Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points

Acoustic dampers are efficient and cost-effective means for suppressing thermoacoustic instabilities in combustion chambers. However, their design and the choice of their purging air mass flow is a challenging task, when one aims at ensuring thermoacoustic stability after their implementation. In the present experimental and theoretical study, Helmholtz (HH) and Quarter-Wave (QW) dampers are considered. A model for their acoustic impedance is derived and experimentally validated. In a second part, a thermoacoustic instability is mimicked by an electro-acoustic feedback loop in a rectangular cavity, to which the dampers are added. The length of the dampers can be adjusted, so that the system can be studied for tuned and detuned conditions. The stability of the coupled system is investigated experimentally and then analytically, which shows that for tuned dampers, the best stabilization is achieved at the exceptional point. The stabilization capabilities of HH and QW dampers are compared for given damper volume and purge mass flow.Comment: 34 pages, 19 figures, acepted in the Journal of Sound and Vibratio

Forcing of globally unstable jets and flames

In the analysis of thermoacoustic systems, a flame is usually characterised by the way its heat release responds to acoustic forcing. This response depends on the hydrodynamic stability of the flame. Some flames, such as a premixed bunsen flame, are hydrodynamically globally stable. They respond only at the forcing frequency. Other flames, such as a jet diffusion flame, are hydrodynamically globally unstable. They oscillate at their own natural frequencies and are often assumed to be insensitive to low-amplitude forcing at other frequencies. If a hydrodynamically globally unstable flame really is insensitive to forcing at other frequencies, then it should be possible to weaken thermoacoustic oscillations by detuning the frequency of the natural hydrodynamic mode from that of the natural acoustic modes. This would be very beneficial for industrial combustors. In this thesis, that assumption of insensitivity to forcing is tested experimentally. This is done by acoustically forcing two different selfexcited flows: a non-reacting jet and a reacting jet. Both jets have regions of absolute instability at their base and this causes them to exhibit varicose oscillations at discrete natural frequencies. The forcing is applied around these frequencies, at varying amplitudes, and the response examined over a range of frequencies (not just at the forcing frequency). The overall system is then modelled as a forced van der Pol oscillator. The results show that, contrary to some expectations, a hydrodynamically self-excited jet oscillating at one frequency is sensitive to forcing at other frequencies. When forced at low amplitudes, the jet responds at both frequencies as well as at several nearby frequencies, and there is beating, indicating quasiperiodicity. When forced at high amplitudes, however, it locks into the forcing. The critical forcing amplitude required for lock-in increases with the deviation of the forcing frequency from the natural frequency. This increase is linear, indicating a Hopf bifurcation to a global mode. The lock-in curve has a characteristic ∨ shape, but with two subtle asymmetries about the natural frequency. The first asymmetry concerns the forcing amplitude required for lock-in. In the non-reacting jet, higher amplitudes are required when the forcing frequency is above the natural frequency. In the reacting jet, lower amplitudes are required when the forcing frequency is above the natural frequency. The second asymmetry concerns the broadband response at lock-in. In the non-reacting jet, this response is always weaker than the unforced response, regardless of whether the forcing frequency is above or below the natural frequency. In the reacting jet, that response is weaker than the unforced response when the forcing frequency is above the natural frequency, but is stronger than it when the forcing frequency is below the natural frequency. In the reacting jet, weakening the global instability – by adding coflow or by diluting the fuel mixture – causes the flame to lock in at lower forcing amplitudes. This finding, however, cannot be detected in the flame describing function. That is because the flame describing function captures the response at only the forcing frequency and ignores all other frequencies, most notably those arising from the natural mode and from its interactions with the forcing. Nevertheless, the flame describing function does show a rise in gain below the natural frequency and a drop above it, consistent with the broadband response. Many of these features can be predicted by the forced van der Pol oscillator. They include (i) the coexistence of the natural and forcing frequencies before lock-in; (ii) the presence of multiple spectral peaks around these competing frequencies, indicating quasiperiodicity; (iii) the occurrence of lock-in above a critical forcing amplitude; (iv) the ∨-shaped lock-in curve; and (v) the reduced broadband response at lock-in. There are, however, some features that cannot be predicted. They include (i) the asymmetry of the forcing amplitude required for lock-in, found in both jets; (ii) the asymmetry of the response at lock-in, found in the reacting jet; and (iii) the interactions between the fundamental and harmonics of both the natural and forcing frequencies, found in both jets.Gates Cambridge Trust, Emmanuel College, Trinity Colleg

Response of a swirl-stabilized flame to transverse acoustic excitation

This work addresses the issue of transverse combustion instabilities in annular gas turbine combustor geometries. While modern low-emissions combustion strategies have made great strides in reducing the production of toxic emissions in aircraft engines and power generation gas turbines, combustion instability remains one of the foremost technical challenges in the development of next generation combustor technology. To that end, this work investigates the response of a swirling flow and swirl-stabilized flame to a transverse acoustic field is using a variety of high-speed laser techniques, especially high-speed particle image velocimetry (PIV) for detailed velocity measurements of this highly unsteady flow phenomenon. A description of the velocity-coupled transverse instability mechanism is explained with companion measurements describing each of the velocity disturbance pathways. Dependence on acoustic frequency, amplitude, and field symmetry is discussed. Significant emphasis is placed on the response of a swirling flow field to a transverse acoustic field. Details of the dynamics of the vortex breakdown bubble and the shear layers are explained using a wide variety of measurements for both non-reacting and reacting flow cases. This thesis concludes with an overview of the impact of this work and suggestions for future research in this area.PhDCommittee Chair: Tim Lieuwen; Committee Member: Ari Glezer; Committee Member: Jerry Seitzman; Committee Member: Lakshmi Sankar; Committee Member: Suresh Meno

Prediction and control of combustion instabilities in real engines

This paper presents recent progress in the field of thermoacoustic combustion instabilities in propulsion engines such as rockets or gas turbines. Combustion instabilities have been studied for more than a century in simple laminar configurations as well as in laboratory-scale turbulent flames. These instabilities are also encountered in real engines but new mechanisms appear in these systems because of obvious differences with academic burners: larger Reynolds numbers, higher pressures and power densities, multiple inlet systems, complex fuels. Other differences are more subtle: real engines often feature specific unstable modes such as azimuthal instabilities in gas turbines or transverse modes in rocket chambers. Hydrodynamic instability modes can also differ as well as the combustion regimes, which can require very different simulation models. The integration of chambers in real engines implies that compressor and turbine impedances control instabilities directly so that the determination of the impedances of turbomachinery elements becomes a key issue. Gathering experimental data on combustion instabilities is difficult in real engines and Large Eddy Simulation (LES) has become a major tool in this field. Recent examples, however, show that LES is not sufficient and that theory, even in these complex systems, plays a major role to understand both experimental and LES results and to identify mitigation techniques

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer

Advanced Fluid Dynamics

This book provides a broad range of topics on fluid dynamics for advanced scientists and professional researchers. The text helps readers develop their own skills to analyze fluid dynamics phenomena encountered in professional engineering by reviewing diverse informative chapters herein

Self-oscillation

Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a "relaxation oscillator," i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized ("entrained"). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot's theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.Comment: 68 pages, 33 figures. v4: Typos fixed and other minor adjustments. To appear in Physics Report

Investigation of the Effects of Oxidizer Temperature on the Stability of a Gas-Centered Swirl Coaxial Injector

Rocket engines achieve extraordinary high energy densities within the chamber in the form of high pressure turbulent combustion. Successful design of these engines requires sustained, stable operation of a combustor exposed to extreme thermal loads. Slight deviations in operating conditions can then incur consequences ranging from reduced performance up to catastrophic failure in the face of excess heat loading. Sustained periodic oscillations, termed combustion instabilities, are often encountered during development, as fluctuations produced by combustion noise couple with heat release modes by way of modulation of the feed system, injector hydrodynamics, chemical kinetics, and mixing and atomization process. Successful development of reliable, high performance rocket engines can be achieved either through a thorough understanding of both injector and combustor dynamics to mitigate these instabilities or through the laborious design/test iteration process. This document describes a two-fold work by the author. The first objective considers the acquisition of high-fidelity data sets of a single gas-centered swirl coaxial injector for use in the validation of computational models. Secondly, the stability of this injector was studied at two oxidizer inlet temperatures. Combustion stability was assessed through variation of the combustor geometry. Previous research shows that varying this geometry can either drive or dampen pressure oscillations. Testing was conducted on an experimental test bed equipped with modular sections to accommodate changing oxidizer post and chamber lengths. A single gas-centered swirl coaxial injector was used, with operating parameters based on the RD-180 injector element, such as equivalence and momentum flux ratios. Two oxidizer inlet temperatures were chosen. The first was oxygen combusted with gaseous hydrogen at lean conditions in a preburner to produce hot oxidizer near 700 K. The second was pure oxygen delivered at room temperature. Results from the test campaign revealed the system to be classically stable across all configurations and inlet conditions tested, with pressure perturbations less than 10% of the mean chamber pressure. Discriminating behavior was observed between the two oxidizer inlet temperatures. At elevated temperatures, peak-to-peak pressure oscillations observed throughout the system were small at less than 4% of the mean chamber pressure. There was no observed dependency of the amplitude on geometry. At ambient temperatures, the pressure oscillations ranged from 4% up to 7%. The increase in amplitudes were similar to that of the acoustic refection coefficient between the oxidizer and chamber gas, based on their acoustic specific impedance. An increase in the acoustic transmission coefficient was also observed, going from hot to ambient oxidizer. The increase in these two values would not necessarily lead to enhanced coupling between the chamber and resonance behavior in the post, but is expected to amplify pressure oscillations. At the ambient condition, clear variation in amplitudes were generated through manipulation of the geometry. The general trend matched previous experiments but was not followed by all tested configurations. It was determined that a methodology solely based on the effective resonator wavelength was not sufficient to predict the amplitude of pressure oscillations. Instead, a better predictor of amplitude was found based on the alignment of the system with postulated vortex generation from the injector face and impingement on the chamber walls. The time between local pressure oscillations and final impingement of the resulting vortices fell between one and two cycles of the fundamental longitudinal chamber mode, increasing linearly in strength as phase lag increased