Proper Orthogonal Decomposition (POD) has been implemented in processing of highspeed movies of combustion light emission from two combustion instability experiments. Using the method of singular value decomposition, analysis produces a series of POD modes -orthogonal bases of linked spatial and temporal modes which are sorted based on decreasing singular value or "energy," which indicates the variation and descriptivity contained within each POD mode. Without initially specified conditions or functional forms beyond raw data, the POD modes identify the measured frequencies of the chamber acoustic modes and show the physical behavior of the light emission associated with each POD mode. The major behaviors of the combustion light emission can be reconstructed using select POD modes, serving as an effective low-order approximation of high-order data. Based on this effectiveness, POD analysis shall be extended to the determination of flame describing functions from the temporal POD modes and measured pressure signals.
Nomenclature= M-term approximation = temporal POD mode component = spatial POD mode component = singular value or "energy" of POD mode = number of POD modes used in approximation
An automated data isolation and reduction method has been developed to generate meaningful graphical combustion response functions from a combination of pressure amplitude and various image analysis metrics. It was developed and tested using pressure measurements and high speed imaging of combustion light taken from an unstable high pressure subscale single element longitudinal combustor. The code was used to isolate time slices of near stationary pressure amplitude, and process the corresponding images into combustion response approximated by Global I', Center of Intensity, POD, and DMD. Overall the generated combustion response functions generally agreed with expected behavior of an element located at the pressure antinodes of multiple modes of a longitudinal combustor. The response functions generally showed positively correlated linear behavior with pressure amplitude. Results from POD and DMD both successfully isolated the prominent spatial and temporal light emission behavior.
Combustion response functions describe the magnitude and time lag behavior of a §ame in response to unsteady pressure and velocity. By understanding the feedback between unsteady §ow¦elds and heat release, the growth and decay of combustion instability can be better predicted. An automated data isolation and reduction method has been developed to generate meaningful graphical combustion response functions from a combination of pressure amplitude and various image analysis metrics. It was developed and tested using pressure measurements and high-speed imaging of combustion light taken from a single element at the midspan of an unstable high-pressure subscale transverse combustor. The code was used to isolate time slices of near stationary pressure amplitude and to process the corresponding images into combustion response approximated by aggregate intensity, intensity weighted spatial center, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD). Overall, the generated combustion response functions generally agreed with expected behavior of an element located at a ¦rst width (1W) velocity antinode and second width (2W) pressure antinode. Results from both POD and DMD successfully isolated the prominent spatial and temporal light emission behavior.
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