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. 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 ohoku 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 ongues 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 » C. Huygens (1629-1695) f 1 ≠ f 2 f 1 = f 2 f 1 = f 2 ● 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. Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

1.- Introduction 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 Synchronization in Thermoacoustics Abel et al. (PRL, 2009) ● 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] Topic of this study = synchronisation of thermoacoustic oscillator 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] 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 mm 2 ), porosity = 0,85 Heat resistance (NiCr): diameter = 0,25 mm, resistivity=7 Ω /foot, length 36 cm) Onset frequency f 0 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 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]) 1.- Fix d and d s 2.- Switch heat power on (fix Q above onset), wait for about 1 h (steady state acoustic pressure, natural frequency f 0 ). 3.- Switch louspeaker on, and fix louspeaker voltage U and frequency f forc =f 0 4.- Decrease forcing frequency f forc , 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=f 0 , then repeat steps 4 and 5 with increasing f forc until loss of synchonization 8.- Repeat steps 3 to 7 around f forc =f 0 /2, f forc =f 0 /3, f forc =2f 0 9.- Increase U and repeat steps 3 to 8. Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

2.- Experimental apparatus and signal processing 2.3.- Signal processing A p (t) ● Sampling frequency f s =30f, duration (30- 60 s) ● Measure both p(t) and U(t). ● From p and U, compute: p ana (t)=p(t)+ip H (t)=A p (t)e i Φ p (t) i Φ U (t) U ana (t)=U(t)+iU H (t)=U p (t)e ● The quantities of interest for data analysis are: Frequency spectra p(f) and U(f) ✗ The amplitude modulation A p (t) ✗ The phase difference Ψ (t)= Φ p (t)- Φ U (t) ( Φ p (t)=2 π f nat +c te ) ✗ Different possible states Synchronization 1:1 Phase Modulation 1:1 Loss of synchonisation 1:1 (or n:1, resp.) (or n:1, resp.) (or n:1, resp.) f nat =f forc (or f nat =nf forc ) f nat ≠ f forc (or f nat ≠ nf forc ) f nat ≠ f forc (or f nat ≠ nf forc ) A p (t)=c te A p (t) ≠ c te A p (t) ≠ c te Ψ (t)=c te Ψ (t) ≠ c te but bounded Ψ (t) ≠ c te and not bounded Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results 3.1.- Example of Arnold tongues - Q=22,6 W, d s =19 cm, d=5mm - Before measurements f 0 =173,7±0,04 Hz, L p = 144,8 dB SPL - After 13 h, f 0 = 174,33±0,04 Hz, L p = 144,3 dB SPL - Increase U from U rms =40 mV to U rms =10 V - define L U =20log 10 (U rms /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) f forc =173,8 Hz f forc =174 Hz Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results 3.2.- Transition to synchronization for weak forcing (saddle-node bifurcation) = Max  A  t   − Min  A  t    A Max  A  t   A max   . dt  p  t − U  t    = 1 T T ∫ 2  f 0 0 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) = Max  A  t   − Min  A  t    A Max  A  t   A max   . dt  p  t − U  t    = 1 T T ∫ 2  f 0 0 Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »

3.- Experimental results 3.4.- Influence of stack position and coupling distance - Q=22,6 W, d s =8 cm, d=5mm - Before measurements f 0 =171,96±0,04 Hz, L p = 143,3 dB SPL - After 12 h, f 0 = 172,6±0,04 Hz, L p = 144,3 dB SPL - Increase U from U rms =40 mV to U rms =10 V - define L U =20log 10 (U rms /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, d s =8 cm, d=1mm - Before measurements f 0 =171±0,04 Hz, L p = 141,4 dB SPL - After 13 h, f 0 = 171,7±0,04 Hz, L p = 142,8 dB SPL - Increase U from U rms =40 mV to U rms =10 V - define L U =20log 10 (U rms /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, d s 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 d s ), 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 Acoustics 2012,Nantes, 26 April 2012 session « Thermoacoustics »