Saturday, April 4, 2020

On the Covid-19 Pandemic

The current pandemic is a disease about which we know little,  for which we have no vaccine,  and for which we have no real treatments.  After this is over,  we will know more,  but for now,  the only thing we can do is to use the same thing we have used for centuries:  quarantining at one level or another,  to slow its spread.  Calling it "social distancing" makes no difference,  it is still a simple quarantine.

Here is what we do know,  as of this writing,  learned the hard way as the epidemic sickens and kills people.  It seems similar to,  but not the same as,  the 1918 "Spanish Flu" pandemic.  We have not seen this dangerous a disease since then.  It is a once-in-a-century event.

Covid-19 seems to be at least as contagious as,  and perhaps more contagious than,  the 1918 flu.  It seems to have a similar death rate (the number who die compared to the number thought to be infected),  which is somewhere around 10 to 20 times higher than ordinary influenzas.  Those are seriously-dangerous characteristics.

There seems to be another unusual characteristic that combines with the other two to make Covid-19 a truly dangerous threat.  It seems to be more generally spread by people showing no symptoms,  than by people who are just getting sick and beginning to run a fever. 

That makes all of us potential "Typhoid Mary" carriers of the disease.  It also makes taking temperature rather useless as a screening tool to determine who might be infected,  and who might not be. Without massively-available testing,  one must presume that all other persons are contagious,  which argues for using stricter levels of quarantine.

So far,  it is thought that the Covid-19 virus is spread within the moisture droplets ejected by sneezing or coughing,  or even by talking.  5 minutes talking spews the same droplet numbers and size distribution as one cough.  A sneeze just spews a lot more.  The Covid-19 virus does not seem to be able to remain airborne outside of those droplets,  the way a chickenpox or measles virus does.

Masks vary in their effectiveness against particle sizes.  It is hard to breathe through a mask that stops particles the size of a large bacterium.  No mask stops a virus particle.  But even a simple cloth bandana will stop most of the moisture droplets from coughing or sneezing,  as does about 6 feet of space (the droplets quickly fall to the floor).  See Figure 1 at end of article.  

What that means is that the new CDC recommendation to wear masks in public is not to prevent the infection of the mask wearer,  but to stop the mask wearer from infecting others.  It would protect the wearer only when someone got right in their face to sneeze,  cough,  or talk at very close range.  The 6 foot distance rule already stops that effect.

The recommendation to wear a mask is actually based on this uncomfortable reality:  that many seemingly-well people are actually infected,  just not showing symptoms,  and are walking around spreading the disease.  This "Typhoid Mary" effect is not common,  but may well be the case with this particular virus.

As already indicated,  a simple bandana will work.  Leave the real surgical masks for the health professionals.  They need them.  We ordinary citizens do not.  When you go to the store,  wear a bandana or a home-made mask.  That's all you need,  to protect others.  The 6 foot rule protects you.

And for Heaven's sake,  quit panic-buying toilet paper and other supplies!  There is plenty being made,  and plenty in the supply chain,  for everybody's needs.  The shelves are bare because so many folks panicked and took far more than their share (their "share" being what they really need).  Shame on you!

Predictions about this pandemic are still guesswork.  The CDC figures show a peak of 100,000 or more deaths in about another month.  Maybe a month or two after that,  it will be more-or-less over,  and we can safely re-open our lives and businesses.  But that's a guess,  and it will likely change.  See Figure 2 at end of article.  

Had we started with the quarantining a month or two sooner than we did,  the death totals would have been lower,  but the time to the end of this gets longer.  Time spent shut down costs all of us money and jobs. 

That is the inevitable tradeoff:  lives versus money. And it is quite the serious effect,  make no bones about that.  Job losses are already beginning to resemble those of the Great Depression of the 1930's.

But almost all of your mothers and churches taught you to value lives over money,  that valuing money over lives was evil!  Think about that,  when you vote.  Not just next time,  but from now on.

 Figure 1 -- Data on Particles Versus Filter Pore Sizes
Figure 2 -- How Quarantining Works,  and What It Does

Update 4-5-2020:                                                                       

The best numbers I have seen on Dr. Fauci’s curves and predictions,  as of end-of-March,  say that with “social distancing” quarantining in place,  US deaths may accumulate to 100,000 to 240,000 people lost.  That death rate trend should peak out somewhere in early May.  Without the quarantining measures,  something like 2 million deaths would be expected.  Maybe more.

Just to “calibrate” the threat of this thing,  the US lost 407,300 soldiers in WW2,  for a 1939 population of 131 million.  That’s 0.31% of the population dead from war

With Covid-19 at a population of 325 million today,  it is 0.03-0.07% of the population dead with quarantining,  and something like about 0.6% of the population dead without quarantining.  You don’t credibly compare this pandemic to yearly traffic deaths or the H1N1 epidemic.  You compare it to the casualties of a major world war.

Based on the numbers published in the newspaper,  the US death rate appears to be near 2% of known cases of infection.  For Dr. Fauci’s predicted death accumulation numbers,  that corresponds to something like 5 to 12 million accumulated known infections.  That’s about 1.5-3.7% of the US population infected,  and 0.03-0.07% of the population dying of it.  These numbers are clouded by uncertainty,  because without widespread testing,  we cannot know the real number of infections.

Using the rough-estimate 2 million deaths for no quarantining,  and the same 2% death rate of those infected,  the accumulated infections would be about 100 million,  which is 31% of the US population.  Quarantining is thus very,  very important,  by about a factor of 10 on the total infections,  and on total deaths.  So,  those who deny or ridicule the risk are dead wrong,  if you will forgive my choice of words.

According to Wikipedia,  the 1918 Spanish flu killed something like 1-6% of the world population.  The same article gives these statistics for the US:  about 28% of the population became infected,  and about 1.7% of those infected died of it. 

The death rate among those infected is quite comparable between Covid-19 and the 1918 flu.  The number of expected Covid-19 infections is lower,  probably because of our quarantining efforts,  despite our delay getting started.  The estimate of infections without quarantining is actually quite comparable to 1918. 

The Covid-19 pandemic really is an event comparable to the 1918 flu pandemic.  We have not seen such a thing in 102 years.

This is quite serious,  so I reiterate the recommendations I gave above:

#1. Stay away from crowds and gatherings,  and when you must go out,  stay at least 6 feet apart (which is what protects you from infection,  not any mask you might wear).

#2. If you must go out where 6 feet apart is not feasible,  wear a bandana or home-made mask to protect others in case you are unknowingly contagious (save the real masks for the health care folks who need them).

               Corollary:  if you are sick in any way,  DO NOT GO OUT.

#3. Stop panic-buying and hoarding supplies,  there is no need for that.


#4. Watch what your public leaders do (not what they say) to judge whether they values lives over money,  or not.  Then stop re-electing those with the wrong priorities. 

Wednesday, April 1, 2020

Entry Heating Estimates


The following discussions define the various heating and cooling notions for entry stagnation heating,  in terms of very simple models that are known to be well inside the ballpark.  How to achieve the energy conservation balance among them is also addressed.  This is more of an “understand how it works” article than it is a “how to actually go and do” article.

Convective Stagnation Heating

The stagnation point heating model is proportional to density/nose radius to the 0.5 power,  and proportional to velocity to the 3.0 power.  The equation used here is H. Julian Allen’s simplest empirical model from the early 1950’s,  converted to metric units.  It is:

qconv, W/sq.cm = 1.75 E-08 (rho/rn)^0.5 (1000*V)^3.0,  where rho is kg/cu.m,  rn is m,  and V is km/s

The 1000 factor converts velocity to m/s.  This is a very crude model,  better correlations are available for various shapes and situations.  However,  this is very simple and easy to use,  and it has been "well inside the ballpark" since about 1953.  This is where you start.  See Figure 1. 


 Figure 1 – Old,  Simple Model for Entry Stagnation Convection Heating

Plasma Radiation Stagnation Heating

There are all sorts of correlations for various shapes and situations.  However,  to get started,  you just need a ballpark number.  That comes from the widely-published notions that (1) radiational heating varies with the 6th power of velocity,  and (2) radiation dominates over convection heating at entry speeds above 10 km/s.  What that means is you can use a very simple radiational heating model,  and "calibrate" it with your convection model:

qrad,  W/sq.cm = C (1000*V)^6,  where V is input as km/s 

The 1000 factor converts speed to m/s.  The resulting units of the constant C are W-s^6/sq.cm-m^6.  You have to "calibrate" this by evaluating C with your convective heating result at 10 km/s,  and a "typical" entry altitude density value,  for a given nose radius for your shape:

find qconv per above at V = 10 km/s with "typical" rho and rn,  then

C, W-s^6/sq.cm-m^6 = (qconv at 10 km/s)(10^-24)

This should get you into the ballpark with both convective and radiation heating.  Figure both and then sum them for the total stagnation heating.  Below 10 km/s speeds,  the radiation term will be essentially zero.  Above 10 km/s it should very quickly overwhelm the convective heating term. 

As an example,  I had data for an Apollo capsule returning from low Earth orbit.   I chose to evaluate the peak stagnation heating point,  which occurred about 56 km altitude,  and about 6.637 km/s velocity.   See Figure 2.  Dividing that convective heating value of 55.72 W/sq.cm by the velocity cubed,  and then multiplying by 10 km/s cubed,  I was able to estimate stagnation convective heating at 10 km/s and 56 km altitude as 190.59 W/sq.cm. 

Dividing that value by 10 km/s to the 6th power gave me a C value of 1.90588 x 10-4to use directly with velocities measured in km/s,  for estimating radiation heating from the plasma layer adjacent to the surface.  The resulting trends of convective,  radiation,  and total stagnation heating versus velocity (at 56 km) are shown in Figure 3.

 Figure 2 – Relevant Peak Convective Stagnation Heating Data for Apollo From LEO

 Figure 3 – Estimated Apollo Stagnation Heating Trends Versus Velocity at 56 km Altitude

Radiational Cooling

This is a form of Boltzmann's Law.  The power you can radiate away varies as the 4th power of the surface temperature,  but gets modified for an effective temperature of the surroundings receiving that radiation (because that gets radiated back,  and emissivity is equal to absorptivity):

qrerad,  BTU/hr-ft^2 = e sig (T^4 – TE^4) for T’s in deg R and sig = 0.1714 x 10-8 BTU/hr-ft^2-R^4

For this equation,  T is the material temperature,  TE is the Earthly environment temperature (near 540 R = 300 K),  e is the spectrally-averaged emissivity (a number between 0 and 1),  and sig is Boltzmann’s constant for these customary US units.  

This radiation model presumes transparency of the medium between the radiating object and the surroundings.  That assumption fails rapidly above 10 km/s speeds,  as the radiating plasma in the boundary layer about the vehicle becomes more and more opaque to those wavelengths

Therefore,  do not attempt radiationally-cooled refractory heat protection designs for entry speeds exceeding about 10 km/s.  They won't work well (or at all) in practice.  Ablative protection becomes pretty much your only feasible and practical choice.

Heat Conduction Into The Interior

This is a cooling mechanism for the exposed surface,  and a heating mechanism for the interior structure.  In effect,  you are conducting heat from the high surface temperature through multiple layers of varying thermal conductivity and thickness,  to the interior at some suitable "sink" temperature. 

The amount of heat flow conducted inward in steady state depends upon the temperature difference and the effective thermal resistance of the conduction path.  The electrical analog is quite close,  with current analogous to heat flow rate per unit area,  voltage drop analogous to temperature difference,  and resistance analogous to thermal resistance. 

In the electrical analogy to 2-D heat transfer,  conductance which is the inverse of resistance is analogous to a thermal conductance which is a thermal conductivity divided by a thickness

Resistances in series sum to an overall effective resistance,  so the effective thermal resistance is the sum of several inverted thermal conductances,  one for each layer. Each resistance sees the same current,  analogous to each thermal resistance layer seeing the same thermal flux,  at least in the 2-D planar geometry.

Like voltage/effective resistance = current,  heat flow per unit area (heat flux) is temperature drop divided by effective overall thermal resistance.  (The geometry effect gets a bit more complicated than just thickness in cylindrical geometries.)  In 2-D:

qcond = (Tsurf - Tsink)/effective overall thermal resistance

For this the effective overall thermal resistance is the sum of the individual layer resistances,  each in turn inverted from its thermal conductance form k/t:

eff. th. resistance (2-D planar) = sum by layers of layer thickness/layer thermal conductivity

Using the electrical analogy, the current (heat flux) is the voltage pressure (temperature difference) divided by the net effective resistance (thermal resistance).  The voltage drop (temperature drop) across any one resistive element (layer) is that element's resistance (layer thermal resistance) multiplied by the current (heat flux).  See Figure 4.

 Figure 4 – Modeling the Thermal Resistances of Multiple Layers for Conduction

What that says is that for a given layering with different thicknesses and thermal conductivities,  there will be a calculable heat flux for a given overall temperature difference. Each layer has its own temperature drop once the heat flux is known,  and the sum of these temperature drops for all layers is the overall temperature drop. 

Any layer with a high thermal resistance will have a high temperature drop,  and vice versa. High thermal resistance correlates with high thickness,  and with low thermal conductivity.  A high temperature drop over a short thickness (a high thermal gradient) requires a very low thermal conductivity indeed,  essentially about like air itself.

On the other hand,  any high-density material (like the monolithic ceramics) will have high thermal conductivity,  and thus the thermal gradients it can support are inherently very modest.  Such parts trend toward isothermal behavior.  Their high meltpoint does you little practical good,  if there is no way to hang onto the "cool" end of the part.  In point of fact,  there may not be much of a “cool” end.

Active Liquid Cooling

In effect,  this is little different than the all-solid heat conduction into a fixed-temperature heat sink,  as described just above.  The heat sink temperature becomes the allowable coolant fluid temperature,  and the last “layer” is the thermal boundary layer between the solid wall and the bulk coolant fluid.  The thermal conductance of this thermal boundary layer is just its “film coefficient” (or “heat transfer coefficient”).  The simple inverse of this film coefficient is the thermal resistance of that boundary layer.  See Figure 5.

 Figure 5 – Modifying the Thermal Conduction Model for Active Liquid Cooling

The main thing to worry about here is the total mass of coolant mcoolant recirculated,  versus the time integral (for the complete entry event) of the heating load conducted into it.  That heat is going to raise the temperature of the coolant mass  and indirectly the pressure at which it must operate.  That last is to prevent boiling of the coolant. 

∫ qcond dt = mcoolant Cv (Tfinal – Tinitial)  where Tfinal is the max allowable Tsink

Balancing the Heat Flows: Energy Conservation

A patch of heat shielding area sees convective heating from air friction,  and may see significant radiation heating if the entry speed is high enough.  That same patch can conduct into the interior,  and it can radiate to the environment,  if the adjacent stream isn't opaque to that radiation.  If the heat shield is an ablative,  some of the heating rate can go into the latent heat of ablation.  See Figure 6.

 Figure 6 – The Energy Conservation Balance

The correlations for convective and radiation stagnation heating given above depend upon vehicle speed,  not plasma temperature.  The equation for conduction into the interior depends upon the surface and interior temperatures.  Re-radiation to the environment depends upon the surface and environmental temperatures.  Of these,  both the environmental and heat sink temperatures are known fixed quantities.

If the heat shield is ablative,  then the surface temperature is fixed at the temperature at which the material ablates;  otherwise,  surface temperature is free to "float" for refractory materials that cool by radiation. 

The way to achieve energy conservation for refractories is to adjust the surface temperature until qconv + qrad - qcond - qrerad = 0.  For ablatives,  the surface temperature is set,  and you just solve for the rate of material ablation (and the recession rate):  qabl = qconv + qrad - qcond - qrerad.

The heating flux rate qabl that goes into ablation,  divided by the latent heat of ablation Labl times virgin density ρ, can give you an estimate of the ablation surface recession rate  r (you will want to convert to more convenient units):

(qabl BTU/ft^2-s)/(Labl BTU/lbm)(ρ lbm/ft^3) =  ft^3/ft^2-s = r, ft/s

(qabl W/m^2)/(Labl W-s/kg)(ρ kg/m^3) = m^3/m^2-s =  r, m/s

Other Locations

Those require the use of empirical correlations or actual test data to get accurate answers.  However,  to just get in the ballpark,  any guess is better than no guess at all!  For lateral windward-side heating,  try about half the heat flux as exists at the stagnation point.  For lee-side heating in the separated wake,  try about 10-20% of the stagnation heating. 

Clarifying Remarks

Bear in mind that these equations are for steady-state (thermal equilibrium) exposure.  The conduction into the interior is the slowest to respond to changes.  Transient behavior takes a finite-difference solution to analyze.  There is no way around that situation. 

But if that conduction effect is small compared to the applied heating terms because there is lots of re-radiation or there is lots of ablation to balance them,  you can then approximate things by deleting the conduction-inward term.  You simply cannot do that if there is no ablation or re-radiation.  And your conduction effect will not be small compared to the heating,  if you are doing active liquid cooling.

If you are entering from Earth orbit at speeds no more than 8 km/s,  you can reasonably ignore the plasma radiation stagnation heating term.   On the other hand,  for entry speeds above 8 km/s,  your re-radiation cooling term will rapidly zero as the plasma layer goes opaque to thermal radiation.  Its transmissibility must necessarily zero,  in order for its effective emissivity to become large.  The zero transmissibility is what zeroes the re-radiation term.

If you choose to do a transient finite-difference thermal analysis,  what you will find in the way of temperature distributions within the material layers has little to do with steady-state linear temperature gradients.  Instead,  there will be a “humped” temperature distribution that moves slowly like a wave through the material layers.  This is called a “thermal wave”.  It forms because heat is being dumped into the material faster than it can percolate through by conduction.  See Figure 7.  


Figure 7 – The Thermal Wave Is a Transient Effect

This humped wave of temperature will decrease in height and spread-out through the thickness,  as it moves through the material.  But,  usually its peak (even at the backside of the heat shield) is in excess of the steady-state backside temperature estimates.  It may take longer to reach the backside than the entire entry event duration,  but it will certainly tend to overheat any bondlines or substrate materials.

Material properties such as thermal conductivity are actually functions of material temperature.  These are usually input as tables of property versus temperature,  into the finite-difference thermal analyses.   Every material will have its own characteristics and property behavior.  I did not include much material data in this article,  in the way of typical data,  for you to use.  As I said at the beginning,  this article is more about “understanding” than it is “how-to”. 

The local heating away from the stagnation point is lower.  There are many correlations for the various shapes to define this variation,  but for purposes of finding out what “ballpark you are playing in”,  you can simply guess that windward lateral surfaces that see slipstream scrubbing action will be subject to crudely half the stagnation heating rate.  Lateral leeward surfaces that face a separated wake see no slipstream scrubbing action.  Again,  there are lots of different correlations for the various situations,  but something between about a tenth to a fifth of stagnation heating would be “in the ballpark”. 

Low density ceramics (like shuttle tile and the fabric-reinforced stuff I made long ago) are made of mineral flakes and fibers separated by considerable void space around and between them.  The void space is how minerals with a high specific gravity can be made into bulk parts with a low specific gravity:

sgmineral * solid volume fraction = sgmineral *(1 – void volume fraction) = bulk effective sg

The low effective density confers a low thermal conductivity because the conduction paths are torturous,  and of limited cross-section from particle to particle,  through the material.   Such thermal conductivity will be a lot closer to a mineral wool or even just sea level air,  than to a firebrick material. 

This low effective density also reduces the material strength,  which must resist the wind pressures and shearing forces during entry.  A material of porosity sufficient to insulate like “mineral wool-to-air” will thus be no stronger than a styrofoam. 

So,  typically,  these low density ceramic materials are weak.  And they are very brittle.  The brittleness does not respond well to stress- or thermal expansion-induced deflections in the substrate,  precisely because brittle materials have little strain capability.  That fatal mismatch has to be made up in how the material is attached to the substrate.  If bonded,  considerable flexibility is required of the adhesive.

Related Thermal/Structural Articles On This Site

Not all of these relate directly to entry heat transfer.  The most relevant items on the list are probably the high speed aerodynamics and heat transfer article,  and the article taking a look at nosetips and leading edges. 

The “trick” with Earth orbit entry using refractories instead of ablatives is to maximize bluntness in order to be able to use low density ceramics at the stagnation zone without overheating them.  That leaves you dead-broadside to the slipstream,  and thus inevitably ripping off your wings,  unless you do something way “outside the box”. 

The pivot wing spaceplane concept article is a typical “outside the box” study restricted to 8 km/s or less.  The older folding wing spaceplane article is similar.  In both studies,  the wings are relocated out of the slipstream during entry,  which is conducted dead broadside to the oncoming flow. 

The reinforced low density ceramic material that I made long ago is described to some extent in the article near the bottom of the list (about low density non-ablative ceramic heat shields).  It is like the original shuttle tile material that inspired it,  but is instead a heavily reinforced composite analogous to fiberglass.  This information was also presented as a paper at the 2013 Mars Society convention.

The fastest way to access any of these is to use the search tool left side of this page.  Click on the year,  then on the month,  then on the title.  It is really easy to copy this list to a txt or docx file,  and print it.

1-2-20…On High Speed Aerodynamics and Heat Transfer  
4-3-19…Pivot Wing Spaceplane Concept Feasibility            
1-9-19…Subsonic Inlet Duct Investigation                        
1-6-19…A Look At Nosetips (Or Leading Edges)                
1-2-19…Thermal Protection Trends for High Speed Atmospheric Flight  
7-4-17…Heat Protection Is the Key to Hypersonic Flight     
6-12-17…Shock Impingement Heating Is Very Dangerous     
11-17-15…Why Air Is Hot When You Fly Fast                         
6-13-15…Commentary on Composite-Metal Joints                 
10-6-13…Building Conformal Propellant Tanks,  Etc.             
8-4-13…Entry Issues                                                         
3-18-13…Low-Density Non-Ablative Ceramic Heat Shields   
3-2-13…A Unique Folding-Wing Spaceplane Concept        
1-21-13…BOE Entry Analysis of Apollo Returning From the Moon  
1-21-13…BOE Entry Model User’s Guide                            
7-14-12…Back of the Envelope Entry Model                       


There are also several studies for reusable Mars landers that I did not put in the list.  They are similar to the two spaceplane studies,  but entry from Mars orbit is much easier than entry from Earth orbit.  Simple capsule shapes work fine without stagnation zone overheat for low density ceramics,  even for the large ballistic coefficients inherent with large vehicles.

Final Notes

I’ve been retired for some years now,  and I have been retired out of aerospace work much longer than that.   I’ve recently been helping a friend with his auto repair business,  but that won’t last forever. 

Not surprisingly,  I am not so familiar with all the latest and greatest heat shield materials,  or any of the fancy computer codes,  and I have little beyond these paper-and-pencil-type estimating techniques to offer (which is exactly “how we did it” when I first entered the workforce long ago).   Yet these simple methods are precisely what is needed to decide upon what to expend the effort of running computer codes!  Today’s fresh-from-school graduates do not know these older methods.  But I do.

Sustained high speed atmospheric flight is quite distinct from atmospheric entry from orbit (or faster),  but if you looked at that high speed aerodynamics and heat transfer article cited in the list,  then you already know that I can help in that area as well.

Regardless,  it should be clear that I do know what to worry about as regards entry heat protection,  and how to get into the ballpark (or not) with a given design concept or approach in either area (transient entry or sustained hypersonic atmospheric flight)!  I can help you more quickly screen out the ideas that won’t work,  from those that might. 

And if you look around on this site,  you will find out that I also know enough to consult in ramjet and solid rocket propulsion,  among many other things.  I’m pretty knowledgeable at alternative fuels in piston and turbine engines,  too.

If I can help you,  please do contact me.   I do consult in these things,  and more.  

More?  More:  I also build and sell cactus eradication farm implements that really work easier,  better,  and cheaper than anything else known.  I turned an accidental discovery into a very practical family of implements.  It’s all “school of hard knocks” stuff.

Thursday, March 19, 2020

Whoa! Calm Down!

Update 4-5-2020:

This one is pretty much superseded by "On the Covid-19 Pandemic" dated 4-4-2020.

Update 3-24-2020:

The production of foodstuffs,  paper goods,  and other products is just as high now as it was before the COVID-19 scare began.  There was plenty to go around,  and still should be.  Panic buying strips the shelves bare because those who panicked acquire way more than they did before.

THAT is why there is seemingly not enough to go around now:  those who panicked took far more than their fare share.  SHAME ON YOU!

As for masks,  what the following article shows is that wearing a mask will NOT keep you well.  What it shows is that masks keeps sick people from infecting those around them.  In a hospital setting,  it therefore makes far more sense to put the masks on the sick people in the beds.  That would greatly lower the airborne virus-bearing particles in the air in those rooms where they are.

That conclusion goes against what people have been taught and trained to do,  but you cannot argue with science and math.  For well people to wear filter masks is only a psychological "sky hook" to make them feel better.  Do it if you like,  but you should know that it is scientifically pointless (you could not breathe through a mask that would actually stop a virus particle).  Simple as that.

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Update 3-29-20:

When faced with an epidemic of an infectious disease for which there is no cure,  no preventative,  and little in the way of known effective treatment,  the only possible method of the coping is the same method of quarantining at one or another level that we have used for centuries.  THAT is what "social distancing" and "shelter-at-home" are all about.

Op-Ed Page Cartoon from Waco "Trib" for Sunday 3-29-20

Those same centuries' experiences clearly indicate that this method works far better if you recognize the problem early and get started early with the quarantining.  Delay,  and more folks die.  A lot more.  We've known for sure this was coming since late December.  We did nothing until mid-March.

It becomes a rock-and-a-hard-place choice:  quarantine and wreck the economy,  or don't quarantine and kill a lot of people.  And don't end the quarantine too soon,  or the epidemic comes roaring back. Centuries of experience say so.  The lies from some politicians do not change those facts.

Your mothers and your churches all told you to value lives above money,  that not to do so is evil!  Yet we have politicians in office who clearly value money above lives.  Don't listen to their excuses,  look at what they do,  or advocate doing.  Then judge for yourself:  do they advocate evil or not?

You do not need politicians who would do such evil,  making decisions that control your lives.  Those clearly do not care whether you live or die.  Stop re-electing them!  You don't need an amendment to have term limits.  You have your vote.

Now,  get on with the quarantine,  and quit panic-buying and hoarding supplies!

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Original start of posting:  

The American response to COVID-19 has been somewhat irrational,  once the delays and denials ended.  There has been a rash of panic-buying of supplies that has emptied store shelves.  Here's my take on that.

*****************************

The widespread panic-buying of supplies is nonsense.  Here's why,  starting with stripping store shelves of paper goods:

Filters are a way to remove particles from a gas or liquid stream.  The pore size of the filter determines the sizes of the particles removed. 

Particles smaller than the pore size go right through,  while larger ones get hung up in the filter material.  This is just common sense physics.  No point in denying it. 

Paper inherently has pore sizes,  which is why it is used for the various filter grades,  including coffee filters.  These pore sizes range from 2 microns to 25 microns.  A micron is one millionth of a meter,  or 0.001 mm,  which is just about 0.00004 inches.

The so-called N-95 surgical mask,  which is difficult to breathe through,  is close to the 2 micron pore size.  Most toilet and tissue paper,  coffee filter,  and kitchen paper towel materials would be closer to the 25 micron pore size. Automotive air,  oil,  and fuel filter elements fall in between.

I got this data from Wikipedia on 3-18-2020,  specifically from the article titled "Filter Paper".

A sneeze generates up to 40,000 droplets varying from 0.5 to 12 micron diameter.  A cough (or talking for 5 minutes) generates about 3000 of the same kind of droplets.  Most of the droplets tend toward the large end of the size distribution (nearer 10 micron than 1). 

So, any paper filter whatsoever will stop most, but not every, droplet from sneezes,  coughs,  and talking. This keeps confined the droplets from the person wearing the mask. It keeps those droplets from reaching those around the mask wearer.

It does very little to keep the droplets from other people off of the mask wearer,  unless those others are very close indeed.  In other words,  surgeons wear masks not to keep themselves well,  but to keep from getting their patients sick with anything they themselves might have!

I got this information off the internet 3-18-2020 at: https://www.ncbi.nlm.nih.gov/books/NBK143281/,  for which the book title is: Natural Ventilation for Infection Control in Health-Care Settings,  and the specific section in the book is: Annex C Respiratory Droplets.

So what dangerous things could be in those droplets,  or floating around in the air,  or on surfaces other people have touched?  Bacteria and viruses come to mind. Not much else.

The typical bacteria sizes range 0.5 to 5 micron,  with the very smallest about 0.3 micron.  I got this information from the Wikipedia article "Bacteria",  as of 3-18-2020.  Many of these will go through even the highest-quality paper filter,  including the N-95 surgical masks.  All of them will definitely go right through toilet paper,  or a kitchen paper towel!

Viruses typically range from 0.02 to at most 0.4 micron in size.  Most definitely all of these go right through even the highest-quality paper filter.  I got this information off the internet 3-18-2020 from:  https://www.britannica.com/science/virus/Size-and-shape.

So,  given that situation,  what is the point of well persons wearing masks to protect themselves from viruses,  when those masks absolutely cannot protect them from viruses? 

And what is the point of raiding stores for toilet paper and paper towels to make improvised masks,  when they absolutely cannot protect you from viruses? 

People seem to be doing that,  on the basis of Facebook posts and YouTube videos.  Those are claiming you can protect yourself that way,  when it is simply not true. 

Why are they lying to you?  For profit. 

The business model for those media has nothing to do with truth.  They get paid when you click on their stuff,  whether true or false.  They get paid more when they feed you more and more of the same kind of stuff you already clicked on.

There are no enforcers-of-truth out there,  because there are no rules governing the truth of anything posted. You have a better chance of getting the truth from mainstream media whose reporters are trained to journalistic standards,  and who interview the real scientists and doctors.

We all need to stay away from crowds,  and wash our hands thoroughly and frequently.  (Plain soap and water is at least as effective as any hand sanitizer,  if not more effective.)  We do not need to panic-buy and hoard supplies,  based on internet and social media lies-for-profit. This thing will pass.

But here's something else to think about.  If your favorite internet and social media sources have been lying to you about coronavirus COVID-19,  what else have they been lying to you about?

Tuesday, March 3, 2020

Ramjet Flameholding

Genesis of this article lies in some of the discussions in “One of Several Ramjets That I Worked On”,  dated 4 February 2020,  on this site.  This topic of flameholding is far bigger than most folks suspect. 

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.

 Fig. 1 – Hypergolic vs Non-Hypergolic Ignition

The Known Flame Stabilizer Geometries

The known,  well-proven,  stabilizer geometries for ramjets are depicted in Figure 2.  

 Fig. 2 – The Known Flame Stabilizer Geometries

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 ramjetssolid-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.

 Fig. 3 – Fundamentals of Liquid Systems vs Solid Gas Generator Systems

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

               Coaxial Dump

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 rangeThe 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.  

 Fig. 4 – One 4-Inlet Air Entry Flow Field With and Without Flamehold Capability

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.

 Fig. 5 – Two-Inlet Side Dump Asymmetrical and Symmetrical Flow Fields

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.

 Fig. 6 – Related Side Dump Flow Fields

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 limitSo,  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. 

There are a lot of very important characteristics of the fuel propellant that depend critically on its composition,  beyond just those important to flameholding.  Some hint of that is shown in Figure 8

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

Just for completeness,  two typical hypergolic high-magnesium propellant compositions are given in Figure 10.  One is a pressed composition found in the old SA-6 SAM gas generator. 

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. 

Trying to penetrate directly through the entering air is difficult:  these air streams are almost a dam,  unless the fuel jet is very forceful (high PGG/P3).  The effect of this jet on the strength and organization of the RZ vortex is not so very high.  Being on the centerline,  it neither aids nor opposes vortex rotation.  This is the geometry that works well experimentally with a subsonic GG throat for passive flow rate control.  Use injection port Mach < 0.5,  and propellant burn rate exponent n ~ 1.

 Fig. 11 – Center Injection in the Asymmetric Twin

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.

 Fig. 12 – Vertical Twin Injection in the Asymmetric Twin

 Fig. 13 – Dual Adjacent Injection in the Asymmetric Twin

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.  

 Fig. 14 – Dual Opposite Injection in the Asymmetric Twin

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 systemthere 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.

Date                   Title
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.