Theoretical and numerical study of symmetry breaking effects on azimuthal thermoacoustic modes in annular combustors

A large range of physical problems, from molecules to giant stars, contains rotating symmetry and can exhibit azimuthal waves or vibrations. When this symmetry is broken, the system can become unstable with chaotic behaviors. Symmetry breaking is investigated in annular combustors prone to azimuthal thermo-acoustic instabilities. First, theories reveal that two types of symmetry breaking exist : due to different burner types distributed along the chamber or due to the flow itself . It leads to frequency splitting, fixes the mode structure and can destabilize the configuration. A UQ analysis is also performed to quantify the symmetry breaking effect due to uncertainties of flame descriptions or behaviors. To complete theory, Large Eddy Simulations are performed on a single-sector as well as on a complete 360° configuration of the annular experiment of Cambridge. Numerical results are compared to experimental data showing a good agreement. In particular, an unstable azimuthal mode at 1800 Hz grows in both LES and experiment. However, LES cannot investigate the limit cycle because of its extreme cost. To tackle this problem, a new methodology is developed, called AMT, where theory or Helmholtz solver predictions are injected into LES or DNS. This method allows to study symmetry breaking, mode nature and dynamics as well as evaluating damping in realistic annular configurations

Étude théorique et numérique des effets de brisures de symétrie sur les modes thermo-acoustiques azimutaux dans les chambres annulaires

Une large gamme de problèmes physiques, des petites molécules aux étoiles géantes, contiennent des symétries de rotation et sont sujets à des oscillations azimutales ou transverses. Quand cette symétrie est rompue, le système peut devenir instable. Dans cette thèse, les brisures de symétries sont étudiées dans les chambres de combustion annulaires, sujettes à des instabilités thermo-acoustiques azimutales. En premier lieu, deux types de brisures sont obtenus analytiquement : la première en répartissant des bruleurs différents le long de la chambre et la seconde provoquée par le champ moyen lui-même. Ces ruptures de symétries entraînent une séparation des fréquences, fixe la structure du mode et peut déstabiliser le système. De plus, une approche Quantification d’Incertitudes (UQ) permet d’évaluer l’effet de la rupture de symétries provoquée par les incertitudes sur la description ou le comportement des flammes. Pour compléter cette théorie, des Simulations aux Grandes Echelles (SGE) sont réalisées sur un mono-secteur ainsi que sur une configuration complète 360° de l’expérience annulaire de Cambridge. Les résultats numériques sont comparés aux données expérimentales et montrent un bon accord. En particulier, un mode instable à 1800 Hz croît dans les deux cas. Cependant, la SGE, limitée par son coût important, ne permet pas l’étude du cycle limite s’établissant après plusieurs centaines de millisecondes. Pour pallier à ce problème, une nouvelle approche, appelée AMT, est développée : les résultats d’une théorie ou d’un solveur acoustique sont injectés dans une simulation SGE. Cette approche permet d’étudier les brisures de symétries, la nature et la dynamique des modes acoustiques, ainsi que d’évaluer l’amortissement dans des configurations réalistes. ABSTRACT : A large range of physical problems, from molecules to giant stars, contains rotating symmetry and can exhibit azimuthal waves or vibrations. When this symmetry is broken, the system can become unstable with chaotic behaviors. Symmetry breaking is investigated in annular combustors prone to azimuthal thermo-acoustic instabilities. First, theories reveal that two types of symmetry breaking exist : due to different burner types distributed along the chamber or due to the flow itself . It leads to frequency splitting, fixes the mode structure and can destabilize the configuration. A UQ analysis is also performed to quantify the symmetry breaking effect due to uncertainties of flame descriptions or behaviors. To complete theory, Large Eddy Simulations are performed on a single-sector as well as on a complete 360° configuration of the annular experiment of Cambridge. Numerical results are compared to experimental data showing a good agreement. In particular, an unstable azimuthal mode at 1800 Hz grows in both LES and experiment. However, LES cannot investigate the limit cycle because of its extreme cost. To tackle this problem, a new methodology is developed, called AMT, where theory or Helmholtz solver predictions are injected into LES or DNS. This method allows to study symmetry breaking, mode nature and dynamics as well as evaluating damping in realistic annular configurations

Progress in analytical methods to predict and control azimuthal combustion instability modes in annular chambers

Longitudinal low-frequency thermoacoustic unstable modes in combustion chambers have been intensively studied experimentally, numerically, and theoretically, leading to significant progress in both understanding and controlling these acoustic modes. However, modern annular gas turbines may also exhibit azimuthal modes, which are much less studied and feature specific mode structures and dynamic behaviors, leading to more complex situations. Moreover, dealing with 10–20 burners mounted in the same chamber limits the use of high fidelity simulations or annular experiments to investigate these modes because of their complexity and costs. Consequently, for such circumferential acoustic modes, theoretical tools have been developed to uncover underlying phenomena controlling their stability, nature, and dynamics. This review presents recent progress in this field. First, Galerkin and network models are described with their pros and cons in both the temporal and frequency framework. Then, key features of such acoustic modes are unveiled, focusing on their specificities such as symmetry breaking, non-linear modal coupling, forcing by turbulence. Finally, recent works on uncertainty quantifications, guided by theoretical studies and applied to annular combustors, are presented. The objective is to provide a global view of theoretical research on azimuthal modes to highlight their complexities and potential

Analytical methods for azimuthal thermo-acoustic modes in annular combustion chambers

Large power densities in gas turbines can be accompanied by combustion instabilities (Culick & Kuentzmann 2006; Lieuwen & Yang 2005) due to a coupling between the flames and acoustics, creating high pressure and heat release oscillations in the chamber. Such oscillations may destroy the whole propulsion system and combustion instabilities have been a key issue for aeronautics and propulsion systems (Candel 2002; Culick & Kuentzmann 2006; Lieuwen & Yang 2005) especially in high-performance engines (Harrje & Reardon 1972; Culick 1987) for a long time. Full-scale experiments in this field are difficult (Poinsot et al. 1987; Lee & Lieuwen 2003; Lee & Anderson 1999) and numerical simulations have been used heavily to replicate the complex mechanisms involved in combustion instabilities in full-scale geometries (Wolf et al. 2009; Staffelbach et al. 2009; Wolf et al. 2010). These simulations are not sufficient to understand or control unstable modes: low-order models and theory on simplified geometries (Dowling 1995, 1997; Kopitz et al. 2005; Nicoud et al. 2007) are needed to guide both large-eddy simulations (LES) and experiments. Annular chambers used in gas turbines sometimes exhibit a specific class of unstable modes: azimuthal modes (Figure 1) propagating along the azimuthal direction eθ and not only in the longitudinal direction ez (Candel 1992; Crighton et al. 1992; Lieuwen & Yang 2005; O’Connor et al. 2015). Mechanisms leading to azimuthal instabilities are more complex than those encountered in longitudinal configurations

Route to chaos on a dragonfly wing cross section in gliding flight

The route from linear towards nonlinear and chaotic aerodynamic regimes of a fixed dragonfly wing cross section in gliding flight is investigated numerically using direct Navier-Stokes simulations (DNSs). The dragonfly wing consists of two corrugations combined with a rear arc, which is known to provide overall good aerodynamic mean performance at low Reynolds numbers. First, the three regimes (linear, nonlinear, and chaotic) are characterized, and validated using two different fluid solvers. In particular, a peculiar transition to chaos when changing the angle of attack is observed for both solvers: The system undergoes a sudden transition to chaos in less than 0.1 degree. Second, a physical insight is given on the flow interaction between the corrugations and the rear arc, which is shown as the key phenomenon controlling the unsteady vortex dynamics and the sudden transition to chaos. Additionally, aerodynamic performances in the three regimes are given, showing that optimal performances are closely connected to the transition to chaos

Discharge coefficient of an orifice jet in cross flow: influence of inlet conditions and optimum velocity ratio

International audienceThe present work aims to characterize the discharge performance of aircraft door vent flaps. For this purpose, three different configurations with increasing complexity are studied with a RANS and a LES solver. The first configuration consists of an orifice plate in a duct for which experimental pressure loss data are available in the literature. This configuration is used as a reference for the validation of the RANS and LES setups. The duct placed downstream of the orifice is then removed to produce an unconfined geometry in which the orifice jet discharges either into an open atmosphere or a transverse flow. Finally, a classic jet in cross flow is also studied. The main objective is to analyze the discharge coefficient variations depending on three key parameters: (i) the jet Reynolds number, (ii) the inlet velocity profile, and (iii) the velocity ratio between the jet and the cross flow. Results show that for cases without cross flow, the jet Reynolds number has no influence on the discharge performance whereas a steady decrease of the orifice pressure loss is observed as the duct inlet velocity profile is deformed from that of a flat profile. The Poiseuille profile is found to minimize the pressure loss. In addition, numerical data of the reference configuration compare well with experimental values when such a profile is prescribed. Finally, simulations with a cross flow evidence an optimal velocity ratio for which the discharge coefficient is maximum and exceeds the freejet value

Sensitivity analysis of thermo-acoustic eigenproblems with adjoint methods

International audienceThis paper outlines two new applications of adjoint methods in the study of thermoacoustic instability. The first is to calculate gradients for the active subspace method, which is used in uncertainty quantification. The second is to calculate gradients in a nonlinear thermo-acoustic Helmholtz solver. Two methods are presented. The first, which uses the discrete adjoint approach, is specifically for nonlinear Helmholtz eigenvalue problems that are solved iteratively. The second, which uses a hybrid adjoint approach, is more general and can be applied to both problems

Saturation of a turbulent mixing layer over a cavity: response to harmonic forcing around mean flows

Turbulent mixing layers over cavities can couple with acoustic waves and lead to undesired oscillations. To understand the nonlinear aspects of this phenomenon, a turbulent mixing layer over a deep cavity is considered and its response to harmonic forcing is analysed with large-eddy simulations (LES) and linearised Navier–Stokes equations (LNSE). The Reynolds number is Re=150 000. As a model of incoming acoustic perturbations, spatially uniform time-harmonic velocity forcing is applied at the cavity end, with amplitudes spanning the wide range 0.045–8.9% of the main channel bulk velocity. Compressible LES provide reference nonlinear responses of the shear layer, and the associated mean flows. Linear responses are calculated with the incompressible LNSE around the LES mean flows; they predict well the amplification (both measured with kinetic energy and with a proxy for vortex sound production in the mixing layer) and capture the nonlinear saturation observed as the forcing amplitude increases and the mixing layer thickens. Perhaps surprisingly, LNSE calculations based on a monochromatic (single frequency) assumption yield a good agreement even though higher harmonics and their nonlinear interaction (Reynolds stresses) are not negligible. However, it is found that the leading Reynolds stresses do not force the mixing layer efficiently, as shown by a comparison with the optimal volume forcing obtained from a resolvent analysis. Therefore they cannot fully benefit from the potential for amplification available in the flow. Finally, the sensitivity of the optimal harmonic forcing at the cavity end is computed with an adjoint method. The sensitivities to mean flow modification and to a localised feedback (structural sensitivity) both identify the upstream cavity corner as the region where a small amplitude modification has the strongest effect. This can guide in a systematic way the design of strategies aiming at controlling the amplification and saturation mechanisms

Three-Dimensional Modeling of Annular Cascade Trailing-Edge Noise

The paper addresses various aspects of an analytical methodology for the modeling of the sound transmission through the outlet guide vanes of an axial-flow fan architecture, in view of predicting the trailing-edge noise with a proper account of the cascade effect. The first part extends a previous two-dimensional model by including the stagger and the curvature of the vanes. This is achieved by iteratively solving matching equations at the leadingedge and trailing-edge interfaces of the stator, with a multiple-scale analysis between two iterations, considering the inter-vane channels as bifurcated waveguides of slowly varying cross-section. The second part is aimed at extending a previous two-dimensional cascade trailing-edge noise model to an annular cascade described in cylindrical coordinates. For this the trailing-edge noise sources of a vane section are replaced by an equivalent lift dipole, the direct sound of which is expanded as a series of annular-duct modes. The scattering of each mode by the complete cascade is calculated by a three-dimensional mode-matching technique and the complete radiation of the trailing-edge source obtained by summing all modal contributions. The last part explains how the aforementioned two-dimensional model of curved-channel can be generalized in the three-dimensional annular geometry at the price of some approximations. Only preliminary results are given at each step, the paper being aimed at demonstrating the methodology but not yet at simulating a complete configuration. The objective is to formulate three-dimensional blade/vane row aeroacoustic problems without resorting to a strip-theory approach

An analytical model for azimuthal thermoacoustic modes in an annular chamber fed by an annular plenum

This study describes an analytical method for computing azimuthal modes due to flame/acoustics coupling in annular combustors. It is based on a quasi-one-dimensional zero-Mach-number formulation where N burners are connected to an upstream annular plenum and a downstream chamber. Flames are assumed to be compact and are modeled using identical flame transfer function for all burners, characterized by an amplitude and a phase shift. Manipulation of the corresponding acoustic equations leads to a simple methodology called ANR (annular network reduction). It makes it possible to retain only the useful information related to the azimuthal modes of the annular cavities. It yields a simple dispersion relation that can be solved numerically and makes it possible to construct coupling factors between the different cavities of the combustor. A fully analytical resolution can be performed in specific situations where coupling factors are small (weak coupling). A bifurcation appears at high coupling factors, leading to a frequency lock-in of the two annular cavities (strong coupling). This tool is applied to an academic case where four burners connect an annular plenum to a chamber. For this configuration, analytical results are compared with a full three-dimensional Helmholtz solver to validate the analytical model in both weak and strong coupling regimes. Results show that this simple analytical tool can predict modes in annular combustors and investigate strategies for controlling them