Rate Of Propane Diffusion In Air

When fueling a combustion spudgun one question that occasionally arises is; "How long does it take to equilibrate (fully mix) the fuel with the air in the chamber?" To get the most oomph from a canon the fuel and air in the chamber need to be well mixed. If most of the fuel is at one end of the chamber the cannon's power will be reduced, indeed it may not fire at all.

I've noticed that a cannon, without a chamber fan, and fueled with a syringe is much more powerful on a warm summer day than it is on a cool winter day. With a chamber fan the cannon's performance is much less sensitive to the temperature. Perhaps the temperature dependence, in the absence of a fan, is due to slower mixing of the fuel and air on a cold day.

It would be handy to have an estimate of how fast propane diffuses (mixes) with air. To this end, I have constructed a simple combustion chamber specifically designed to mix slowly. The chamber has a large aspect ratio (length to width ratio), no chamber fan, and is fuel by slow injection of propane near the end of the chamber opposite the spark gap end.

Chamber Construction

The test chamber was constructed from a 46" long by 1.69" diameter (aspect ratio 27:1) polycarbonate fluorescent lamp protector tube. These clear polycarbonate tubes are available at most hardware stores for a couple bucks each. The setup is shown below.

I closed the ends of the polycarbonate tube with plastic wrap held in place with rubber bands (see photo below of the spark gap end of the chamber). The chamber could be described as a "semi-open" tube; at low pressures the chamber is well sealed, a modest rise in pressure will blow the plastic wrap end caps off the chamber and limit the peak pressure in the chamber.

The spark gap consists of a pair of "un-popped" pop rivets hot glued into holes in the tube. The ignition source was a "100KV" stun gun.

To make the small (0.05"D) filling vent hole visible I highlighted it with a black marker (visible in the photo above).

The tests were carried out at temperatures that  ranged from about 41F to 52F.

68cc of propane (4% of the chamber volume) was measured with a syringe and injected over about 10 seconds into the small hole on the end of the tube opposite from the spark gap. The small vent hole on the spark end was also open during injection. The holes were covered with blue painter's tape after fueling. The blue tape survived repeated firings of the tube, without perforating or being dislodged, even though it was peeled back and then reapplied for each refueling. The tube was held horizontal while fueling and was left to sit, without being disturbed, for the times described below. 

Diffusion Time Tests

In the first test the chamber was fueled and the first ignition attempt was 5 minutes after fueling. The chamber did not ignite. Four more attempts were made at times up to 54 minutes without ignition. The chamber then sat for an additional 38 minutes (92 minutes total) before another attempt was made at which time it ignited, blowing both of the rubber banded plastic wrap end caps.

For the second test the chamber was purged with a fan, fueled as before and ignition attempted at 19, 37, 47, 56, ... minutes up to a last test at 6hrs after fueling. The chamber never ignited. This suggests to me that there is some problem associated with multiple unsuccessful attempts at ignition. It appears that unsuccessful ignition attempts in some way consume the fuel and/or oxygen in the chamber. Perhaps some of the fuel is burned even though the chamber doesn't fully ignite. Alternatively, the spark converts some of the oxygen in the chamber to ozone, which then reacts slowly with the polycarbonate chamber or with some of the propane fuel. Repeated nonproductive firings ends up reducing the fuel and/or oxygen level below the lower combustion limit of propane in air.

To over come this problem I changed the testing procedure. In the new method ignition is only attempted once per fueling cycle. If the chamber does not ignite then it is purged and refueled and a new test is started.

Tests using this new method successfully ignited after 111, 77, 62, 57, 49 and 42.5 minutes. The next attempt was at 31 minutes which failed to ignite (the chamber also didn't ignite at 44 min but did ignite at 176 minutes).

The next tests ignited at 37, 33 and 25 minutes.

Though I was trying to keep the refueling method as consistent as possible there is still significant variability in the mixing rate. There were ignition failures at 19 and 31 minutes and success at 25 minutes. Given this variability, a precise measurement of the diffusion rate is not possible. It is possible to estimate an approximate diffusion rate. It appears that the time to diffuse the ~44 inches between the inlet port and the spark gap is between 25 and 31 minutes. Therefore, the rate of diffusion is 1.4 to 1.8 inch/min. Note that this time does not represent the time needed to fully equilibrate the gases in the chamber. Instead, it is the time required to get a combustible mixture at the spark gap. Since the lower flammability limit of propane in air is about 3% the observed time to ignition may represent the equivalent of two diffusional half-lifes. The first half-life gets the propane concentration at the spark gap to 2% (50% equilibration) which won't ignite, the second half-life to 3% (75% equilibration) which will ignite.

It appears that propane diffuses in air with a half-life rate of 0.28 to 0.35 minutes per inch at temperatures in the range of 41F to 52F. To get the fuel mixture to 97% of full equilibration will require 5 half-lifes (calculated as [1 - 1/2⁵]), roughly 1.5 min/inch length between the fuel injection point and the spark gap.

Speeding Mixing Up

In the studies above I was trying to get the fuel to diffuse as slowly as possible, the resulting diffusion rate is a worst case scenario for this particular chamber. I then examined how much the diffusion rate can be increased by simply injecting the fuel in a way that will maximize mixing. The fastest that I can inject the 68cc fuel from the syringe is about 1 second, roughly ten times faster than in the previous studies. To see if a higher injection rate increases the mixing rate, I did a series of firings using the higher fuel inject rate. To reduce the back pressure in the system I added an additional 0.101" diameter vent hole to the spark gap end of the chamber in addition to the original 0.052" hole. The chamber now has five times greater vent area at the spark gap end.

The syringe needle is 1.5" long and has an OD of 0.049". I estimate that the ID of the needle is about 0.043". Injecting 68cc (4.15in³) of gas through a needle with an area of Pi(0.043/2)² = 0.00145in² in one second gives a gas velocity of;

As before, the fuel was injected, the holes covered with tape and, after a waiting period, the chamber was ignited. Under these conditions the chamber fired at 22, 19 and 14 minutes. The chamber didn't ignite at 10 minutes (this loading also didn't ignite at 11 but did ignite at 14 minutes). The next test failed to ignite at 12 and 13 but did ignite at 15 minutes. Assuming that only the first attempt at ignition is a valid measurement, it appears the diffusion time to a combustible mixture over the 44" distance is more than 12 and less than 14 minutes. So, the t_1/2 is about 0.15min/inch and 5t_1/2 is 0.75 min/inch. Expressed as a diffusion velocity instead of a rate we get  6.7inch/min.

Fast injection of the fuel increased the apparent diffusion rate by a factor of two for this combustion chamber.

Literature Values for Propane Diffusion in Air

Table 1 (below) contains various physical and combustion properties for propane, methane and gasoline (Data from http://wps.com/LPG/WVU-review.html).

Table 1. Some Physical and Combustion Properties of Propane, Methane and Gasoline

The measured diffusion velocity of 6.7inch/min agrees reasonable well with the value of ~8.0inch/min from Table 1.

How Fast Would Other Fuel Gases Diffuse

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of the gas's molecular weight. We can use this relationship to estimate how much faster, or slower, other fuel gases would diffuse in this chamber.

Conclusions

This study was designed to measure the worst case diffusion rate. In practice, there are several things that can be done to increase the mixing rate of propane in air. A chamber fan should give complete mixing in just a few seconds. Inverting the chamber slowly several times should also significantly increase the diffusion rate as will injecting the fuel at high velocity. Injecting the fuel at the center of the chamber, instead of the end, will cut the distance the fuel has to diffuse in half and give adequate mixing in half the time.