Browsing by Author "Sen, Rahul"

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    Acoustic scattering by discontinuities in waveguides
    Sen, Rahul (Virginia Polytechnic Institute and State University, 1988)
    The scattering of acoustic waves by boundary discontinuities in waveguides is analyzed using the Method of Matched Asymptotic Expansions (MAE). Existing theories are accurate only for very low frequencies. In contrast, the theory developed in this thesis is valid over the entire range of frequencies up to the first cutoff frequency. The key to this improvement lies in recognizing the important physical role of the cutoff cross-modes of the waveguide, which are usually overlooked. Although these modes are evanescent, they contain information about the interaction between the local field near the discontinuity and the far-field. This interaction has a profound effect on the far-field amplitudes and becomes increasingly important with frequency. The cutoff modes also present novel mathematical problems in that current asymptotic techniques do not offer a rational means of incorporating them into a mathematical description. This difficulty arises from the non-Poincare form of the cross-modes, and its resolution constitutes the second new result of this thesis. We develop a matching scheme based on block matching intermediate expansions in a transform domain. The new technique permits the matching of expansions of a more general nature than previously possible, and may well have useful applications in other physical situations where evanescent terms are important. We show that the resulting theory leads to significant improvements with just a few cross-mode terms included, and also that there is an intimate connection with classical integral methods. Finally, the theory is extended to waveguides with slowly varying shape. We show that the usual regular perturbation analysis of the wave regions must be completely abandoned. This is due to the evanescent nature of the cross-modes, which must be described by a WKB approximation. The pressure field we so obtain includes older results. The new terms account for the cutoff cross-modes of the variable waveguide, which play a central role in extending the dynamic range of the theory.
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    Acoustic wave propagation in a circular cosh duct carrying a mean flow
    Thompson, Charles; Sen, Rahul (Acoustical Society of America, 1987-09-01)
    An analysis of acoustic wave propagation in a waveguide carrying an incompressible mean flow is presented. The radius of the waveguide is taken to vary slowly as a function of axial location. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the small parameter where is the ratio of the typical duct radius R 0 and the wall wavelength L 0. An analytical solution for the pressure field in the duct is given in terms of a regular perturbation expansion in The method of matched asymptotic expansions is used to evaluate the refractive effect of a thin mean-flow boundary layer on the acoustic pressure field. It is shown that in the case where the duct geometry conforms to that of a circular cosh duct the effect of higher-order turning points in the wave equation can be effectively handled by a closed-form solution that approximately solves the governing equations. The results of analysis are compared to those obtained using numerical methods. 1987 Acoustical Society of America
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    Scattering of acoustic waves in a waveguide
    Sen, Rahul; Thompson, Charles (Acoustical Society of America, 1987)
    The problem of scattering from boundary discontinuity in a waveguide is discussed. The relationship between the static and dynamic representations of the scattered pressure field will be investigated for those frequencies falling below the first cross mode of the duct. Special attention is paid to the influence of cutoff cross modes to the solution of the pressure field. It is shown that the method of matched asymptotic expansions can be successfully used to determine globally valid pressure field junction conditions near a boundary discontinuity. The matching of exponentially decaying terms of the inner solution is shown to, in turn, contribute to the junction impedance and extend the frequency range of the solution's validity.