New mouthpiece for our Artist Series Irish Whistle – Simulation and analysis

This is part III in which we are going to deep dive into some simulations and analysis methods. Most importantly, which simulations are important when designing a musical part. The obvious elements in simulation are of course air flow, air speed, turbulence in and over the mouthpiece. More closely, we are going to have a look at the chamber, how does the air behave in the body and around tone holes? Do all the added features make sense? Does what we thought made sense, make a difference? Can we measure acoustical characteristics and how do we do this? Does it make sense to add mass to a mouth piece? Are we better off printing in PLA, ABS or copper, bronze and aluminium?

Part I – Introduction | Part II – The design | Part III – Simulations

Written by Ruud Roelofsen (3D, design)

Air stream simulation

In order to get a representation of an air-stream blown into the windway, we first need to establish the speed at which a musician blows air into a whistle mouth piece. We have seen that this is around 1-1,5 mtr/s. When blowing octaves, the speed increases. We do think it makes too much difference here, but we’re going to assume the air has a temperature of 37C or 310K. Here are my main conclusions.

These parameters are then added to the simulation. The starting point (the origin) of the air stream is obviously the beginning of the mouth piece. But first we’re are going add a body to our mouthpiece, complete with correct tone hole diameters and distances. Next, we need a so called ‘computational domain”a calculation bounding box around the instrument. The computational domain can be see as a box around the whistle:

The air stream parameters are as follows:

For completeness, we going to add the relative humidity of exhaled air: set to 50%. We don’t think it is important unless you want to measure material characteristics maybe.

Let’s start with just ‘blowing in’ an air stream that lasts 10 seconds. Maybe there is something obvious blocking or distorting the air stream, forcing us to make adaptations at this stage.

In the graphic above you can see that the air is split at the tip of the blade. In reality we know that the air is oscillating at high speed at this point. This means that one moment the air is escaping outside, and inside at another. It alternates below and above the blade. Some people think that all air is contributing to a note; in absolute sense it does, but some air leaves the mouth piece an does not stay inside the body. Don’t worry, all air is needed to produce a note. In fact, this constant battle of air staying inside or going outside the mouthpiece is music to our ears! The blue indicates that the air loses its speed. What we are seeing as well is that most of the air (in this simulation) is going downward, although the tip of the blade is exactly aligned with the lowest part of the wind-way. The reason is two-fold: the wind-way has a slight funnel shape; it has a lowered ceiling at an angle. This is done on purpose for this very reason. It results in easy blowing of the mouth piece. In addition to this – although less significant – is that the air is sucked into the chamber by air that is already circulating there.

Turbulent energy

Next, we are going to take a look at the turbulent energy being generated by the air the musician has blown in (well, virtually that is). Looking at the wind-way, there is not much turbulent energy, maybe slightly towards the end (of the wind-way); this is where the green color turns slightly yellow. As the air enters the chamber we see the turbulent energy increasing and spreading in all directions. This is quite normal as the air tries to find its way outside to an area with the least (less) resistance. By blowing air into he mouth piece at high speed, we direct the air over the blade into the chamber and the body, and partly outside of the mouthpiece.

Air through the body of the whistle


Looking at a cross section again, we are seeing a circular motion of air in the chamber. It seems as though the air blown into the mouth piece is about to enter the body, but some of it returns, makes one or more saltos and only then enters the body.

In the design of the chamber, I tried to introduce a few optimizations; the bottom and the walls of the chamber are rounded (fillet-ed) , causing the air to tumble and eventually enter the body. I have seen that without these optimizations, the air was less directed and made sharp angles bouncing from the walls.

Now let’s see what happens around a tone hole when air passes through:

We are seeing clearly that the air is drawn to a tone hole, then drops and is drawn to the next tone hole.

Basics of a flute

The air stream, caused by a musician blowing into the mouth piece moves ove the blade. As we have seen earlier, air starts to oscillate; the air stream is distorted. This in turn results in the mouth piece to produce sound; an acoustic wave makes its way through the tube.

The speed a t which this wave moves is about half of the speed at which the air is blown into the entry speed at the beginning of the wind-way. In order to produce a low sounding note, the musician blows gently into the mouth piece. The travel speed of the acoustic wave through the body is low, as the notes produces are low in frequency. To play high notes, the time at which the acoustic wave travels through the body must increase; it requires the air to move faster, and this is done by blowing harder into the mouth piece.

Another interesting thin we are seeing is that at each tone hole, again the air is oscillating, caused by the sharp edge of the tone hole. This is more or less the same what we saw happening at the mouth piece blade; the part of the air that stays inside causes oscillation, which in its turn causes the different acoustic waves. The air oscillates over the entire length of the tube and the locations of the (closed and open) tone holes change this oscillation, thus the acoustic waves. This is what is causing different sounding notes.

Conclusion

From doing some basic simulations, we can see everything functions as it should – in theory. I realize I haven’t explained everything in depth, and what I also did not cover extensively is comparing different shapes and features while doing simulations. True, I have only shown you the end results, but I did uncover some of the unique features we added to this mouth piece…

These new features seem to work. Next is to make sure we have a prototype!

Prototyping

To get our hands on this prototype, we are going to print our design with our trusty 3D printer. Sounds cool, right? Of course, it’s very nice to immediately be able to create a prototype. However, there are some downsides to 3D-printing. We’ll discuss this in part IV, so stay tuned!

This was part III in a series about our new Artist Whistle mouthpiece. Part IV is all about 3D printing.

Part I – Introduction | Part II – The Design | Part III – Simulations