Impedance models in time domain including the extended Helmholtz resonator model

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111 Citaten (Scopus)
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The problem of translating a frequency domain impedance boundary condition to time domain involves the Fourier transform of the impedance function. This requires extending the definition of the impedance not only to all real frequencies but to the whole complex frequency plane. Not any extension, however, is physically possible. The problemshould remain causal, the variables real, and the wall passive. This leads to necessary conditions for an impedance function. Various methods of extending the impedance that are available in the literature are discussed. A most promising one is the so-called z-transform by Ozyoruk & Long, which is nothing but an impedance that is functionally dependent on a suitable complex exponent e-i¿¿. By choosing ¿ a multiple of the time step of the numerical algorithm, this approach fits very well with the underlying numerics, because the impedance becomes in time domain a delta-comb function and gives thus an exact relation on the grid points. An impedance function is proposed which is based on the Helmholtz resonator model, called Extended Helmholtz Resonator Model. This has the advantage that relatively easily the mentioned necessary conditions can be satisfied in advance. At a given frequency, the impedance is made exactly equal to a given design value. Rules of thumb are derived to produce an impedance which varies only moderately in frequency near design conditions. An explicit solution is given of a pulse reflecting in time domain at a Helmholtz resonator impedance wall that provides some insight into the reflection problem in time domain and at the same time may act as an analytical test case for numerical implementations, like is presented at this conference by the companion paper AIAA-2006-2569 by N. Chevaugeon, J.-F. Remacle and X. Gallez. The problem of the instability, inherent with the Ingard-Myers limit with mean flow, is discussed. It is argued that this instability is not consistent with the assumptions of the Ingard-Myers limit and may well be suppressed.
Originele taal-2Engels
Titel12th AIAA/CEAS Aeroacoustics Conference (Cambridge MA, USA, May 8-10, 2006)
Aantal pagina's20
StatusGepubliceerd - 2006
Evenement12th AIAA/CEAS Aeroacoustics Conference - Cambridge, Verenigde Staten van Amerika
Duur: 8 mei 200610 mei 2006


Congres12th AIAA/CEAS Aeroacoustics Conference
LandVerenigde Staten van Amerika

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  • Citeer dit

    Rienstra, S. W. (2006). Impedance models in time domain including the extended Helmholtz resonator model. In 12th AIAA/CEAS Aeroacoustics Conference (Cambridge MA, USA, May 8-10, 2006) [AIAA-2006-2686]