# Experimental Investigation on Self-Excited Thermoacoustic Instability in a Rijke Tube
## 3 Experimental Facility  
Figure 4 demonstrates a schematic of the experiment facility employed to perform measurements of temperature, chemiluminescence and pressure in the Rijke tube during thermoacoustic instability. The setup consisted of a TDLAS system for temperature detection, a microphone for pressure detection, a high-speed camera for chemiluminescence detection, a Rijke tube with length of 800 mm and diameter of 30 mm and a Bunsen burner, whose exit diameter was 10 mm. Furthermore, a J-type thermocouple (not shown in the figure) in the Rijke tube was employed for temperature reference. The fundamental frequency of the Rijke tube employed in this experiment under standard conditions is 215 Hz, which is determined by \(f=c/(2L_{T})\)[31]. \(f\) is the fundamental frequency, \(c\) the sound speed, assuming to be 343 m/s and \(L_{T}\) the length of the Rijke tube. It is important to also mention that the fundamental frequency will be increased with the temperature rising.  
The TDLAS system works as follows: a function generator (Rigol 4102, Rigol, Beijing, China) generated sawtooth waveforms to drive two diode laser controllers (Arroyo 6305, Arroyo), which enable the output of two DFB diode lasers' (NEL, NTT, Tokyo, Japan) wavelengths around 7444.35 cm\({}^{-1}\) and 7185.59 cm\({}^{-1}\), respectively, corresponding to two absorption transitions of H\({}_{2}\)O. The time division multiplexing strategy was employed, and the repetition rate was 5 kHz to capture the fluctuations of temperature. The lights coming from the two DFB lasers were combined and then divided into two beams by a fiber splitter. One was directed through a Fabry-Perot interferometer (Thorlabs SA200-12B, Thorlabs, Newton, MA, USA) and detected by a photodetector (Thorlabs PDA20 CS2, Thorlabs, Newton, MA, USA) to obtain the wavelength of lights. The other was directed to a customized fiber bundle. The fiber bundle contained a single mode fiber (9 \(\upmu\)m core diameter) for transmitting the laser light, which was surrounded by six multimode fibers (105 \(\upmu\)m core diameter) for collecting reflected lights and pitching it onto a photodetector. The fiber-coupled beam was collimated to a beam diameter of -2 mm by a fiber collimator (Thorlabs F220 APC-1310, Thorlabs, Newton, MA, USA) and passed through the region of interest. Subsequently, it was reflected by a flat mirror and coupled into multimode fibers by the collimator. Ultimately, the transmitted light was directed onto another photodetector.  
The heat source was provided by a Bunsen burner with butane as fuel, with a volume flow rate of 200 mL/min. The exit of the Bunsen burner was located 200 mm away from one end of the Rijke tube, corresponding to a quarter of tuber length to enable the occurrence of thermoacoustic instability. The fuel and air were premixed before entering the burner. The chemiluminescence of flame was recorded by a high-speed camera (Fastcam SA-Z 2100K, Photron, Tokoyo, Japan) with 3000 fps to demonstrate the flame response to thermoacoustic instability. The pressure at the exit of the Rijke tube was monitored by a microphone to capture the variation in pressure with a measurement rate of 3 kHz.