Weakly nonlinear thermoacoustics for stacks with slowly varying pore cross-sections

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

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

A general theory of thermoacoustics is derived for arbitrary stack pores. Previous theoretical treatments of porous media are extended by considering arbitrarily shaped pores with the only restriction that the pore cross-sections vary slowly in the longitudinal direction. No boundary-layer approximation is necessary. Furthermore, the model allows temperature variations in the pore wall. By means of a systematic approach based on dimensional analysis and small parameter asymptotics, we derive a set of ordinary differential equations for the mean temperature and the acoustic pressure and velocity, where the equation for the mean temperature follows as a consistency condition of the assumed asymptotic expansion. The problem of determining the transverse variation is reduced to finding a Green's function for a modified Helmholtz equation and solving two additional integral equations. Similarly the derivation of streaming is reduced to finding a single Green's function for the Poisson equation on the desired geometry
Original languageEnglish
Pages (from-to)41-70
JournalJournal of Fluid Mechanics
Volume618
DOIs
Publication statusPublished - 2009

Fingerprint

Thermoacoustics
porosity
Green's function
cross sections
Helmholtz equation
Green's functions
Poisson equation
Ordinary differential equations
Temperature
Integral equations
Helmholtz equations
Porous materials
dimensional analysis
Boundary layers
Acoustics
temperature
integral equations
boundary layers
constrictions
differential equations

Keywords

  • driven acoustic-oscillations
  • porous-media
  • performance
  • equations
  • engine
  • tubes
  • flow

Cite this

in 't Panhuis, P.H.M.W. ; Rienstra, S.W. ; Molenaar, J. ; Slot, J.J.M. / Weakly nonlinear thermoacoustics for stacks with slowly varying pore cross-sections. In: Journal of Fluid Mechanics. 2009 ; Vol. 618. pp. 41-70.
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Weakly nonlinear thermoacoustics for stacks with slowly varying pore cross-sections. / in 't Panhuis, P.H.M.W.; Rienstra, S.W.; Molenaar, J.; Slot, J.J.M.

In: Journal of Fluid Mechanics, Vol. 618, 2009, p. 41-70.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Molenaar, J.

AU - Slot, J.J.M.

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AB - A general theory of thermoacoustics is derived for arbitrary stack pores. Previous theoretical treatments of porous media are extended by considering arbitrarily shaped pores with the only restriction that the pore cross-sections vary slowly in the longitudinal direction. No boundary-layer approximation is necessary. Furthermore, the model allows temperature variations in the pore wall. By means of a systematic approach based on dimensional analysis and small parameter asymptotics, we derive a set of ordinary differential equations for the mean temperature and the acoustic pressure and velocity, where the equation for the mean temperature follows as a consistency condition of the assumed asymptotic expansion. The problem of determining the transverse variation is reduced to finding a Green's function for a modified Helmholtz equation and solving two additional integral equations. Similarly the derivation of streaming is reduced to finding a single Green's function for the Poisson equation on the desired geometry

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KW - performance

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