Cooling

I haven't posted recently, as you'll no doubt have noticed. A great deal has happened to me since the last time I made an entry here, almost none of it related to rocketry. Those who need to know, know. Suffice it to say, I'm in a much better frame of mind now than I was and I am ready to take up my project where I left off, and begin sharing ideas with all of you.

What I want to talk about today is cooling. Apparently, the engineer who was in charge of the tube bundle development for the Rocketdyne F1 was told to "make sure it doesn't melt". The goal of rocket motor cooling can't really be stated any clearer than that, so here are my thoughts on the subject.

All of my earlier attempts to estimate cooling requirements were based on the approach given in Krzycki, and I tried to compare my engine design to similar sized ones in the literature to get some idea of the heat flux that might be encountered. I decided to adopt a slightly more stringent approach. To that end, I studied various sources on the subject, the chief ones being Huzel & Huang and Humble, Henry and Larson. I also dipped into a lot of the NTRS papers, as well as The RAE's Beta Project report.

The best amateur analysis of the regenerative cooling problem I have found online is that by G N Sortino at Fubarlabs, "Thermal Analysis of Steady State Engines" which can be found here:- wiki.fubarlabs.org/fubarwiki/Thermal-Analysis-of-Steady-State-Engines.ashx

I quickly found, as did the above author, that there are a lot of tricky variables in these equations, and it is not at all easy to know where to begin. Luckily, Huzel and Huang's approach to cooling design is eminently practical. By combining their approach with an engine concept that I felt could be fabricated, I started to make some small headway.

I began by thinking about an engine composed of a tube bundle and with a thrust of 1000lbf. I arbitrarily decided on a tube ID of 6mm, purely on a rule of thumb basis. I then ran a simulation on RPA of this hypothetical engine, the propellants being a 90% ethanol/water mix with Nitrous Oxide. Here are the leading particulars for this thrust chamber as calculated by RPA:-

#---------------------------------------------------------------------------------------------------
#
# Table 1. Thermodynamic properties
#---------------------------------------------------------------------------------------------------
# Parameter Injector Nozzle inl Nozzle thr Nozzle exi Unit
#---------------------------------------------------------------------------------------------------
Pressure 2.0684 2.0661 1.1392 0.1015 MPa
Temperature 1867.3657 1867.1488 1646.1334 995.3005 K
Enthalpy -1347.9581 -1348.3832 -1778.8090 -3060.6928 kJ/kg
Entropy 11.1984 11.1986 11.1986 11.1986 kJ/(kg·K)
Internal energy -2117.3892 -2117.7249 -2457.0646 -3469.2680 kJ/kg
Specific heat (p=const) 1.9622 1.9622 1.9364 2.5923 kJ/(kg·K)
Specific heat (V=const) 1.5496 1.5496 1.5241 2.0981 kJ/(kg·K)
Gamma 1.2663 1.2663 1.2705 1.2356
Isentropic exponent 1.2662 1.2662 1.2705 1.2270
Gas constant 0.4120 0.4120 0.4120 0.4105 kJ/(kg·K)
Molecular weight (gas) 20.1788 20.1788 20.1793 20.2543
Molar mass (gas) 0.0202 0.0202 0.0202 0.0203 kg/mol
Molar mass (total) 0.0202 0.0202 0.0202 0.0203 kg/mol
Density 2.6883 2.6856 1.6796 0.2484 kg/m³
Sonic velocity 987.0341 986.9786 928.2780 708.0312 m/s
Velocity 0.0000 29.1568 928.2780 1850.8024 m/s
Mach number 0.0000 0.0295 1.0000 2.6140
Area ratio 19.9000 19.9000 1.0000 3.3900
Mass flux 78.3036 78.3036 1559.0966 459.7134 kg/(m²·s)
Viscosity 0.0001 0.0001 0.0001 0.0000 kg/(m·s)
Conductivity, frozen 0.2122 0.2122 0.1908 0.1306 W/(m·K)
Specific heat (p=const), frozen 1.9240 1.9240 1.8840 1.7340 kJ/(kg·K)
Prandtl number, frozen 0.5869 0.5869 0.5868 0.5600
Conductivity, effective 0.2177 0.2168 0.1919 nan W/(m·K)
Specific heat (p=const), effective 1.9550 1.9610 1.8920 nan kJ/(kg·K)
Prandtl number, effective 0.5814 0.5855 0.5860 nan
#---------------------------------------------------------------------------------------------------

The first step in the heat transfer calculation was to find the gas side heat transfer coefficient, hg. Before doing this, figures for adiabatic wall temperature and the actual gas side cooled wall temperature were derived.

The adiabatic wall temperature may be found at any point in the chamber by multiplying the stagnation temperature by a stagnation recovery factor, typically 0.9. I decided to model the cooling on the throat case as this would be the most stringent. At the throat, the stagnation recovery factor is 1, so it can be seen from this and the figures above that the adiabatic wall temperature at the throat is about 1867.15 K.

Taw = 1867.15 K

The next figure to determine was the gas side cooled wall temperature, or Twg. Of course there is no way to know what this is, so the approach is to state a figure that it is within the wall material's ability to withstand. I envisaged a tube wall bundle made of 316L tubes welded together. I wanted to keep this below 400 deg C so I decided on a figure for Twg of 300 deg C or 573.15 K.

Twg = 573.15 K

Next, to calculate hg:-

hg = 0.026k (pv/u)^0.8 (1/Dt)^0.2 (Cpu/k)^0.4

Where:-

k = gas thermal conductivity
p = gas density
v = gas velocity
u = gas dynamic viscosity
Dt = throat diameter
Cp = gas specific heat at constant pressure

All of the above values can be got from the RPA table, apart from Dt. For the engine under consideration, standard design equations put the throat diameter at 45mm i.e. 45 x 10^-3m.

With these values in the hg equation, the following values resulted:-

hg = 0.00494 x 861439.4 x 1.859 x 0.0516

hg = 408.2 W/m^2K

Using hg, Taw and Twg the calculation can now be moved on further to gain the throat heat flux, q:-

q = (Taw - Twg) x hg

q = (1867.15 - 573.15) x 408.2

q = 528.2 x 10^3 W/m^2

It is now possible to calculate the temperature of the cooled side of the wall Twc, as follows:-

Twc = Twg - qt/k

Where:-

t = wall thickness
k = wall material thermal conductivity

I had decided to use metric hydraulic tubing for the bundle material. Tube of 10mm OD has a 6mm ID hence the wall thickness t is 2mm. The thermal conductivity of 316L at 300 deg C is about 16 W/m^2.

Hence:-

Twc = 573.15 - [(528.2 x 10^3 x 2 x 10^-3)/16]

Twc = 573.15 - 66

Twc = 507.15 K

This figure of 507.15 K for Twc is rather apposite, as it corresponds to 234 deg C. We know that the oxidiser, nitrous oxide, sits at about 760 psi at STP. We will want to pressurise it above and beyond this value for reasons of both safety and flow homogeneity. If we assume a figure of 800 psi as our pressurant level, then we can use this for the fuel as well. The boiling point of pure ethanol at 800 psi is about 240 deg C. The wall temperature on the cooled side is below this, and this with ethanol/water. By adjusting the coolant pressure we can tune the response to induce some nucleate boiling.

It is now possible to calculate the required coolant heat transfer coefficient to permit the calculated gas side heat transfer and temperature differential. Huzel and Huang give a practical method of doing this:-

hc = q/(Tcw - Tco)

where Tco = coolant temperature. What figure must be used for this? In Huzel and Huang it is assumed that the coolant flowing through the throat tube is in a two pass circuit and has already been through the throat once. A value of 600 deg R is assigned for Tco. This is 60 deg C. I was troubled by this figure as I felt it would be neccesary to account for the temperature increase the coolant would see as it traversed the chamber, let alone the throat. As the flow of the coolant through the tubes is turbulent and is constantly being renewed, it would seem that the instantaneous coolant temperature would be unlikely to approach the values of Tcw in the various parts of the chamber. Therefore I decided to use a "film temperature" for the Tco figure. Film temperature of the coolant can be defined as:-

Tfilm = 0.5(Tcw - Tcs)

Where Tcs = coolant static temperature, i.e. the temperature on entering the coolant circuit.

So for the above case, Tfilm = 0.5(507.15 K - 293.15 K)

Tfilm = Tco = 380.15 K i.e. ~ 100 deg C

So the hc required to achieve steady state in the cooling circuit becomes:-

hc = q/(Tcw - Tco)

hc= 528.2 x 10^3/(507.15 - 380.15)

hc = 4159 W/m^2K 

Recall now that I was talking about using 316L tubes in this design. The tubes have a 10mm OD. For a 1000lbf engine, the fuel flowrate will be about 0.84 Kg/sec. The chamber diameter will be about 200mm. This means a total of 63 tubes to form the chamber. Now, the formula to calculate hc for a given flowrate and tube diameter is:-

hc = 0.023 (Cp m/A) (u/Dpv)^0.2 (k/uCp)^0.66

Where:-

Cp = coolant specific heat
m = coolant flowrate
A = coolant flow area
D = coolant flow diameter
u = coolant dynamic viscosity
k = coolant thermal conductivity
p = coolant density

The coolant transport properties (density, specific heat and so on) were all calculated at the Tco value of 380.15 K. They are detailed below:-

Density = 755.6Kg/m^3

Thermal conductivity = 0.185 w/mK

Specific heat = 3.39 x 10^3 J/KgK

Dynamic viscosity = 0.3 x 10^-3 N-s/m^2

These values were calculated for 90% ethanol/water at Tco of 380.15 K. The thermal conductivity was calculated using the Fillipov equation. Dynamic viscosity was found by using the Refutas equation to find kinematic viscosity and then multiplying this by the density.

Going back to the practical aspect of 316L tubes, I envisaged the coolant circuit as consisting of a series of tubes joined by manifolds to allow the coolant to pass up and down the chamber, thereby splitting the 63 tubes up into groups of coolant passages. It can be seen that the values to be used in the hc calculation are essentially constants. Only changing the number of tubes in a coolant passage group will alter the coolant flowrate and thus velocity. So the problem then became one of iteration to come as close to an hc value of 4159 W/m^2K as was practicable.

It was found that by splitting the 63 tubes up into 21 coolant passage groups of 3 tubes each, the following result was gained:-

21 groups of 3 tubes, each group of 3 tubes forming one coolant passage

0.84 kg/sec / 21 = 0.04 kg/sec 

0.04 kg/sec through a 6mm ID tube gives a velocity of 1.87 m/sec

then:-

hc = 0.023 ((3.39x10^3 x 0.04)/2.83x10^-5) (0.3x10^-3/(6x10^-3 x 755.6 x 1.87))^0.2 (0.185/0.3x10^-3 x 3.39x10^3)^0.66 

hc = 0.023 x 4791519.4 x 0.129 x 0.325

hc = 4620.3 W/m^2K

Recall that the figure required was 4159 W/m^2K. Do these calculations mean that this hypothetical system would be steady state? I'd say yes, tentatively. They are as far as I've got up to now and they feel right. I'm open to all comments and that is why I have posted them here. I'd be very grateful for any thoughts on all of this.

Nitrous Oxide

Apologies, Dear Reader, for the dearth of entries just lately. As you might imagine from the post title, I have finally relented. It is happening. More to follow, do stay tuned.

Hydrogen Peroxide

Definitely not.

Hydrogen Peroxide

Well, maybe...watch this space.

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.