Supersonic Wind Tunnel part 1

 

Previously I had mentioned the use of water flow to simulate supersonic flow, however after having done some research I’ve abandoned this approach for now in favour of building a supersonic wind tunnel. The main reason for this is I’d like to some investigation on combustion stability at the small scale I want to operate at, and I will have issues trying to match Reynolds and Strouhal Numbers aft of the intake with a water channel, so that would require a separate experiment. I will almost certainly be using a separate experiment to do combustion analysis anyway, but I quite like the idea of running a micro-ramjet engine, even for a second, in supersonic flow in a wind tunnel small enough to sit on my desktop.

So there are a number of choices I can use regarding supersonic wind tunnels and they fall under two main categories; continuous and intermittent. Continuous tunnels tend to be a closed system, where the air recirculates within the tunnel and does not exhaust into the atmosphere. They also tend to be expensive and consume large amounts of power. They may require several hours of run time before they achieve the desired flow regime but they do offer finer flow control and a large range of Mach numbers can be achieved. Another concept I looked at was the use of a continuous open-system type using multiple vacuum cleaner motors, staged so that the required pressure ratio could be achieved and the air flowing into the impellers would have to pass through the test section first, but again the cost of assembling such a thing would be prohibitive let alone the cost of running several 240 Volt, 1600 Watt motors in unison, that’s also assuming the electrical wiring in my house could cope with drawing large amounts of Amps without setting something on fire! The power requirements vs test section size are unfavourable at these small scales, the small, continuous tunnel used by aerospace students at Toronto University [1], uses a 550V, 15kW motor for a 30 mm test section height.

concept-cont-ss-tunnel
Schematic of a multi-blower indraft tunnel briefly explored

The intermittent tunnels all work on the same principle, create a large pressure difference either side of the test section and let physics do the rest until such time  the pressure equalises. Shock tubes are probably the simplest form and can be driven by explosives, or a burst disk set to release at a certain gas pressure. These operate for very short durations, and at the scales I’m interested in would be useless.

The next arrangements are the most interest for my own needs, these are the blow down and indraft tunnels. The former makes use of a compressed air tank, which is then discharged through a nozzle, relying on the difference between the atmospheric and tank pressure to accelerate the flow through the section, discharging the air into the atmosphere. The latter relies on a tank placed aft of the test section, and is then reduced to as near vacuum as possible. A valve is then opened and atmospheric pressure is then enough to create sonic conditions in the nozzle throat. There is a hybrid of these two tunnels whereby high pressure air and a vacuum are used to maximise the pressure difference, but for the sake of another atmosphere of pressure difference, I didn’t think it was worth the extra complication.

The advantage of an indraft tunnel is the inherit safety of operating close to the tank, which if it should fail, simply implodes, whereas a pressure tank tends to resolve anything close by into its component parts, human bodies included. However there are problems, the sourcing of a large tank sturdy enough to resist imploding and creating the vacuum. I did draw up some plans to use an old oil barrel and a cheap vacuum pump, but a few back of the envelope calculations suggest I wouldn’t get anything like a low enough pressure before the barrels failed, meaning I’d need several barrels. There are plenty of YouTube videos showing barrels imploding after filling them with steam, sealing them and then letting them cool. So this idea was also discounted.

beadblaster
Tyre bead blaster, note the large diameter pipe fitting and valve

The blow down tunnel does mean I can use a compressed air tank, designed for the purpose so giving me an acceptable safety margin. However most compressed air tanks within my budget are the types sold by DIY stores, and don’t come supplied with fittings of a sufficient diameter to create the required mass flow rates, that was until I stumbled on ‘tyre bead blasters’. Small compressed air tanks of around 5 – 10 gallons in volume, with 30 mm pipe fittings and a valve, once filled the entire air supply is literally blasted at the rim of a tyre to seat it onto the wheel rim. These seem to be the ideal pressure vessel, but how long would one of these run a modestly sized supersonic tunnel for……..

A schematic of a simple desktop supersonic tunnel is shown below, with so few parts it can be made from easily available materials, and instrumentation should also be fairly easily come by or made.

blowdownScmtc
Proposed Desktop Sized Supersonic Tunnel

 

Modelling blow down time

A number of strategies were explored to model the time it takes for the tank to empty, so I know whether the idea is feasible or not as I didn’t want a test section height smaller than 30mm and a running time of less than a second.

The first approach was to use steady one-dimensional flow equations to give an approximate time as a benchmark, based on the following:

Variables-ssonic-flow
Constants and variables used in the analyses
eqns-ssonic-flow
Steady one-dimensional analysis of blow down time

Just under a second, this doesn’t seem too promising, but this was assuming a 15 mm square throat. So rather than repeating the same calculations over and over it’s time to dive into Excel.

I looked at a number of papers on the topic of leaking pressure vessels [2,3], and compiled them into workable models in Excel, see below, I’m not going to discuss the finer points of these models as they’re adequately explained in the papers, but I do have some doubts about its accuracy for simulating large pressure drops in small tanks, as the models were originally designed to model leaks of large tanks over many minutes and hours, although both cases rely on choked flow at the source of the leak.

The plot shows the results for the methods outlined by Bird et al, and Rasouli and Williams papers, together with the mean data of both models between the two, the horizontal line indicating the minimum pressure to maintain sonic flow in the throat. They predict low run times of around half a second, which while workable, is a bit too low, and is somewhat lower than the 1D-steady flow equation previously calculated.

I did have some doubts with these results, as expressed earlier, so another trawl through Google had another paper on gas discharge in my hands [4], describing a simpler isothermal model based on exponential decay. The isothermal behaviour best fitted this work as the duration the tunnel will be in operation will negate any heat transfer. The authors had also carried out numerous blow down tests for various nozzle sizes and tank combinations, the results of which match the numerical model well. Adding the results of this new model to the spreadsheet, the data suggest a runtime closer to one and a half seconds. Due to the validation carried out in the paper, I have more confidence in these new results and so that means I can carry on with the design!

Once I design the test section nozzle, which will accelerate the flow to the desired Mach number, I can fine tune the nozzle area, as a reduction of 5 mm in throat width gives an estimated blow down time of two seconds.

blowdowngraph
Results from various blow-down modelling methods

Refs:

1.  http://www.aerospace.utoronto.ca/pdf_files/supersonic.pd

2. Rasouli, F., and Williams, T.A., Journal Air & Waste Management Assoc., March 1995.

3. Bird, R.B., Stewart, W.E., and Lightfoot, E.N., Transport Phenomena, John Wiley & Sons, New York 1960.

4. Dutton, C.J., and Coverdill, R.F., Experiments to Study the Gaseous Discharge and Filling of Vessels, 1996.

 

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