Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH
Keyword(s):  
Mach Number ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Heat Release ◽  
Acoustic Field ◽  
Release Rate ◽  
Governing Equations ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acceleration Term

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.

scholarly journals Thermoacoustic Instability in a Rijke Tube with a Distributed Heat Source

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaochuan Yang ◽  
Ali Turan ◽  
Shenghui Lei
Keyword(s):  
Heat Source ◽  
Heat Release ◽  
Method Of Lines ◽  
Nonlinear Behaviour ◽  
Heat Sources ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acoustic Perturbation ◽  
The Stability ◽  
The Galerkin Method

A Rijke tube with a distributed heat source is investigated. Driven by the widely existing thermoacoustic instability in lean premixed gas turbine combustors, this work aims to explore the physicochemical underpinning and assist in the elucidation and analysis of this problem. The heat release model consists of a row of distributed heat sources with individual heat release rates. The integrated heat release rate is then coupled with the acoustic perturbation for thermoacoustic analysis. A continuation approach is employed to conduct the bifurcation analysis and capture the nonlinear behaviour inherent in the system. Unlike the conventional approach by the Galerkin method, the acoustic equations are originally discretized using the Method of Lines (MOL) to build up a dynamic system. The model is first validated and shown to yield good predictions with available experimental data. Influences of multiple heat sources, time delay, and heat release distribution are then studied to reveal the extensive nonlinear characteristics involved in the case of a distributed heat source. It is found that distributed heat source plays an important role in determining the stability of a thermoacoustic system.

Thermoacoustic instability as mutual synchronization between the acoustic field of the confinement and turbulent reactive flow

2017 ◽  
Vol 827 ◽  
pp. 664-693 ◽  
Author(s):  
Samadhan A. Pawar ◽  
Akshay Seshadri ◽  
Vishnu R. Unni ◽  
R. I. Sujith
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Acoustic Field ◽  
Heat Release Rate ◽  
Release Rate ◽  
Bluff Body ◽  
Acoustic Pressure ◽  
Mutual Synchronization ◽  
Periodic Oscillations ◽  
Thermoacoustic Instability

Thermoacoustic instability is the result of a positive coupling between the acoustic field in the duct and the heat release rate fluctuations from the flame. Recently, in several turbulent combustors, it has been observed that the onset of thermoacoustic instability is preceded by intermittent oscillations, which consist of bursts of periodic oscillations amidst regions of aperiodic oscillations. Quantitative analysis of the intermittency route to thermoacoustic instability has been performed hitherto using the pressure oscillations alone. We perform experiments on a laboratory-scale bluff-body-stabilized turbulent combustor with a backward-facing step at the inlet to obtain simultaneous data of acoustic pressure and heat release rate fluctuations. With this, we show that the onset of thermoacoustic instability is a phenomenon of mutual synchronization between the acoustic pressure and the heat release rate signals, thus emphasizing the importance of the coupling between these non-identical oscillators. We demonstrate that the stable operation corresponds to desynchronized aperiodic oscillations, which, with an increase in the mean velocity of the flow, transition to synchronized periodic oscillations. In between these states, there exists a state of intermittent phase synchronized oscillations, wherein the two oscillators are synchronized during the periodic epochs and desynchronized during the aperiodic epochs of their oscillations. Furthermore, we discover two different types of limit cycle oscillations in our system. We notice a significant increase in the linear correlation between the acoustic pressure and the heat release rate oscillations during the transition from a lower-amplitude limit cycle to a higher-amplitude limit cycle. Further, we present a phenomenological model that qualitatively captures all of the dynamical states of synchronization observed in the experiment. Our analysis shows that the times at which vortices that are shed from the inlet step reach the bluff body play a dominant role in determining the behaviour of the limit cycle oscillations.

Smart Passive Control of Thermoacoustic Instability in a Bluff-Body Stabilized Combustor: A Lagrangian Analysis of Critical Structures

2020 ◽  
Author(s):  
C. P. Premchand ◽  
Manikandan Raghunathan ◽  
Midhun Raghunath ◽  
K. V. Reeja ◽  
R. I. Sujith ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Flow Field ◽  
Heat Release ◽  
Shear Layer ◽  
Heat Release Rate ◽  
Release Rate ◽  
Sound Production ◽  
Bluff Body ◽  
Passive Control ◽  
Thermoacoustic Instability

Abstract The tonal sound production during thermoacoustic instability is detrimental to the components of gas turbine and rocket engines. Identifying the root cause and controlling this oscillatory instability would enable manufacturers to save in costs of power outages and maintenance. An optimal method is to identify the structures in the flow-field that are critical to tonal sound production and perform control measures to disrupt those “critical structures”. Passive control experiments were performed by injecting a secondary micro-jet of air onto the identified regions with critical structures in the flow-field of a bluff-body stabilized, dump, turbulent combustor. Simultaneous measurements such as unsteady pressure, velocity, local and global heat release rate fluctuations are acquired in the regime of thermoacoustic instability before and after control action. The tonal sound production in this combustor is accompanied by a periodic flapping of the shear layer present in the region between the dump plane (backward-facing step) and the leading edge of the bluff-body. We obtain the trajectory of Lagrangian saddle points that dictate the flow and flame dynamics in the shear layer during thermoacoustic instability accurately by computing Lagrangian Coherent Structures. Upon injecting a secondary micro-jet with a mass flow rate of only 4% of the primary flow, nearly 90% suppression in the amplitude of pressure fluctuations are observed. The suppression thus results in sound pressure levels comparable to those obtained during stable operation of the combustor. Using Morlet wavelet transform, we see that the coherence in the dominant frequency of pressure and heat release rate oscillations during thermoacoustic instability is affected by secondary injection. The disruption of saddle point trajectories breaks the positive feedback loop between pressure and heat release rate fluctuations resulting in the observed break of coherence. Wavelet transform of global heat release rate shows a redistribution of energy content from the dominant instability frequency (acoustic time scale) to other time scales.

scholarly journals Analysis on the Fire Growth Rate Index Considering of Scale Factor, Volume Fraction, and Ignition Heat Source for Polyethylene Foam Pipe Insulation

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3644
Author(s):  
Jung Wook Park ◽  
Ohk Kun Lim ◽  
Woo Jun You
Keyword(s):  
Growth Rate ◽  
Heat Source ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Volume Fraction ◽  
Fire Retardant ◽  
Scale Factor ◽  
Fire Growth ◽  
Pipe Insulation

The fire growth rate index (FIGRA), which is the ratio of the maximum value of the heat release rate (Qmax) and the time (tmax) to reach the maximum heat release rate, is a general method to evaluate a material in the fire-retardant performance in fire technology. The object of this study aims to predict FIGRA of the polyethylene foam pipe insulation in accordance with the scale factor (Sf), the volume fraction of the pipe insulation (VF) and the ignition heat source (Qig). The compartments made of fireboard have been mock-up with 1/3, 1/4, and 1/5 reduced scales of the compartment as specified in ISO 20632. The heat release rate data of the pipe insulation with the variation of Sf, VF, and Qig are measured from 33 experiments to correlate with FIGRA. Based on a critical analysis of the heat transfer phenomenon from previous research literature, the predictions of Qmax and tmax are presented. It is noticeable that the fire-retardant grade of the polyethylene foam pipe insulation could have Grade B, C, and D in accordance with the test conditions within ±15% deviation of the predicted FIGRA. In case of establishing the database of various types of insulation, the prediction models could apply to evaluate the fire-retardant performance.

Dynamical Characterization of Thermoacoustic Oscillations in a Hydrogen-Enriched Partially Premixed Swirl-Stabilized Methane/Air Combustor

2021 ◽  
Author(s):  
Abhishek Kushwaha ◽  
Praveen Kasthuri ◽  
Samadhan A. Pawar ◽  
R. I. Sujith ◽  
Ianko Chterev ◽  
...  
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Acoustic Pressure ◽  
Thermal Power ◽  
Frequency Locking ◽  
Thermoacoustic Instability ◽  
Period 2 ◽  
Partially Premixed ◽  
Hydrogen Enrichment

Abstract In this study, we systematically analyze the effects of hydrogen enrichment in the well-known PRECCINSTA burner, a partially premixed swirl-stabilized methane/air combustor. Keeping the equivalence ratio and thermal power constant, we vary the hydrogen percentage in the fuel. Successive increments in hydrogen fuel fraction increase the adiabatic flame temperature and also shift the dominant frequencies of acoustic pressure fluctuations to higher values. Under hydrogen enrichment, we observe the emergence of periodicity in the combustor resulting from the interaction between acoustic modes. As a result of the interaction between these modes, the combustor exhibits a variety of dynamical states, including period-1 limit cycle oscillations (LCO), period-2 LCO, chaotic oscillations, and intermittency. The flame and flow behavior is found to be significantly different for each dynamical state. Analyzing the coupled behavior of the acoustic pressure and the heat release rate oscillations during the states of thermoacoustic instability, we report the occurrence of 2:1 frequency-locking during period-2 LCO, where two cycles of acoustic pressure lock with one cycle of the heat release rate. During period-1 LCO, we notice 1:1 frequency-locking, where both acoustic pressure and heat release rate repeat their behavior in every cycle.

Lagrangian Saddle Point Analysis in the Flow-Field of a Bluff-Body Stabilized Combustor

2019 ◽  
Author(s):  
C. P. Premchand ◽  
Nitin B. George ◽  
Manikandan Raghunathan ◽  
Vishnu R. Unni ◽  
R. I. Sujith ◽  
...  
Keyword(s):  
Saddle Point ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Bluff Body ◽  
Leading Edge ◽  
Mean Flow ◽  
Acoustic Frequency ◽  
Thermoacoustic Instability ◽  
Point Analysis

Abstract Experiments are performed in a partially-premixed bluff-body stabilized turbulent combustor by varying the mean flow velocity. Simultaneous measurements obtained for unsteady pressure, velocity and heat release rate are used to investigate the dynamic regimes of intermittency (10.1 m/s) and thermoacoustic instability (12.3 m/s). Using wavelet analysis, we show that during intermittency, modulation of heat release rate occurring at the acoustic frequency fa by the heat release rate occurring at the hydrodynamic frequency fh results in epochs of heat release rate fluctuations where the heat release is phase locked with the acoustic pressure. We also show that the flame position during intermittency and thermoacoustic instability are essentially dictated by saddle point dynamics in the dump plane and the leading edge of the bluff-body.

Onset of thermoacoustic instability in turbulent combustors: an emergence of synchronized periodicity through formation of chimera-like states

2016 ◽  
Vol 811 ◽  
pp. 659-681 ◽  
Author(s):  
Sirshendu Mondal ◽  
Vishnu R. Unni ◽  
R. I. Sujith
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Large Amplitude ◽  
Local Heat ◽  
Combustion Noise ◽  
Periodic Oscillations ◽  
Thermoacoustic Instability ◽  
Chimera State ◽  
Rate Oscillations

Thermoacoustic systems with a turbulent reactive flow, prevalent in the fields of power and propulsion, are highly susceptible to oscillatory instabilities. Recent studies showed that such systems transition from combustion noise to thermoacoustic instability through a dynamical state known as intermittency, where bursts of large-amplitude periodic oscillations appear in a near-random fashion in between regions of low-amplitude aperiodic fluctuations. However, as these analyses were in the temporal domain, this transition remains still unexplored spatiotemporally. Here, we present the spatiotemporal dynamics during the transition from combustion noise to limit cycle oscillations in a turbulent bluff-body stabilized combustor. To that end, we acquire the pressure oscillations and the field of heat release rate oscillations through high-speed chemiluminescence ($CH^{\ast }$) images of the reaction zone. With a view to get an insight into this complex dynamics, we compute the instantaneous phases between acoustic pressure and local heat release rate oscillations. We observe that the aperiodic oscillations during combustion noise are phase asynchronous, while the large-amplitude periodic oscillations seen during thermoacoustic instability are phase synchronous. We find something interesting during intermittency: patches of synchronized periodic oscillations and desynchronized aperiodic oscillations coexist in the reaction zone. In other words, the emergence of order from disorder happens through a dynamical state wherein regions of order and disorder coexist, resembling a chimera state. Generally, mutually coupled chaotic oscillators synchronize but retain their dynamical nature; the same is true for coupled periodic oscillators. In contrast, during intermittency, we find that patches of desynchronized aperiodic oscillations turn into patches of synchronized periodic oscillations and vice versa. Therefore, the dynamics of local heat release rate oscillations change from aperiodic to periodic as they synchronize intermittently. The temporal variations in global synchrony, estimated through the Kuramoto order parameter, echoes the breathing nature of a chimera state.

Lagrangian Analysis of Flame Dynamics in the Flow Field of a Bluff Body-Stabilized Combustor

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
C. P. Premchand ◽  
Nitin B. George ◽  
Manikandan Raghunathan ◽  
Vishnu R. Unni ◽  
R. I. Sujith ◽  
...  
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Bluff Body ◽  
Leading Edge ◽  
Mean Flow ◽  
Lagrangian Analysis ◽  
Acoustic Frequency ◽  
Thermoacoustic Instability ◽  
Flame Dynamics

Abstract Experiments are performed in a partially premixed bluff body-stabilized turbulent combustor by varying the mean flow velocity. Simultaneous measurements obtained for unsteady pressure, velocity, and heat release rate are used to investigate the dynamic regimes of intermittency (10.1 m/s) and thermoacoustic instability (12.3 m/s). Using wavelet analysis, we show that during intermittency, modulation of heat release rate occurring at the acoustic frequency fa by the heat release rate occurring at the hydrodynamic frequency fh results in epochs of heat release rate fluctuations where the heat release rate is phase locked with the acoustic pressure. We also show that the flame position during intermittency and thermoacoustic instability are essentially dictated by saddle point dynamics in the dump plane and the leading edge of the bluff body.

The Effect of Sauter Mean Diameter Fluctuations on the Heat Release Rate in a Lean-Burn Aero-Engine Combustor

2019 ◽  
Author(s):  
Nicholas C. W. Treleaven ◽  
Andrew Garmory ◽  
Gary J. Page
Keyword(s):  
Heat Release ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Release Rate ◽  
Release Rate ◽  
Sauter Mean Diameter ◽  
Lean Burn ◽  
Thermoacoustic Instability ◽  
Mean Diameter

Abstract It has been shown that the fluctuations of pressure caused by a thermoacoustic instability can affect the mass flow rate of air and atomisation of the liquid fuel inside a gas turbine. Tests with premixed flames have confirmed that the fluctuations of the mass flow rate of air can affect the heat release rate through purely aerodynamic phenomenon but little work has been done to test the sensitivity of the heat release rate to changes in the fuel atomisation process. In this study, a lean-burn combustor geometry is supplied with a fuel spray fluctuation of SMD (Sauter mean diameter) of 20% with respect to the mean value and the heat release rate predicted using Large Eddy Simulation (LES) with combustion predicted using a presumed probability density function (PPDF), flamelet generated manifolds (FGM) method. Previous work has shown that at atmospheric conditions the SMD may fluctuate by up to 16% percent and at low frequencies may be reasonably well predicted by using a correlation based on the instantaneous velocity and mass flow rate of air close to the air-blast atomiser. Analysis of the flow fields highlights a complicated spray, flame and wall interaction as being responsible for this observed fluctuation of heat release rate. The heat release rate predicted by the LES shows a 20% fluctuation which implies that even small fluctuations of SMD will significantly contribute to thermoacoustic instabilities.

Comparison of Unsteady Heat Release Rate by Measurements From Chemiluminescence and Two Microphone Techniques

2015 ◽  
Author(s):  
Rajbir Verma ◽  
Sathesh Mariappan
Keyword(s):  
Heat Source ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Combustion Instability ◽  
Broad Band ◽  
Premixed Flames ◽  
Black Body Radiation ◽  
Acoustic Resonator ◽  
Acoustic Velocity

In the reaction zone of flame, electronically excited species are formed such as CH*, OH* etc. During de-excitation these radicals emit electromagnetic radiation of certain wavelength. This process is called chemiluminescence. The intensity of chemiluminescence, is in general captured using a photo multiplier tube (PMT), which is used to measure unsteady heat release rate from premixed flames. This technique is well established and is now a standard for unsteady heat release rate measurements in the parlance of combustion instability, however has certain limitations. In fuel rich mixtures, unreacted heated carbon emits broad band black body radiation, which in some cases large enough to mask the chemiluminescence signal. Hence, this technique is not valid for fuel rich conditions. Moreover, it cannot be applied, when the heat source is diffusion/partially premixed flames or electrically heated wires. We propose an alternative in this regard: two microphone technique. In this technique, we relate the acoustic velocity jump across the heat source to measure the unsteady heat release rate. The up and downstream acoustic velocity, in turn is obtained by two microphone technique. Experiments are performed in a premixed multiple flame burner at fuel lean conditions. This burner is enclosed in a duct, which acts as an acoustic resonator. Results indicate that the magnitude of the unsteady heat release rate obtained from both the techniques is found to agree within 18 %. Experiments are conducted for various lengths of the duct, thereby changing the oscillating frequency. This method is valid as long as the heat source is compact in comparison to the duct, which is true in most of the combustors during combustion instability and is irrespective of its type.

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