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7997 results in Fluid dynamics and solid mechanics

Page 48 of 400

  • 1 - Some Preliminaries

  • Erkan Dokumacı
  • Book:
    Duct Acoustics
    Published online:
    11 May 2021
    Print publication:
    13 May 2021, pp 1-22

  • Summary

    This chapter describes the basic analytic concepts and operations which are invoked throughout the book. Mathematical models of sound wave motion in ducts come from the solutions of the linearized forms of the basic fluid dynamic equations of unsteady fluid flow in frequency and wavenumber domains. The process of linearization is discussed in depth and the frequency and wavenumber transformations are defined rigorously. A quantity that is often of interest in duct acoustics is the acoustic power transmitted in a duct. Calculation of time-averaged acoustic power transmitted in ducts is described a unified manner. Finally, we describe the mathematical link with the analyses presented in the book and linear system dynamics. These topics are collected in this preliminary chapter as primer and also to avoid interruption of the continuity of discussions on the principal subjects.

  • 4 - Transmission of One-Dimensional Waves in Coupled Ducts

  • Erkan Dokumacı
  • Book:
    Duct Acoustics
    Published online:
    11 May 2021
    Print publication:
    13 May 2021, pp 125-172

  • Summary

    Some coupled-duct configurations occur recurrently in practical systems. In view of the conditions of continuity and compatibility of the acoustic fields, ducts may or may not be connected as individual units. In this chapter we present one-dimensional intermediate acoustic models for basic coupling configurations such as area changes and junctions, and continuous and discrete acoustic models for packs of coupled perforated ducts. These are multi-port elements and they can be connected at their ports to the one-dimensional duct elements given in Chapter 3.

Duct Acoustics
  • Fundamentals and Applications to Mufflers and Silencers
  • Erkan Dokumacı
  • Published online:
    11 May 2021
    Print publication:
    13 May 2021
  • foundations of duct acoustics to the acoustic design of duct systems, through practical modeling, optimization and measurement techniques. Discover in-depth analyses of one- and three-dimensional models of sound generation, propagation and radiation, as techniques for assembling acoustic models of duct systems from simpler components are described. Identify the weaknesses of mathematical models in use and improve them by measurement when needed. Cope with challenges in acoustic design, and improve understanding of the underlying physics, by using the tools described. An essential reference for engineers and researchers who work on the acoustics of fluid machinery ductworks.

  • SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING

  • Part of
  • DAVID GALLOWAY, DAVID IVERS
  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 1 / January 2021
    Published online by Cambridge University Press:
    30 April 2021, pp. 23-38

  • DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.

Page 48 of 400