Tuesday, 28 February 2012

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. 

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