M.K. Myers

Bio: M.K. Myers is an academic researcher from George Washington University. The author has contributed to research in topics: Mach number & Duct (flow). The author has an hindex of 6, co-authored 9 publications receiving 766 citations.

Nonlinear effects on sound in nearly sonic duct flows

Abstract: A nonlinear theory for sound propagation in nearly sonic flows in variable area ducts is outlined. The theory is based on a quasi-one-dimensional model and the use of matched asymptotic expansions. The problem of an acoustic source located in the throat region of a duct with a converging section is treated. It is shown that the near-sonic region has a marked nonlinear effect on sound propagation in the duct.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Impedance Models in Time Domain including the Extended Helmholtz Resonator Model

Abstract: 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 problemshouldremain causal, the variables real, andthe 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 −iωκ . By choosing κ 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.

Transport of energy by disturbances in arbitrary steady flows

Abstract: An exact equation governing the transport of energy associated with disturbances in an arbitrary steady flow is derived. The result is a generalization of the familiar concept of acoustic energy and is suggested by a perturbation expansion of the general energy equation of fluid mechanics. A disturbance energy density and flux are defined and identified as exact fluid dynamic quantities whose leading-order regular perturbation representations reduce in various special cases to previously known results. The exact equation on disturbance energy is applied to a simple example of nonlinear wave propagation as an illustration of its general utility in situations where a linear description of the disturbance is inadequate.