Impact of PVC Dynamics on Shear Layer Response in a Swirling Jet

2017 ◽  
Author(s):  
Mark Frederick ◽  
Joshua Dudash ◽  
Jacqueline O’Connor ◽  
Kiran Manoharan ◽  
Santosh Hemchandra ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Combustion Instability ◽  
Forced Response ◽  
Coupling Mechanism ◽  
Longitudinal Acoustic ◽  
Acoustic Forcing ◽  
The Impact

Combustion instability, or the coupling between flame heat release rate oscillations and combustor acoustics, is a significant issue in the operation of gas turbine combustors. This coupling is often driven by oscillations in the flow field. Shear layer roll-up, in particular, has been shown to drive longitudinal combustion instability in a number of systems, including both laboratory and industrial combustors. One method for suppressing combustion instability would be to suppress the receptivity of the shear layer to acoustic oscillations, severing the coupling mechanism between the acoustics and the flame. Previous work suggested that the existence of a precessing vortex core (PVC) may suppress the receptivity of the shear layer, and the goal of this study is to first, confirm that this suppression is occurring, and second, understand the mechanism by which the PVC suppresses the shear layer receptivity. In this paper, we couple experiment with linear stability analysis to determine whether a PVC can suppress shear layer receptivity to longitudinal acoustic modes in a non-reacting swirling flow at a range of swirl numbers. The shear layer response to the longitudinal acoustic forcing manifests as an m = 0 mode since the acoustic field is axisymmetric. The PVC has been shown both in experiment and linear stability analysis to have m = 1 and m = −1 modal content. By comparing the relative magnitude of the m = 0 and m = −1,1 modes, we quantify the impact that the PVC has on the shear layer response. The mechanism for shear layer response is determined using companion forced response analysis, where the shear layer disturbance growth rates mirror the experimental results. Differences in shear layer thickness and azimuthal velocity profiles drive the suppression of the shear layer receptivity to acoustic forcing.

Impact of Precessing Vortex Core Dynamics on Shear Layer Response in a Swirling Jet

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Mark Frederick ◽  
Kiran Manoharan ◽  
Joshua Dudash ◽  
Brian Brubaker ◽  
Santosh Hemchandra ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Combustion Instability ◽  
Forced Response ◽  
Longitudinal Acoustic ◽  
Precessing Vortex Core ◽  
Acoustic Forcing

Combustion instability, the coupling between flame heat release rate oscillations and combustor acoustics, is a significant issue in the operation of gas turbine combustors. This coupling is often driven by oscillations in the flow field. Shear layer roll-up, in particular, has been shown to drive longitudinal combustion instability in a number of systems, including both laboratory and industrial combustors. One method for suppressing combustion instability would be to suppress the receptivity of the shear layer to acoustic oscillations, severing the coupling mechanism between the acoustics and the flame. Previous work suggested that the existence of a precessing vortex core (PVC) may suppress the receptivity of the shear layer, and the goal of this study is to first, confirm that this suppression is occurring, and second, understand the mechanism by which the PVC suppresses the shear layer receptivity. In this paper, we couple experiment with linear stability analysis to determine whether a PVC can suppress shear layer receptivity to longitudinal acoustic modes in a nonreacting swirling flow at a range of swirl numbers. The shear layer response to the longitudinal acoustic forcing manifests as an m = 0 mode since the acoustic field is axisymmetric. The PVC has been shown both in experiment and linear stability analysis to have m = 1 and m = −1 modal content. By comparing the relative magnitude of the m = 0 and m = −1,1 modes, we quantify the impact that the PVC has on the shear layer response. The mechanism for shear layer response is determined using companion forced response analysis, where the shear layer disturbance growth rates mirror the experimental results. Differences in shear layer thickness and azimuthal velocity profiles drive the suppression of the shear layer receptivity to acoustic forcing.

On the Impact of Shear Flow Instabilities on Global Heat Release Rate Fluctuations: Linear Stability Analysis of an Isothermal and a Reacting Swirling Jet

2012 ◽  
Author(s):  
Kilian Oberleithner ◽  
Sebastian Schimek ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Heat Release ◽  
Shear Layer ◽  
Linear Stability ◽  
Heat Release Rate ◽  
Release Rate ◽  
Linear Stability Analysis ◽  
Amplitude Dependence ◽  
Swirling Jet ◽  
The Impact

The prediction of large-scale flow structures in combustor flows and their impact on the flame dynamics is of great importance to avoid thermoacoustic instabilities in modern gas turbine design. The streamwise growth of these so-called coherent structures depends on the receptivity of the shear layers, which can be predicted numerically by means of linear stability analysis. We demonstrate this approach on an isothermal swirling jet that is dominated by a self-excited helical mode that features a precessing vortex core, showing that this theoretical concept successfully predicts the frequency, the source, and the shape of this mode. The analysis is further applied to a reacting flow with a swirl-stabilized flame, pointing out important connections between the shear layer receptivity and the measured amplitude dependence of the flame transfer function. The theoretical findings suggest that the saturation of the global heat release rate fluctuations observed at moderate forcing amplitudes is caused by vanishing shear layer receptivity.

scholarly journals Modelling waving crops using large-eddy simulation: comparison with experiments and a linear stability analysis

2010 ◽  
Vol 652 ◽  
pp. 5-44 ◽  
Author(s):  
S. DUPONT ◽  
F. GOSSELIN ◽  
C. PY ◽  
E. DE LANGRE ◽  
P. HEMON ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Large Eddy Simulation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Coupled Model ◽  
Wind Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Eddy Structures ◽  
The Impact

In order to investigate the possibility of modelling plant motion at the landscape scale, an equation for crop plant motion, forced by an instantaneous velocity field, is introduced in a large-eddy simulation (LES) airflow model, previously validated over homogeneous and heterogeneous canopies. The canopy is simply represented as a poroelastic continuous medium, which is similar in its discrete form to an infinite row of identical oscillating stems. Only one linear mode of plant vibration is considered. Two-way coupling between plant motion and the wind flow is insured through the drag force term. The coupled model is validated on the basis of a comparison with measured movements of an alfalfa crop canopy. It is also compared with the outputs of a linear stability analysis. The model is shown to reproduce the well-known phenomenon of ‘honami’ which is typical of wave-like crop motions on windy days. The wavelength of the main coherent waving patches, extracted using a bi-orthogonal decomposition (BOD) of the crop velocity fields, is in agreement with that deduced from video recordings. The main spatial and temporal characteristics of these waving patches exhibit the same variation with mean wind velocity as that observed with the measurements. However they differ from the coherent eddy structures of the wind flow at canopy top, so that coherent waving patches cannot be seen as direct signatures of coherent eddy structures. Finally, it is shown that the impact of crop motion on the wind dynamics is negligible for current wind speed values. No lock-in mechanism of coherent eddy structures on plant motion is observed, in contradiction with the linear stability analysis. This discrepancy may be attributed to the presence of a nonlinear saturation mechanism in LES.

Pulsatile flow in stenotic geometries: flow behaviour and stability

2009 ◽  
Vol 622 ◽  
pp. 291-320 ◽  
Author(s):  
M. D. GRIFFITH ◽  
T. LEWEKE ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Base Flow ◽  
Arterial Stenosis ◽  
Working Fluid ◽  
Absolute Instability ◽  
Straight Tube ◽  
Instability Modes

Pulsatile inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted pulsatile flows. The Reynolds number is varied between 50 and 700 and the stenosis degree by area between 0.20 and 0.90. Numerically, a spectral element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. For low Reynolds numbers, the flow is characterized by a vortex ring which forms directly downstream of the stenosis, for which the strength and downstream propagation velocity vary with the stenosis degree. Linear stability analysis is performed on the simulated axisymmetric base flows, revealing a range of absolute instability modes. Comparisons are drawn between the numerical linear stability analysis and the observed instability in the experimental flows. The observed flows are less stable than the numerical analysis predicts, with convective shear layer instability present in the experimental flows. Evidence is found of Kelvin–Helmholtz-type shear layer roll-ups; nonetheless, the possibility of the numerically predicted absolute instability modes acting in the experimental flow is left open.

Effect of enclosure height on the structure and stability of shear layers induced by differential rotation

2015 ◽  
Vol 765 ◽  
pp. 45-81 ◽  
Author(s):  
Tony Vo ◽  
Luca Montabone ◽  
Gregory J. Sheard
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Differential Rotation ◽  
Shear Layers ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Axisymmetric Model ◽  
Two Dimensional Model

AbstractThe structure and stability of Stewartson shear layers with different heights are investigated numerically via axisymmetric simulation and linear stability analysis, and a validation of the quasi-two-dimensional model is performed. The shear layers are generated in a rotating cylindrical tank with circular disks located at the lid and base imposing a differential rotation. The axisymmetric model captures both the thick and thin nested Stewartson layers, which are scaled by the Ekman number ($\mathit{E}\,$) as $\mathit{E}\,^{1/4}$ and $\mathit{E}\,^{1/3}$ respectively. In contrast, the quasi-two-dimensional model only captures the $\mathit{E}\,^{1/4}$ layer as the axial velocity required to invoke the $\mathit{E}\,^{1/3}$ layer is excluded. A direct comparison between the axisymmetric base flows and their linear stability in these two models is examined here for the first time. The base flows of the two models exhibit similar flow features at low Rossby numbers ($\mathit{Ro}$), with differences evident at larger $\mathit{Ro}$ where depth-dependent features are revealed by the axisymmetric model. Despite this, the quasi-two-dimensional model demonstrates excellent agreement with the axisymmetric model in terms of the shear-layer thickness and predicted stability. A study of various aspect ratios reveals that a Reynolds number based on the theoretical Ekman layer thickness is able to describe the transition of a base flow that is reflectively symmetric about the mid-plane to a symmetry-broken state. Additionally, the shear-layer thicknesses scale closely to the expected ${\it\delta}_{vel}\propto A\mathit{E}\,^{1/4}$ and ${\it\delta}_{vort}\propto A\mathit{E}\,^{1/3}$ for shear layers that are not affected by the confinement ($A\mathit{E}\,^{1/4}\lesssim 0.34$ in this system, the ratio of tank height to shear-layer radius). The linear stability analysis reveals that the ratio of Stewartson layer radius to thickness should be greater than $45$ for the stability of the flow to be independent of aspect ratio. Thus, for sufficiently small $A\mathit{E}\,^{1/4}$ and $A\mathit{E}\,^{1/3}$, the flow characteristics remain similar and the linear stability of the flow can be described universally when the azimuthal wavelength is scaled against $A$. The analysis also recovers an asymptotic scaling for the normalized azimuthal wavelength which suggests that ${\it\lambda}_{{\it\theta},c}^{\ast }\propto (|\mathit{Ro}|/\mathit{E}\,^{2})^{-1/5}$ for geometry-independent shear layers at marginal stability.

scholarly journals The impact of heating the breakdown bubble on the global mode of a swirling jet: Experiments and linear stability analysis

2016 ◽  
Vol 28 (10) ◽  
pp. 104102 ◽  
Author(s):  
Lothar Rukes ◽  
Moritz Sieber ◽  
C. Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Global Mode ◽  
Swirling Jet ◽  
The Impact

Impact of Flow Non-Axisymmetry on Swirling Flow Dynamics and Receptivity to Acoustics

2015 ◽  
Author(s):  
Samuel Hansford ◽  
Jacqueline O’Connor ◽  
Kiran Manoharan ◽  
Santosh Hemchandra
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Flow Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Swirling Flow ◽  
Forced Response ◽  
Experimental Results ◽  
Transverse Acoustic ◽  
Jet Axis

In this study, we experimentally investigate both the intrinsic instability characteristics and forced response to transverse acoustic excitation of a non-reacting, swirling flow for application to combustion instability in annular gas turbine engines. The non-axisymmetry of the velocity field is quantified using an azimuthal mode decomposition of the time-averaged velocity field that shows that (1) the flow field is largely axisymmetric, (2) axisymmetry decreases with downstream distance, and (3) forcing does not significantly alter the time-averaged shape of the flow field. The flow field is analyzed in a companion linear stability analysis that shows that the most unstable modes in the flow field are m=−1 and m=−2, which agrees with the experimental observations and shows that the intrinsic dynamics of this flow field are non-axisymmetric with respect to the jet axis. The linear stability analysis captures the spatial variation of mode strength for certain modes, particularly mode m=−1, but there are some deviations from the experimental results. Most notably, these deviations occur for mode m=0 at radii away from the jet axis. Experimental results of the forced response of the flow indicate that the intrinsic instability characteristics of the flow field have an impact on the forced-response dynamics. Response of the flow field to a velocity anti-node in a standing transverse acoustic field shows non-axisymmetric vortex rollup and the dominance of the m=−1 and m=1 azimuthal modes in the fluctuating flow field. In the presence of a pressure anti-node, the m=0 mode of the fluctuating flow field is very strong at the jet exit, indicating an axisymmetric response, and ring vortex shedding is apparent in the flow measurements from high-speed PIV. However, further downstream, the strength of the axisymmetric mode decreases and the m=−1 and m=1 modes dominate, resulting in a tilting of the vortex ring as it convects downstream. Implications for flame response to transverse acoustic fields are discussed.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties, and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a 1-D model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function. By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

Global linear stability analysis of jets in cross-flow

2017 ◽  
Vol 828 ◽  
pp. 812-836 ◽  
Author(s):  
Marc A. Regan ◽  
Krishnan Mahesh
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Implicitly Restarted Arnoldi

The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275–307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between $R=2$ to $R=4$ observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129), where $R=\overline{v}_{jet}/u_{\infty }$ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when $R=2$, whereas downstream shear-layer instabilities are shown to dominate when $R=4$.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a one-dimensional (1D) model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function (FTF). By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

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