Ground Testing Ramjets

This is an expanded version of a posting I made over on LinkedIn 20 November 2022. There is a wordcount limit there,  that I do not have here.

A ramjet comprises air inlets,  a combustor chamber,  a nozzle,  and a fuel supply.  Historically,  these have pushed missiles.  They scoop up air by the ram effect in high-speed flight,  which both raises its pressure,  and raises its temperature. 

There are basically three ways to test such a device on the ground.  The first is the “freejet test”,  which is basically a high-speed wind tunnel with heated air,  in which the entire missile is placed.  This tests for the inlet performance including vehicle attitude effects,  the sized inlet/nozzle balance,  and the efficiency and performance of the combustor.  What is important besides simple supersonic airspeed is the right wind tunnel air temperature so that the air total temperature as captured within the inlet is at the correct value,  same as it would have been in flight at that speed.  A very large quantity of supersonic air must be sent through the wind tunnel,  compared to the quantity of air that the inlets actually capture.  This is the most expensive mode of ground testing.

The second is the “semi-freejet test”,  which is also basically a high-speed wind tunnel test,  in which only the inlets are submerged within the heated supersonic airstreams.  Only the propulsion system (inlets,  combustor,  and nozzle) need be tested.  This tests for the inlet performance excluding vehicle attitude effects,  the sized inlet/nozzle balance,  and the efficiency and performance of the combustor.   The total wind tunnel airstream quantity is large compared to that captured by the inlets,  and it must produce the right total temperature as captured within those inlets.  But the total supersonic air quantity is far less than that of the freejet test.  This is still quite expensive,  but it costs a lot less than a freejet test.

The third is the “direct-connect” (or “connected-pipe”) test,  in which a heated air supply delivers the flight quantity of air,  at the flight total temperature,  to only the subsonic portion of the flight inlets.  This does not test for inlet capture and recovery performance or the vehicle attitude effects upon them,  and it does not test for the sized balance of inlet and nozzle.  It only tests for the efficiency and performance of the combustor,  under the presumption that inlet performance (with vehicle attitude effects) is already known separately.  The quantity of air is only that which would have been captured by the inlets,  at the flight total temperature,  and it is delivered to the inlets contained in piping flowing subsonically,  not as a free supersonic jet.  This is the most economical way to test for combustor efficiency and performance.  The relative effects of fuels,  insulations,  injection schemes,  and materials of construction can also be tested most cost-effectively this way,  as this is the least-expensive test mode,  by far.

---------------------------  only this far on linkedin,  due to wordcount limit

Heating the Air

There are two ways to heat the air that is delivered to the test article in direct-connect testing:  “vitiation” and pebble-bed heaters.  In vitiation,  the airstream gets a gas fuel added to it,  and combusted,  then makeup oxygen gets added back to the stream.  The inert gas in this “vitiated air” stream includes the vitiation combustion products,  not just the nitrogen and argon and trace gases that are in real air.  This requires precise real-time computer control,  to achieve the airflow quantity and total temperature simultaneously,  and still hold the oxygen content to exactly that of air.  That type of control is not cheap.  For some fuels containing reactive metals,  it is not chemically correct:  the carbon dioxide and water vaper combustion products are additional sources of oxygen,  besides the basic oxygen content.  That can lead to massively-erroneous test results,  especially if magnesium is involved!

The pebble bed heater is a large and massive pre-heated bed of particles through which the airstream is percolated,  to heat it up to essentially the pebble bed preheat temperature.  The result is chemically correct air at the pre-heated bed temperature.  This does not require any precise computer control at all,  and so is much,  much less expensive than vitiation,  and it can be used reliably with metallized fuels. 

The airflow can be fed through two lines,  each with its own pebble bed heater at two different pre-heat temperatures,  and then combined into a single mixed stream fed to the test combustor’s inlets.  In this way,  by controlling the two airflows,  a variable mixed temperature can be delivered to the test article,  as well as a variable airflow rate.  This only requires the pre-programming of simple linear controls on the metering venturi pressures,  and can even be done manually,  if exacting precision is not required in the delivered airflow and total temperature.

Pebble bed heaters are usually best done as metal balls pre-heated electrically,  but those will have more severe max temperature limitations than vitiation.  Higher temperatures closer to vitiation capabilities are possible with combustion-gas preheat of the pebble bed,  using rock or ceramic pebbles,  but this risks a dusting problem that can cause erosion of structures downstream.

These testing modes are simply not appropriate for scramjet articles at speeds above about Mach 5 or 6,  as the air heating methods are simply incapable of supplying the necessary extreme temperatures.  The usual limitations correspond with speeds nearer Mach 3 to 4.

Altitude Simulation

There is the issue of open-air nozzle testing versus high altitude simulation.  If the ambient atmospheric pressure is too high,  it will cause shock-separation of the flow in the supersonic portion of the nozzle,  and perhaps even unchoking of its throat.  Using a sonic-only test nozzle profile avoids shock separation at the cost of incorrect nozzle thrust,  but cannot stop unchoke,  if the backpressure is high enough.  Open-air nozzle testing does allow very informative photography. 

For the freejet and semi-freejet test modes,  if the test cabin is sealed,  it is possible to operate the system at a low-enough test cabin pressure so as to maintain the choke or even the full-flowing nozzle of a test article at high-altitude conditions.  The exact pressure corresponding to desired alrtitude is not necessary,  only one such that a choked and full-flowing nozzle is maintained.  Not all such facilities can do this.  If the test cabin is vented to the atmosphere,  then only lower altitude conditions may be tested that correspond to a choked,  full-flowing nozzle.

Direct-connect testing is different.  If the ambient backpressure precludes a choked and full-flowing test nozzle,  then a supersonic diffuser can be installed,  along with an ejector.  This precludes tailpipe flame and plume photography,  but it does allow high-altitude testing in terms of airflow rates and achieved engine pressures.  The diffuser can be sealed to the test article with a rolling diaphragm seal.  Again,  exact backpressure at the nozzle is not required,  only a pressure such that a choked and full-flowing nozzle is maintained.  The diffuser has a supersonic compression convergence,  followed by a friction decelerator at constant area down close to Mach 1,  but not actually subsonic.  This is followed by a divergence in which subsonic shockdown occurs,  followed by a significant degree of subsonic diffusion. 

The subsonic stream at the diffuser outlet will likely not be diffused all the way back up to ambient atmospheric pressure,  so this is coupled to an ejector pump that raises the pressure the rest of the way.  The working fluid for this ejector could be steam from a boiler,  or it could be air from the blowdown air supply that feeds the test article,  since test article air flows are much lower at high altitude,  than they are nearer sea level.   

Performance Determination

Combustor efficiency can be calculated from post-combustion static pressures just before the nozzle entrance (termed station 4),  or from measured thrust calibrated for tare forces,  or both.  Note that both require a choked and full-flowing nozzle,  which is why the backpressure unchoke is to be avoided at all costs.  There is no such thing as a tare pressure,  so if the sources of data disagree on the efficiency,  trust the data derived from static pressure;  you simply do not have your facility tare forces properly calibrated.

For pressure-based performance,  your nozzle entrance contraction ratio and expected combustion gas specific heat ratio provide the ratio of chamber combusted stagnation pressure P_t4 to the measured combusted static pressure P₄.  You need to know very precisely the flowrates of air w_a and fuel w_f and any ablated liner massflow w_abl.  Their sum is the total massflow at station 4 w₄.  You will also need the value of the discharge coefficient C_D at the ramjet throat (station 5),  something determined separately by flow calibration testing.  But for good nozzle designs,  it is never very far from 0.98.

The choked massflow equation determines combusted characteristic velocity c*₄ = P_t4 C_D A₅ g_c/w₄,  where g_c is the gravity constant that makes the units consistent.  The fuel to air ratio,  the inlet total temperature T_t2,  and theoretical thermochemical calculations done at the measured P₄ will produce a theoretical combusted characteristic velocity c*^o₄.  Their ratio is the stream thrust combustion efficiency η_cSA = c*₄/c*^o₄.

For thrust-based performance,  you will need the same estimates of P_t4,  A₅,  and specific heat ratio as were used in the pressure-based analysis,  the tare-corrected thrust measurement also corrected for any supersonic diffuser forces (thus being the actual nozzle thrust F_noz),  the exit area A₆,  the half-angle of that exit cone a,  and the ambient or altitude diffuser pressure around the nozzle exit P₇.  The nozzle kinetic energy efficiency calculates as η_KE = 0.5*(1 + cos(a)),  where a is simple if a conical nozzle,  or the average of near-throat and exit-lip values,  if a curved bell.  

The nozzle exit ratio A₆/A₅,  kinetic energy efficiency,   and combustion gas specific heat ratio allow you to compute the vacuum thrust coefficient C_Fvac by standard ballistic methods.  That plus the values of A₆ and P₇ allow you to compute the actual thrust coefficient C_F.  Then the thrust-effective P_t4 = F_noz/C_F A₅.  From there,  the analysis is exactly the same as pressure-based,  all the way to η_cSA.

To meet combustion efficiency definition reporting requirements per the Chemical Propulsion Information Agency (CPIA) standards,  you must convert these stream thrust efficiencies (both bases) to the temperature-rise basis that is considered standard for ramjet work,  where T^o_t4 is the theoretical combusted total temperature from your thermochemical calculation:  

η_cΔT = (T^o_t4*η_cSA² – T_t2)/(T^o_t4 – T_t2).

Final Comments

I’ve tried to describe the bare bones of testing ramjets on the ground.  There’s a whole lot of nitty-gritty details I left out.  Describing all of that is closer to a book than just an article.