Tuesday, 28 February 2012

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)


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. 

Wednesday, 22 February 2012

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)

nC*vap = f [(Vg - Vl) / MRVl]  (2)

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.