Further Swirl Investigations

I have spent the last few weeks gaining a deeper understanding of the processes governing swirl atomisation. I want to report on that now, together with giving a bit more information on the gas centred swirl coaxial concept.

I have been using the following principal references in my study of swirl atomisation:-

• Theory and Practice of Swirl Atomizers, Yuri I. Khavkin, Taylor & Francis, 2004
• Atomization and Sprays, Arthur H. Lefebvre, CRC Press, 1988
• An Appraisal of Swirl Atomizer Inviscid Flow Analysis Part 1 & 2, Dr. John J. Chinn, Journal of Atomization and Sprays, 1993

My studies of swirl theory led me to believe that if the swirl chamber and outlet orifice were of the same diameter then the coefficient of discharge would be unity for all practical purposes.

Here is a photograph of the swirl inducer used in the trials:-

As previously mentioned, this swirler was formed by generating a two start, 3mm pitch metric trapezoidal thread on a 12mm diameter brass bar. The finished turned diameter of the swirler was 11.55mm. Due to the particular geometry of the profile tool used to cut this thread, it was not possible to depth it fully with a two start helix. Hence various precision measuring instruments and techniques were used to determine the key passage dimensions. The total equivalent flow area of the passages was calculated, using the equivalent diameter as defined in the last post. The total equivalent diameter of the swirl inducer above was 2.426 x 10^-3 metres.

Where EA = Equivalent Area, this gave:-

EA = 4.62 x 10^-6 metre square (0.007 inch square)

The swirler was made a transition fit in a short cylindrical body. The extremity of the inducer protruded approximately 1mm from the base of the body. In this way any swirl effects on the flow were eliminated. The measured flow would be the baseline level through the swirl inducer passages.

The assembled unit was tested using mains water at a pressure of 500kPa (72psi). The first test was a simple check of pressure drop. This was measured as 70kPa (10 psi) using an in line gauge.

The theoretical flow rate of the swirl inducer was then calculated using the standard pipe flow relation and the equivalent area:-

m = A (2p deltaP)^0.5  (1)

Where:-

m = mass flow

A= flow area

p = fluid density

deltaP = Pressure drop

Cd was not included as at this stage an ideal flow rate was being calculated. Substituting the known values in (1):-

m = 4.62 x 10^-6 (2 x 1000 x 70 x 10^3)^0.5

m = 4.62 x 10^-6 x 11.832 x 10^3

m = 0.0547 kg/sec (0.120 lb/sec)

The actual flow rate was then measured by timed discharge into an 8 litre bucket. The bucket was filled in an average time of 143.4 seconds, giving a flow rate of:-

8/143.4 = 0.0557 kg/sec (0.122 lb/sec)

This is a reasonable agreement given the limits of accuracy of both the flow area and flow rate measurement methods.

Reading Khavkin, I found vindication for my choice of equivalent diameter to calculate the swirler flow rate. Khavkin gives the following relation for swirl atomiser equivalent diameter, De:-

De = [(4{m/(2p deltaP)^0.5})/pi)]^0.5  (2)

Substituting the relevant values into (2) shows an equivalent diameter De of 2.433 x 10^-3 metres. This compares well with the calculation shown above.

Next the swirl inducer was fitted into a body having a 15mm long x 11.5mm diameter swirl chamber. The swirl chamber was parallel all the way to the outlet orifice, creating a so called "open" swirl atomiser.

This set up was trialled and the by now familiar thin swirling cone was produced:-

The break up length gives some indication of the swirl angular velocity. Due to the 15mm length of the swirl chamber, friction has reduced the velocity to the extent that the liquid viscosity and surface tension is able to resist the centrifugal disturbing force and produce a longer cone.

The discharge time for 8 litres with this set up was 146 seconds. This gives a flow rate of 0.0547 kg/sec. This compares very well with the calculated value for the swirler and the baseline figure without interference from the swirl chamber. If anything, a Cd value of around 0.97 to 0.98 is being displayed. This is so close to 1 that it is tempting to write this off to measurement and timing errors. That said, for all practical purposes the Cd can be considered to be unity.

The next trial was to investigate the length of the swirl chamber on the break up length and stability of the swirling cone. It should be emphasised here that a swirling external cone is not important in terms of the operation of a gas centred swirl coaxial injector. Rather the presence and condition of the cone is a metric of the quality of the internal swirling liquid film, which is an important parameter for a gas centred swirl device. The swirl chamber dimensions were reduced in 2mm increments by moving the swirl inducer towards the exit. It was found that the absolute minimum swirl chamber length for a stable cone was about 4mm. At 2mm swirl length the cone showed signs of instability (tearing). This could have been a symptom of shorter break up due to the reduced friction, but I believe that this explanation would produce an intact shorter cone, rather than the tear displayed.

The shorter cone produced by the 4mm swirl length:-

And the cone produced by the 2mm swirl length:-

The shorter cone length can be seen here, as can the tear in the fabric of the cone.

The flow rate for all of the swirl chamber length trials were of the order of 0.055 kg/sec.

It has been mentioned that the quality of the internal swirling liquid film is an important performance parameter for the gas centred swirl injector. There are various empirically derived film thickness relations in Lefebvre. Performance of swirl atomisers is highly dependant on specific geometry. None of the methods in Lefebvre related to an open swirl atomiser. Not surprisingly they did not give very sensible results when tried. 

According to Dr. John Chinn of UMIST, the air core within a swirl atomiser adjusts itself to permit the maximum flow rate. This is known as the principle of maximum flow, and is analogous to the flow of water over a weir.

This means that the exit diameter of the swirl atomiser is reduced by the diameter of the air core and effectively becomes an annulus. It was shown earlier that a swirl inducer equivalent diameter of 2.426 x 10^-3 metres was required to flow 0.055 kg/sec. As the same flow rate is exiting the atomiser, then the area of this annulus must be of the order of 4.62 x 10^-6 metres square. The air core in a standard swirl atomiser tapers outwards towards the exit diameter. In an open swirl atomiser the air core is parallel.

The photograph below shows the body with the swirl inducer pressed into position. It has been highlighted to show the air core annulus concept:-

The swirling liquid film thickness may be estimated as follows. If the flow area is A1 and the air core area A2, then the air core area A2 may be found by subtracting A1 from the total exit area Ae:-

Given that De is 11.5 x 10^-3 m,

Ae = 0.1038 x 10^-3 metres square

A1 = 4.62 x 10^-6 metres square

Hence A2 = Ae - A1 

A2 = 0.09918 x 10^-3 metres square

This means the air core diameter Dac is 11.23 x 10^-3 m. Subtracting this from the exit diameter De and dividing by two gives the thickness t of the liquid film:-

t = (D - Dac)/2

t = (11.5 x10^-3 - 11.23 x 10^-3)/2

t = 0.135 x 10^-3 m

t ~135 microns

Obviously I have no practical way of measuring this dimension apart from the assumption that particle size reflects film thickness to some degree. I had speculated in the previous post that the film thickness was of the order of 180 microns based on particle size. What does seem clear is that if the exit diameter is increased then film thickness should decrease. That would have a positive effect on atomisation and would also shorten the cone due to the thinner sheet having less resistance to inertial forces. That said, the friction from the larger swirl chamber wall surface area would tend to retard the angular velocity, somewhat negating this effect.

I trialled this by opening the last 10mm of the swirl chamber to 13mm. The swirler was installed to make the total swirl chamber length 15mm, as in the first trial which gave a cone length of 52mm. Here is a photograph of the 13mm De unit:-

It can be seen that the cone length has approximately halved. In addition, tearing can be seen on the cone surface suggesting it has been thinned. The discharge rate was still of the order of 0.055kg/sec.

The approximate swirling liquid film thickness for the 13mm De value is 115 micron, so approximately half of that when the De was 11.5mm.

For an effective gas centred swirl coaxial injector, a stable, thin swirling liquid film is essential. When this thin film is sheared by the central gas flow, very small droplets result. The possibility of swirling the central gas flow has occurred to me. I tried running compressed air at 690 kPa (100psi) through the swirl test unit. This produced a strong vacuum at the centre of the swirler, presumably where the air core was being generated. I suspect that in a production device this vacuum would disrupt the swirling film and lead to coalescence and droplet size increase. It may also lead to recirculation and attendant flow instabilities.

To conclude, the investigations so far carried out on swirl atomisation have shown the following:-

• The Cd of the open swirl atomiser can be considered unity for all practical purposes
• The equivalent diameter of the swirl inducer can be used to predict output flow
• With the current swirl inducer, a minimum swirl length of 4mm is required for a stable film
• Increasing swirl length increases stability of the film but increases cone length, decreasing swirl length decreases stability and decreases cone length
• For the current swirl inducer it appears possible to approximate the liquid film thickness
• Increasing the exit diameter of the swirler appears to decrease the liquid film thickness   
• Halving the film thickness appears to halve the cone length (tentative)

These trials have provided some excellent information, all of which is highly pertinent to the design of a gas centred swirl coaxial injector. The design of this device can now commence. Keep watching this space.

Swirl Investigations

Detailed results from the shear coaxial injector trials are now ready and will be published in due course. That said I have been making progress in the workshop based on the conclusions of the shear tests. I will report on that now.

The salient points of the shear tests were as follows:-

• Atomisation in the centre of the liquid stream was poorer than on the periphery, mainly due to the edges of the liquid stream being in closer contact with the gas and hence the greatest shearing force
• Droplet sizes were smaller when momentum flux ratio was increased (by using denser gas) but not by an order of magnitude
• Pulsing, with suspected mass flow fluctuation, was encountered in all the shear tests. This was thought to be due to recirculation of the gas in the injector cup - which could feed into combustion instabilities
•  The smallest droplet sizes were encountered when an element of swirl was induced in the liquid flow - pulsing was absent with swirl - the swirl seemed to stabilise the system

These observations make it fairly clear that swirl on the liquid phase appears to be advantageous in terms of droplet size reduction and spray stabilisation. It would seem obvious that a good method to reduce droplet size is to use the pressure of the liquid to effect primary atomisation prior to the stream being hit by the gas. The mechanism of stabilisation is less clear.

 Swirl atomisers work by using the pressure of the fluid to impart tangential velocity to the flow. The fluid then exits the atomiser in a swirling, air cored, thin walled cone. The following images (Rocco, Goncalves and Iha) show the classical swirl atomiser disintegration mechanism. The image with three shadowgraphs of a swirling cone shows the swirl angle increasing with inlet pressure and the break up length decreasing (which corresponds to a thinning of the swirling sheet). This is due to the greater tangential velocity produced by the higher pressure. The conical sheet exhibits longitudinal and lateral waves on it's surface. These are in fact Kelvin-Helmholtz waves. The second image (line drawing) shows that droplet formation proceeds from the break off of toroidal ligaments whose thickness is of the order of the film thickness and whose length corresponds to the wavelength of the surface waves on the sheet. 

If this thinned swirling sheet is sheared by a co-flowing gas, then it seems logical that smaller droplets should be produced than just with shearing alone.  In a rocket motor where the oxidiser is a gas, encapsulating the oxidiser with the fuel prevents any unmixed oxidiser reaching the chamber walls and reacting with them. Since the oxidiser in the Thunderchild system is the gas, a gas centred injector is seen to be desirable.

Such a gas centred swirl coaxial injector could be characterised as a straight post for the gas, surrounded by the liquid swirl inducer. Intuitively it would seem to be advantageous to allow the swirling flow to develop fully before subjecting it to the gas stream. The gas would shear the thin swirling sheet before it had exited the atomiser body, meaning primary atomisation would take place inside the injector cup.

The swirl inducer is the key component in this system. Swirl can be produced either by tangential drillings or a helical element. I looked at methods of drilling tangential holes, but ruled this out as being too hit and miss. I had done some preliminary experiments with swirl in 2011. The swirl inducers were simply made by cutting sections from double start wood screws. This was the method of producing tangential flow in the swirl portions of the shear coaxial tests. A more reproducible means would be to screw cut multiple start helical swirl inducers. That way a number of inducers could be manufactured to fit into a single common body. The dimensions of the  helical passages would also conform to a nominal standard.

As I already had the tooling to cut metric trapezoidal threads, I decided this was the way to go in terms of producing serviceable elements. The last post shows a swirler made in this way. I obtained the carbide inserts from Associated Production Tooling in Glasgow:- www.shop-apt.co.uk

 As previously mentioned, the metric trapezoidal thread is similar to acme, but with a thread angle of 30 degrees instead of 29 degrees.The image below shows the thread profile. The full specification is given in BS 5346 and more information can be found here:- www.roymech.co.uk/Useful_Tables/Screws/Trapezoidal.html

After studying swirl atomiser theory I decided to try to simplify the flow calculation by removing the effect of discharge coefficient. This could be achieved by sizing the outlet orifice much larger than would be required to deliver the flow rate from the trapezoidal helical passages.

This should make it possible to use standard pipe flow equations to calculate the flow through the helical passages, the dimensions of which could be found from the relevant standard. The image below shows the formula for the area of a trapezium:-

To find the flow through the trapezoidal passages, the equivalent flow area was calculated from the equivalent diameter. Equivalent diameter is defined as:-

ED = 4 x (A/WP) (1)

Where:-

ED = Equivalent diameter

A = Area 

WP = Wetted perimeter

The wetted perimeter in this instance is the sum of all four sides. The length of the angled sides was calculated using trigonometric relations.

The first swirler manufactured was shown in the previous post. This was a two start 2mm nominal pitch metric trapezoidal thread on an 8mm diameter brass bar. I decided to scale this up slightly for the test units and ultimately the prototype injector. I went with 12mm bar and 3mm nominal pitch, again with a two start thread. I reasoned that the 12mm diameter inducer would be easier to get a gas post through. I also had hopes that the wider swirler would lead to a thinner liquid film, and hence smaller droplets.

The actual pitch of the thread was increased to 6mm to allow a double start. The machining method was as described in the previous post. A simple body was made to carry the swirler. This was of 25.4mm diameter BS230M07 steel. An 8mm long, 7.5mm diameter outlet orifice was drilled. This has a conical lead in from the swirl inducer. The inducer is a transition fit in the body and a 1/4 inch BSPT fitting introduces the test liquid, water in this case. Here is a high speed flash photograph of the assembled device on test:-

A well defined cone can be seen, as can toroidal ligaments tearing off and forming droplets. The cone angle is approximately 110 degrees.

The better images were taken from above the cone, also at high speed and with flash:-

It is instructive to compare this image with the shadowgraphs taken from Rocco, Goncalves and Iha. The lateral and longitudinal waves can be seen on the surface of the cone. The break away and subsequent disintegration into droplets of the toroidal ligaments is prominently displayed.

Here is the same photograph with some droplet sizes measured using the same software as in the shear coaxial tests:-

Droplet sizing is seen here over one of the toroidal ligaments. This was just a rough attempt to get some idea of the sizes produced. It can be seen that the smallest resolvable drop sizes seem to be a definite improvement on those in the shear coaxial tests.

From the droplet sizes it would appear that the film thickness is in the region of 180 - 220 microns.

The flow rate for this two start swirler was calculated at 0.047 kg/sec, using the equivalent diameter as defined in (1) above. The actual flow rate measured by timed discharge was 0.05 kg/sec. Allowing for timing and measurement errors this seems like a reasonable level of agreement. It looks as though the assumptions made regarding flow calculation were plausible. 

Finally, here is a triple start swirler that has been machined on a 12mm brass bar. This is also 3mm nominal pitch. For a three start thread, 3mm metric trapezoidal would need a pitch of 9mm. The Harrison M250 can cut a maximum pitch of 8mm. Hence the compound had to be advanced by 2.6mm per start, as opposed to 3mm. This is of little importance in this application. In the second photograph, the three starts have been marked in black, green and red ink to make them more visible. The image of Her Majesty the Queen gives the scale:-

The next stage will be to construct a prototype gas centred swirl coaxial injector for testing. Keep watching this space.

Workshop Update

I am still working on the results of the shear coaxial injector tests. In the meantime, here is what I have been up to in the workshop.

I have gone a little further down the road to producing a swirl prototype by machining some swirl inducers.

A two start metric trapezoidal thread was generated on a section of round brass bar. The metric trapezoidal thread form is similar to acme, though with a thread angle of 30 degrees as opposed to 29 degrees.

The photograph shows a swirl inducer that has just been machined. The insert tool can also be seen. The thread is of 2mm pitch, meaning that the Harrison was set up to cut a 4mm pitch for the first start, and then the compound was advanced by 2mm to put the second start in between the first.

The liquid will be swirled through the annulus, thereby creating a thin film which will be atomised very completely by the high speed gas flow through the core. High swirl and high momentum flux ratio are the keys to this system.

Coaxial Shear Injector - Particle Sizing Update

This morning I completed the last of the Coaxial Shear Injector particle sizing experiments. I now have a sizable and interesting data set that is going to take no small amount of processing.

With that in mind, this post will be a combination of a description of the experiments carried out and the photographic method adopted. I will also give some initial speculative conclusions based on the results as analysed thus far.

The tests were carried out using air and argon respectively, and four different basic injector configurations were tested. These were as follows:-

• 2.5mm (0.098") liquid orifice with 1Dl recess
• As above but with 2Dl recess
• 3.5mm (0.137") liquid orifice with 1DL recess
• As above but with 2Dl recess

These set ups were all run with air and then argon to test the effect of varying momentum flux ratio and aerodynamic Weber number, as well as velocity ratio. The liquid simulant was water. The 2.5mm orifice gave a liquid velocity of 5.6 m/s (18.4 ft/sec) whereas the 3.5mm orifice gave 2.86 m/s (9.4 ft/sec).

Another subset of experiments was run with the 2Dl recess using air with a swirl inducer in the central orifice. Both water and air were run through the central orifice to check the effect of the swirl. In addition, air was also run through the central orifice without swirl.

The gas/liquid ratio was the same as the design o/f ratio, namely 1.2. This meant that the water flow rate was increased fractionally when running the argon tests in order to maintain  some degree of verisimilitude. The injector was mounted on a simple bracket which was then held in a machine vice.

It took several days of experimentation to come up with a photographic technique that provided suitable images for droplet analysis. As mentioned previously, I had thought to use a backlit technique to illuminate the spray and thereby image the droplets. I set up the camera, injector and an opaque perspex screen. The backlighting came from a Yongnuo Y560 speedlight flash unit situated behind the screen. The flash unit was mounted on a tripod and connected to the camera by means of a hot shoe extension cable. This arrangement, minus the flash unit, is shown below:-

The camera used was a Nikon D70s DSLR. The backlit photographs, whilst showing the break up length to good effect, proved to be ineffective for imaging the droplets. This is a typical backlit image produced:-

As can be seen, the break up length is visible but little else. I experimented with various techniques and I found that the best spray and droplet images were produced by directing the flash onto the spray from the front, using the perspex screen as an opaque background.

For each injector and gas configuration, I took a general overview image using a Canon IXUS IS95 digital camera. This was followed by droplet imaging shots using the Nikon, from two different positions. Both were perpendicular to the injector face, the first being 40mm from the face and the second 140mm from the face. The image below shows the general overview of an injector run with argon and the 3.5mm liquid orifice with a 1Dl recess:-

It can be seen that the spray appears to consist of two discrete cones; a relatively translucent outer cone with an optically more dense core. This core consisted of a variety of sizes of droplet ranging from about 160 microns to 600 microns. The major droplet clusters appear to be around the 250 - 300 micron size. The droplets in the outer cone could not be resolved with the camera and lenses at my disposal. They form the vast majority of the droplets in the spray, and I believe that they are very small indeed, certainly 60 microns and smaller. Hence conclusions on spray quality can only be made based on the droplets that can be resolved. 

Some tenuous preliminary conclusions? Resolved droplet sizes ranged from 160 to 600 microns. There appeared to be a considerable number of smaller droplets that could not be resolved. Increasing momentum flux ratio appears to produce overall smaller droplets. Decreasing velocity ratio seems to produce coarser atomisation, with a faster liquid speed creating smaller droplets. This points to the liquid Reynolds number creating more and smaller initial disturbances. Oscillation or pulsing of the spray was observed in all the basic injector configurations, to a greater or lesser degree. Increasing Dl tends to increase the severity of the pulsing (amplitude increases whilst frequency seems to remain stable). I suspect the pulsing is driven by some sort of recirculation at the point of the gas/water interface, and recessing the centre post makes this worse. The initial results seem to be confirming those predicted from study of shear coaxial injector theory, as well as those from the earlier tests carried out in 2010 - 2011.

I know that you will all want to see a picture of the spray showing droplet sizes. so I've included one below. I have to stress at this point that I am still processing the images from the experiments and another post will follow detailing the droplet distributions and average sizes for each configuration,  along with more detailed conclusions. I will also describe the droplet sizing software used. 

This image is a slice from the Position 1 shot taken from a run using the 3.5mm orifice with air and a 1Dl recess.

To reiterate, I've compiled this post to get some initial results "out there" and a description of the experimental method. A more detailed one will follow giving droplet sizes and distributions for all of the configurations tested, along with more in depth conclusions regarding the various injector configurations.

I hope to have the detailed post ready in the next few weeks. Do keep watching.

Shadow Sizing

I have mentioned before that I am playing catch up with this blog; the initial experiments with the Shear Coaxial Injector took place over several months between 2010 and 2011. My original intention was to analyse the results of these experiments and post them here. However, I have decided on a much more interesting and hopefully illuminating course of action.

I am going to repeat the Shear Coaxial experiments, but this time I am going to attempt to set up a rudimentary particle sizing arrangement. At the start of the project I wrote to Dr Matt Stickland at the Mechanical Engineering Department of Strathclyde University, asking for advice on particle sizing. He very kindly wrote back and advised that the best method is Laser Doppler Interferometry - equipment costing hundreds of thousands of pounds. That aside, he also outlined a method that seemed to be within the grasp of the amateur workshop. This technique is called Shadow Sizing.

The basic premise is to take a backlit photograph of the spray with a very short depth of focus. The back lighting comes from a speedlight flash unit that is well diffused by a sheet of frosted glass or perspex. If the speed of the flash and the camera shutter are fast enough, the result should be a photograph of the shadow of the spray with the droplets frozen in mid flight. Software can then be used to measure the size of the droplets with reference to a known dimension in the frame, for example part of the injector structure.

I have all the items needed to carry out this test either on order or in place. The camera in use will be a Nikon D70s DSLR. I also have a piece of software that can be pressed into service to perform the droplet measurements.

So hopefully in the next few weeks you will see an analysis of the Shear Coaxial Injector based on the theory outlined so far, as well as some droplet sizes to compare with the empirical predictive relations.

Once I have covered the Shear Coaxial Injector, I shall go on to explain the measures taken to improve its performance, including the introduction of swirl. I can hear your hearts beating faster at the very thought.

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.