Numerical Techniques in Linear Duct Acoustics—A Status Report

Abstract

A review is presented covering both finite difference and finite element analysis of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turbojet engine duct, muffler, or industrial ventilation system. Both steady-state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.

Acoustic Finite Element Analysis of Duct Boundaries

“…Thus, the governing equations are reduced to "1^ + V"(pu) = 0 (2)(3) and P ("^ + u-Vu) = -vp. (2)(3)(4) To obtain a single equation for pressure from the two existing equations, which also involve the velocity, the divergence of to. (2)(3)(4) is found .…”

“…(2)(3)(4) To obtain a single equation for pressure from the two existing equations, which also involve the velocity, the divergence of to. (2)(3)(4) is found . (2)(3)(4)(5)(6) This equation governs situations in which flow is present but the effects of viscosity, body forces, and volume sources may be neglected.…”

“…The finite difference method is probably best suited to non-linear problems and problems in the time domain (4).…”

Transfer matrix of conical waveguides with any geometric parameters for increased precision in computer modeling

“…For computational methods of modeling waveguides and ducts, the reader is referred to. [9][10][11] For applications of computational methods for modeling wind instruments in musical acoustics, refer to. 3,6,7,[12][13][14] Applications of numerical techniques in the design of mufflers in exhaust systems are discussed in Refs.…”

A finite difference solution for the propagation of sound in near sonic flows

“…Such direct methods, whether based on finite element or finite difference methodology (ref. 2), produce a large set of coupled linear equations, which are usually solved by matrix manipulations, that is, inversion/ decomposition procedures. However, many practical aeroengine duct modeling situations require extremely large numbers of degrees-of-freedom for accurate resolution.…”