Eigenmodes of lined flow ducts with rigid splices

Abstract

This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure eigenmodes is given in terms of an azimuthal Fourier sum, with the Fourier coefficients given by a recurrence relation. Since this expression is derived using a Green’s function method, the completeness of the expansion is guaranteed. A numerical procedure is described for solving this recurrence relation, which is found to converge exponentially with respect to number of Fourier terms used and is in practice quick to compute; this is then used to give several numerical examples for both uniform and sheared mean flow. An asymptotic expression is derived to directly calculate the pressure eigenmodes for thin splices. This asymptotic expression is shown to be quantitatively accurate for ducts with very thin splices of less than 1 % unlined area and qualitatively helpful for thicker splices of the order of 6 % unlined area. A thin splice is in some cases shown to increase the damping of certain acoustic modes. The influences of thin splices and thin boundary layers are compared and found to be of comparable magnitude for the parameters considered. Trapped modes at the splices are also identified and investigated.

Isentropic wave propagation in a viscous fluid moving along a lined duct with shear flow and its implication for ultrasonic flow measurement

“…which is the classical Ingard-Myers boundary condition [4,27]. If the acoustic impedance is independent of the time, one obtains…”

“…However, such method neglected the viscous dissipation in the fluid. By analyzing the acoustic wave propagating in a viscous boundary layer, different improved models of the boundary condition were proposed by Brambley et al [4], Rienstra and Darau [27], and Auregan et al [2,24], to mention a few. Although the viscous dissipation was taken into consideration at the viscous boundary layer, the governing equation of wave propagation was established in the framework of the inviscid fluid.…”

Linear Stability with Respect to the Initial Value Perturbations in the Presence of Solutions of the Linearized Equation Having Strictly Positive Exponential Growth Rate

“…For describing the instantaneous acoustic perturbation propagation in a gas flowing through a lined duct, the authors of [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] consider the nonlinear Euler equations governing the gas flow and the solution of these equations describing the gas flow. After that, the…”

Theoretical model of scattering from flow ducts with semi-infinite axial liner splices

“…the influence of splices has mainly been examined in terms of induced spinning modes with respect to their numbers and width in the circumferential axis, using either numerical simulations (McAlpine & Wright 2006;Tam, Ju & Chien 2008) or analytical methods, such as mode matching (Fuller 1984;Elnady, Boden & Glav 2001;Yang & Wang 2008), multi-modal method (Bi et al 2006), Green's function approach (Brambley 2009) and eigenmode analysis (Fuller 1984;Brambley, Davis & Peake 2012). We should say that the above literature review is not exhaustive.…”