# Experimental Investigation on Self-Excited Thermoacoustic Instability in a Rijke Tube
## 1 Introduction  
Thermoacoustic instability has drawn great attention in the design and operation of gas-turbine combustors [1]. It originates from the closed feedback between fluctuations of acoustic waves and heat release. The feedback typically consists of three steps depicted in Figure 1[2]. Heat release rate fluctuations provide an energy source for acoustic waves, resulting in velocity and pressure oscillations propagating throughout combustors. Then, acoustic fluctuations stimulate the ratio of fuel to air variations, which contribute to further heat release rate fluctuations. Consequently, closed feedback is maintained. Under some conditions, the occurrence of thermoacoustic instability is inevitable and its resulting powerful pressure oscillations and significant temperature variations are potential dangerous for the structural strength and performance of gas turbines [3] and rocket engines [4]. Therefore, it necessitates comprehension of the essence of thermoacoustic instability to predict and control it. Rijke tube, which is typically composed of an open-ended vertical or horizontal tube and a heat source inside it, has been widely employed to obtain the fundamental understanding of the dynamics in the thermoacoustic instability phenomena by numerous researchers. [PERSON] et al. [5] deduced the liner theory including driving and damping effects from the observation of two types of thermoacoustic instability. The predictions of the theory were shown to be in great agreement with experimental results. [PERSON] et al. [6] simulated non-linear self-excited thermoacoustic instability numerically within different types of Rijke tubes. The oscillations of pressure were found to be stimulated at the tube'snatural frequencies. The obtained results were coincident with experiments. [PERSON] et al. [7] focused on characteristics of thermoacoustic behavior in Rijke-type combustors. It was found that oscillation amplitudes of pressure achieved the maximum in fuel-rich flames. [PERSON] et al. [8] developed a model based on the physical analysis about heat release and gas dynamics to describe the thermoacoustic instability phenomenon in electrically heated Rijke tubes. For the purpose of predicting the amplitude and frequency of the thermoacoustic instability, [PERSON] et al. [9] captured the reaction flow physics in the Rijke tube by solving conservation equations numerically and compared the numerical and experimental results. [PERSON] et al. [10] reported the contributions of nonlinearity and non-normality to thermoacoustic instability in Rijke tubes. To acquire some understanding of the evolution of flow disturbances in initiating thermoacoustic instability, a generalized model of Rijke tubes was presented by [PERSON] et al. [11]. Furthermore, he developed a thermo-acoustic-piezo system based on Rijke-Zhao to extend the application for energy harvesting [12]. [PERSON] [13] combined the nonlinear governing equations with an optimized procedure to reveal the lowest initial energy which triggers self-sustained oscillations in a horizontal Rijke tube. Although the procedure is developed in a simple thermoacoustic system, it is still available for more complicated thermoacoustic models. [PERSON] et al. [14] studied the impacts of dispersion of heaters on Rijke tubes via altering heating property and the numerical simulation was performed to acquire temperature and flow field distribution with different heat sources. [PERSON] et al. [15] utilized the high-voltage microsecond plasma discharge for suppression of the thermoacoustic instability in Rijke tubes. More recently, [PERSON] et al. [16] conducted experimental measurements upon the heat conduction transfer function during thermoacoustic instability in a horizonal Rijke tube. The findings demonstrated that the transfer function was influenced significantly by heater power as well as mean air flow velocity. However, previous measurements are mainly concerned with pressure or velocity. The instantaneous temperature measurements in the Rijke tube are rarely reported.