Shear Coaxial Injector - A Review of My Early Research

As previously mentioned, I had decided to opt for a coaxial injector for the Thunderchild project. My goals were and are a high C* efficiency and durability. This implies a high rate of energy release but with due consideration to injector face and chamber wall compatibility.


The NASA series of Special Publications (SP's) are well known to all in the amateur rocket engine community. For a gas/liquid injection scenario, NASA SP-8089 "Liquid Rocket Injectors" cites the concentric tube (i.e. coaxial) type injector, with or without swirl, for use in situations where wall compatibility and efficiency, that is to say good atomisation, are paramount.


In the interests of simpler fabrication, I decided at this point to restrict my investigations to the shear coaxial injector. The primary references given in SP-8089 for this type of injector are NASA CR-120936 and NASA CR-120968, by A.Y. Falk and R.J. Burick. These studies were completed by Rocketdyne in 1972 and 1973 respectively. Both form part of a research effort into space stored propellant systems. The propellants in question were gaseous methane (CH4) and a mixture of 86% Liquid Fluorine and Liquid Oxygen (yes, really) known as FLOX.


So far in these musings I have used SI units throughout. In my studies of injection methods I have tended to swap from SI to Imperial, dependent on the text I am using as a reference. On September the 14th 1970, NASA policy document NPD 2240.4 stated that measurement systems employed in all NASA and contractor reports should be expressed in SI units. To their credit, most NASA contractors seem to have studiously ignored this directive. As CR-120936 and CR-120968 use Imperial units, I will do so in this post. I will of course give the SI equivalents in brackets.


CR-120936 was an attempt to characterise the coaxial shear injector whilst CR-120968 formed a set of design guidelines based on the latter documents' findings. CR-120936 is dominated by empiricism; there is no real attempt made to quantify the physical mechanisms of atomisation. Rather the Authors' efforts were focused on producing a set of experimentally derived design equations that could be used to produce reliable, functional injector units.  


Falk and Burick produced a sizable data set that is often referenced in later studies. They began with the premise that the injector is ultimately responsible for the delivered C* efficiency value, and that this value can be expressed as a product of the C* efficiency due to vapourisation, nC*vap, and the C* efficiency due to mixing, nC*mix. Cold flow and hot fire experiments were carried out to determine the effect of varying injector parameters on nC*mix and nC*vap. Now, vapourisation is essentially atomisation in the presence of combustion. Having made that distinction, for the purposes of cold flow testing the two terms amount to the same thing.  

Falk and Burick co-related nC*vap using an early computerised combustion model called K-Prime, written in FORTRAN. A streamwise model was used to co-relate nC*mix to a mixing factor, Em, originally developed by Rupe.

Rupe defined Em as the summation of the mass weighted value of the difference between the local mass fraction ratio and the nominal mass fraction ratio. The value of Em is expressed as a percentage. Falk and Burick graphed Em versus nC*mix, enabling the value of Em for any value of nC*mix to be determined. The results of the K-Prime modelling were also graphed to give a percentage value of nC*vap against injector mass median drop size, in microns. 


Relating these results to the cold flow and hot fire experiments, Falk and Burick managed to reduce nC*mix and nC*vap to functions of the following expressions:-

nC*mix = f [(pgVg)^2 / MRVl]  (1)

and:-

nC*vap = f [(Vg - Vl) / MRVl]  (2)

Where:-

Vg = Gas velocity

pg = Gas density

Vl = Liquid velocity

MR = Mixture ratio (o/f)

Despite CR-120936 being an empirical study, straight away one can see that the inclusion of the term (pgVg)^2 in (1) implies a Reynolds number type relationship for nC*mix. Likewise, the term Vg - Vl in (2) has Weber number related implications for nC*vap. The graphs presented show that the expressions give reasonable, though not exactly precise, correlation to the mixing and vapourisation data.

The expressions in (1) and (2) above produce non dimensional numbers. In CR-120936 and CR-120968 these are then cross referenced to graphs giving values for Em and a mass median drop size, in microns. The mass median drop size is given as a fraction of the liquid injection orifice diameter, D.

Broadly speaking, Falk and Buricks' findings indicated that mixing and atomisation are primarily influenced by gas and liquid velocity ratio. Altering parameters that increase mixing tended to decrease atomisation, and vice versa. For example, increasing liquid jet diameter decreases the liquid velocity, which improves the velocity ratio and thereby improves mixing. However, it also increases the initial droplet size, since this is related to the liquid jet diameter, D. Though in theory the Vg - Vl parameter increases, the increase in the size of D tends to cancel this benefit out. Reducing the injected gas density also decreased mixing, tending to point to a mass flux ratio related relationship. The K-Prime combustion model predicted a required initial drop size of 300 microns for an nC*vap of 95%. This was based on combustion in a 40 inch (1.016 m) L* chamber. Theoretically, it is safe to assume that the Thunderchild chamber would perform better with this drop size, having an L* of 60 inch (1.52 m). The findings also showed that reducing the mixture ratio MR increased atomisation and mixing quality.

 From a standpoint of injector geometry, the Authors found that liquid post recess had a beneficial effect on mixing and atomisation quality, with an optimum recess value of around one liquid injection diameter. 

 The cold flow models that were tested in this study had flow rates in line with a thrust value of 70lbf (311N). Hot fire single element tests showed a C* efficiency of 92%. Wall heat flux levels in the test chamber were in the region of 2-3 BTU/in^2-sec (37-49 MW/m^2). This figure is in line with that mentioned in Krzycki. Injector face heat flux was found to be approximately 0.5 BTU/in^2-sec (8.2MW/m^2-sec). These tests also showed that recesses greater than 1.5 times the liquid diameter led to combustion within the cup region. This is the volume enclosed by the tip of the liquid post and the face of the injector.

It is tempting to suspect that the flow of cryogenic FLOX into the injector had some bearing on the low face heat flux. That said, these results seem to show that the assumptions made about the coaxial shear injector in terms of efficiency coupled with wall compatibility are grounded in fact. 

After studying CR-120936, I decided to use the design precepts and data presented as a starting point for my own investigations into shear coaxial injection. I had already begun speculating on the physical principles that I considered were affecting the atomisation and mixing process. I've mentioned some of these ideas already in this post. The use of the relations in (1) and (2) would enable me to build a prototype for testing which could then be used as a basis for further research. This would allow me to gain more insight into these physical mechanisms and how they could be optimised.

In the cold flow tests Falk and Burick used CH4 as the gas and either water or hot wax as FLOX simulants. I had decided to use water as the simulant for ethanol and either air or argon as gaseous oxygen simulants. A comparison of the densities for the propellants/simulants used in CR-120936 and the Thunderchild project follows:-

• CH4 density @ 500psi (34.5 bar)  = 1.45lb/ft^3 (23.2 kg/m^3)
• FLOX density = 89lb/ft^3
• Hot Wax (Shell wax 270) density = 47.1 lb/ft^3 (754.46 kg/m^3)
• Water density = 62.43 lb/ft^3 (1000kg/m^3)
• Ethanol density = 49.25 lb/ft^3 (789 kg/m^3)
• 70% Ethanol/Water density = 54.12 lb/ft^3 (867 kg/m^3)
• Air density @ 100psi (6.9 bar) = 0.54lb/ft^3 (8.65 kg/m^3)
• Argon density @ 400psi (27.6 bar) = 2.83 lb/ft^3 (45.3 kg/m^3)
• Gaseous oxygen density @ 400 psi = 2.26 lb/ft^3 (36.2 kg/m^3)

It can be seen that the densities of the simulants chosen for the Thunderchild project approximate the propellants quite well. For a given flow rate, injection velocities should resemble the propellant design ones fairly closely. There is also a reasonable level of parity between the Thunderchild simulants/propellants and those of CR-120936, particularly for the hot wax. The thrust value of the single element test units in CR-120936 was 70lbf, not too dissimilar to the 50lbf of Thunderchild. 


All this bodes well for the use of the relations in CR-120936 to design a prototype injector for further study. Falk and Buricks' chamber pressure was 500psi. I have given densities for argon and oxygen at 400psi. This is because the Thunderchild project design chamber pressure is 300psi and the projected pressure drop to avoid instabilities is 100psi. Air density is given at 100psi as the compressor I have could only supply 100psi.

It is worth noting that CR-120936 looked briefly at swirling the liquid through the central post. As mentioned earlier, at this point I was concentrating my efforts on shear coaxial injection. A comprehensive study is being made of swirl injection. All the best swirl literature is by the Russians, and though it took me some time to source this, I eventually got my hands on it. 

The study of Falk and Buricks' work took place in the summer of 2009. I then went on to use their work as the basis for a prototype injector, which was completed by the summer of 2010. In the next post I will move on from this review of CR-120936 and describe the design and construction of this prototype.

Injection, Injection

At long last.

The fuel injector of a rocket engine is without doubt the single most important component in the entire system. This is because it exercises influence over all of the closely coupled key performance arbiters. These are:-

• Combustion efficiency
• Combustion stability
• Heat transfer and cooling

If this were not enough, the unit also has to endure the aggressive, high temperature environment of the combustion chamber whilst conforming to a specified form factor.

Over the years injector design has combined approaches of both meticulous research and "try it and see what happens". I have travelled a similar road. Fortunately today there is a vast literature on atomisation, mixing and sprays, both rocket specific and general. Hence my experimental efforts have been guided at each stage by reference to published works.

Injectors for rocket engines fall into two main categories:-

• Impinging Stream
• Coaxial Jet

These two types are further broken down into a number of distinct subsets.

An important subset of the Impinging Stream type is the so called Shower Head injector; this may be regarded as an impinging stream injector in which the impingement angle is zero. Impinging stream types are further subdivided by impingement component and pattern. Types include fuel on fuel, fuel on oxidiser, oxidiser on oxidiser and combinations of these. Patterns used are many and various, including doublet, triplet, pentad, and numerous combinations of these. The main mechanism of stream break up and atomisation in the impinging stream type is momentum exchange. Impinging stream types are primarily used in systems where both fuel and oxidiser are liquids.

Coaxial injectors are the chief choice when one of the propellants is in a gaseous state. They are split into two main groups, shear and swirl. In the shear type, a low velocity central liquid flow is stripped and atomised by a higher velocity annular gas flow. The main mechanism of atomisation in this type is induced Kelvin-Helmholtz instability. The most important performance controlling variable in the shear coaxial unit is the gas/liquid relative velocity. Surface tension of the liquid resists the deforming force of the gas momentum, hence high gas/liquid Reynolds Numbers are common in efficient shear coaxial injectors. Shear coaxial injectors are almost always liquid centred.

The swirl coaxial injector imparts a tangential velocity to either the gas or liquid flow, and in some cases to both. They may be liquid or gas centred. Centrifugal force due to tangential velocity causes liquid ejected from the injector to form a cone shaped, thin sheet spray. Under the influence of the centrifugal force ligamentation and droplet formation rapidly occur in the thin swirling sheet. The key formation mechanism here is Rayleigh Instability, with the centrifugal force standing in for gravity. These droplets are then further broken down by the gas flow induced Kelvin-Helmholtz type mechanism of the shear injector. In the case where both gas and liquid are swirled, momentum exchange also plays a part in the spray formation.

 High gas to liquid Reynolds numbers are again a feature of this type of unit. Swirl atomisation is governed by the efficiency with which the potential energy of the flowing stream is converted to a tangential velocity. Key to this is the minimisation of friction in the flow path.

A quick survey of amateur liquid rocket engines on the internet showed the proliferation of the impinging type injector. My view was that the multiplicity of small holes needed would be difficult to drill accurately at the angles required, as well as being difficult to deburr effectively. This would lead to stream misimpingement and hydraulic flip as well as many broken drills. The impinging stream type injector would also be more difficult to manifold.

As the present project is using a gaseous oxidiser, I decided to go with a Coaxial injector design. I felt that this would be easier to manufacture and be more amenable to performance enhancing modifications. It would also be a unique feature of the Thunderchild Project.

Here is a photograph of an early mock up to illustrate the coaxial principle:-

Next I'll look at how this principle was developed.



An Update

First of all let me apologise for not having posted anything in the last few months. Rest assured, things have been moving steadily onward with the Thunderchild Project!

I have been very busy in the workshop and with nozzle and injector design. This coupled with the generalities of everyday life has meant  I have had little time to post.

Workshop wise I have been re-acquainting myself with screwcutting in the lathe. As well as being important to the project generally, my acquisition of threading tools for the Harrison has allowed me to radically re-design and improve the injector. I've also had some excellent input on the injector design front from Dr. John Chinn, of the University of Manchester Institute of Science and Technology (UMIST). Dr. Chinn is an authority on atomisation and sprays and was kind enough to take time to clarify a few points for me.

To try to get some idea of the efficiency of the injector design, I've been looking at a technique called "Shadow Sizing". Essentially this involves taking a photograph of the spray against a brightly illuminated graticule. It is then possible (with some effort) to gauge droplet size, distribution and number. I've been trying to work out a scheme to implement this, and thinking about software to automate the particle counting/sizing task. As an aside, I have put this notion forward for the BBC Radio 4 "So You Want to be a Scientist" search for amateur research ideas. I don't hold out much hope for it, as there usually seems to be an environmental, or "primary school nature table science" type of bias to the chosen entries. Still, you never know.

The design of the nozzle and convergence is well advanced, and this will most likely be the next component to be machined. The extra area required to achieve the design L* figure was calculated using the formula for the frustum of a cone. I will post the full nozzle and convergence design calculations in due course.

Some time ago I told you about the new tilting rotary table, well here it is:-

And here, tilted:-

Last but not least...the British Reaction Research workshop is moving! Yes, I have bought a new, larger house, and the space for the workshop is insulated and has access from inside the house. It will be much more comfortable in the colder months...I still get chills when I think about machining the components for the chamber last winter, when it was minus 10 degrees celsius outside!

Inevitably, it will take some time to get the workshop up and running again. I will give you some pictures of the move and set up, and I'll try to use some of the time to start giving you the much vaunted injector details. Do stay tuned.



Fuel Concerns

Before I start going into details about nozzle design and dimensions I had better say a few things about fuel choice. I was minded to tell you about this when I visited a friend recently. Michael is a technical horologist. Together with his wife Maria, they run The House of Automata http://www.thehouseofautomata.com/ . Michael asked me what fuel I am using...I suddenly realised that as yet I hadn't made any mention of this all important subject.  

The list of substances that can be used as rocket engine fuels and oxidisers is a long one. Few of these are easily obtainable. For an amateur rocket project we can discount such exotic animals as hypergolics, acids and amines. Likewise peroxides. An out of control fire or explosion would not endear us to our neighbours, or indeed the authorities.

That leaves commonly available gaseous and liquid hydrocarbons or alcohols as fuels. We have the choice of gaseous oxygen or oxides of nitrogen as oxidisers.

Availability is not the only desirable property for a fuel and oxidiser to possess. A good fuel should be safe to store and handle. As the fuel will also be used as a coolant, it should have a good specific heat capacity.This latter requirement rules out the use of gaseous fuels in a safe rocket engine. The choice then comes down to petrol (gasoline) and kerosine in the hydrocarbon camp and methanol, ethanol or IPA representing the alcohols.

As for the choice of oxidiser, gaseous oxygen for welding is widely available and easily obtainable. It requires no special handling or storage requirements beyond those dictated by common sense. This is in contrast to LOX which is a non starter in a semi residential workshop setting. That said, cryogenics are not neccesarily out of the question. Nitrous oxide is readily available due to its use in car performance enhancement. It is stored in liquid form under pressure in cylinders. It is also relatively safe and easy to handle. When released under control of a regulator the liquid rapidly changes state to a gas.

Gaseous oxygen seems to be the best option at this stage. Its ease of availability, handling and storage contribute to moving the project forward in a timely fashion. That said, I wouldn't rule out the use of nitrous oxide. I will be able to make a much more informed decision once the engine is built and hot fire experience has been gained.

Petrol, kerosine and the alcohols, methanol, ethanol and IPA have been widely used as rocket engine fuels. For comparison, here are some performance figures for these three fuels, when burned with gaseous oxygen:-

Kerosine

O/F ratio = 2.2

Isp = 255

Flame temperature = 3200 Celsius (5800 Fahrenheit)

Petrol

O/F ratio = 2.5

Isp = 260

Flame temperature = 3170 Celsius (5740 Fahrenheit)

Alcohol (Methanol)

O/F ratio = 1.2

Isp = 240

Flame temperature = 2810 Celsius (5090 Fahrenheit)

 These fuels are readily available in almost every community. Hydrocarbons give good performance when burned with oxygen, as can be seen. Unfortunately they make poor coolants. Kerosine and petrol have a tendency to "crack" at high temperatures and leave sooty, solid carbon deposits. These can block coolant and injector channels, thereby causing problems. I am trying to construct a safe and reliable engine and so hydrocarbons are out, at least for the time being.

As shown, alcohol gives decent performance with a lower flame temperature. It is also chemically stable when in contact with the hot walls of the chamber cooling jacket. The flame temperature could be reduced further by increasing the ratio of fuel to oxygen, that is to say producing a rich mixture. This would be the only option with hydrocarbon fuels. With alcohol, the flame temperature can be reduced further and the cooling properties greatly increased by diluting the alcohol with water, with which it mixes in all proportions. 

 In 1948 the Aeronautical Research Council published report 2816. Authored by ABP Beeton, it dealt with "The Calculated Performance of Ethyl Alcohol - Water Mixtures as Rocket Fuels with Liquid Oxygen". It states that a combination of 100% ethyl alcohol and LOX gives an Isp of 250. By contrast, a 70% ethyl alcohol - water and LOX combination results in an Isp of 240. For the 100% ethyl alcohol combination the combustion temperature is given as 3000 celsius. With 70% ethyl alcohol the temperature is 2820 celsius. Thus it can be seen that the hot gas temperature is some 180 Celsius lower for a decrease in Isp performance of only 4%.

To conclude, it can be seen that gaseous oxygen is a good choice of oxidiser for the Thunderchild Project. It is readily and cheaply available due to its use in welding. Similarly, ethanol is a good choice of fuel. It is easily available and relatively inexpensive. It gives good performance and is a good coolant. Dilution with water increases the cooling capacity and eases the cooling problem for a very small decrease in performance.  

Exemplar

An exemplar is defined as an excellent model or typical example, worthy of imitation. In my last post I spoke about manufacturing a banjo type fitting. Now, it struck me that there may be many who have never heard this term and have no idea what a banjo fitting is. A recent visit to the Royal Air Force Museum at Cosford, in Shropshire, gave me the chance to rectify the situation.

The Cosford museum is well worth a visit if you are in the West Midlands with an afternoon to spare. You can read about it here:-  www.rafmuseum.org.uk/cosford/

The collection includes the National Cold War Exhibition, including excellent examples of the "V" bomber type in the form of a Vulcan, Valiant and Victor. Cosford perfectly complements the Southern Branch of the Royal Air Force Museum in Hendon, North London.

The Cosford Museum has an excellent collection of British Rocket Engines, including a De Havilland Sprite RATO unit and a De Havilland Spectre. It is also possible to see the Saunders Roe SR 53 aircraft, the mixed power interceptor that the Spectre was designed for. Both the Spectre and Sprite were Kerosine/HTP units. Incidentally, you can see a cutaway of the Sprite in the second edition of Sutton, on page 36.

Both engines included good examples of banjo fittings and I took some photographs to illustrate the type:-

This is a banjo fitting on the top of the Sprites' Hydrogen Peroxide tank. The purpose of this fitting and its' associated pipeline was to charge the tank with compressed air from the air distributor valve. The fitting is composed of a cylindrical outer portion that is fixed to the tank by means of a hollow "banjo bolt". This has a perpendicular drilling that allows the hole in the centre of the bolt to communicate with the cylindrical portion. By this means the fluid entering the cylindrical portion is delivered through the bolts' central hole. The cylindrical portion is sealed at the top and bottom with Dowty Washers. Copper or aluminium crush washers are used in some instances. This photograph also shows a frankly beautiful example of TIG welding.

The next example is taken from the De Havilland Spectre:-

The fitting in this picture is of an AGS type. As a matter of fact, it is an AGS 1130 banjo body and an AGS 1135 banjo bolt. AGS stands for "Aircraft General Standard". This is a standard for various aircraft detail components. It was used on British Aircraft for many years. Threaded components were based around the BA system for smaller than 0.25 inch and BSF for 0.25 inch and larger. For fluid power systems, the BSP parallel thread was used.

Here is an AGS 1132 banjo body:-

And here is an AGS 1136 banjo bolt:-

This image clearly shows the central hole communicating with the perpendicular hole. These images come from the website of LAS Aerospace Ltd, on which you can see and learn more about AGS parts:- http://www.lasaero.com/

I am going to be in the workshop all next week so with any luck the next photographs I show you should be of parts that I have made. I  am still working on the posting detailing the nozzle design calculations, so do look out for that.



Fasteners

I just wanted to mention that when I returned home I had received a delivery of stainless steel fasteners and a new piece of workshop equipment.

I had bought a selection of metric stainless bolts, mainly M8 and M14. These are destined to play a part in the further development of the injector.

I found a new supplier for stainless fasteners. I used to use Stagonset. According to various forums, they have gone out of business. The former employees have started up again, calling themselves Westfield Fasteners. You can find them at:- http://www.westfieldfasteners.co.uk/

As for the workshop equipment, I now have a tilting rotary table. It is a Vertex one which I got from RDG tools:-
 http://www.rdgtools.co.uk/
 I had decided to get one as I was struggling to drill perpendicular, conjoined holes with my existing one. Once I get a chance to clean the grease off it and take a photograph, you'll get to see it.

Back in the Real World

Once again I have returned from one of my globetrotting escapades. After a few days to decompress, I will be able to get back into the workshop. Work on the rocket motor will resume, as will regular postings to let you know what is going on.

Whilst I was away, I did some work on the design of the convergence and nozzle. The plan is to get it fabricated this time home. I will post the design equations for it in due course. I have also been thinking about an idea for a banjo type fitting that will be based on commonly available hardware. At the moment the design of the motor includes various BSP to Swagelok fittings. These are quite expensive, so if I could devise a means of replacing them it would be a definite plus.

Time permitting, you should also start to see a few postings regarding injection. I think this is the holy grail; whenever I find a new site devoted to rocket engine construction, my first thought is to find out what their injector is like. So in the next few weeks you'll be able to read about the design, evolution and testing of mine. An evolution that is still ongoing, I hasten to add.

Plenty there to keep me busy and to hopefully be of interest to the likeminded. Thank you for following and keep watching this space. I will endeavour to use the one between my ears.