Systematic derivation of the weakly non-linear theory of thermoacoustic devices

P.H.M.W. Panhuis, in 't, S.W. Rienstra, J. Molenaar

Research output: Book/ReportReportAcademic

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Abstract

Thermoacoustics is the field concerned with transformations between thermal and acoustic energy. This paper teaches the fundamentals of two kinds of thermoacoustic devices: the thermoacoustic prime mover and the thermoacoustic heat pump or refrigerator. Two technologies, involving standing wave and traveling wave modes, are considered. We will investigate the case of a porous medium and two heat exchangers placed in a gas-filled resonator, in which either a standing or traveling wave is maintained. The central problem is the interaction between the porous medium and the sound field in the tube. The conventional thermoacoustic theory is reexamined and a systematic and consistent weakly non-linear theory is constructed based on dimensional analysis and small parameter asymptotics. The difference with conventional thermoacoustic theory lies in the dimensional analysis. This is a powerful tool in understanding physical effects which are coupled to several dimensionless parameters that appear in the equations, such as theMach number, the Prandtl number, the Laucret number and several geometrical quantities. By carefully analyzing limiting situations in which these parameters differ in orders of magnitude, we can study the behavior of the system as a function of parameters connected to geometry, heat transport and viscous effects.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages39
Publication statusPublished - 2006

Publication series

NameCASA-report
Volume0604
ISSN (Print)0926-4507

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derivation
dimensional analysis
standing waves
traveling waves
heat pumps
refrigerators
sound fields
Prandtl number
heat exchangers
resonators
tubes
heat
geometry
gases
interactions

Cite this

Panhuis, in 't, P. H. M. W., Rienstra, S. W., & Molenaar, J. (2006). Systematic derivation of the weakly non-linear theory of thermoacoustic devices. (CASA-report; Vol. 0604). Eindhoven: Technische Universiteit Eindhoven.
Panhuis, in 't, P.H.M.W. ; Rienstra, S.W. ; Molenaar, J. / Systematic derivation of the weakly non-linear theory of thermoacoustic devices. Eindhoven : Technische Universiteit Eindhoven, 2006. 39 p. (CASA-report).
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abstract = "Thermoacoustics is the field concerned with transformations between thermal and acoustic energy. This paper teaches the fundamentals of two kinds of thermoacoustic devices: the thermoacoustic prime mover and the thermoacoustic heat pump or refrigerator. Two technologies, involving standing wave and traveling wave modes, are considered. We will investigate the case of a porous medium and two heat exchangers placed in a gas-filled resonator, in which either a standing or traveling wave is maintained. The central problem is the interaction between the porous medium and the sound field in the tube. The conventional thermoacoustic theory is reexamined and a systematic and consistent weakly non-linear theory is constructed based on dimensional analysis and small parameter asymptotics. The difference with conventional thermoacoustic theory lies in the dimensional analysis. This is a powerful tool in understanding physical effects which are coupled to several dimensionless parameters that appear in the equations, such as theMach number, the Prandtl number, the Laucret number and several geometrical quantities. By carefully analyzing limiting situations in which these parameters differ in orders of magnitude, we can study the behavior of the system as a function of parameters connected to geometry, heat transport and viscous effects.",
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Panhuis, in 't, PHMW, Rienstra, SW & Molenaar, J 2006, Systematic derivation of the weakly non-linear theory of thermoacoustic devices. CASA-report, vol. 0604, Technische Universiteit Eindhoven, Eindhoven.

Systematic derivation of the weakly non-linear theory of thermoacoustic devices. / Panhuis, in 't, P.H.M.W.; Rienstra, S.W.; Molenaar, J.

Eindhoven : Technische Universiteit Eindhoven, 2006. 39 p. (CASA-report; Vol. 0604).

Research output: Book/ReportReportAcademic

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N2 - Thermoacoustics is the field concerned with transformations between thermal and acoustic energy. This paper teaches the fundamentals of two kinds of thermoacoustic devices: the thermoacoustic prime mover and the thermoacoustic heat pump or refrigerator. Two technologies, involving standing wave and traveling wave modes, are considered. We will investigate the case of a porous medium and two heat exchangers placed in a gas-filled resonator, in which either a standing or traveling wave is maintained. The central problem is the interaction between the porous medium and the sound field in the tube. The conventional thermoacoustic theory is reexamined and a systematic and consistent weakly non-linear theory is constructed based on dimensional analysis and small parameter asymptotics. The difference with conventional thermoacoustic theory lies in the dimensional analysis. This is a powerful tool in understanding physical effects which are coupled to several dimensionless parameters that appear in the equations, such as theMach number, the Prandtl number, the Laucret number and several geometrical quantities. By carefully analyzing limiting situations in which these parameters differ in orders of magnitude, we can study the behavior of the system as a function of parameters connected to geometry, heat transport and viscous effects.

AB - Thermoacoustics is the field concerned with transformations between thermal and acoustic energy. This paper teaches the fundamentals of two kinds of thermoacoustic devices: the thermoacoustic prime mover and the thermoacoustic heat pump or refrigerator. Two technologies, involving standing wave and traveling wave modes, are considered. We will investigate the case of a porous medium and two heat exchangers placed in a gas-filled resonator, in which either a standing or traveling wave is maintained. The central problem is the interaction between the porous medium and the sound field in the tube. The conventional thermoacoustic theory is reexamined and a systematic and consistent weakly non-linear theory is constructed based on dimensional analysis and small parameter asymptotics. The difference with conventional thermoacoustic theory lies in the dimensional analysis. This is a powerful tool in understanding physical effects which are coupled to several dimensionless parameters that appear in the equations, such as theMach number, the Prandtl number, the Laucret number and several geometrical quantities. By carefully analyzing limiting situations in which these parameters differ in orders of magnitude, we can study the behavior of the system as a function of parameters connected to geometry, heat transport and viscous effects.

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Panhuis, in 't PHMW, Rienstra SW, Molenaar J. Systematic derivation of the weakly non-linear theory of thermoacoustic devices. Eindhoven: Technische Universiteit Eindhoven, 2006. 39 p. (CASA-report).