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 $R=4$.

Numerical investigation of the saturation process in an incompressible cavity flow

2017 ◽  
Vol 837 ◽  
pp. 182-209 ◽  
Author(s):  
N. Vinha ◽  
F. Meseguer-Garrido ◽  
J. de Vicente ◽  
E. Valero
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Saturation Process ◽  
Wall Boundary Conditions

A numerical study of the saturation process inside a rectangular open cavity is presented. Previous experiments and linear stability analysis of the problem completely described the flow in its onset, as well as in a saturated regime, characterized by three-dimensional centrifugal modes. The morphology of the modes found in the experiments matched the ones predicted by linear analysis, but with a shift in frequencies for the oscillating modes. A three-dimensional incompressible direct numerical simulation (DNS) is employed for a detailed investigation of the saturation process inside a cavity with dimensions similar to the one used in the experiments, to further explain the behaviour of these modes. In this work, periodic boundary conditions are first imposed to better understand the effect of the saturation process far from the walls. Then, the effects of spanwise solid wall boundary conditions are investigated with a DNS reproducing the full dynamics of the experiments. The main flow structures are identified using the dynamic mode decomposition technique and compared with previous experimental and linear stability analysis results. The main reason for the aforementioned shift in frequency is explained in this paper, as it is a function of the velocity of the main recirculating vortex.

scholarly journals Analysis of V-Gutter Reacting Flow Dynamics Using Proper Orthogonal and Dynamic Mode Decompositions

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4886 ◽  
Author(s):  
Yang Yang ◽  
Xiao Liu ◽  
Zhihao Zhang
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Wake Instability ◽  
Shedding Frequency ◽  
Proper Orthogonal

The current work is focused on investigating the potential of data-driven post-processing techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) for flame dynamics. Large-eddy simulation (LES) of a V-gutter premixed flame was performed with two Reynolds numbers. The flame transfer function (FTF) was calculated. The POD and DMD were used for the analysis of the flame structures, wake shedding frequency, etc. The results acquired by different methods were also compared. The FTF results indicate that the flames have proportional, inertial, and delay components. The POD method could capture the shedding wake motion and shear layer motion. The excited DMD modes corresponded to the shear layer flames’ swing and convect motions in certain directions. Both POD and DMD could help to identify the wake shedding frequency. However, this large-scale flame oscillation is not presented in the FTF results. The negative growth rates of the decomposed mode confirm that the shear layer stabilized flame was more stable than the flame possessing a wake instability. The corresponding combustor design could be guided by the above results.

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.

Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body

2011 ◽  
Vol 676 ◽  
pp. 110-144 ◽  
Author(s):  
P. BOHORQUEZ ◽  
E. SANMIGUEL-ROJAS ◽  
A. SEVILLA ◽  
J. I. JIMÉNEZ-GONZÁLEZ ◽  
C. MARTÍNEZ-BAZÁN
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Velocity Ratio ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Direct Numerical Simulations ◽  
The Body ◽  
Stream Velocity

We investigate the stability properties and flow regimes of laminar wakes behind slender cylindrical bodies, of diameter D and length L, with a blunt trailing edge at zero angle of attack, combining experiments, direct numerical simulations and local/global linear stability analyses. It has been found that the flow field is steady and axisymmetric for Reynolds numbers below a critical value, Recs (L/D), which depends on the length-to-diameter ratio of the body, L/D. However, in the range of Reynolds numbers Recs(L/D) < Re < Reco(L/D), although the flow is still steady, it is no longer axisymmetric but exhibits planar symmetry. Finally, for Re > Reco, the flow becomes unsteady due to a second oscillatory bifurcation which preserves the reflectional symmetry. In addition, as the Reynolds number increases, we report a new flow regime, characterized by the presence of a secondary, low frequency oscillation while keeping the reflectional symmetry. The results reported indicate that a global linear stability analysis is adequate to predict the first bifurcation, thereby providing values of Recs nearly identical to those given by the corresponding numerical simulations. On the other hand, experiments and direct numerical simulations give similar values of Reco for the second, oscillatory bifurcation, which are however overestimated by the linear stability analysis due to the use of an axisymmetric base flow. It is also shown that both bifurcations can be stabilized by injecting a certain amount of fluid through the base of the body, quantified here as the bleed-to-free-stream velocity ratio, Cb = Wb/W∞.

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.

A numerical study of shear layer characteristics of low-speed transverse jets

2016 ◽  
Vol 790 ◽  
pp. 275-307 ◽  
Author(s):  
Prahladh S. Iyer ◽  
Krishnan Mahesh
Keyword(s):  
Velocity Profile ◽  
Shear Layer ◽  
Convective Instability ◽  
Numerical Study ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Dominant Frequencies

Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129) at velocity ratios ($R=\overline{v}_{j}/u_{\infty }$) of 2 and 4 and Reynolds number ($Re=\overline{v}_{j}D/{\it\nu}$) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ($St=0.65$) is dominant along the length of the shear layer for $R=2$, whereas the dominant frequencies change along the shear layer for $R=4$. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

Global Stability Analysis of an Academic Rotor/Stator Cavity Subject to Periodic and Simple Wall Oscillations

2021 ◽  
Author(s):  
Mark Noun ◽  
Laurent Gicquel ◽  
Gabriel Staffelbach
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Pressure Fluctuations ◽  
Dynamic Mode Decomposition ◽  
Forced Flow ◽  
Dynamic Mode ◽  
Global Stability Analysis ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Spatio Temporal

Abstract Complex unsteady phenomena can appear in turbomachinery components and result in the self-sustained oscillatory motion of the fluid as found in aeronautical engines or rocket turbopumps for example. The origin of these oscillations often results from the complex coupling between flow non linearities and structure motion generating major risks for the operation of the engine and even undermining its components. For instance, in turbines, the internal components that are most liable to vibrate are the blades and discs. In this context, it is critical to understand the effect of the vibrating components on the flow stability in rotor/stator cavities. In order to address this problem, an academic rotor/stator cavity subject to periodic wall oscillations is investigated in the current paper where the frequency of the vibrations are imposed and correspond to the previously identified unstable fluid modes inside the cavity. The objective is to understand the behavior of the flow when subject to a periodic forcing imposed by the rotor motion. To do so, predictive numerical strategies are established based on Large Eddy Simulation (LES) in conjunction to a global stability analysis which seem to be a promising method to capture flow instabilities. Focus is here brought to the underlying pressure fluctuations found inside the cavity using spectral analysis complemented with the global stability analysis, demonstrating that such tools can address forced flow problems. More specifically and for all simulations, the results of the global stability analysis are compared to a Dynamic Mode Decomposition (DMD) of LES predictions by reconstructing the corresponding modes through a spatio-temporal approach showing that the new fluid limit cycles present modes that shift or completely disappear compared to the unforced case, the forcing mechanism altering the stability of the entire system.

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.

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.

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