I am using 2 ultrasonic assembly for cleaning purpose and I want to increase cavitation intensity.
(1) a ceramic transducer with a diameter of 30 mm and a horn with a end diameter of 8 mm.
(2) a ceramic transducer with a diameter of 40 mm and a horn with a end diameter of 8 mm.
Since the input power of (2) is higher than that of (1), I expected that the sound pressure of (2) is higher than that of (1), but it was not.
I think it is because the acoustic impedance of (2) is much lower than that of (1) (even though the power is high, sound pressure can be lower since Z=p/v is lower).
1. Am I misunderstanding something??
2. If not, how to increase the acoustic impedance of the ultrasonic assembly??
3. How can I estimate the acoustic impedance of the ultrasonic assembly??
4. What is the best?? the acoustic impedance of the ultrasonic assembly should be equal to the acoustic impedance of the media (water in my case) or as high as possible?
You can't change the impedance of the fluid, unless you use a different fluid. That means if you want larger pressure variation, there has to be higher amplitude. Increasing both of these together requires higher power density. Higher power density requires either more power or less area.
You can reduce the area by reducing the area of the horn, of by focusing the waves into a small volume using a shaped horn. While doing this you need to keep the impedance matched so that most of the transducer power gets into the fluid.
Malcolm White Thank you for your helpful answer. Currently, I am studying the design of acoustic horns with Jaedeok Seo. Relatedly, I have a few questions regarding acoustic impedance matching.
1. Is there a specific horn design method for matching acoustic impedance? Could you recommend relevant literatures?
2. We aim to transmit acoustic waves in water. For this purpose, do we need to match the acoustic impedance of the horn to a similar value as the characteristic impedance of water (known as the product of density and speed of sound)?
I am not an acoustics expert, and cannot recommend any books.
If something with a high impedance has to transmit power to something with a low impedance, then it either has to move the same area with a lot more amplitude or more area with the same amplitude, so that it seems as hard to move. The horn can also direct the wave. You will need to read what you can find on the internet, such as this https://tspace.library.utoronto.ca/bitstream/1807/76180/3/Amini_Mohammad_Hossein_201611_PhD_thesis.pdf,
who describes a quarter-wave transformer,
and transmission line theory or the theory of wave propagation.
Microwave propagation is similar to ultrasonics in some ways, although there are some important differences.
I think the best bet is to add a matching layer to the end of the horn that will maximize the transfer of power from horn to water. If you look up matching layers in general, you will find that they are quarter wave (in the matching layer material) thick and of impedance (Zh*Zw)^.5, where Zh is the acoustic impedance of the horn material and Zw the acoustic impedance of the water (1.5 MRayls). Ideally, you should also have a matching layer from the transducer into the horn as well, same formula but using the impedances of the ceramic and horn material. The matching layer is designed for one frequency (where the matching layer is a quarter-wave thick) so will not help a lot for high bandwidth (very short) pulses.
Hope that helps.
If you know the power density needed to cavitate, and the power available from the transducer, you can work out the maximum area over which you can achieve cavitation, if you use all the power available. The power density is easily calculated from the required pressure and the impedance of the water. It is no good trying to get cavitation over an area bigger than this, without more power.
Malcolm White David Vilkomerson I appreciate both of you. I think I know a little bit now. Both answers have been very helpful in understanding ultrasound excitation.
If I may add something to the previous valuable comments:
1) as soon as cavitation occurs, the medium impedance drops dramatically -more air than water... Impedance matching will further degrade accordingly and appear an unachievable goal - anyway the lower the better!
2) increasing power density is a good way ahead, but then comes the depolarization threshold of the piezo-ceramic: you have to chooses it very carefully to boost without damage your driving voltage. This power density maximization might not favour piezo-composites! If cost is not an issue, single crystal piezo-materials might enable a far superior power density...
3) better than looking only to the diameter, maximizing the radial velocity of the piezo-ceramic assembly is a good criterion to maximize sound radiation efficiency thus cavitation: e.g. consider using piezo-ceramic benders instead of solid ceramics (maybe it is already your case?); by the way a bender has by design a much lower matching impedance than a tonpilz stack.
4) a simple way to augment cavitation is to reduce the ambient static pressure - if you put your whole assembly in a depressed enclosure e.g. 0.5bar, you will increase cavitation without much technological burden!
So my advice is just to broaden your transducer lay-out analysis beyond the only issue of impedance matching...
I'm glad that Bernard Garnier has been able to bring some experience to this discussion rather than my general principles. Thank you!
Barnard Garnier's comments are of great value -- but in operation what will happen is the cavitation will produce a mismatch, power density will do down, cavitation will cease, power density will increase until cavitation again reduces the matching, and cycle repeats -- i.e. a pulsing rather than CW operation.
I expect cyclic operation will be fine - as you describe it, there will be cavitation some of the time.
David might be a bit optimistic as the cavitation bubbles persist by oscillating for several seconds (they collapse and grow again cyclically at their own rate depending of their diameter and the static pressure; this is why they have an important eroding power). Only the bigger bubbles migrate to the surface rapidly, but the small one affect as much the medium impedance: I really doubt the impedance mismatch would be restored between successive ultrasonic pulses!
This discussion remains rather theoretical anyway: in any case the more you reduce the impedance mismatch the better...
However, If you look up matching layers in general, you will find that they are quarter wave (in the matching layer material) thick and of impedance (Zh*Zw)^.5, where Zh is the acoustic impedance of the horn material and Zw the acoustic impedance of the water (1.5 MRayls). Ideally, you should also have a matching layer from the transducer into the horn as well, same formula but using the impedances of the ceramic and horn material. The matching layer is designed for one frequency (where the matching layer is a quarter-wave thick) so will not help a lot for high bandwidth (very short) pulses.
It doesn't seem that you will require short pulses that require high bandwidth, but if you do, matching layers can have broad bandwidth by making the impedance change in stages, as the bandwidth is inversely proportional to the ratio of the new-old impedance. You make the first matching layer increase the impedance by half (assuming you are matching into water from a higher impedance), and add a second matching layer that matches the now increased impedance to the transducer. As this is done on every medical transducer -- to match PZT to tissue -- there's good literature on this. See, for example, papers by DeSilets.
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