Linearized Euler Equations for the Prediction of Linear High-Frequency Stability in Gas Turbine Combustors

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Moritz Schulze ◽  
Tobias Hummel ◽  
Noah Klarmann ◽  
Frederik Berger ◽  
Bruno Schuermans ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Gas Turbine ◽  
Linear Stability ◽  
Euler Equations ◽  
Linear Stability Analysis ◽  
High Frequency ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Gas Turbine Combustors ◽  
Transversal Mode

A novel methodology for linear stability analysis of high-frequency thermoacoustic oscillations in gas turbine combustors is presented. The methodology is based on the linearized Euler equations (LEEs), which yield a high-fidelity description of acoustic wave propagation and damping in complex, nonuniform, reactive mean flow environments, such as encountered in gas turbine combustion chambers. Specifically, this work introduces three novelties to the community: (1) linear stability analysis on the basis of linearized Euler equations. (2) Explicit consideration of three-dimensional, acoustic oscillations at screech level frequencies, particularly the first-transversal mode. (3) Handling of noncompact flame coupling with LEE, that is, the spatially varying coupling dynamics between perturbation and unsteady flame response due to small acoustic wavelengths. Two different configurations of an experimental model combustor in terms of thermal power and mass flow rates are subject of the analysis. Linear flame driving is modeled by prescribing the unsteady heat release source term of the linearized Euler equations by local flame transfer functions, which are retrieved from first principles. The required steady-state flow field is numerically obtained via computational fluid dynamics (CFD), which is based on an extended flamelet-generated manifold (FGM) combustion model, taking into account heat transfer to the environment. The model is therefore highly suitable for such types of combustors. The configurations are simulated, and thermoacoustically characterized in terms of eigenfrequencies and growth rates associated with the first-transversal mode. The findings are validated against experimentally observed thermoacoustic stability characteristics. On the basis of the results, new insights into the acoustic field are discussed.

Linearized Euler Equations for the Prediction of Linear High-Frequency Stability in Gas Turbine Combustors

2016 ◽  
Author(s):  
Moritz Schulze ◽  
Tobias Hummel ◽  
Noah Klarmann ◽  
Frederik Berger ◽  
Bruno Schuermans ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Gas Turbine ◽  
Linear Stability ◽  
Euler Equations ◽  
Linear Stability Analysis ◽  
High Frequency ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Gas Turbine Combustors ◽  
Transversal Mode

A novel methodology for linear stability analysis of high-frequency thermoacoustic oscillations in gas turbine combustors is presented. The methodology is based on the linearized Euler equations, which yield a high-fidelity description of acoustic wave propagation and damping in complex, non-uniform, reactive mean flow environments, such as encountered in gas turbine combustion chambers. Specifically, this work introduces three novelties to the community: (1) Linear stability analysis on the basis of linearized Euler equations. (2) Explicit consideration of three-dimensional, acoustic oscillations at screech level frequencies, particularly the first transversal mode. (3) Handling of non-compact flame coupling with LEE, that is, the spatially varying coupling dynamics between perturbation and unsteady flame response due to small acoustic wavelengths. Two different configurations of an experimental model combustor in terms of thermal power and mass flow rates are subject of the analysis. Linear flame driving is modeled by prescribing the unsteady heat release source term of the linearized Euler equations by local flame transfer functions, which are retrieved from first principles. The required steady state flow field is numerically obtained via CFD, which is based on an extended Flamelet-Generated Manifold combustion model, taking into account heat transfer to the environment. The model is therefore highly suitable for such types of combustors. The configurations are simulated, and thermoacoustically characterized in terms of eigenfrequencies and growth rates associated with the first transversal mode. The findings are validated against experimentally observed thermoacoustic stability characteristics. On the basis of the results, new insights into the acoustic field are discussed.

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

scholarly journals The Growth and Saturation of Submesoscale Instabilities in the Presence of a Barotropic Jet

2018 ◽  
Vol 48 (11) ◽  
pp. 2779-2797 ◽  
Author(s):  
Megan A. Stamper ◽  
John R. Taylor ◽  
Baylor Fox-Kemper
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Boussinesq Equations ◽  
Small Region ◽  
Computational Domain ◽  
Mean Flow ◽  
The Mean

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.

scholarly journals Theoretical Investigation of the Atlantic Multidecadal Oscillation

2015 ◽  
Vol 45 (9) ◽  
pp. 2189-2208 ◽  
Author(s):  
Florian Sévellec ◽  
Thierry Huck
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Atlantic Multidecadal Oscillation ◽  
Meridional Overturning Circulation ◽  
Internal Mode ◽  
Mean Flow ◽  
Coupled Models ◽  
Basin Scale ◽  
Level Model

AbstractA weakly damped mode of variability, corresponding to the oceanic signature of the Atlantic multidecadal oscillation (AMO) was found through the linear stability analysis of a realistic ocean general circulation model. A simple two-level model was proposed to rationalize both its period and damping rate. This model is extended here to three levels to investigate how the mode can draw energy from the mean flow, as found in various ocean and coupled models. A linear stability analysis in this three-level model shows that the positive growth rate of the oscillatory mode depends on the zonally averaged isopycnal slope. This mode corresponds to a westward propagation of density anomalies in the pycnocline, typical of large-scale baroclinic Rossby waves. The most unstable mode corresponds to the largest scale one (at least for low isopycnal slope). The mode can be described in four phases composing a full oscillation cycle: 1) basin-scale warming of the North Atlantic (AMO positive phase), 2) decrease in upper-ocean poleward transport [hence a reduction of the Atlantic meridional overturning circulation (AMOC)], 3) basin-scale cooling (negative AMO), and 4) AMOC intensification. A criterion is developed to test, in oceanic datasets or numerical models, whether this multidecadal oscillation is an unstable oceanic internal mode of variability or if it is stable and externally forced. Consistent with the classical theory of baroclinic instability, this criterion depends on the vertical structure of the mode. If the upper pycnocline signature is in advance of the deeper pycnocline signature with respect to the westward propagation, the mode is unstable and could be described as an oceanic internal mode of variability.

Guiding Actuator Designs for Active Flow Control of the Precessing Vortex Core by Adjoint Linear Stability Analysis

2018 ◽  
Author(s):  
Jens S. Müller ◽  
Finn Lückoff ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Combustion Chamber ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Stereoscopic Particle Image Velocimetry ◽  
Axial Position ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Lock In

The fundamental impact of the precessing vortex core (PVC) as a dominant coherent flow structure in the flow field of swirl-stabilized gas turbine combustors has still not been investigated in depth. In order to do so, the PVC needs to be actively controlled to be able to set its parameters independently to any other of the combustion system. In this work, open-loop actuation is applied in the mixing section between the swirler and the generic combustion chamber of a non-reacting swirling jet setup to investigate the receptivity of the PVC with regard to its lock-in behavior at different streamwise positions. The mean flow in the mixing section as well as in the combustion chamber is measured by stereoscopic particle image velocimetry and the PVC is extracted from the snapshots using proper orthogonal decomposition. The lock-in experiments reveal the axial position in the mixing section that is most suitable for actuation. Furthermore, a global linear stability analysis is conducted to determine the adjoint mode of the PVC which reveals the regions of highest receptivity to periodic actuation based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity data and the applicability of the adjoint-based model for the prediction of optimal actuator designs is discussed.

scholarly journals Examining the Effect of Geometry Changes in Industrial Fuel Injection Systems on Hydrodynamic Structures With BiGlobal Linear Stability Analysis

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner ◽  
Laurent Selle ◽  
Thierry Poinsot
Keyword(s):  
Stability Analysis ◽  
Shape Optimization ◽  
Linear Stability ◽  
Turbulent Flows ◽  
Linear Stability Analysis ◽  
Fuel Injection ◽  
Injection System ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Center Body

Abstract Shape optimization with respect to the suppression or enhancement of dynamical flow structures is an important topic in combustion research and beyond. In this paper, we investigate the flow in an industrial fuel injection system by experimental means, as well as large eddy simulation (LES) and linear stability analysis (LSA) for two configurations of the swirler. In the first configuration, the reference geometry, a precessing vortex core (PVC) occurs. In the second configuration, a center body is mounted in the interior of the injector. It is shown by both experiments and LES that the PVC is suppressed by the presence of the center body, while the mean flow remains nearly unaffected. The method of LSA is applied in order to explain the effect of the geometry change. The work shows that LSA is capable of explaining the occurrence or disappearance of coherent structures evolving on the turbulent flows if the geometry is changed. This is an important step in using LSA in the context of shape optimization of industrial fuel injectors.

Guiding Actuator Designs for Active Flow Control of the Precessing Vortex Core by Adjoint Linear Stability Analysis

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Jens S. Müller ◽  
Finn Lückoff ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Combustion Chamber ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Stereoscopic Particle Image Velocimetry ◽  
Axial Position ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Lock In

The fundamental impact of the precessing vortex core (PVC) as a dominant coherent flow structure in the flow field of swirl-stabilized gas turbine combustors has still not been investigated in depth. In order to do so, the PVC needs to be actively controlled to be able to set its parameters independently to any other of the combustion system. In this work, open-loop actuation is applied in the mixing section between the swirler and the generic combustion chamber of a nonreacting swirling jet setup to investigate the receptivity of the PVC with regard to its lock-in behavior at different streamwise positions. The mean flow in the mixing section as well as in the combustion chamber is measured by stereoscopic particle image velocimetry (SPIV), and the PVC is extracted from the snapshots using proper orthogonal decomposition (POD). The lock-in experiments reveal the axial position in the mixing section that is most suitable for actuation. Furthermore, a global linear stability analysis (LSA) is conducted to determine the adjoint mode of the PVC which reveals the regions of highest receptivity to periodic actuation based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity data, and the applicability of the adjoint-based model for the prediction of optimal actuator designs is discussed.

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