Shear Coaxial Injector - Further Background and Theory

As mentioned earlier, CR120936 was primarily an empirical study. As the tests with the prototype Shear Coaxial Injector began, I realised I would have to conduct further research into the mechanisms of coaxial atomisation and the physical parameters governing it. Prior to examining the actual tests it would be well to look at these principles.

The basic mechanism of coaxial atomisation is stripping of the liquid stream by the higher velocity co-flowing gas. Atomisation is initiated by internal vortices in the liquid stream producing ripples or waves on the surface of the stream. These are accelerated by the co-flowing gas, aerodynamic forces inducing and reinforcing Kelvin-Helmholtz instability.The crests of these waves are hence stretched, forming ligaments and eventually droplets. This Kelvin-Helmholtz instability driven atomisation can often be seen at the seaside on a windy day. If the sea is choppy enough, as the wind blows it will atomise surface instabilities from the crest of each wave. The photograph below shows this happening:-

When I took this photograph the day was perfect for making this type of observation; bright sunshine and a 30 knot wind.

So much for the sea. Let us return to coaxial atomisation. In attempting to disrupt a liquid stream with a co-flowing gas stream, aerodynamic forces tend to perturb the stream. Surface tension and viscosity tend to preserve it. So it can be seen that gas and liquid stream Reynolds Number and Weber Number are important parameters.

The Reynolds number of a fluid gives a measure of the ratio between aerodynamic and viscous forces. The Weber number relates aerodynamic forces to surface tension. The Weber number is particularly important when considering fluid flows where there is an interface between fluids of two different phases, i.e. a liquid and a gas.

Gas and liquid Weber numbers are cited as a key performance arbiters in the literature. Hardalupas and Whitelaw (1) and later Lasheras, Villermaux and Hopfinger (2) stressed the importance of the so called Aerodynamic Weber Number, defined as:-

We = pg (Vg - Vl)^2 Dl/o  (1)

Where:-

We = Aerodynamic Weber Number

pg = Gas density

Vg = Gas velocity

Vl = Liquid velocity

Dl = Liquid orifice diameter

o = Surface tension

Gas or Liquid Reynolds number can be written as:-

Re = V D/v  (2)

Where, with the appropriate subscripts:-

Re = Gas or liquid Reynolds number 

v = Gas or liquid kinematic viscosity 

V = Gas or liquid velocity

D = Gas or liquid orifice diameter

Hardalupas and Whitelaw along with Lasheras, Villermaux and Hopfinger also showed the importance of Gas/Liquid Momentum Flux Ratio, and Mass Flux Ratio.

Lasheras, Villermaux and Hopfinger define these as:-

M = pgVg^2 / plVl^2 (3)

Where:-

M = Momentum Flux Ratio

pg = Gas density

Vg = Gas velocity

pl = Liquid density

Vl = Liquid velocity

And:-

m = plVlAl / pgVgAg (4)

Where:-

m = Mass flux ratio

Al, Ag = Gas and liquid orifice areas

Mayer (3) showed that a high liquid Reynolds number is essential for the production of atomisation initiating instabilities on the surface of the liquid stream. He also found that the transition Reynolds number, between smooth and disrupted flow surface, is similar to that for turbulent flow in pipes, that is to say Re > 4000. The following photographs are taken from Mayer and illustrate this point:-

Flow direction is from left to right. Stream diameter is 2mm, comparable to that of the prototype Shear Coaxial Injector. The top photograph shows a laminar flow. Here, Re = 800, Vl = 0.4 m/s. The centre photograph shows a turbulent flow with surface asperities and wave growth well established. Here, Re = 10,000 and Vl = 5 m/s. The bottom picture shows much more turbulent flow with very well developed wave growth. Here Re = 40,000, corresponding to a Vl of 20 m/s.

Kenny and Moser et al (4) showed that for coaxial shear injectors, a definite atomisation regime exists. The onset of this regime is generally acknowledged as the point at which the liquid jet is fully disintegrated at the injector face, or within a very short distance of it. This condition is important for good performance, since the existence of an intact length in the liquid jet may lead to a combustion free zone at the start of the chamber. This would effectively reduce the available L*, leading to inefficient and possibly unstable combustion. Using the definition for Aerodynamic Weber number given in Hardalupas and Whitelaw, Kenny and Moser et al defined this atomisation region to exist where We > 1000 and Liquid Re > 10,000.

Looking at the photographs from Mayer above, it can be seen that the stream where Re = 40,000 has a short portion just after the orifice outlet that is undisturbed. This illustrates another important and contradictory point. Eroglu, Chigier and Farago (5) showed that intact length decreases with increasing liquid Re, up to a point, and then begins to increase. Increasing liquid Re also implies increasing Vl. It is known that shear coaxial injectors depend on the velocity difference between the gas and liquid streams. So a slower liquid velocity is desirable, at the expense of liquid Re. Lasheras, Villermaux and Hopfinger showed that as the Aerodynamic Weber number increases for similar Reynolds numbers, the crucial parameter is Momentum Flux Ratio. Obviously increasing Aerodynamic Weber number implies increasing Vg which also increases Momentum Flux Ratio. Indeed, Hopfinger and Lasheras (6) further report that the liquid stream is completely disintegrated when Momentum Flux Ratio > 10. For M > 20 however, recirculation can occur which may cause oscillation of the spray. This can also initiate combustion instabilities.

The final piece in the puzzle is the central post recess. It will be remembered from Falk and Burick that central post recess improved atomisation for all conditions. This is explained by the work of Juniper and Candel (7). They showed that the recessing of a slow moving dense liquid stream inside a fast moving, coaxial, lighter stream causes the central fluid to behave like a wake within the annular flow. This induces a sinusoidal instability on the surface of the fluid. The photograph below is from Juniper and Candel and illustrates this phenomenon:-

Juniper and Candel demonstrate mathematically that recessing the central tube of a coaxial injector always leads to self sustaining wake like instabilities of the central stream. Clearly, these instabilities would augment the internal vortices described in Mayer, thereby enhancing the general break up mechanism.

Three controlling variables are defined. These are the ratio between the annular width and half the central stream width h, a density ratio S and a velocity ratio L. They are defined as:-

S =  pl/pg (5)

L = (Vl - Vg) / (Vl + Vg) (6)

Juniper and Candel plot convective and absolute instability lines for values of h varying from 1 to 7. The graphs plot L against log10 S. The variable h is seen to be close to 1 for most coaxial injectors. This will be proved for the prototype Shear Coaxial Injector later in this exposition.

To conclude, the primary mechanism of coaxial atomisation is the stripping of the stream by the initiation of Kelvin Helmholtz type instabilities on the surface of the liquid stream. These are accelerated and eventually disintegrated into droplets. These instabilities are enhanced by recessing the central liquid post, which induces a global wake mode instability. A large Aerodynamic Weber number is desirable, as is a high Momentum Flux and Mass Ratio. The Reynolds number of the liquid stream must be kept high, but not so high as to lead to an intact length at the orifice outlet. Essentially, these conditions can be satisfied by operating the unit at a high gas to liquid velocity ratio.  

I have tried to give as complete a picture of the mechanisms involved in coaxial shear atomisation, as well as the factors that control it, as I can. The Kelvin Helmholtz model is something of a simplification of what is an extremely complex process. In the next post we will look at the actual experiments with the prototype Shear Coaxial Injector and apply the principles outlined here to analyse its' performance.

References

(1) Coaxial Airblast Atomisers, Hardalupas and Whitelaw, Imperial College London, 1993.

(2) Break-up and atomisation of a round liquid jet by a high speed annular air jet, Lasheras, Villermaux and Hopfinger, Journal of Fluid Mechanics, 1998.

(3) Coaxial atomisation of a round liquid jet in a high speed gas stream: A phenomenological study, W. O. H Mayer, Experiments in Fluids, 1994.

(4) Cold Flow Testing for Liquid Propellant Rocket Injector Scaling and Throttling, Kenny, Moser et al, AIAA, 2006.

(5) Coaxial atomiser liquid intact lengths, Eroglu, Chigier and Farago, Physics of Fluids, 1990.

(6) Breakup of a Water Jet in High Velocity Co-Flowing Air, Hopfinger and Lasheras, Proceedings of ICLASS 94, 1994.

(7) The stability of ducted compound flows and consequences for the geometry of coaxial injectors, Juniper and Candel, Journal of Fluid Mechanics, 2003.

  

Update and Lathe Works

The postings detailing the experiments with the Shear Coaxial Injector are now ready and will follow in due course. Over the last few months I have been concentrating on setting up the new workshop. This is now 90% complete. Work on the engine will recommence very soon. The new workshop will be a far more comfortable environment to be in as the winter approaches.

Obviously part of setting up the workshop was installing the Harrison M250. During functional tests I found that there was an issue with the torque limiter driving the power shaft. Should the saddle or cross slide be obstructed in any way, causing an over torque condition, this device protects the power shaft and saddle from damage by slipping.

Though not strictly an engine related issue, I have decided to post the details of this problem and the solution here. As a member of the Yahoo Harrison Lathe Group, I hope that others will find the information given useful.

The problem was that stopping the saddle with moderate hand pressure was enough to disengage the torque limiter. The torque limiter works by means of two spring loaded balls engaging with slots on the feed gearbox driving feature. Corresponding holes on the power shaft driven member transmit the drive to the power shaft. An over torque causes the balls to ride around the driven member, coming out of their detent position and thereby disengaging the drive.  On rotating the power shaft with a suitable spanner I could hear and feel the balls disengaging at a very low torque. I surmised the problem was due to insufficient spring loading. This despite the fact that the unit had operated perfectly since I bought the lathe in 2009.

Throughout this exposition I will give Harrison part numbers of the components described in brackets. The spring loading is produced by a pack of 12 Belleville washers in the torque limiter housing (D102H3004). I have often seen Belleville washers fracture, so that was my initial thought as to the cause of the fault.

First of all the torque limiter housing was separated from the feed gearbox driving feature (903013) by removing the two countersunk M4 securing screws. The torque limiter housing was then carefully slid along the power shaft. The two balls were removed from the slots in the driving feature. Below is the driving feature showing the distance piece (D001H2082) and the power shaft partially withdrawn from the latter assembly. The two ball engagement slots can be seen:-

In order to slide the torque limiter housing assembly off the power shaft it is necessary to fully withdraw the power shaft from the feed gear box driving feature. The tailstock end of the power shaft is borne in a steel top hat section bush (906008) which runs in a bore in the power shaft/leadscrew support bracket (906001). This bore is sealed by a plug (906009) that is a transition fit in the support bracket. After slackening the M5 securing grub screw it was possible to withdraw the top hat bush:-  

There was now sufficient latitude to get a punch in to drive out the transition fit plug. A copper drift would have been ideal to prevent damaging the plug. I placed a pad of insulating tape on a standard punch to achieve the same effect:-

Here is the plug partially removed:-

Once the plug is out the power shaft can be withdrawn and the torque limiter housing removed. The housing has an adjusting barrel nut (D021H3001) threaded in the end. This is used to load the Belleville washers and can be removed using a suitable peg spanner or two punches inserted into the driving holes. On dismantling the torque limiter I discovered that the Belleville washers were not fractured. Rather they had been assembled in the incorrect orientation.

 Whilst I appreciate that Belleville washers can be installed in different orientations to affect a coarse adjustment, I do not think this was the case. The washers had been installed in a random fashion. I do not think this would have been done by Harrisons so I can only assume it was the work of the previous owner. Here is the disassembled and cleaned torque limiter assembly:-

The picture shows the housing, driven feature (903028) 6 mm dia. balls x 2, M4 countersunk securing screws x 2, threaded adjuster with locking M4 grub screws x 2, all 12 Belleville washers and the transition fit plug.

The Belleville washers were in good condition. The driven feature abuts the step that can be seen inside the housing. When the washers are slid over the driven feature and the adjuster is threaded in, they effectively spring load the unit.

The washers were next assembled to the driven feature in the correct orientation:-

The complete unit was then reassembled ready to be slipped back on to the power shaft:-

This rebuilt unit was slid back on to the power shaft and reassembled to the feed gear box driving feature. A blob of grease on each ball helped them stay put in the driving features' slots. The tailstock end top hat bush was reinstated and the transition fit plug refitted. 

A full and successful test of the surfacing and facing power feeds ensued. For the life of me, I cannot understand how the unit had functioned for so long, given how it had been assembled.

And here is the complete article:-

The next postings will detail the results of the Shear Coaxial Injection experiments. Stay tuned.

Thermocouple Experiment and an Update

I know that many of you will be anxious to see pictures and video footage of the tests I did on the prototype Shear Coaxial Injector. I am working on that post and editing the video footage to ensure the salient points are presented.


I am also still working on reinstating my workshop. In the meantime I decided to try to make some progress on the development of the sensor suite and data acquisition system for the completed engine.


At the start of this month I received some 0-60 bar (0-870 psi) pressure sensors and some ruggedised K type thermocouples. The pressure sensors are Parker ASIC Performer types. These units are 1-6 Volt output. This is accessed by means of a micro DIN connector. The thread on the business end is 1/4 inch BSPP. Here is a photograph of one of the units:-

I intend to use these devices to measure fuel, oxidiser, pressurant and chamber pressure on the test bed. I haven't trialled one yet as I will have to get one plumbed into my Enerpac, which will have to wait until the workshop has been set up.


The K type thermocouples came from Rachel McGill of McGill Motorsports, in Kirkcaldy, Fife. The units are designed for use in performance cars to give an indication of exhaust gas temperature. In the Thunderchild Engine they will be embedded in the injector and the chamber flanges, to try to get an idea of chamber wall and injector face temperature. Mounting is by means of a stainless steel adaptor threaded to 1/8 inch NPT at one end. When assembled, the opposite end of the adapter looks similar to a JIC or AN fitting. The resemblance is superficial however, as the barrel nut hides a brass ferrule. This arrangement grips the thermocouple and allows it to be set at any depth in the measurement port. This will be easy to integrate into the Thunderchild chamber flanges and injector plate. Here is an exploded photograph of the thermocouple assembly:-

I have done a lot of work with microcontrollers over the years, primarily with the BASIC Stamp and PIC devices. Whilst these are capable systems, I have decided to move over to the mbed NXP LPC1768 device. This is a 40 pin DIP packaged device based on an ARM 32 bit Cortex core. It is a highly capable device intended for rapid prototyping and supports a wide variety of analogue and digital input and outputs as well as all the popular communications protocols, i.e. USB, RS232, CAN, Ethernet, SPI and I2C. The unit is very well supported via an excellent website. A Handbook gives detailed information and programming examples whereas a Cookbook allows users to share code and other project information. The user friendly compiler is online based, which allows the user to develop projects anywhere, on any machine.


Communication with the device is via a virtual RS232 port over a USB connection. The unit looks like a USB memory stick to the host computer, and firmware is loaded onto the device from the compiler by dragging and dropping, as one would do to save any file type to a memory stick. More information can be found at:- www.mbed.org

I interfaced the thermocouple to my mbed unit using a MAX6675 Thermocouple to Digital converter IC. This is a fantastic little device that applies the cold junction compensation on-chip and then transmits the measured temperature using the SPI protocol. The device is only available in an SO package and so I got mine on a break out board from AdaFruit:- www.adafruit.com


Here is a photograph of the breadboard with the mbed microcontroller and the MAX6675 break out board connected:-

Here is a close up of the MAX6675 break out board:-

The mbed is programmed in C. I am much more familiar with PBASIC and I am finding C quite a trial to learn; compared to the average C program, PBASIC looks like a lost work of Shakespeare!


Fortunately the mbed website includes a wealth of example programs and I downloaded the "Hello World" example for the MAX6675. This reads the temperature from the thermocouple and then constantly transmits this to the host computer via the built in pseudo RS232 port. I used TeraTerm to display the results. This is a fine, workmanlike freeware terminal emulator:- logmett.com/freeware/TeraTerm.php

Here is a shot of TeraTerm with the displayed temperature of my kitchen!

I am going to continue setting up the workshop this week, and working on the blog post detailing the results of the Shear Coaxial Injector experiments. This will be followed by more on injection - how and why I decided to move towards swirl coaxial types.


Keep watching.

Shear Coaxial Injector - Constructing the Prototype Injector for Research

The previous post gave details of the design and the dimensions of the research injector. I will now go on to describe its' construction. As mentioned, I decided to make the body of the unit from BS230M07 steel. This is a free cutting mild steel. I know a lot of my readers are in the United States, so for their benefit the nearest equivalent would be AISI 1213.

The centre fuel post started out as a 316 stainless steel  M8 x 50mm hex head screw. I manufactured a threaded bush to hold this and then faced the end:-

Next I centre drilled the end of the screw and then generated the 1.85mm injection hole. I had to use a cobalt drill on the hard 316 stainless steel:-

The next thing to do was to set the screw up and turn the thread back to leave 15mm of it remaining:-

Once this step was completed the fuel post was reversed in the chuck and a 4mm fuel feeder hole was drilled for approximately 40mm:-

Once the fuel post was complete, I started bringing the body of the unit to size. There was no need to have the full chamber flange diameter for the research unit:-

Once the unit was to size it was time to start boring the various diameters required:-

First of all a 6.8mm hole was put right through, this is the tapping drill for an M8 x 1.25 thread:-

Next a flat bottomed hole of diameter 14mm x 25mm deep was generated using a slot drill in the tailstock. I found 14.5mm to be the optimum tapping drill size for a 3/8 inch BSPT fitting, without reaming the hole. The hole was bored to final size:-

Next step was to tap the 6.8mm hole to M8 for 15mm to accept the fuel post:-

The 3/8 inch BSPT thread was then generated for the fuel inlet fitting:-

Then the part was reversed and parted to length.The 6.8mm hole in the end of the unit was then bored out to the design diameter of 8.17mm, for 35mm:-

The body of the unit was now almost complete. After lathe clean up cuts, the next step was to drill and tap the 90 degree hole to 1/4 inch BSPT, into the annulus bore for the oxygen inlet:-

The unit was then assembled using an M8 viton/stainless steel bonded washer to seal the fuel post bolt. It was now ready for testing to commence. The study of CR-120936 and the design of the research injector took place between June and August 2009. The construction work shown in this post took place in June of 2010. In the next post I will look at the first tests of this research injector.

Shear Coaxial Injector - A Prototype for Practical Research

In the last post we saw that the shear coaxial injection presents a good choice when we are concerned with high C* efficiency yet benign chamber wall conditions. After careful study of Falk and Buricks' work, I decided to build a prototype injector to gain more insight into the mechanisms of shear coaxial atomisation and mixing.


The prototype was built using the design propellant flow rates. Calculated from the usual relations, for the 50lbf Thunderchild motor these are:-

• Ethanol = 0.098 lb/sec (0.044 kg/sec)
• Gaseous Oxygen = 0.118 lb/sec (0.053 kg/sec)

It can be seen that the mixture ratio, MR (o/f) is 1.2. This is the nominal optimum value for this propellant combination, as predicted by Alexander Ponomarenkos' Rocket Propulsion Analysis software. Given chamber pressure, nozzle parameters and propellant types, this useful simulation calculates chemical and thermodynamic properties as well as theoretical and predicted performance. It can be found here:- http://www.propulsion-analysis.com

I went with the figure given in Krzycki for the gaseous oxygen injection velocity, 200 ft/sec (61 m/sec). The gas density chosen is that for oxygen at 400psi, 2.26 lb/ft^3. For the initial experiments I decided to start by optimising mixing, as defined by Falk and Burick. It will be remembered that Falk and Buricks' empirical relation for mixing is:-

(pgVg)^2 / MRVl  (1)

Where:-

pg = gas density

Vg = gas velocity

MR = mixture ratio

Vl = liquid velocity

The graph in figure 29, page 53 of CR-120936 shows that for the maximum Em achieved of 92-95%, the figure for the relation in (1) above lies between 2000 and 4000. Setting Vl to 68 ft/sec (20.7 m/sec) gives a value of 2500. Interpolating from figure 29 shows that this gives an Em of 95%. This figure is for a liquid post recess of 1Dl. 


The relation given for atomisation in CR-120936 is:-

(Vg-Vl) / MRVl  (2)

Substituting the relevant values into (2) gives 1.6. Transferring this to the graph in figure 38, page 67, it can be seen that the initial drop size will be in the region of 0.225Dl microns. Again this figure is for a liquid post recess of 1Dl.


I came up with a design for the coaxial injector using a standard ISO metric hex socket head screw for the centre post. This screw would have the thread turned off it for a section of its length, to give a smooth post, and the remaining thread would then form the securing feature. I went with an M8 x 50mm screw. This diameter scaled well with that of the chamber, particularly when the size of the hole for the gas annulus is taken into account.


The liquid injection hole in the end of the post was sized as follows:-

Vl = 68 ft/sec  

pl = 49.25 lb/ft^3

wl = 0.098 lb/sec

inch conversion factor = 144

Al = liquid injection area

Formula to calculate the area for design flow rate at design velocity:-

Al = wl/plVl  (3)

Substituting the values given into (3):-

Al = [0.098/(49.25x68)]x144  (4)

= 0.0042 in^2

= 2.7 mm^2

Therefore Dl = 1.85 mm

The final dimensions were converted to metric units to make life easier in the workshop. Using the equation in (3) above the metric diameter of the gas orifice for the design flow and velocity came out as 5.5mm. This theoretical diameter had to be converted to a larger diameter so that the gas annulus hole could be drilled. Then when the central post was fitted the effective area would give a flow diameter of 5.5mm. 

According to BS3692, an ISO metric bolt has a minimum minor diameter of 6.23mm. When turning the bolts down, I discovered that the rolled thread meant I had to take the bolt to 6mm in order to remove all trace of it. The area of the 6mm plain portion was thus 28.27mm^2. The area of the theoretical gas flow diameter is 24.26mm^2. Adding these two gives 52.53mm^2. This gives a dimension for the gas annulus diameter of 8.17mm. Thus when the 6mm liquid post is inserted, the area left gives an effective flow diameter of 5.5mm. The bolt was also shortened to give a post recess of 1Dl, as mentioned in CR-120936. I anticipated making various bolts to check recess effects, as well as changes in Dl to study the effect of liquid velocity.

A set of dimensions was now coming together for the research injector. For the main body of the unit I decided to use BS230M07 mild steel, due to its' free cutting properties. The fuel post bolt was made from 316 stainless steel, so that it could be hot fired in any future production design. The fuel post was to be sealed with a viton/stainless steel bonded washer. The fuel inlet was through a 1/4 inch swagelok to 3/8 inch BSPT fitting directly above the bolt. This was done to give enough space to get the bolt head in. The diameter of an M8 hex socket head bolt is about 13mm, and the tapping drill for 3/8 BSP is 14.7mm. The oxygen flow entered the annulus through a 1/4 inch swagelok to 1/4 inch BSPT fitting.  

To summarise the key dimensions of the research injector:-

Fuel post diameter = 6mm

Annulus hole diameter = 8.17mm

Dl = 1.85mm

Dg (theoretical) = 5.5mm

These dimensions were sized from the premise of maximising mixing as defined by the relations in CR-120936. According to this report, the Dl value of 1.85mm (0.07 inch) gives an initial drop diameter of 416 microns (Dl x 0.225). I had, and still have, no way of verifying this. It can be seen however that this is quite coarse, so straight away the assertion that optimising mixing has a detrimental effect on atomisation seems to ring true.

Here is a photo of the completed unit:-

The oxidiser inlet can be seen, as can the annulus hole. The unit is minus the central post and the fuel inlet fitting. In the next post I will show the construction of this research injector. 

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.