Methods and techniques for precise and accurate in-duct aero-acoustic measurements : Application to the area expansion

Sammanfattning: During the design and commissioning of combustion equipment, combustion associated instabilities are commonly encountered. These thermo-acoustic instabilities can cause undesirable noise, vibrations, local thermal and mechanical stresses in the combustor and are prominent in lean combustion. An often used mathematical tool to predict the instability in combustors is the so called network model where the system under study is subdivided in several subsystems and the acoustic state variables are regarded as the input/output of these subsystems. Solving this system of equations gives rise to the complex Eigen-frequencies of the system which tell if the complete system will have an unstable/stable response for specific operating conditions. In such a model it is critical to know what the influence of each subpart is on the acoustic wave propagation to correctly predict the unstable frequencies of the system. The area expansion is a common element found in combustors and the acoustic properties of the area expansion under quiescent conditions are well known, however in the presence of flow, acoustic flow interactions may occur. These interactions change the acoustic properties and are challenging to model and accurate experimental data is needed to validate the modelling. In this study, measurements of the aero-acoustic properties of an area expansion are presented, however the focus is on the experimental techniques and methods used to obtain accurate and precise measurement data in the plane wave frequency regime. The measurement accuracy of the setup used to determine the passive aero-acoustic properties of the area expansion is assessed by measuring a known impedance. Several sources of errors are identified and methods to account for these error sources are given. It is shown that the microphone impedance affects the measurement results and the upper limit of the measurement accuracy for quiescent measurements is governed by this error. The measurement precision of the setup is assessed using a multi-variate analysis and compared with results obtained from a Monte-Carlo simulation. Also the problem to determine the uncertainty of the measured complex pressures receives attention. Using a framework based on the Hilbert-transform, expressions are derived which estimate the uncertainty on the measured complex value from the background signal spectrum. The obtained knowledge is used to determine the scattering matrix of the area expansion. For the quiescent case, the measured results agree within 1.5% of the absolute values and within 1 degree in comparison with the analytical models. In the case with flow, the errors are slightly larger due to the increased flow-noise but a good correspondence with analytical models is found. Also a sudden sound absorption at high flow speeds and low frequencies is observed.