Study of Thermoacoustic Instability using Rijke Tube

Author(s):  
Subhash Kumar ◽  
MSN Murthy ◽  
Sheshadri Sreedhara
2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.


1989 ◽  
Vol 202 ◽  
pp. 83-96 ◽  
Author(s):  
C. Nicoli ◽  
P. Pelcé

We develop a simple model in which longitudinal, compressible, unsteady heat transfer between heater and gas is computed in the small-Mach-number limit. This calculation is used to determine the transfer function of the heater, which plays an important role in the stability limits of the thermoacoustic instability of the Rijke tube. The transfer function is determined analytically in the limit of small expansion parameter γ, and numerically for γ of order unity. In the case ρμ/cp = constant, an analytical solution can be found.


Author(s):  
Jianchang Feng ◽  
Wen Ao ◽  
Peijin Liu

Dynamical systems theory has been often employed to study nonlinear flow and flame dynamics in combustion systems. However, the corresponding studies using nonlinear dynamics to analyze the Rijke tube thermoacoustic system are still occasional. Little study has been performed to elucidate the characteristics of triggering phenomenon in the bistable region of the thermoacoustic system. In this regard, the main objectives of the present research are to contribute analysis for the lack of literature in these areas, especially to study the bistability and triggering properties of a thermoacoustic system. The thermoacoustic model of a horizontal Rijke tube is firstly established. The governing equations are expanded and solved by using Galerkin method. The analysis of the system is carried out by using nonlinear dynamics theory. Linear and nonlinear stability boundaries for the variation of non-dimensional heater power, damping coefficient and the relative heater location are obtained for different values of non-dimensional time lag in the system. Regions of global stability, global instability and bistability are characterized. The bistable region in the relative heater location is distributed symmetrically with xf=0.25. It is observed that the bistable region in the relative heater location firstly decreases with an increase in the non-dimensional time lag, reaching a minimum value at a certain critical value of τ, then increases. The situation for the bistable region in the damping coefficient presents a reverse variation, And the bistable region reach the maximum at τ=0.5. The triggering phenomenon and limit cycle of the system in the bistable region are studied. The critical triggering values are determined with the changes of the non-dimensional heater power, the damping coefficient and the relative heater location. The critical triggering value of velocity perturbation decreases with the increase of non-dimensional heater power, whereas an increasing trend is observed with the increase of damping coefficient. Interestingly, the critical triggering value firstly decreases and then increases with the increase of the relative heater location. The variation of critical triggering value for pressure perturbation is found to correspond with velocity perturbation. In the bistable region, the amplitude and frequency of the steady limit cycle oscillation of the system are independent of the initial perturbation values, but the perturbation value has strong effect on the duration needed to achieve the steady limit cycle, and the time required for the system to reach the limit cycle under the perturbation of U1=0.4 is about 3 times longer than that of U1=0.8.


Author(s):  
Chandrachur Bhattacharya ◽  
Asok Ray

Abstract Transfer learning (TL) is a machine learning (ML) tool where the knowledge, acquired from a source domain, is 'transferred' to perform a task in a target domain that has (to some extent) a similar setting. The underlying concept does not require the ML method to analyse a new problem from the beginning, and thereby both the learning time and the amount of required target-domain data are reduced for training. An example is the occurrence of thermoacoustic instability (TAI) in combustors, which may cause pressure oscillations, possibly leading to flame extinction as well as undesirable vibrations in the mechanical structures. In this situation, it is difficult to collect useful data from industrial combustion systems, due to the transient nature of TAI phenomena. A feasible solution is the usage of prototypes or emulators, like a Rijke tube, to produce largely similar phenomena. This paper proposes symbolic time series analysis (STSA)-based transfer learning, where the key idea is to develop a capability of discrimination between stable and unstable operations of a combustor, based on the time series of pressure oscillations from a data source that contains sufficient information, even if it is not the target regime, and then transfer the learnt models to the target regime. The proposed STSA-based pattern classifier is trained on a previously validated numerical model of a Rijke-tube apparatus. The knowledge of this trained classifier is 'transferred' to classify similar operational regimes in: (i) an experimental Rijke-tube apparatus and (ii) an experimental combustion system apparatus. Results of the proposed transfer learning have been validated by comparison with those of two shallow neural networks (NN)-based TL and another NN having an additional long-short-term-memory (LSTM) layer, which serve as benchmarks, in terms of classification accuracy and computational complexity.


2010 ◽  
Vol 2 (4) ◽  
pp. 325-355 ◽  
Author(s):  
Priya Subramanian ◽  
Sathesh Mariappan ◽  
R. I. Sujith ◽  
Pankaj Wahi

Author(s):  
Umut Zalluhoglu ◽  
Nejat Olgac

This paper brings a novel mathematical perspective in assessing the rise of the secondary dynamic modes to prominence during the suppression of thermoacoustic instability. This phenomenon is observed by many earlier investigators; however, without a complete analytical reasoning. We consider a Rijke tube with both a passive Helmholtz resonator and an active feedback control to suppress instabilities. The core dynamics is represented as a linear time-invariant multiple time-delay system of neutral type. Parametric stability of the resulting infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots paradigm. This tool reveals the stability outlook of such systems exhaustively and non-conservatively in the parameter space of the system. First, we examine the stability with and without the Helmholtz resonator. We then select an unstable operation for the resonator-mounted Rijke tube, impose a time-delayed integral feedback control over it and reveal the stabilizing controller parameters using the cluster treatment of characteristic roots methodology. When high control gains are inappropriately selected, the new analytical procedure declares how the secondary dynamic modes of the system exhibit instability although the initially unstable mode is now stabilized. All of these stability assessments are cross-validated using experimental results from a laboratory-scale Rijke tube set-up.


2008 ◽  
Vol 20 (4) ◽  
pp. 044103 ◽  
Author(s):  
Koushik Balasubramanian ◽  
R. I. Sujith

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