Figure 5 - available via license: Creative Commons Attribution-NonCommercial 4.0 International
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Reflection coefficient for the plane wave mode (left) and the first higher order mode (right) as function of frequency for two different acoustic excitations, case 1 () and case 2 ( ). The vertical lines denote the cut-on frequencies of the higher order modes.
Source publication
To be able to compare the measured scattering matrices with model predictions, the quality of the measurements has to be known. Uncertainty analyses are invaluable to assess and improve the quality of measurement results in terms of accuracy and precision. Linear analyses are widespread, computationally fast and give information of the contribution...
Contexts in source publication
Context 1
... Figure 5, the reflection coefficient of the plane wave mode and the first higher order mode are shown for two different excitation configurations. For the first configuration, only one loudspeaker was used, situated on the top wall. For the second configuration, two loudspeakers mounted in the side walls and facing each other were used. Doak 38,39 investigated the exci- tation of higher order modes in rectangular ducts and showed that the excitation strength of the specific modes is sensitive to both the spatial distribution of the excitation sources and the end conditions of the duct. Therefore, the two different configurations lead to different amplitudes of the ingoing waves. From the reflection coefficients it can be seen that after the cut-on of the second higher order mode, the plane wave and first higher order mode reflection coefficients for the second configuration show more scatter compared to the results from the first ...
Context 2
... the bottom row of Figure 5, the relative difference between the calculated covariance matrix for the reflec- tion coefficient using the Monte-Carlo method and the multi-variate method is shown. The figure shows that after the second cut-on frequency, the covariance matrix for the plane waves is not correctly described by the linear analysis. The relative difference between the covariance matrices for the reflection coefficient for the first higher order mode is large for almost all frequencies, and the results obtained from the multi- variate method cannot be ...
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Citations
This master’s thesis ‘Sensitivity Analysis of Flame Transfer Function Measurements’ deals with the uncertainty propagation and sensitivity analysis in the context of experimental thermoacoustics. The relationship between velocity fluctuation and heat release (flame transfer function) is a central aspect when predicting combustion instabilities. The flame transfer function was determined using a transfer matrix description of the flame and spray combustion chamber at realistic in-flight-conditions (elevated temperature and pressure).These measurements yield uncertainties, which are propagated onto the flame transfer function. Even though the computation of the flame transfer function mainly consists of simple matrix operations, the analytical approach is not feasible and consequently a Monte-Carlo approach is chosen. The static temperature, static pressure, mass flow, complex dynamic pressure and the axial position of the dynamic pressure sensors, are taken into account as uncertain input distributions. The estimation of the spreads of these uncertain entities are based on experience in industrial burner tests. It is found that the flame transfer function is noticeably uncertain below 150 Hz and between 600 Hz and 1000 Hz. A sensitivity analysis revealed, that the main contributors are the amplitude and phase uncertainties of the dynamic pressure sensors, the uncertainty in the exact axial position of such towards higher frequencies and the static temperature in the inlet section. The contribution of the static pressure and mass flow towards the global uncertainty are found to be negligible. Using numerically determined sensitivity coefficients, the results can be used for different input uncertainties without the need for repeated Monte Carlo simulations. The implementation can be easily adapted to calculate the uncertainty and sensitivity of other entities of in-duct-measurements such as scatter matrices or dissipation coefficients and is thus applicable in a broader sense.
