Synchronization of a standing wave thermoacoustic prime-mover by an - - PowerPoint PPT Presentation

Synchronization of a standing wave thermoacoustic prime-mover by an external sound source.

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

• G. Penelet(a), T. Biwa(b)

(a) Laboratoire d'Acoustique de l'Université du Maine, UMR CNRS 6613, avenue Olivier Messiaen,

72085 Le Mans cedex 9, France

(b) Department of Mechanical Systems and Design, T

• hoku University, 980-8579 Sendai, Japan

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

PLAN

1.- Introduction 2.- Experimental apparatus and signal processing

2.1.- Experimental apparatus 2.2.- Experimental protocol 2.3.- Signal processing

3.- Experiments

3.1.- Example of Arnold T

• ngues

3.2.- T ransition to synchronization for weak forcing 3.3.- T ransition to synchronization for strong forcing 3.4.- Influence of stack position and coupling distance 3.5.- About the quenching phenomenon

4.- Conclusion, future prospects

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

1.- Introduction

• First observations of the synchronization phenomenon made by

Huygens (1665) => « sympathy of two pendulum clocks »

• Use or observation of synchonization phenomena are abundant in nature and science,
• biology,medicine (singing crickets, circadian rythm, cardiac pacemaker...)
• electronics engineering (synchronization of triode generators for radio communications,

Larsen effect...)

• mechanics (clocks, organ pipes...)
• physics or chemistry (Belousov–Zhabotinsky reaction, ...)
• social life (applauding audience)

« These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics »

• A. Pitkovsky, M. Rosenblum, J. Kurths, « Synchonization: A Universal Concept in

Nonlinear Science », Cambridge University Press, NY, 2001.

• C. Huygens

(1629-1695)

f1≠f2 f1=f2 f1=f2

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

1.- Introduction Topic of this study = synchronisation of thermoacoustic

• scillator by an external sound source

Why making such a study?

1.- Because the experiment is easy to build, highly demonstrative, and it points out some universal concepts about synchronisation. => original experiment for master courses in dynamics systems? 2.- Might be of interest for optimizing thermoacoustic engines by means of active control process [C. Desjouy, G. Penelet, P

. Lotton, J. Appl. Phys. 108:114904, 2010]

Synchonization phenomena in acoustics

Synchronization of Organ pipes

• Former study by Lord Rayleigh ((in « the theory of sound ») : mutual

synchronization of two organ pipes and the quenching effect (oscillation death)

• But even recent studies:

[Abel et al, J. Acoust. Soc. Am. 119:2467, 2006] [Abel et al. Phys. Rev. Let., 103:114301, 2009]

Sketch of the experiment by Abel et al. (PRL, 2009)

Synchronization in Thermoacoustics

• Spoor and Swift : Use of synchonization of two thermoacoustic engines to cancel vibration

[P . Spoor et al., J. Acoust. Soc. Am. 108:588, 2000]

• Muller and Lauterborn: Synchronization of a thermoacoustic Oscillator by a loudspeaker

[Muller et al., Proc. Intern. Symp. of Musical acoustics, pp 178-183, 1995]

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

2.- Experimental apparatus and signal processing

2.1.- Experimental apparatus

The thermoacoustic oscillator

Resonator (Pyrex): length=49 cm, inner diameter= 52 mm Stack (Cordiérite): 600 CPSI (0,45 x 0,45 mm2), porosity = 0,85 Heat resistance (NiCr): diameter = 0,25 mm, resistivity=7 Ω/foot, length 36 cm)

Onset frequency f0 of about 171-173 Hz

(depends on Q, and on the coupling with the loudspeaker)

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

2.- Experimental apparatus and signal processing

2.1.- Experimental apparatus

The experimental apparatus

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

2.- Experimental apparatus and signal processing

2.2.- Experimental protocol

1.- Fix d and ds 2.- Switch heat power on (fix Q above onset), wait for about 1 h (steady state acoustic pressure, natural frequency f0). 3.- Switch louspeaker on, and fix louspeaker voltage U and frequency fforc=f0 4.- Decrease forcing frequency fforc, wait for 2 to 5 minutes 5.- Proceed to data acquisition (measure p(t) and U(t)) 6.- Repeat steps 4 and 5 until loss of synchonization 7.- Return to f=f0, then repeat steps 4 and 5 with increasing fforc until loss of synchonization 8.- Repeat steps 3 to 7 around fforc=f0/2, fforc=f0/3, fforc=2f0 9.- Increase U and repeat steps 3 to 8. One session of measurements => about 13 hours of measurements within one day!

(Automatizing experiments would be worth considering, e.g. in [Abel et al., PRL 103:114301, 2009])

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

2.- Experimental apparatus and signal processing

2.3.- Signal processing

• Sampling frequency fs=30f, duration (30- 60 s)
• Measure both p(t) and U(t).
• From p and U, compute:
• The quantities of interest for data analysis are:

✗

Frequency spectra p(f) and U(f)

✗

The amplitude modulation Ap(t)

✗

The phase difference Ψ(t)=Φp(t)-ΦU(t) (Φp(t)=2πfnat+cte)

Ap(t)

Synchronization 1:1 (or n:1, resp.)

fnat=fforc (or fnat=nfforc) Ap(t)=cte Ψ(t)=cte

Phase Modulation 1:1 (or n:1, resp.)

fnat≠fforc (or fnat≠nfforc) Ap(t)≠cte Ψ(t)≠cte but bounded

Loss of synchonisation 1:1 (or n:1, resp.)

fnat≠fforc (or fnat≠nfforc) Ap(t)≠cte Ψ(t)≠cte and not bounded

pana(t)=p(t)+ipH(t)=Ap(t)eiΦp(t) Uana(t)=U(t)+iUH(t)=Up(t)e

iΦU(t)

Different possible states

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.1.- Example of Arnold tongues

• Q=22,6 W, ds=19 cm, d=5mm
• Before measurements f0=173,7±0,04 Hz, Lp= 144,8 dB SPL
• After 13 h, f0= 174,33±0,04 Hz, Lp= 144,3 dB SPL
• Increase U from Urms=40 mV to Urms=10 V
• define LU=20log10(Urms/4.10-2)

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.2.- Transition to synchronization for weak forcing (saddle-node bifurcation)

fforc=173,8 Hz fforc=174 Hz

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.2.- Transition to synchronization for weak forcing (saddle-node bifurcation)

 A Amax =Max  At−Min  At  Max  At = 1 T ∫

T



pt −Ut  2f 0

.dt

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.3.- Transition to synchronization for strong forcing (Hopf bifurcation)

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.3.- Transition to synchronization for strong forcing (Hopf bifurcation)

 A Amax =Max  At−Min  At  Max  At = 1 T ∫

T



pt −Ut  2f 0

.dt

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.4.- Influence of stack position and coupling distance

• Q=22,6 W, ds=8 cm, d=5mm
• Before measurements f0=171,96±0,04 Hz, Lp= 143,3 dB SPL
• After 12 h, f0= 172,6±0,04 Hz, Lp= 144,3 dB SPL
• Increase U from Urms=40 mV to Urms=10 V
• define LU=20log10(Urms/4.10-2)

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.4.- Influence of stack position and coupling distance

• Q=22,6 W, ds=8 cm, d=1mm
• Before measurements f0=171±0,04 Hz, Lp= 141,4 dB SPL
• After 13 h, f0= 171,7±0,04 Hz, Lp= 142,8 dB SPL
• Increase U from Urms=40 mV to Urms=10 V
• define LU=20log10(Urms/4.10-2)

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.5.- About the quenching phenomenon

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.5.- About the quenching phenomenon

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results

3.6.- Influence of d

s and d: summary

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

4.- Conclusion

4.1.- Concluding remarks

• Main results:

✗

Synchronisation is controlled by d, ds and U

✗

For large U and small d: the Arnold tongue becomes asymetric and quenching is observed

✗

n:1 are more easyly observed than 1:n synchronization

• A simple (but long) experiment which points out

✗

some universal effects in synchronisation: frequency locking, phase locking, phase modulation, quenching...

✗

some effects which are intrinsic to the thermoacoustic oscillator itself

• The experimental results are complementary (influence of d and ds), but also significantly

different from those obtained by Muller and Lauterborn

[Muller et al., Proc. Intern. Symp. of Musical acoustics, pp 178-183, 1995]

Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

4.- Conclusion

4.2.- Future prospects

• Derive a simplified theory to reproduce the experiments ?
• Make further experiments (=> Automate them?)
• Investigate mutual synchonization of 2 thermoacoustic oscillators