This document discusses the use of Proper Orthogonal Decomposition (POD) to analyze combustion instability by reducing high-dimensional flame data. The experiment used a low-swirl burner and methane to create a flame at various acoustic frequencies (85hz, 125hz, 167hz) while taking high-speed pictures. POD was able to reconstruct the flame dynamics from heat release data alone, validating results from the Rayleigh method which requires simultaneous heat release and pressure measurements. Key modes from the POD analysis matched structures seen in the Rayleigh results, demonstrating POD can effectively analyze thermoacoustic instability without pressure data.

1. Application of Proper Orthogonal Decomposition in
Combustion Instability Analysis
Proper Orthogonal Decomposition (POD) is a statistical data analysis
method that takes high-dimensional data and reduces it to low-dimen-
sional approximations. This method is often used to reduce a large se-
ries of data into its different basic modes. These different modes rep-
resent how the “energy” of the data is distributed; a useful technique
in showing the dynamics of flow. The majority of the energy can be
captured within a finite amount of modes, allowing for a simplified re-
duction of complex data.
In this experiment, we used a low-swirl burner and meth-
ane to create a flame. Then by using a laser we were able
to take a cross section of the flame and take high-speed
pictures of the flame. We use laser induced fluorescence
to excite the OH radical to monitor the heat release. With
the Rayleigh data we took the pressure data simultane-
ouslywiththeheatreleasedatabutwiththePODweonly
had to take the heat release data. The 85 hz and 125 hz
cases have higher pressure amplitudes so it allowed for
clearer results as compared to the 167 hz case.
Acoustic Frequency: 85 hz, 125 hz, and 167 hz
Rayleigh: 300 pictures, 6 cases for each frequency
POD: 1800 pictures continuously for each frequency
In the experiment, we want to confirm the Rayleigh results by using
POD. The Rayleigh method shows flame instability by comparing the
heat release oscillations to the pressure oscillations. If the flame and
heat oscillations are in phase, the magnitude of the thermoacoustic
instability is maximized, if they are out of phase (negative value), the
thermoacoustic instability is dampened. With the Rayleigh method,
we must obtain heat release data and pressure data. If the pressure
data isn’t accurate, this can cause uncertainty in our results. In the POD
method we only need to monitor the heat release. When we solely
use the heat release data we can compare the Rayleigh results with the
POD results.
With the POD results you can see similar structures as with the Rayleigh
results. In the Rayleigh results, the negative values represent stability
and the postive values show instability. With POD, the results soley
show the heat release. Mode 1 shows the average flame picture. Mode
2 contains a majority of the energy and it shows similar coupling struc-
tures as with the Rayleigh results. Mode 3 also shows similar structures
to the Rayleigh results. A flame in natural conditions will be asymmet-
rical, however in our experiment we can control the petrebations so
the asymmetry is not shown until the 5th mode in the 85 hz and 125 hz
case, and the 4th mode in the 167 hz case. The asymmetry is the result
of the swirling flow.
I N T R O D U C T I O N M E T H O D S
A I M S
CO N C LU S I O N S
Daniel Lin, Jianan Zhang, Dr. Albert Ratner// University of Iowa
85 hz
125 hz
167 hz
Mode 2 Mode 3 Mode 4Rayleigh Mode 5
E X P E R I M E N T S E T U P
PRMS = 1.7262
PRMS = 3.7407
PRMS = 0.5883
Mode 1
Rayleigh POD
OH-PLIF laser system