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.
