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
Combustion dynamics are controlled by the coupling between heat addition and gas dynamic modes, hence their direct measurement and comparisons with prediction are key to improving computational tools as well as our fundamental understanding of the problem. Whereas gas dynamic modes are relatively easy to measure and compare, measurement and characterization of heat addition are much more difficult due to its complexity and the lack of any direct means of measurement. This paper demonstrates several methods for characterizing and comparing heat release from experiment and simulation. A model rocket combustor is used for the study. Comparisons are made for two configurations, one stable and one unstable. High-speed, line-of-sight imaging of OH* emission from the experiment was first phase averaged, and then treated with an Abel inversion routine to produce a dynamic, two-dimensional field of heat addition. The field before inversion could be compared to line-integrated calculations of heat release rate from three-dimensional large eddy simulations, and after inversion to azimuthally averaged cross-sections from simulations. Modal decomposition analysis of the two-dimensional fields were performed. The applicability and limitations of each comparison approach are assessed. Nomenclature J 0 = zero-order Bessel function of the first kind L op = length of oxidizer post, mm|inch p′ = dynamic pressure, MPa P cc = chamber pressure, MPa Φ = equivalence ratio ′ = unsteady term of a variable ω = frequency, Hz
A two-dimensional chamber containing seven ox-centered shear coaxial injector elements was designed to generate and modulate an unsteady transverse flowfield. A single Study element was placed in the middle of this unsteady flowfield so its response can be measured using pressure measurement and high speed imagery. The initial characterization of this combustor entailed the effect of post length configurations on pressure amplitude. With all other conditions held constant, a long oxidizer post configuration was stable, and a short oxidizer post configuration was unstable. These post lengths were scaled from a comparable longitudinal combustor and have consistent stability behavior for the individual scaled post lengths. Phase lag behavior between the high frequency measurements in the oxidizer posts and the combustion chamber indicated that consistent phase lags near half of the chamber acoustic mode period between posts and local chamber regions were necessary to sustain a high amplitude unsteady flowfield, suggesting a coupling of post resonance with the chamber unsteady flowfield. a
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