The subject of this thesis is the acoustic properties offlow duct area expansions and the influence of flow-acousticcoupling at sharp edges. For low Mach number flow, significantinteraction between the sound field and the flow field canoccur at such points of flow separation. A linear analyticalmodel is used to describe the sound field, whereas the meanflow field is modelled as a jet issuing into the larger duct.The scattering coefficients for sound waves incident on thearea expansion are determined by the Wiener-Hopf techniquetogether with a building block method. To achieve a uniquesolution, the unsteady Kutta condition is applied at the sharpedge. The results have been verified through comparison withexperimental data, and the agreement is excellent. Thereflection and transmission coefficients for the plane wave, aswell as the absorption coefficient have been studied, and aquasi-stationary model for the scattering coefficient have beenderived from the analytical model.
The shear layer emanating from the edge is modelled as avortex sheet, with zero thickness. The vortex sheet is unstablefor all frequencies, and as a real shear layer is unstable onlyup to a critical frequency disturbances, it is a low frequencymodel. In fact, it is the Strouhal number, based on thethickness of the shear layer that determines the stabilityproperties of the shear layer. The dynamics of a finite shearlayer is included in the model by adjusting the edge condition,thus extending the model to higher Strouhal numbers. Inaddition, a method to calculate the absorption of sound due tothe vortex shedding gives a good prediction of experimentaldata. The promising result for the adjusted edge condition andthe possibility to predict the transmitted acoustic far fieldimplies that the jet expansion region, which is neglected inthe model, has indeed a negligible influence on the plane wavesound transmission. Apparently, linear theory is sufficient topredict these phenomena, at least in the low frequencyregion.
New results, both experimental and theoretical, for the endcorrection of an area expansion are presented. It is shown thatthe end correction varies significantly when the duct widthStrouhal number is around one. For large Strouhal numbers, thenon-flow results are retrieved. An analysis of the duct modesindicates a regime where the flowacoustic coupling via ahigher order acoustic mode is important. It is shown that thisphenomenon is governed by the Strouhal number and not by theclassical acoustic variables Helmholtz number and Mach number.Finally, the influence of the flow-acoustic coupling on theenergy flow is discussed. It is shown that non-orthogonal ductmodes indicate the Strouhal number region where theflow-acoustic coupling has the strongest influence on the soundfield. Strong coupling to a higher orderacoustic mode isanalysed in some detail. A method to construct a conservativesystem, regarding the vortex sheet as a source/sink term isalso presented.
Keywords:sound, vortex sheet, flow separation, endcorrection, Strouhal number, non-orthogonal modes, energybalance
Stockholm: KTH , 2003. , 10 p.
sound, vortex sheet, flow separation, end correction, Strouhal number, non-orthogonal modes, energy balance