A classification of duct modes based on surface waves

Rienstra, SW Sjoerd

doi:10.1016/s0165-2125(02)00052-5

Cited by 159 publications

(120 citation statements)

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“…where σ HI is the value of σ for the surface mode that is a potential candidate for an instability [4], and is a Kutta-condition factor. = 0 corresponds to σ HI being considered stable and not present in x > 0, and leads to a boundary streamline cusp at x = 0 of w = O(x 1/2 ).…”

Section: The Scattering Problem and Its Solutionmentioning

confidence: 99%

“…For finite Z , most modes are acoustic modes and have nearly real α mµ . Rienstra [4] identified and characterized surface modes localized close to the duct boundary, for which α mµ has a large imaginary part (this analysis having been subsequently extended in [6]). Using the mass-spring-damper lining model, Rienstra tentatively suggested that one of these surface modes, present only with nonzero mean flow, might be interpreted as a downstream-growing instability, and termed this mode a hydrodynamic instability (HI) mode.…”

mentioning

confidence: 98%

“…Some common models for the dependence of Z on ω will be considered here. The first is the mass-spring-damper model, as used by Rienstra [1,4], which treats the boundary as a locally-reacting simple harmonic oscillator with mass per unit area a * , spring constant per unit area b * , and damping constant per unit area R * . Hence, when forced by the fluid pressure p * , the boundary behaves according to…”

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confidence: 99%

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Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow

Brambley

2009

J Eng Math

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The low-frequency limit of the reflection coefficient for downstream-propagating sound in a cylindrical duct with uniform mean flow at a sudden hard-soft wall impedance transition is considered. The scattering at such a transition for arbitrary frequency was analysed by Rienstra (2007, J Eng Maths 59:451-475), who, having derived an exact analytic solution, also considered the plane-wave reflection coefficient, R 011 , in the low-frequency limit, and it is this result that is reconsidered here. This reflection coefficient was shown to be significantly different with or without the application of a Kutta-like condition and the corresponding inclusion or exclusion of an instability wave over the impedance wall, assuming an impedance independent of frequency. This analysis is here rederived for a frequency-dependent locally-reacting impedance, and a dramatic difference is seen. In particular, the Kutta condition is shown to have no effect on R 011 in the low-frequency limit for impedances with Z (ω) ∼ −ib/ω for some b > 0 as ω → 0, which includes the mass-spring-damper and Helmholtz resonator impedances, although, interestingly, not the enhanced Helmholtz resonator model. This casts doubt on the usefulness of the low-frequency plane-wave reflection coefficient as an experimental test for the presence of instability waves over the surface of impedance linings. The plane-wave reflection coefficient is also derived in the low-frequency limit for a thin shell boundary, based on the scattering analysis of Brambley and Peake (2008, J Fluid Mech 602:403-426), who suggested the model as a well-posed regularization of the mass-spring-damper impedance. The result might be interpretable as evidence for the nonexistence of an instability over an acoustic lining.

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Section: The Scattering Problem and Its Solutionmentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow

Brambley

2009

J Eng Math

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“…In acoustics, cylindrical ducts are of special interest for pressure wave propagation and turbocharger applications [33][34][35][36]. In photonics, axially symmetric media can be found in single-and multicore optical fibers, optical couplers, laser arrays, modulators, and Bragg gratings [37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Transformations in Optical Fibers

2018

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Supersymmetry (SUSY) has recently emerged as a tool to design unique optical structures with degenerate spectra. Here, we study several fundamental aspects and variants of one-dimensional SUSY in axially symmetric optical media, including their basic spectral features and the conditions for degeneracy breaking. Surprisingly, we find that the SUSY degeneracy theorem is partially (totally) violated in optical systems connected by isospectral (broken) SUSY transformations due to a degradation of the paraxial approximation. In addition, we show that isospectral constructions provide a dimension-independent design control over the group delay in SUSY fibers. Moreover, we find that the studied unbroken and isospectral SUSY transformations allow us to generate refractive-index superpartners with an extremely large phase-matching bandwidth spanning the S þ C þ L optical bands. These singular features define a class of optical fibers with a number of potential applications. To illustrate this, we numerically demonstrate the possibility of building photonic lanterns supporting broadband heterogeneous supermodes with large effective area, a broadband all-fiber true-mode (de)multiplexer requiring no mode conversion, and different mode-filtering, mode-conversion, and pulse-shaping devices. Finally, we discuss the possibility of extrapolating our results to acoustics and quantum mechanics.

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“…For certain impedance models Z(ω), including the mass-spring-damper impedance [4,16] for which Z = R + imω − iK/ω and the Extended Helmholtz Resonator impedance [5,17] for which Z = R + imω − iβ cot(ωL − iε/2), time-domain versions of the frequency-domain boundary condition (1) are possible. However, high-frequency numerical instabilities are invariably present in time-domain simulations [4,17,18] when such impedances are used with slipping mean flow using the Myers boundary condition (1).…”

Section: Introductionmentioning

confidence: 99%

Time-domain implementation of an impedance boundary condition with boundary layer correction

Gabard

2016

Journal of Computational Physics

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A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley [ , AIAA J. 49(6), pp. 1272[ -1282. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

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A classification of duct modes based on surface waves

Cited by 159 publications

References 13 publications

Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow

Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow

Supersymmetric Transformations in Optical Fibers

Time-domain implementation of an impedance boundary condition with boundary layer correction

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