 8, to at most 9, “step heights” from the sudden area-expansion, to where the dividing streamline hits the combustor wall. This is under burning conditions.
In this context, “step height” is the difference in combustor and inlet radii, or half the difference in combustor and inlet diameters. Curran found that step height also turns out to be an important parameter for estimating or correlating the flame stability of coaxial dump configurations.
Within the separated zone, there is a vortex flow oriented such that the vortex axis is a closed circle in a ring about the entering jet. This vortex is distorted and stretched, in the sense that its long dimension is more-or-less the length of the separation zone, and its short dimension is more-or-less the step height.
There is a mixing layer between the entering jet of air and the recirculation zone flow, that widens downstream. This is how fresh air (and any fuel already mixed into it) gets entrained into the recirculation zone, and also how the hot gas products from the recirculation zone combustion leave that zone, and get mixed into the periphery of the main flow.
This mixing is mostly turbulence-driven, so the percentage massflow of RZ-entrained air is rather low. Curran also found that there are ways to estimate exactly how much entrainment occurs, which is something I documented in my ramjet ”how-to” book, rather than here.
Now, what Curran found experimentally is that if the flow velocity V in the inlet duct gets too high, or the inlet static pressure P too low, or the inlet air total temperature Tt too low, or the step height h too small, then stable combustion is not possible. Thus, the correlating parameter can be of the form
parameter = Va/Pb Ttc hd
which, when plotted for a great many lean and rich blowout tests as the ordinate, with an abscissa of equivalence ratio, forms a loop. That is, it forms a complete loop if there is enough data at a variety of possible flight conditions. This loop looks crudely like an inverted parabola in shape. Inside the loop is the regime of stable combustion, and outside there can be no stable combustion.
The left (lean) branch is the lean blowout limit, and the right (rich) branch is the rich blowout limit, all other things being equal. If altitude is high enough (low P), or flight speed slow enough (low Tt), or size small enough (low h), then you are trying to operate above the peak of the loop. Again, stable combustion is infeasible.
The exact values of the correlating exponents depend upon which fuel you are using. Curran was working with liquid fuels, mostly JP-4 wide-cut fuel (same as Jet-B). He found inlet velocity less important than the other variables for this geometry class. The other details of his best correlation are given in my ramjet “how-to” book, not here.
One thing about this geometry that is very important to understand is that all surfaces exposed to flame are (1) insulated from the hot gas, and (2) have no heating on the reverse side. These are inherently survivable at flight speeds well into the hypersonic range. The side-dump geometries share this ability.
Another important characteristic pertains to inlet air stream flows that are pre-mixed with all the injected liquid fuel: in that case the entrained fraction of the air is also the entrained fraction of the fuel, and in the same ratio. Thus, the RZ local equivalence ratio is identical to the overall engine equivalence ratio. The only exception would be to add extra fuel injection directly into the annular RZ, which would cause it to run a richer local equivalence ratio than the overall engine.
V-Gutter Blockage Element
The next-simplest flow field to understand is that of the V-gutter stabilizer, which is one of the blockage-element stabilizers shown in Figure 2 above. The recognized expert for these was Robert Ozawa at Marquardt, in the 1960’s and 1970’s. I also knew Bob.
Actually, the flow field picture looks very much like that of the coaxial dump, just turned “inside-out”, and made two-dimensional, instead of axisymmetric, behind each branch of the stabilizer grid. There are two oppositely-turning vortices in the wake zone behind each branch of the V-gutter stabilizer. These vortex cores connect to those of other grid branches, or terminate upon the wall of the combustor, just as the flow physics of stable, persistent vortices requires.
Again, there are ways to estimate the rather limited turbulence-driven entrainment of air into these RZ volumes, balanced by the hot gas flow output from these volumes. And there are ways to compute a stability loop parameter from the same basic variables V, P, and Tt, plus d, where d is the V-gutter element width edge-to-edge.
This parameter forms the same sort of stability loop that looks like an inverted parabola, when plotted as parameter-at-blowout vs equivalence ratio. The meaning of that stability loop is exactly the same as that for the coaxial dump. Only the details are different: for the V-gutter, inlet duct velocity V is the most sensitive variable, not the least sensitive.
I document those details in my ramjet “how-to” book. Not here.
It is also very important to understand the survivability limits of this stabilizer geometry. On the upstream side, each element is washed by the air stream, whose recovery temperature (very nearly the air stagnation temperature) is the driving temperature for heat transfer to the surface from the air.
On the downstream side, each element is washed by hot combustion gases, whose recovery temperature (very nearly the stagnation temperature) is the driving temperature for heat transfer to the surface from the hot gases.
Thus, the steady-state soaked-out material temperature for the V-gutter element is going to be somewhere in between the air recovery and hot gas recovery temperatures. Since the exposed areas are crudely about the same, that soak-out temperature is not far from the arithmetic average of the two recovery temperatures. In turn, that is not very far from the average of the two total temperatures.
That average is a large number for material temperature. Which neatly explains why no ramjet has ever flown faster than about Mach 3 in the stratosphere, with this kind of stabilization system, and slower yet at lower altitudes. No practical material can survive being that hot.
Another important characteristic pertains to inlet air streams that are pre-mixed with all the injected liquid fuel: in that case the entrained air fraction is also the entrained fuel fraction, and in the same ratio. Thus, the RZ local equivalence ratio is identical to the overall engine equivalence ratio.
The only exception would be to add extra fuel injection directly into the V-gutter element RZ’s, which would cause them to run richer local equivalence ratios than the overall engine. That requires a small fuel spray tube at the inside corner of the V-gutter element, on the downstream side.
Can Stabilizers and Inverted-Can Stabilizers
The can stabilizer takes the form of a can with one end open and the other closed, plus perforations through its lateral sidewalls. The closed end faces upstream. The inlet duct airstream is directed into the annulus around the outside of the can, and prevented from bypassing it to go downstream. This the flow must proceed through the perforations into the interior of the can, and only from there is it free to proceed downstream.
Each of these perforation flows resembles the coaxial-dump flow field situation, except that there is no separation-reattachment downstream, because there is no surface to which reattachment can be made. These are just multiple jets into a “cloud” that increasingly moves faster downstream toward the open end of the can, as its massflow total adds up.
Stability correlations would resemble those discussed above, where the dimension variable might be the average perforation diameter, or the can inside diameter. I have not researched those stability correlations, it being a topic long considered obsolete for ramjet application. However, it is current technology in gas turbine engines.
For fuel injection into the airstream upstream of the can stabilizer, then entrainment into the perforation recirculation zones applies to both air and fuel, same as for the coaxial dump. To enrich the space within the can, one must inject fuel directly into the can, from the upstream closed end.
In most modern gas turbine applications, this is in fact where all of the fuel injection occurs, so that the local equivalence ratio within the can varies from all-fuel forward, to very lean at the can outlet. Initial combustion occurs somewhere in between, where the equivalence ratio is close to unity.
Downstream of that zone the effects of perforation flows are mostly just gas temperature reduction by air dilution, down to something tolerable at the turbine inlet.
Like the V-gutter, the can stabilizer is washed by air on its upstream (outer) surfaces, and at least locally, by hot flame on its downstream (inner) surfaces. Thus the equilibrium material soak-out temperature must fall somewhere near the average of inlet air total temperature and hot gas total temperature, perhaps locally increased somewhat by the very non-uniform gas temperature distribution that occurs with fuel injection directly into the can.
So, among all the other potential limitations from compressor and turbine blading temperatures, there is also a survivability limitation on can combustors, to flight speeds of about Mach 3.5 or so, in gas turbine applications. And so also there is a survivability limit, even in ramjet applications.
The inverted can stabilizer shown in Figure 2 above has the closed end downstream, with the inlet air directed into the interior of the can, and prevented from bypassing downstream around its periphery. The jets from the perforations are directed radially outward, instead of inward.
This geometry was used in the “Talos” ramjet combustor about 1950 to “fold” the flow geometry for smaller volume and length. That proved to be doable, but difficult, experimentally. It has not been applied widely since. In “Talos”, it did require an additional pilot flame into the outer annulus.
This geometry is subject to essentially the same survivability limits due to overheat as the can and V-gutter stabilizers, and for exactly the same reasons. At least theoretically, one could get a richer local equivalence ratio distribution by direct fuel injection into the inverted can, similar to that by direct injection into the plain can. This was not done in “Talos”.
Side Dump Inlets
The 4-inlet form could be either a flameholding configuration, or a non-flameholding configuration for hypergolic fuel, as indicated in Figure 4 below. The overall configurations look to be very similar, until one notes whether there is a volume provided, in which a recirculation zone (RZ) might exist.
The main discussions in the article on this site titled “One of Several Ramjets I Worked On”, dated 4 February 2020, pertain to the hypergolic magnesium-fueled SA-6, and correlate with the lower part of the figure. There is no significant volume for any RZ, as the gas generator aft dome protrudes well into the airbreathing combustor.
If instead, one provides a volume in which recirculation flow may occur, as in the upper part of the figure, then flame stabilization is possible with this geometry. This was very well-proven in flight by the “ALVRJ” long-range strike missile flight tests in the 1970’s, and underlies the performance of the Russian “Sunburn” and “Krypton” anti-ship systems flying today. All three are liquid-fueled ramjets.
What is unique about the side entry geometries (all of them, not just this one) is that local momentum balance provides much larger entrainment fractions of the airflow into these recirculation zones. The steeper the air entry angle off of axial, the larger these entrainment fractions tend to be. They are significantly larger entrainment fractions than those seen in the coaxial dump or blockage-element stabilizers (details are in the ramjet “how-to” book, not here).
The same higher entrainment fractions mean that there must be very significant paths for the much larger hot gas product flows from these RZ’s to the downstream regions of the combustor. This effect greatly exceeds that of turbulent mixing layers between streams. The actual hot gas “leak paths” to downstream are between the entering air streams, as indicated in Figure 4 above.
The same steeper entry angles lead to higher stream total pressure losses. These higher pressure losses also lead to faster mixing rates in the flow downstream of the side entry. Higher asymmetry in the inlet placement also leads to higher total pressure losses, leading in turn to higher mixing rates downstream. Again, details are given in the ramjet “how-to” book, not here. A comparison of such symmetry vs asymmetry of inlet entry is illustrated in Figure 5, for two 2-inlet configurations.
In the “2 at 45o 90o apart” configuration (“asymmetric twin”), top of the figure, the two entering airstreams impinge upon each other, before the combined streams impinge upon the far side of the combustor. The two streams impinging upon each other do create a finer-scale turbulent “dithering” motion, but the greater effect by far is a sort of self-stabilization of the far wall impingement point, so that it does not wander around significantly at all. That stabilization of the wall impingement point also stabilizes the single large RZ vortex, whose axis terminates upon the two “cheekwalls” of the RZ. It is very persistent.
From the impingement point, the two main streams climb up the far walls opposite each other, making oppositely-rotating vortices aligned downstream, essentially bringing a degree of swirl to the mixing. It’s not a lot of swirl: only about 1 turn gets made before the flow reaches the nozzle, at L/D ~ 5. These flow patterns are seen in both flow visualizations (if mass and momentum are both modeled), and in the burn and erosion patterns seen in the combustor ablative insulation from actual tests.
In contrast, the “2 at 45o 180o” apart (“symmetric twin”) configuration in the lower part of the figure creates a different flow pattern. The streams impinge only upon themselves to create the turn downstream. This point has some “dither” to its location, so the impinging streams and everything they touch moves about somewhat. There is no definite swirl created downstream.
This entry tends to create a pair of RZ vortices, of much smaller overall dimension than the one in the asymmetric twin. Because of the less stable positioning of the impingement location, these RZ vortices are also less stable. They do tend to “come-and-go”, meaning break apart and reform. All these effects can be seen in the visualizations, if mass and momentum ratios are modeled correctly.
As shown in Figure 6 there are related configurations with similar flow patterns to those of the asymmetric and symmetric twin configurations of Figure 5. The “1 at 45o” configuration (“single side inlet”) has an overall flow pattern somewhat similar to the asymmetric twin, except that no persistent swirl is created. The lack of stabilizing stream impingement means the far wall impingement location is much less stable. The RZ vortex is large like the asymmetric twin but much less stable.
The “4 at 45 equally-spaced” configuration (“4-inlet”) in the bottom of the figure is similar to the symmetric twin in its flow pattern, except that the four RZ vortices are even smaller than the symmetric twin’s two. Although one ring vortex driven by the 4 entering streams is theoretically possible, in practice, there are 4 separate small vortices, each adjacent to its own driving inlet stream. Without solid surfaces upon which the cores can terminate, these are quite unstable, coming and going at random and very rapidly. This is borne out by the visualizations: the vorticity looks random.
All of these RZ vortex configurations serve as effective recirculation flow patterns, as evidenced by the fact that every one of these inlet configurations successfully flameholds when used with properly-vaporized liquid fuels. But they all do NOT successfully serve as flameholders for the GG-fed fuel effluents!
The one that does successfully flamehold with most of the “hydrocarbon” fuel propellants is the asymmetric twin inlet entry. The symmetric twin and 4-inlet configurations only work with fuel propellants that are very high in oxidizer (which makes their effluents far lower in soot, see below). So far, there have been no successful uses of the single-side-inlet with any of these fuel propellants, although seemingly it should work to some extent.
The common thread that links these divergent GG-fed behaviors together is not very intuitive: it is the effects of the soot content in the effluent stream. This burns so slowly that the residence times available in the RZ’s are wildly-wrong (factor 10+ too short). It also sops up so much heat reaching its ignition point with air, that it presents a real quench risk to the combustion in the vortex. The only way around this dilemma is to centrifuge as much of this soot out of the RZ vortex as is possible.
All of these vortices spin with a peripheral fluid velocity V similar to the entering airstream velocity, along the contact surface between the RZ and the air stream(s). It can be different elsewhere around this periphery, especially if elongated in one dimension. Using an average radius figure R for the vortex outer boundary, the average centrifugal acceleration would be crudely V2/R. Since all the V’s are about the same, for the same inlet velocity (or velocities), the smaller vortices should be better expellers of soot by that equation, but in practice they are not. Real life is more complicated.
The intermittency of those vortices in the symmetric twin, 4-inlet, and single side inlet configurations interrupts the expulsion of soot from them. Another complicating factor is to where the soot gets expelled. That can be to the nearby solid surfaces, or downstream to the air streams, or downstream to the hot gas outflow paths. Soot buildup on solid surfaces limits the effectiveness of that path.
In the asymmetric twin, it gets expelled against solid surfaces on 3 sides, and the inlet air streams or downstream flow paths on the fourth. This vortex is very stable and persistent. It can easily expel centrifuged soot downstream, leaving a fuel gas core to burn at fast reaction speed in the RZ.
In the symmetric twin, 2 sides of each vortex expel soot to the solid walls, 1 side to the air stream or downstream flow path, and the fourth side expels soot to the other vortex, which is thus not expulsion at all. Plus, there is the intermittency factor. When the vortex isn’t fully formed, there is no centrifugal effect, and so no expulsion of soot. With reduced ease of soot expulsion, and reduced driving impetus to expel soot, this RZ remains more choked with soot that cannot react significantly once ignited, and which draws much heat to reach its ignition point. It should therefore be quite unsurprising that only the much-lower-soot effluents could successfully flamehold in this geometry.
In the 4-inlet, the situation is much like the symmetric twin, except that the vortex intermittency is even higher, as already described above. Again, it should be quite unsurprising that only the much lower-soot effluents could successfully flamehold in this geometry.
The single side inlet is seemingly most like the asymmetric twin. The difference is the less-stable vortex which is intermittent. There is also a bit less contact area between the airstream and the RZ vortex, so the average speed V could be a bit lower. Unfortunately, this geometry was not the subject of much visualization work, which would indicate how organized and persistent its RZ vortex really is. This geometry was attempted by more than one company for testing, but never successfully burned anything but hypergolic magnesium. Experimentally, it seems to be a real “dog” as a flame stabilizer.
Stirred Reactor Theory for RZ
In the above discussions, both RZ volume and the entrainment fractions of fuel and air (which are not constants) have been highlighted. In effect, there is a fuel-plus-air throughput massflow rate through the RZ volume. This has an effective residence time tRZ which can easily be computed from these data, if one has a value for density:
tRZ = ρ VRZ /(wa + wf) where VRZ is the RZ volume, and wa and wf the entrained massflow rates
This RZ residence time is all the time you have to react the local fuel and air in the RZ, and release their heat, to make an equal massflow of hot gas to be the pilot flame for the main combustor.
The overall engine residence time tR can be computed in a similar fashion from the overall engine volume and flow rates:
tR = ρ Vengine / (wA + wF) where wA and wF are the overall flow rates to the engine
In the blockage-element and coaxial-dump flameholders, entrainment into the RZ is driven by turbulence, with lower entrainment fractions and thus lower entrained massflows. The residence time in the RZ is comparable to the overall engine residence time, at usually 2 to 4 milliseconds in tactical sizes.
The side-dump flameholders are different, with higher entrainment fractions (and entrained massflows) driven by local momentum balance in addition to turbulence. The RZ residence times are in the fractional millisecond range when overall engine residence time is 2-4 milliseconds.
Experience in the tactical-size asymmetric twin with variety of injection geometries and fuel effluents shows that it takes something like 2-3 milliseconds to get the soot burned, lest it show up in the exhaust plume as a bright opaque yellow glare. Soot burning downstream of the nozzle contributes nothing to thrust. At such short RZ timescales, there is little chance of actually burning any of it in the RZ.
This is strongly suggested by simple stirred-reactor modelling of the RZ, using a global effective reaction rate model for the effluent. Those models typically show a peak in local heat release intensity at around 65% of the fuel reacted. Less that that is not stable mathematically, implying no burn is possible. Greater than that is stable, all the way to 100% reacted. With the soot reacting 10 (to maybe 100) times slower than the gaseous fuel component, very little of it has time to react in fractional milliseconds: way under the stability limit. So, it simply cannot burn at all in an RZ environment.
While that model is too simple to be in any way accurate, it is good enough to be very strongly suggestive. Any significant soot in the RZ (1) cannot react, (2) dilutes the gaseous fuel reaction, slowing it down, and (3) draws heat from the gases toward its own ignition point. If the effluent being burned has lots of soot, it is quite unlikely that stable combustion is possible, unless the soot is somehow removed from the RZ before it can have these effects. The only known mechanism for this would be centrifuging the soot out, and experimentally, the asymmetric twin offers the most reliable centrifuge action.
The simplest such model is the one-step one-reactant reaction rate model. The better physical modeling is the one-step two-reactant reaction rate model. Both give roughly the same stability-limit answer. There are a lot more details about stirred reactor modeling, entrainment fractions, and all the other related flameholding phenomena, in my ramjet “how-to” book.
Liquid Fuel Properties Relevant to Flameholding
The stoichiometric (ideal) air/fuel ratio by mass A/Fo is a fundamental fuel characteristic important to all fuels, whether liquid or a GG effluent. The relative richness equivalence ratio ER is computed from the actual fuel/air ratio f/a using this stoichiometry value:
f/a = wf/wa
ER = (f/a) (A/Fo)
This can be done for the overall engine, and if you know the fuel and air entrainment fractions, locally in the RZ. When the mixture is stoichiometric (ideal), one calculates ER = 1. If there is no fuel flow, ER = 0. ER is a number less than 1 if mixture is lean on fuel, and a number greater than 1 if mixture is fuel-rich. This is true no matter what the actual value of A/Fo is, so with ER, mixture strength is obvious at a glance. Plus, fuels with different A/Fo have similar behaviors and combusted-properties data at the same values of ER, including combusted temperatures and combusted c* values.
The other property of a liquid fuel that is fundamentally important to flameholding is its volatility, which has many measures. This is because serious problems ensue, if the fuel is not vaporized by the time it enters into the RZ, up to and including not combusting at all. Since quenching in the RZ is related to heat energy “sucked out” of the RZ hot gases, one such measure is latent heat of evaporation.
The fuel cannot vaporize if the inlet air temperature is too low, so the other relevant measure is its effective boiling temperature. For fuels that are pure substances, this is a definite single boiling temperature. For other fuels that are mixtures (such as petroleum hydrocarbons), this is really the distillation curve (residual liquid temperature vs fraction vaporized).
Some rough-and-ready rules-of-thumb about distillation curves would be using the temperature at the 10% or 20% evaporated point relative to getting RZ ignition, and having the heat balance including flame radiation on droplets reach the 90% evaporation point during steady burning. The pure-fuel analog to this would be heating the droplets to the 10-20% evaporation point for ignition, and evaporating at least 90% in steady burning with flame radiation.
Other factors of some design impact would be the specific heats of the liquid and vapor phases, and the autoignition temperature with air. That last item is more complicated than it initially sounds, because there really is not one “autoignition temperature”. There are “sort-of” two customary values of autoignition temperature reported in the literature: 1-second and 1-millisecond timescales. The millisecond autoignition temperatures are very much higher than the 1-second values.
However, for ramjet work at millisecond-scale residence times, it is the higher millisecond autoignition temperatures that are appropriate. For the gasolines and kerosenes customary in ramjet work, such are on the order of 1000-2000 F, with the 1-second values closer to 400-500 F. 1000 F corresponds to the air total temperature at Mach 3.7 in the stratosphere. 2000 F corresponds to about Mach 5.
Liquid Fuel Flameholding
Most liquid ramjet systems inject fuel into the air stream in the inlet, some distance upstream of the flame stabilizer, whatever it is. This gives the atomized droplets a millisecond-scale time interval to evaporate, using the compression heat in the airstream, and driven by the air temperature being higher than the droplet temperature. This is shown in Figure 7 for the asymmetric twin.
Vaporization needs to be completed by the turn-around point where recirculation motion forward begins. For ignition, there is only the airstream heat available. For steady burning, there is that air heat plus the flame radiation from the RZ striking the droplets, once they are past the stabilizer.
Fig. 7 – Liquid Injection in the Asymmetric Twin Side Dump
If all the fuel injection is into the inlet, then the air stream carries the fuel. Whatever the air entrainment fraction is, that is also the fuel entrainment fraction. For that case, the local ER in the RZ is the same as the overall engine ER. This can be leaned only to the lean blowout point shown conceptually on the figure (there are no correlations available for side dump combustors).
The lean blowout limit can be pushed to a leaner overall ER, if the local RZ ER can be riched-up, at least to a point. This can be done by injecting some of the fuel directly into the RZ, for which that portion’s entrainment fraction is essentially 1. The RZ does not see such a lean ER as the engine, thus allowing leaner overall ER before RZ lean blowout (and engine flameout) occurs.
This applies to the symmetric twin and the 4 inlet, plus the coaxial dump, in exactly the same way as the asymmetric twin shown in the figure: simply by dome injection. For operating the engine at an overall rich ER, one must turn the dome injection off, lest the RZ reach rich blowout sooner than the overall engine. This would be true of any stabilizer configuration.
While direct RZ injection is not so very easily possible to do with V-gutter stabilizers, it is possible with a fuel spray tube nested in the inside corner of the V-gutter element. RZ injection is easily feasible with the can or the inverted can. See again Figure 2 above.
The net result is that liquid fuels can be used in any of the stabilization schemes, with appropriate injection, and an appropriate fuel volatility for the expected inlet temperatures. There are good stability parameter definitions for V-gutters and the coaxial dump, but not for sudden dumps. To fly faster than Mach 3, use a sudden dump configuration (the others will not survive in the hot air).
Solid Fuel Propellant Formulations and Flameholding Characteristics
As with liquid fuels, the stoichiometric air/fuel ratio A/Fo is crucial, in order to look at overall engine and local RZ equivalence ratios ER. Vaporization is not an issue, these GG effluents are mixtures of gases and solids. Among the fuel species in the mix, the dominant gas is usually carbon monoxide, and the solid a very fine carbon soot. Such soot is long-chain carbon fragments, not atomic, which is why it is classed as a solid, and why its global reaction rate is far slower than the gaseous monoxide.
Autoignition temperatures on short timescales are a significant issue, but this is more complicated than with liquids, as two different species are involved. The millisecond-scale autoignition temperature of carbon monoxide is in the 1700-1800 F range (compared to only 1200 F on a 1-second scale). The autoignition temperature of carbon soot on a millisecond time scale is much higher, somewhere in the 4000 F range. Air at 1700-1800 F corresponds to about a Mach 4.8 air total temperature in the stratosphere. That’s about Mach 7 at 4000 F for the soot.
More energy is “sopped up” heating the solid soot from the fairly low temperatures out of the GG to something near 4000 F (near 2000 BTU per pound), than in heating liquid fuel from room temperature to its boiling point, even with the phase change latent heat (near 260 BTU per pound). That is why soot is the greater quench risk than any liquid fuel.
Clearly, getting the soot hot enough to ignite with air, and getting it to react at all (at flameholder residence times), are very, very serious problems! These GG effluent fuels are quite unlike the liquid fuels in that behavior. The amount of soot that must be dealt with is a very strong function of the fuel propellant composition, sometimes an even stronger function than stoichiometric air/fuel ratio. That is exactly why the formulation of the fuel propellant is so intimately linked with what flameholder geometries are even feasible.
One empirical measure of the relative effects of carbon monoxide, carbon soot, and combustion products (whether gaseous or solid) in the GG effluent is an utterly-empirical item that I came up with: the so-called “combustibility index” CI. I defined it to be
CI = (all fuels / effluent) (gas fuels / solid fuels) on a mass fraction basis
The weird thing is that almost regardless of the materials from which the fuel propellant is made, the gaseous fuels are nearly always almost completely carbon monoxide, and the solid fuels carbon soot. There are almost never any liquid fuels in a GG effluent.
What I found experimentally with the better injection geometries in the asymmetric twin is that if CI is 0.7 or more, the effluent burns quite well, even at high altitude and low speed (colder air temperature) conditions, even if combustion aid content is low. If CI is above about 0.3, good behavior is available at low altitude / hot air conditions, but not at high altitude / cooler air conditions, unless there is a large combustion aid content. If CI is less than 0.3, behavior is poorer at low altitude / hot air conditions, and ignition is almost unobtainable at high altitude / cooler air conditions, almost regardless of the type or quantity of combustion aid.
Fig. 8 – Typical “Hydrocarbon” Fuel Propellant Formulation Characteristics
Bear in mind that oxidizer levels from 20% to 60% have been experimentally tested, with the best-performing effluents usually falling in the 30-40% range. So, the “pie slice percentages” shown in the figure are rough guides at best. Further, the “oxidizer+explosives” refers to substituting RDX or HMX for AP. That substitution maxes-out in the 5-10% range, and is most often 0% for a fuel propellant.
The figure does indicate the effects of total solids content upon mix viscosity. That is one way of saying how much of the propellant mix needs to be the liquids, mainly the binder system. Mix viscosity determines what kind of casting must be done. Not shown in the figure is the effect of solids upon strength. The higher the solids content, the better the tensile strength. This influence on strength is why there are usually fuel resin particles included in the composition.
The “metallized combustion aids” could be direct metal powder additions, notably magnesium or aluminum, or they could be more complex compositions enclosed in a separate binder, and granulated into a particulate to be included among the other propellant solids. Aid contents from 0 to 20% have been experimentally tested. Note that raw boron powder is an intense cure catalyst for most binder systems, meaning it must be incorporated within a bound aid particulate.
Magnesium is usually added as a simple metal powder, in percentages from 0 to 12%. It reacts directly with AP-derived oxygen, faster than any other species. Aluminum and boron are usually incorporated within a bound particulate with “fluorinated graphite”. The metal reacts exothermically with the fluorine, leaving the graphite behind as part of the effluent soot.
These metal-fluorinated graphite aid mixtures have been used from 0 to about 20% bound particulate aid. It is also possible to bind up boron-titanium powder mixtures as a combustion aid particulate. The boron-titanium alloying reaction is very exothermic, and titanium is far more reactive with air than plain boron, even when alloyed. The more exothermic the reaction, the more effective the combustion aid.
The explosives substituted for AP also can act as a combustion aid. These include RDX and HMX powders as discussed above, but pelletized nitrocellulose has also been used experimentally, and very successfully! Explosive content must be quite limited in order to achieve class 1.3 hazard.
What happens with a “combustion aid” is an increase in gas generator chamber temperature, leading to better expulsion efficiency, better breakdown of the fuel resin into hydrogen and soot, and quite often a higher burn rate. This has little or nothing to do with reactions in the ramjet, except that at higher effluent temperatures, there is usually a better CI. See the article “Solid Rocket Analysis” dated 16 February on this site, for an understanding of how these various phenomena impact the ballistics and the fabrication processing of the fuel rich solid propellant in the gas generator.
Also shown in the figure is a pie chart of typical effluent composition. Higher oxidizer leads to higher combustion product content, and higher monoxide vs lower soot. You can get these effects at slightly-to-somewhat lower oxidizer by using a combustion aid. Higher oxidizer is directly related to higher A/Fo and density and heating value, regardless of the combustion aid content. This is shown in Figure 9. One usually hits a problem with melting instead of decomposing the resin, before one hits a problem with expulsion, as is also shown in the figure. Experimentally, molten resin won’t burn with air.
The ballistic tailoring aids are usually a mix of carbon black and yellow iron oxide, usually at the 1-to-3% level. The carbon black is an opacifying pigment, and also usually lowers somewhat the sensitivity of burn rate to soak temperature. The yellow iron oxide is a burn rate catalyst that acts to increase the potential range of burn rates, that are usually tailored with oxidizer particle size distributions.
Fig. 9 – Typical Practical “Hydrocarbon” Propellant Formulation Limits
Fig. 10 – Typical Hypergolic High-Magnesium Fuel Propellant Formulation Characteristics
The other is an easily-castable composition that found service as a gas generator fuel propellant, and as a very effective combustor igniter propellant for flameholding systems. It has an unusual two-part silicone rubber binder.
Experimental Results for Air Entry Geometries with Hypergolic Magnesium
These burned in all the side-entry sudden dump geometries, at any ER from very lean to very rich, and with any injection geometry. I never attempted a coaxial dump with them, but they would have burned in it, I feel confident.
They could theoretically burn in a V-gutter or a perforated can, but the very high slagging and erosion effects would seriously damage the V-gutter or the can. Such a combination is definitely NOT recommended!
Experimental Results Regarding Air Entry Geometry with Flameholding Solids
All of these burned successfully in the asymmetric twin inlet geometry, but with significant performance impacts of the different injection geometries. Only the high-oxidizer formulations (AP oxidizer above 45%) ever burned in the symmetric twin or 4-inlet dump configurations. None ever burned successfully in the single side inlet configuration.
None of these were ever tried in the coaxial dump configuration. Given the high-oxidizer restrictions seen in the symmetrical side dumps, it seems rather unlikely that the coaxial dump is a good candidate for general use with flameholding GG effluents. The soot centrifuge effect is quite real, and is as missing from the coaxial dump, as it is in the symmetrical side dump configurations.
Some of these effluents were tried with inlet injection in the asymmetric twin, and they did burn. There were serious problems with slag deposition and orifice erosion, however. Compared to the easier-to-implement dome injection schemes, the inlet injection scheme offers more design problems to solve, than any promised improved performance. It’s just not worth it.
None of these GG effluents were ever tried in a V-gutter or can combustor configuration. While the high-oxidizer forms might indeed burn, the slag and erosion problems seen in inlet injection pose similar (if not greater) risks with the V-gutter and can schemes. Most importantly, there is no soot centrifuge effect available in the can, and at low entrainment fractions and a highly-elongated vortex shape, it is likely missing in the V-gutter as well. These would not seem to be promising choices at all for general application with the more desirable lower-oxidizer propellants.
Injection Choices for Flameholding Solids in Asymmetric Twin Entry Geometry
The simple single center port injection geometry is shown in Figure 11 for the asymmetric twin inlet entry. This works, but the fuel entrainment into the RZ is very sensitive to the ratio of GG pressure to engine forward dome static pressure. Higher pressure ratios equate to greater penetration downstream into the air streams. That in turn equates to lower fuel entrainment fractions and a leaner RZ relative to the overall engine.
A somewhat-related injection geometry is the vertical twin shown in Figure 12. The port nearer the inlets is only a little off centerline, so it aids vortex rotation very little, if at all. The port opposite the inlets opposes vortex rotation. The net effect is a little bit of vortex disruption, but not a whole lot of it.
The port nearer the inlets has the better opportunity to penetrate more at higher PGG/P3 ratio, because the exposed path length in the RZ is shorter. The port opposite the inlets penetrates less effectively, because its exposed path length within the RZ is longer.
The net effects would seem to be a bit less effective centrifuging of the soot, and a bit less RZ lean-down capability at high PGG/P3 ratio, compared to the center port. These predicted effects would have to be confirmed with actual test data. This configuration was only tested with the higher-oxidizer fuel propellant formulations. It burned well with them.
The “dual adjacent” injection geometry in Figure 13 was the most successful of the plain injection port geometries that were tried experimentally. All of the flameholding GG effluents were tested in it, with generally good performance, at “typical” PGG/P3 ratios for the ballistics. The penetration is good in spite of the air dam effect, because of the shorter exposed path length. The location of these jets aids vortex rotation, enhancing the soot centrifuge effect. These are all favorable characteristics.
The only fundamental downside is the variation of the fuel entrainment factor with PGG/P3, not in accordance with desires, when operating across a wide flight envelope. A secondary adverse effect is the need for two throttle valves, in a throttled configuration, or else a single valve feeding a branching point to two fuel passages. These are very inconvenient design problems to have.
The “dual opposite” geometry shown in Figure 14 was suggested by some early visualization work, long before the need for the soot centrifuge effect was known. The RZ in those visualizations showed much finer-scale turbulence, and little evidence of an organized vortex that could act as a centrifuge. While the GG effluents did burn in this configuration, there was very definitely a combustion efficiency decrement, even at the same CI and test conditions. At lower CI, experiment showed a definite loud buzzing combustion instability, as well.
Looking at the figure, it is easy to see that the jets strongly oppose vortex rotation, so the performance problems seen in test are easily understandable, once one understands the effects of the soot centrifuge vs its absence. The ports fire not into the air dam, but the leak paths downstream. This offsets the effects of the longer exposed path length, so the penetration in the dual opposite is not all that different from the dual adjacent.
Not shown is the dual centered configuration. The two ports are on combustor centerline. Only a few tests at higher AP content were run in it. Its geometry and its performance factors are intermediate between the dual adjacent and the dual opposite.
It doesn’t strongly oppose or aid the RZ vortex rotation. Actually, it was fairly similar to the vertical twin and the single center port.
There is an injection configuration that essentially eliminates the strong PGG/P3 dependence of the fuel entrainment fraction seen in the dual adjacent and the other simple dome port configurations. This is the “5-port” injector seen in Figure 15. It was invented at UTC-CSD for a fixed-delivery GG for AMRAAM, and later modified by me for integration with a throttle valve.
As indicated in the figure, the injector tube features 5 ports, one oriented axially downstream into the engine, and the other four laterally. Located off-center toward the inlets, the end port penetrates very well far downstream, with a near-zero entrainment fraction for that portion of the fuel flow.
Two of the lateral ports fire into a surrounding cup structure, where they shock down subsonic, fill the cup, and exit into the RZ at very subsonic speed. This fuel is easily entrained into the RZ vortex, almost entirely. The entrainment fraction for this portion of the fuel flow is very nearly 1. But this fuel is added in the middle, not at the “cheekwalls”, so the fuel distribution across the dome would be a problem, if this were all there was.
It is not: the other two ports are outside the shockdown cup, but angled to strike two fences located upon the dome. These flows direct laterally along the fences, where they impinge upon the “cheekwalls” and shock down subsonic. That allows them to entrain into the sides of the RZ at the “cheekwalls”, without any effective penetration downstream. This pattern is confirmed by both flow visualizations, and the burn and erosion patterns seen on the combustor ablative insulation in tests.
The net effect is that PGG/P3 makes no effective difference to the RZ ER, which is then controlled mostly by the selection of end port area percentage out of the total port area. For a fixed-delivery GG design, the pressure inside the injector tube is essentially the generator chamber pressure. The 5 port areas together are the throat area of the GG. Flow speeds inside the injector tube are subsonic. The flow rate out of each port is essentially proportional to its area.
Fig.15 – 5-Port Injection in the Asymmetric Twin
In a throttled system, the most effective throttling technique proved to be a variable area GG throat. This has to be upstream of the injector tube, and downstream of that throttling throat, pressures are lower than the GG pressure, with supersonic flow speeds that must shock down somewhere in the injector tube. These phenomena affect the flow distribution as no longer proportional to port area.
One has to size the injector ports such that their subsonic shocked-down backpressure forces the shockdown ahead of all the ports. Then the inside flow area of the injector tube has to reduce past each pair of lateral ports, so that the reduced flow does not accelerate to fill the available area, thus maintaining the design high-subsonic Mach number value. I worked out exactly how to do this design, and obtained a patent on this modification for Hercules-McGregor. It was well-verified in many tests to work exactly as intended.
Summary of Results
For liquid fuels, one may use any of the side dump inlet configurations, the coaxial dump, the V-gutter, or the can or inverted-can stabilizer. Take care to select fuel identity such that it has adequate volatility at the coldest inlet air temperatures expected in the flight envelope.
Inject fuel into the inlet(s) far enough upstream of the stabilizer to ensure adequate vaporization for ignition, such that there are no remaining liquid droplets by the time the entrained flow turns around upstream in the recirculation zone. This is without flame radiation heating, at ignition.
Minimum inlet flow speed should be above ~100 ft/sec to prevent flashback of flame upstream of the stabilizer. Maximum inlet speed should never exceed Mach 0.9, or else the limit from the empirical stability correlation, whichever is more restrictive.
If flight speeds will exceed about Mach 3 in the stratosphere, one must use one of the side dump configurations, or the coaxial dump configuration. The inlet air will be too hot to serve as the coolant for any of the blockage-element stabilizers.
If flight speeds will be high enough to cause spontaneous autoignition, then either (1) that portion of the inlet must be insulated against full flame temperatures, or (2) one must use all-dome fuel injection (a configuration for which it is very difficult to get fuel distributed downstream).
For the fuel-rich solid propellants in a GG-fed system, there are two fundamentally-different types treated entirely differently. These are the hypergolic fuels (50+% magnesium), and the flameholding “hydrocarbon” fuels. The hypergolic effluents are largely magnesium vapor polluted with combustion products. The flameholding-fuel effluents are largely mixtures of carbon monoxide and carbon soot, polluted with combustion products; combustibility index CI should exceed 0.5 for good results.
Hypergolic magnesium fuel propellants can be used in any of the coaxial or side dump inlet geometries. They are not recommended for use with the blockage-element stabilizers due to slagging and erosion damage to the stabilizer. With hypergolic magnesium, no flame stabilizer is required, only efficient mixing. No RZ vortex or volume is required. Dome injection is highly recommended.
Flameholding “hydrocarbon” fuel propellants should be used only with the asymmetric twin side dump inlet geometry. With severe composition restrictions, the symmetric twin and 4-inlet forms might be used in the larger diameters. Never use the single side dump inlet. The blockage-element stabilizers might work with severe composition restrictions, but are very vulnerable to slagging and erosion damage, so do not use them.
Always use dome injection of the GG effluent. In the asymmetric twin, the two known best injection configurations are the dual adjacent and the 5-port injectors. The dual adjacent is sensitive to PGG/P3 ratio; the 5-port is not, and integrates far better with a throttle valve, so it is recommended generally. If the GG throat is to be subsonic for passive control, use the single center port injection geometry, and make it large: injection Mach number well under 0.5.
Related Documents and Articles, Etc.
2-4-2020 One of Several Ramjets That I Worked On
1-2-2020 On High Speed Aerodynamics and Heat Transfer
1-9-2019 Subsonic Inlet Duct Investigation
1-6-2019 A Look at Nosetips (or Leading Edges)
1-2-2019 Thermal Protection Trends for High Speed Atmospheric Flight
11-12-2018 How Propulsion Nozzles Work
7-4-2017 Heat Protection Is the Key to Hypersonic Flight
6-12-2017 Shock Impingement Heating Is Very Dangerous
12-10-2016 Primer on Ramjets
11-26-2015 Bounding Analysis: Single Stage To Orbit Spaceplane, Vertical Launch
11-17-2015 Why Air Is Hot When You Fly Very Fast
8-16-2014 The Realities of Air Launch to Low Earth Orbit
11-17-2013 Payload Comparisons
11-6-2013 HTO/HL Launch With Ramjet Assist
8-20-2013 Applying Ramjet to Launch Accelerators
3-18-2013 Low Density Ceramic Non-Ablative Ceramic Heat Shields
12-21-2012 Ramjet Cycle Analyses
8-16-2012 Third X-51A Scramjet Test Not Successful
8-22-2010 Two Ramjet Aircraft Booster Studies
7-23-2010 More Strap-On Pod Ramjet Engine Data
7-11-2010 More Ramjet Performance Numbers for the Strap-On Pod
2-28-2010 Preliminary Acceleration Margins for Baseline Pod
2-20-2010 Ramjet Strap-On Pod Point Performance Mapping
2-20-2010 Ramjet Strap-On Pod Concept
2-20-2010 Inlet Data for Ramjet Strap-On Pod
To easily access these articles, use the search tool at left of the site page. Click on the year, then click on the month, then click on the title.
I have noticed recently that there is very high readership of the article “On High Speed Aerodynamics and Heat Transfer”. For really high-speed atmospheric flight, this topic is indeed the key enabling item. If you do not have a heat protection solution, then you do not have a viable high speed flight design, no matter what its propulsion is.
People interested in calculating ramjet performance might look at “Primer on Ramjets” and then “Ramjet Cycle Analyses”. These will acquaint you with what is actually involved. The article “One of Several Ramjets That I Worked On” is primarily about my work long ago exploiting the SA-6, but includes some discussion of the other systems I worked on, which this article expands upon, particularly with respect to flameholding.
The article “Solid Rocket Analysis” dated 16 February 2020 is primarily oriented toward solid propellant rockets, but those same ballistics and propellant “smarts” apply to the fuel-rich solid-propellant gas generator of a GG-fed ramjet. Those tend to be end-burners, excepting the unchoked-throat systems, which tend to be internal burners.
I had submitted my ramjet “how-to” book to AIAA, but after a long time in limbo, they decided they didn’t want to publish it. I am now looking for ways and means to self-publish the book myself. Watch this space for updates on that.