doi:10.14311/AP.2015.55.0342Acta Polytechnica 55(5):342–346, 2015 © Czech Technical University in Prague, 2015

available online at http://ojs.cvut.cz/ojs/index.php/ap

ELECTRODYNAMIC LOUDSPEAKER-DRIVEN ACOUSTICCOMPRESSOR

Martin Šoltés∗, Milan Červenka

Czech Technical University in Prague, Faculty of Electrical Engineering, Technická 2, Prague, Czech Republic∗ corresponding author: soltes.mail@gmail.com

Abstract. An acoustic compressor is built using the acoustic resonator which shape was optimizedfor a maximum acoustic pressure amplitude and a low-cost compression driver. Acoustic compressor isbuilt by installing a suction port in the resonator wall where the standing wave has its pressure node anda delivery port with a valve in the resonator wall where the standing wave has its pressure anti-node.Different reeds, serving as delivery valves, are tested and their performance is investigated. It was shownthat the performance of such a simple compressor is comparable or better than the acoustic compressorsbuilt previously by other researchers using non-optimally shaped resonators with more sophisticateddriving mechanisms and valve arrangements.

Keywords: acoustic compressor, acoustic resonator, high amplitude acoustic field.

1. IntroductionHigh amplitude standing waves in closed cavities havebeen studied extensively by many researchers (see e. g.[1–4], for the review of the research done on the subjectup to 1996, see [5]). Much of the effort has been devotedto the study of the special case of piston-driven con-stant cross-section resonators driven at or close to oneof its resonance frequencies. However, no matter howstrong the excitation, the maximum acoustic pressureamplitudes obtained in the constant cross-section res-onators were limited. It has been observed and is nowa well-known fact that when resonators of cylindricalshape are excited at their resonant frequency, acousticenergy is transferred from the fundamental resonance tohigher harmonics due to a non-linear properties of fluid,eventually leading to a formation of the shock wave.Due to the fact, that dissipation of acoustic energy isproportional, the shock formation sets the upper limitfor the maximum acoustic pressure in such resonator.

Gaitan and Atchley [3] showed that it is possible toprevent the formation of shock waves in tubes withvariable cross-section, where energy transfer from thefundamental resonance to the higher resonance modesis significantly reduced.

In 1998, Lawrenson et al. [4] published their experi-mental paper in which they introduced the concept ofResonant Macrosonic Synthesis (RMS). They showedthat relative phases and amplitudes of the harmonicscan be controlled by the resonator geometry resultingin shock-free waveforms of extremely high amplitudes.Acoustic pressure amplitudes that they obtained weremore than an order of magnitude larger than it hadbeen possible before.

Ilinskii et al. [6] presented a one-dimensional nonlin-ear model equation for description of high-amplitudestanding waves in axi-symmetric, arbitrarily shapedacoustic resonators in their theoretical paper.

Li et al. [7] presented a method for optimization of the

resonator shapes based on a nonlinear wave equation.They considered resonator shapes described by smoothelementary functions with adjustable parameters only.Červenka et al. [8] proposed an evolutionary

algorithm-based method for optimizing the shape ofthe acoustic resonators for achieving high-amplitudeshock-free acoustic fields. The method is based on a lin-ear model that includes losses due to turbulence in theboundary layer. They used a more general approach ofparametrizing the resonator shape using control pointsinterconnected with cubic splines.

With the progress in both theoretical descriptionas well as experimental results in the field of high-amplitude acoustic fields a number of different prac-tical applications emerged, e. g. acoustic compres-sors, plasma-chemical reactors [9], thermoacoustic de-vices [10], etc.

The possibility of constructing an acoustic compressorhas been investigated by several authors (Bodine [11],Lucas [12], El-Sabbagh [13], Masuda and Kawashima[14] and Hossain et al. [15]). Acoustic compressorsoffer several advantages over the more traditional ones.Most importantly they do not contain moving partsthat require oils to reduce friction and wear — this isimportant in applications where mixing of oil with thecompressed fluid is undesirable. Moving parts also re-duce reliability of the compressor since they are subjectto mechanical fatigue and failure. Another advantageis that acoustic compressors allow using a valvelessconstruction [12]. In all of the experiments researchesused either the piston-driven resonators or the entirely-driven resonators (resonators in which acoustic energyis introduced in the resonator cavity by shaking thewhole resonator along its axis).

In this paper we aim to experimentally demonstratepractical utilisation of high-amplitude acoustic fieldsmade possible by the optimized resonator described inour previous paper [8] by constructing a working exam-

342

vol. 55 no. 5/2015 Electrodynamic loudspeaker-driven acoustic compressor

x [mm] 0 33.3 66.7 100 133.3 166.7 200 233.3 266.7 300r [mm] 5 5 5 5.4 7.6 10.6 15.1 23.1 25 25

Table 1. Coordinates of the ten control points for cubic-spline interpolation describing the shape of the resonator usedin experiments.

Figure 1. Shape of the resonator cavity. Grey crossesdenote positions of the ten control points for cubic-spline interpolation. Part of the resonator to the rightof the dashed line represents the internal waveguideinside the Selenium driver. Resonator is terminated bya rigid wall on its narrow end (at x = 0mm) and by theloudspeaker diaphragm on its wide end (at x = lt ).

ple of an acoustic compressor. We use the commonlyavailable loudspeaker-driver to excite the resonatorsince it is much cheaper and smaller compared with thetraditionally used electromagnetic or electrodynamicshakers to increase the economic attractiveness of theproposed solution.

2. Acoustic compressorconstruction

The experiments were conducted on the system con-sisting of electrodynamic loudspeaker and externalresonator cavity. The compression driver SeleniumDT-405Ti, from which the phase-plug was removed,was used along with a 300mm long external resonator1.External resonator, machined from two pieces of du-ralumin block which were joined together, has an axi-symmetrical cavity, which shape was optimized for theuse with the Selenium loudspeaker for maximal acousticpressure amplitude at the closed end of the resonator(at x = 0mm).

The optimization procedure, described in our previ-ous paper [8] is an evolutionary strategy-based methodthat optimizes the shapes of resonators subject to agiven set of constraints (minimum and maximum ra-dius, minimum and maximum resonance frequency,resonator length). Resonator shape is defined by aset of N control-points (serving as parameters for theoptimization) and is obtained by a cubic-spline inter-polation. We have used N = 10 control points and

1Resonating cavity of the whole system is formed by theshort internal waveguide inside the driver and external resonatorattached to the driver. Total resonator length lt is thereforegiven by lt = lint + lext, where lint is the length of the internalwaveguide and lext is the length of the external waveguide.

Plastic reed

Transparent window

Valve housing

Clamp

Deliveryport

Rotameter

Resonato

r

Pressure gauge Laser vibromoter

Air

Microphone

Hose clamp

Figure 2. Valve housing configuration.

the following constraints: rmin = 5mm, rmax = 25mm,lext = 300mm in the optimization procedure. Res-onance frequency constraints were not applied. Theresulting resonator shape is shown in Figure 1. Coordi-nates of the control points (shown as gray crosses inFigure 1) are listed in Table 1.The acoustic compressor was built by installing a

suction port in the resonator wall where standing wavehas its pressure node (at x = 272mm from the closedend of the resonator in our case) and a delivery portin the resonator wall where the standing wave has itsanti-node (at x = 0mm).

With this arrangement alone, it is already possible toproduce one-way air flow2 [12], however the value of theair flow-rate obtained this way is very small. For thisreason the delivery port was fitted with a valve whichrectifies the flow of the medium and therefore allowsmuch higher values of air flow-rate to be achieved. Inour experiments we have used a reed-type passive valvedue to its simplicity and, more importantly, due to itsability to operate at high frequencies. The valve openswhen acoustic pressure inside the resonator cavity risesabove the static ambient pressure at the other side ofthe reed and closes when the acoustic pressure fallsbellow this static pressure level resulting in one-way airflow.Delivery port — a circular hole of 4mm diameter

with the center at resonator axis of symmetry wasdrilled in the cap closing the resonator at its narrowend (at x = 0mm). Delivery valve, enclosed insidea small metal box, was installed in a way shown in

2This is possible due to nonlinear properties of a fluid — withrising acoustic pressure amplitude inside the resonator, somesmall dc component emerges at the pressure anti-node. Thiscreates static pressure gradient inside the resonator causing airflow between suction and delivery port.

343

Martin Šoltés, Milan Červenka Acta Polytechnica

Figure 3. The acoustic compressor experimental setup.The selenium driver with the resonator attached to itis in the left part of the picture. The delivery valvehousing is attached on the top of the resonator and laservibrometer is placed above. One of the hoses connectsthe pressure gauge and the other one with a hose clampleads to the flow-meter. A microphone is connectedfrom the side of the resonator.

Figure 2. This box (delivery valve housing) features twooutlets for connecting the pressure gauge and air-flowmeter. It also features a transparent glass window inits top wall, which can be used for the measurement ofthe reed displacement using a laser vibrometer. Twoholes of 2mm diameter drilled in the opposite sides ofthe resonator wall at the pressure node serve as thesuction ports.

3. Results3.1. Experimental setupAll measurements were performed at a room tempera-ture and atmospheric pressure using air as a compressedmedium. The electrical signal driving the loudspeakerwas generated with a computer using the LabVIEWenvironment and amplified with the Akiyama AMD400amplifier. Acoustic pressure measurements were madein the LabVIEW environment using the NI PCI-6251data acquisition card and the G.R.A.S. 12AA pre-amplifier with the G.R.A.S. 40DP 1/8 " microphonewhich was attached from the side of the resonator asshown in Figure 2. Static pressure was measured usingthe PTL Prematlak 2010 pressure gauge, air volumeflow-rate was measured using the Rheotest MedingenPG05 rotameter and the µε optoNCDT ILD2300 laservibrometer was used for the reed displacement measure-ment. Figure 3 shows a photograph of the experimentalsetup.

Reed 1 Reed 2 Reed 3 Reed 4

15

19

11

17

6

6

11

11

Figure 4. The valve reeds used in the experiment.Dimensions are in millimetres. Circles in the middle ofeach reed denote the position of the delivery port.

0 1 2 3 4 50

0.2

0.4

0.6

0.8

Driving signal period [−]

Ree

d di

spla

cem

ent [

mm

]

1 2 3 4

Figure 5. Measurement of the displacement versus thetime characteristic for four different valve reeds shownin Figure 4. The displacement was measured with thelaser beam pointing at the center of the delivery port.

3.2. Static pressure with no flowWhen the acoustic pressure is present inside the res-onator, the delivery valve acts as a rectifier — increasingstatic pressure on the other side of the valve. By closingthe hose clamp that controls the air flow (see Figure 2)air is prevented from leaving the delivery valve housingresulting in the static pressure build-up. Since thereis no air-flow out of the delivery valve housing, opti-mally performing valve would eventually produce staticpressure (inside the delivery valve housing) equal tothe acoustic pressure amplitude (inside the resonator).Displacement of the reed should decrease with the ris-ing static pressure and the reed should eventually stopvibrating once the steady-state is reached — whenthe static pressure reaches the value of the acousticpressure amplitude. This is not possible in our simplearrangement where the reed is not allowed to vibratesymmetrically but we can expect better performingreeds having smaller displacement.

A number of different valve reeds were tried and itwas found that dimensions of the reed have a significantimpact on its performance. Results for four differentreeds shown in Figure 4 are presented below. All reedswere made from a 130µm thick PVC foil.

Figure 5 shows a measurement of the steady-statereed displacement versus the time for four differentreeds shown in Figure 4. The resonator was driven withsine-wave signal at resonance frequency fres = 551Hzwith the input voltage amplitude |Uin| = 10V. It canbe observed that the valve reed 1 tracks the acousticpressure well. It opens only for a short interval during

344

vol. 55 no. 5/2015 Electrodynamic loudspeaker-driven acoustic compressor

0 5 10 150

0.05

0.1

0.15

Input voltage amplitude [V]

Pea

k re

ed d

ispl

acem

ent [

mm

]

Figure 6. The valve reed 1 displacement amplitudeversus input voltage characteristic.

Reed number 1 2 3 4Pressure [kPa] 20 16 7 0

Table 2. Static pressures measured inside the deliveryvalve housing, with the resonator driven at the resonancewith the input voltage amplitude |Uin| = 10V.

each cycle with the maximum displacement around0.1mm. Valve reed 4 does not track the acousticpressure very well. It is open during most of the cycleand its maximum displacement is roughly seven timesbigger than the maximum displacement of the valvereed 1. Valve reeds 2 and 3 behave somewhere betweenthese two extremes.

The static pressures inside the delivery valve housingmeasured at these conditions are summarized in theTable 2.

It is clear that the valve reeds which behave closer tothe ideal — exhibiting smaller displacement, which areable to track the acoustic pressure more accurately (i.e.respond faster) produce higher static pressures. Weuse the valve reed 1 in all of the experiments describedbelow.Figure 6 shows the valve displacement versus the

input voltage characteristic. It can be observed that thevalve reed displacement grows roughly proportionatelywith the input voltage suggesting a good — linearbehaviour of the valve.

Figure 7 shows the measured static pressure and theacoustic pressure amplitude versus the input voltagecharacteristic. It can be observed that the systempossesses the desired characteristic — most of theacoustic pressure amplitude is rectified into the staticpressure.

3.3. Resonator with air flowBy gradually releasing the hose clamp, the air is al-lowed to escape the valve housing that results in thedecrease of static (delivery) pressure and one-way airflow through the resonator. Figure 8 shows the air vol-ume flow-rate versus the delivery pressure characteristicmeasured at three different input voltage amplitudes.It was observed that the frequency at which max-

imum air flow is achieved increases with opening of

0 5 10 150

1

2

3

4x 10

4

Input voltage amplitude [V]

[Pa]

Acoustic pressure amplitudeStatic pressure

Figure 7. The acoustic pressure amplitude inside theresonator measured near the delivery port (as shownin Figure 2) and the static pressure measured insidethe delivery valve housing versus the input voltagecharacteristic.

0 2 4 6 8 100

1

2

3

4x 10

4

Flow−rate [l/min]

Del

iver

y pr

essu

re [P

a]

|U

in| = 5V

|Uin

| = 10V

|Uin

| = 15V

Figure 8. The air volume flow-rate versus the deliverypressure measured for the three different input voltageamplitudes.

the hose clamp. However, it does not depend on theabsolute value of the air flow rate or on the deliverypressure. Figure 9 illustrates this frequency shift. Thevertical axis represents frequency at which air flow ismaximal (for a given hose clamp setting) while thehorizontal axis represents this air flow rate as a per-centage of the maximum possible air flow rate — withthe hose clamp removed. This is measured for threedifferent input voltage amplitudes. In other words,Figure 9 illustrates how air flow rate and frequencyat which air flow rate is maximal changes with open-ing of the hose clamp. It can be observed that thefrequency shifts similarly (in relative terms) for allthree input voltages — irrespective of the absoluteair flow rate or static pressure. It seems that thefrequency at which the air flow rate is maximal de-pends only on how much the hose clamp is opened.Possible explanation of this behaviour is that as theclamp is opened the effective geometry of the cavitybehind the delivery valve changes. Since this cavityitself forms an acoustic system the change in its ge-ometry could affect the function of the delivery valve.Similar behaviour was also observed by Masuda andKawashima [14].

345

Martin Šoltés, Milan Červenka Acta Polytechnica

0 20 40 60 80 100550

555

560

565

570

575

580

Flow−rate [%]

Fre

quen

cy [H

z]

|U

in| = 5V

|Uin

| = 10V

|Uin

| = 15V

Figure 9. The shift of the driving signal frequency atwhich the air flow-rate is maximal as the hose clamp isopened. Description of the figure is given in the textabove.

540 560 580 600 6207.5

8

8.5

9

Frequency [Hz]

Flo

w−

rate

[l/m

in]

Figure 10. Frequency characteristic of the air volumeflow-rate at input voltage |Uin| = 15V with the hoseclamp removed.

The measured frequency characteristic of the airvolume flow-rate at the input voltage |Uin| = 15V withthe hose clamp removed is shown in Figure 10. It canbe observed that under these conditions adjusting thedriving frequency from the fres = 551Hz to f = 580Hzresults in roughly 14% increase of the air volume flow-rate.

4. ConclusionsWe have shown that using the optimized resonatordescribed in our previous paper [8] construction ofacoustic compressor is possible even when using a rela-tively inexpensive and simple driving mechanism — acompression driver. Air volume flow-rates and deliverypressures we have been able to achieve (Figure 8) arecomparable or better than the ones reported by otherauthors [13–15].It was observed that the dimensions of the reed,

which acts as a delivery valve, has a significant im-pact on the performance of the compressor with betterperforming reeds exhibiting smaller displacement andfaster response.

The performance of the described compressor couldbe possibly further enhanced by using different (active)valve and by placing a suction port with a valve in theresonator wall where standing wave has its pressure anti-node. Moreover, the shape of the optimized resonator

and the corresponding maximum acoustic pressure am-plitude inside the resonator very much depend on theconstraints used in the optimization procedure. Bychoosing different constraints (especially the minimumradius rmin) optimization procedure would producedifferent resonator shape which could produce higheracoustic pressure amplitude and better performance ofthe acoustic compressor.

AcknowledgementsThis work was supported by GACR grant P101/12/1925.

References[1] B. Coppens, J. V. Sanders. Finite amplitude standingwaves in rigid walled tubes. JASA 52:1024–1034, 1968.

[2] D. B. Cruikshank. Experimental investigation offinite-amplitude acoustic oscillations in a closed tube.JASA 52:1024–1036, 1972.

[3] D. F. Gaitan, A. A. Atchley. Finite amplitude standingwaves in harmonic and anharmonic tubes. JASA pp.2689–2495, 1993.

[4] C. Lawrenson, B. Lipkens, T. S. Lucas, et al.Measurements of macrosonic standing waves in oscillatingclosed cavities. JASA 104:623–636, 1998.

[5] M. Ilgamov, R. Zaripov, R. Galiullin, V. Repin.Nonlinear oscillations of a gas in a tube. AppliedMechanics Reviews 49:137–154, 1996.

[6] Y. A. Ilinskii, B. Lipkens, T. S. Lucas, et al. Nonlinearstanding waves in an acoustical resonator. JASA104:2664–2674, 1998.

[7] X. Li, J. Finkbeiner, G. Raman, et al. Optimized shapesof oscillating resonators for generating high-amplitudepressure waves. JASA 116:2814–2821, 2004.

[8] M. Červenka, M. Šoltés, M. Bednařík. Optimal shapingof acoustic resonators for the generation of high-amplitudestanding waves. JASA 136:1003–1012, 2014.

[9] T. Nakane. Discharge phenomenon in high-intensityacoustic standing wave field. IEEE Trans Plasma Sci .

[10] G. W. Swift. Thermoacoustic engines. JASA84:1145–1180, 1988.

[11] A. G. Bodine. Resonant gas compressor and method,1952. US Patent 2,581,902.

[12] C. Macrosonix. Standing wave compressor, 1991. EPPatent App. EP19,910,301,934.

[13] A. El-Sabbagh. Gas-filled Axisymmetric AcousticResonators. VDM Verlag Dr. Muller Aktiengesellschaft &Co. KG, 2008.

[14] M. Masuda, S. Kawashima. A study on effects of thevalves of acoustic compressors on their delivery flow rate.International congress on acoustics Madrid september2007.

[15] A. Hossain, M. Kawahashi, T. Nagakita, et al.Application of finite amplitude oscillation of air-columnin closed tube to design acoustic compressor. Proceedingof 18th International Congress on Acoustics pp. 381–384,2004.

346