Application of Proper Orthogonal Decomposition to Light Intensity Measurements of Combustion Instability

Abstract

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

Reduced-Order Modeling of Model Rocket Combustors

“…In recent years, modal decomposition techniques have been applied to high-resolution experimental data to extract low-order representations of the combustion dynamics. 15,16 Their successes illustrate the potential of applying reduced order methods to efficiently account for the underlying dynamics.…”

Measuring the phase between fluctuating pressure and flame radiation intensity in a cylindrical combustion chamber

“…The same approach was applied to a rectangular combustion chamber with representative operating conditions and forced acoustics by Hardi et al [17]. Wierman et al [18] performed phase shift studies with research combustors experiencing self-excited combustion instabilities. Proper orthogonal decomposition (POD) techniques were applied to the high-speed imaging of §ame radiation intensity.…”

The change in flow dynamics inside the post chamber of hybrid rocket

“…Turbulent flows are commonly analyzed with POD, where the different scales associated with different kinetic energy can be studied separately. As the importance of understanding the dynamics associated with the combustion have arisen, POD has been applied to the visualization of different combustion systems [11][12][13]. When it is applied to instability problem, it can draw information regarding how each energy level contributes to the instability [11][12][13].…”

“…Visualization techniques are developed and applied to investigate the combustion instability [8,9,[11][12][13]. The representative flow visualization technique is PIV but it requires the incorporation of complex equipment and technical experiences.…”

“…Visualized flow and flame structures are commonly analyzed with Proper orthogonal decomposition (POD) [11][12][13]. POD allows studying the separated specific scales from multiscale phenomena by decomposing the data into spatial and temporal components [13].…”