Experimental study of Rijke-type thermoacoustic instability by using Proper Orthogonal Decomposition method

A low-order modal description of the thermoacoustic instability in a both-end-open Rijke tube with an electrical heater was proposed based on an experimental study using 15 microphones implemented along the tube wall. The simultaneous pressure measurements were decomposed into fluctuations of different eigenmodes (spatial modes) and acoustic (temporal) modes using the Proper Orthogonal Decomposition technique. Three types of pressure fluctuations, which contributed 99% of the total pressure fluctuations, were identified from the reconstructed pressure. The types I and III fluctuations resembled the spatial Fourier modes 1 and 2, respectively, in a unheated tube with slight differences caused by the local inhomogeneity near heater. The type I fluctuation appeared to cause a second type of fluctuation (type II) featured in-phased pressure near the two ends of the tube. The amount of contribution from each type of fluctuation varied with the heater position and the type I appeared to play a dominant role which contributed 85-95% to the total fluctuation. The contribution of type I increased when the heater position approached the midpoint between the pressure node and antinode of the spatial Fourier mode 1, at the same time the contribution of types II increased and the contribution of type III decreased. The phase lag between types I and III changed when the heater position varied, while the phase lag between types I and II remained constant.