Recap from Part 1
Perseverance is all about silent operation, and so reducing the sound of the generator running is all important. The spectrum of the generator with two compementary conventional silencers in series is shown below, with the eight dominant harmonics labelled.
The first order tone of 38Hz is one tenth of the amplitude of the second order, 76Hz, tone. Furthermore, at low frequencies the ear becomes less sensitive, with the ISO standard for perceived loudness indicating a change of about 13dB between these two frequencies. Put another way, at equal pressure levels, the lower frequency sounds one twentieth as loud. Taking these two things together, the 38Hz tone sounds 1/200th as loud as the 76Hz tone, which is why the second harmonic is the most noticeable sound.
In this second installment of the silencing blogs, I shall explain how I tackled this particular issue.
Pressure or Flow?
Going down the exhaust pipe we have the hot exhaust gas and, each time the engine exhaust valves open, there is a pressure pulse that travels down the pipe. These two travel at different speeds, with the gas flowing faster as the engine makes more power, but the pulses always travelling at the speed of sound.
Running at full power, the BetaGen 10 exhaust gas will flow down Perseverance's 1.5in BSP pipework at about 11m/s. The speed of sound is proportional to the square root of the absolute temperature (aviation digression, this is why airliners are limited by Mach number at altitude, and hence why they all fly at about the same speed in the cruise. Except Concorde, but that's stacked digressions, so I best return to the matter in hand).
For an exhaust temperature of 200C, the pressure waves travel at 440m/s. Far faster than the flow of the gas, and little affected by the engine power. It is these pressure pulses that we hear, and which a silencer is trying to suppress.
For most engines (think car, motorbike, diesel narrowboat) the engine speed changes as the speed of the vehicle changes, but on Perseverance I specifically chose a fixed speed generator so I could play tunes on the exhaust. I'm now going to ask you to use your imagination to understand how this works.
Splitting the Pipe
An exhaust tone is a series of pressure peaks and troughs passing down the exhaust in a regular pattern. If we split the exhaust pipe into two parts, with half the flow going down each pipe, the same pressure pattern will pass through each pipe. When the two flows converge again, the peak and trough pattern will be re-established.
Quality graphics, eh?
Now let's give one of the two pipes a longer journey. As the pressure pulses travel at the speed of sound, the pulses going down the shorter pipe arrive at the converging point earlier than the pulses going round the longer pipe. The more the difference in pipe lengths, the greater the time difference. At one special difference in lengths, the pulses travelling down the longer pipe are delayed so much that they arrive exactly as the troughs arrive down the shorter pipe.
The two cancel each other out and there is neither a pulse nor a trough to carry on down the exhaust. The result is blissful silence (at least, for one specific tone). Just to prove this is not entirely nonsense, here is a photo of a long and short path exhaust on an industrial diesel generator.
Things Get Crazy
If you've got your head around that, things now get bizarre. As these are pressure pulses and not flow, we can make them travel both ways down the same pipe. Think of the old fashioned speaking tube - you can speak and listen, with pressure waves travelling in different directions. Better still, you can do both at the same time. My wife and I do this frequently, and without a tube. You get the idea.
We can fold our "longer journey" pipe in half, and make the pulses travel up the pipe, echo off the blank end, and travel back down. On top of which, we don't need to have the short pipe at all. We can let the exhaust gas flow straight down the exhaust, and our longer journey is just a cul-de-sac pipe to one side. It just carries pressure pulses, without any flow, and the echo cancels out the pulses and troughs.
How Long Is This Pipe?
The distance that the sound travels for one pulse-trough-pulse sequence is the length of the sound wave. To cancel the sound out, we needed the longer path to be the distance from a pulse to the following trough, which is half the wave length. But we folded this pipe in half, making use of the sound travelling both ways trick, so our folded longer journey pipe is a quarter of the wavelength. Hence why these are properly called quarter wavelength attenuators, or quarter wave tubes.
The actual length of the pipe depends upon the frequency we are trying to suppress. Remember, this only works for one frequency. At 38Hz the wavelength is about 8 metres, and so a quarter wave tube would have been 2 metres long. This is why I was delighted to find that the dominant tone was at 76Hz, which makes the quarter wave tube only about one metre long; far more manageable. I carried out many tests with pipes of different lengths and geometries and settled on a length of 1020mm.
Speed of Sound
There is a practical problem that I hinted at before, because the speed of sound varies with temperature.The temperature of the air in our tube will be neither ambient, because there is hot exhaust gas going past the open end, nor will it be the temperature of the exhaust, because there is no flow and the pipe will be cooled by the (warm) air in the engine bay. It is not, therefore, possible to calculate the exact length for the pipe.
Also, if the generator changes speed slightly, the frequency we are trying to suppress will vary. This can be compensated for by either having very precise generator speed control (think modern designs) or running at constant load (which suits older mechanical governers, as per the BetaGen). Perseverance will run at constant power while recharging the batteries, which is another reason for using Lithium batteries which can take high charge rates without degrading.
The solution to this temperature problem draws inspiration from the world of music, and specifically from the trombone. The length of the tube is adjustable and we can set it to an optimum length for the normal running conditions. OK, it's not perfect, and the pipe will be slightly "out of tune" when it's cold, but I think it will work fine for most conditions.
Testing Finds a Snag
Beta Marine strongly recommend fitting a flexible section of exhaust pipe immediately as it comes out of the generator, to allow the engine to move on its anti-vibration mounts.
Interestingly the quarter wave tube was absolutely rubbish if fitted after the flexible pipe. Fitting it right on the output of the generator, or further downstream, it worked as expected. I think the reason was that the distance from the engine manifold to the end of the flexible pipe was about a metre, so at that point the quarter wave tube is in fact a half wave from the manifold and will resonate. This is something not mentioned in any of the academic papers on resonant silencers. Fortunately with test results under our belt, we could design the installation to avoid this pitfall.
Here It Is
I found a silencer specialist who had experience of building quarter wave silencers and was prepared to take on this unusual task. BTB Exhausts of Daventy were exceptionally helpful and I strongly recommend them to anyone interested in building a bespoke silencer. They took my hospital silencer and welded on the folded quarter wave tube, with tuning adjuster. Here is the finished item, as first fitted to Perseverance.
This photograph is taken in the bow of Perseverance, looking down, aft and to port. The bowthruster pipe is the grey painted pipe below the hospital silencerwhich is the large silver cylinder at the top of the photo. Exhaust from the generator (mounted behind the photographer) will fit onto the coupling on the right of the photo, and after passing through the silencer, the exhaust passes onto the next absorption silencer out of the photograph to the left. The quarter wave tube comes across the picture, curves downwards and the tuning adjuster allows the distance to the blank end to be varied. A simple pipe clamp holds it in place when "in tune".
Does It Work?
Always a sensible question to ask. I fitted the modified silencer to the generator as part of the test programme. I used a suitable flexible pipe and extension to avoid the known resonant problem, and set up the spectrum analyser to run continuously. I live in a quiet street (especially during Covid lockdowns!) but there are occasional cars going by or wind in the trees can give transient increases in background noise. These cause the base levels of the spectrum to increase, but the generator harmonics remain clear. This speeded-up video of adjusting the tuning length shows the generator tones. The cursor is on the 2nd harmonic.
The values at the cursor are shown at the bottom of the screen, and show levels dropping from -21dB to -35dB and then, as I go past the optimum length, increasing again. An attenuation of -13dB equates to 1/20th. While this has only attenuated one harmonic, it was the most audible, and this 20:1 reduction has been achieved with "just" a bit of pipe.
For the SuperNerds
In theory a quarter wave tube will attenuate all the odd harmonics. The problem of doing sound measurements in the open air is that it's difficult to assess minor changes, and there really is no clear change in the higher harmonics from the test above.
For the UltraNerds
The other arrangement I considered was the Helmholz resonator. For those who don't know what a Helmholz resonator is, grab a bottle and blow across the top. The tone you get depends upon the length of the neck of the bottle and the volume. What is happening is that the lump of air in the neck acts as a weight bouncing on the springy air in the body of the bottle. You can calculate the resonant frequency, and, like the trombone arrangement, make it adjustable, except that in this case it is normal to adjust the volume of the "body" of the resonator.
The snag is that there are more variables to deal with so it is more difficult to design the right shape of resonator. Also, there wasn't much of a space advantage so I went with the simpler bit of pipe.