scholarly journals Local linear stability analysis of cyclone separators

2017 ◽  
Vol 816 ◽  
pp. 507-538 ◽  
Author(s):  
T. A. Grimble ◽  
A. Agarwal ◽  
M. P. Juniper
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Local Stability ◽  
High Speed Photography ◽  
Unstable Flow ◽  
Local Stability Analysis ◽  
Local Linear ◽  
The Stability

Local linear stability analysis is applied to the flow inside a cyclone separator to investigate the unsteady precession of the vortex core. The results of the stability analysis are compared with experimental measurements of the vortex oscillations using high-speed photography with particle seeding and hot-wire anemometry. The experiments reveal distinct spatial variation in the oscillation behaviour within the cyclone. The unsteady motion is focused at each end of the device, at both the narrow cone tip and just below the exhaust duct at the top of the cone, which is known as a vortex finder. The local stability analysis shows that an absolute instability is present throughout the flow for some non-zero azimuthal wavenumbers. The unsteady flow is observed to be driven by coupling between the shear layer and inertial waves confined within the vortex core. Comparison of the stability analysis with experiments shows the same frequency and mode shape behaviour and suggests that the local analysis accurately predicts the unstable modes of the system. The precessing vortex core is responsible for a narrow-band acoustic noise. Comparisons are also drawn with acoustic measurements made on cyclones in which the system is defined by key non-dimensional parameters, such as the swirl number and outlet diameter ratio. The results in this study demonstrate the applicability of local stability analysis to a complex swirling system and yield credible details about the underlying mechanisms of the unstable flow inside the cyclone.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

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.

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 Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

2016 ◽  
Vol 788 ◽  
pp. 549-575 ◽  
Author(s):  
Benjamin Emerson ◽  
Tim Lieuwen ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Acoustic Waves ◽  
Local Stability ◽  
Bluff Body ◽  
Density Ratio ◽  
Global Mode ◽  
Eigenvalue Sensitivity ◽  
Local Stability Analysis ◽  
Measured Time ◽  
The Stability

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Non-parallel linear stability analysis of the vertical boundary layer in a differentially heated cavity

1997 ◽  
Vol 352 ◽  
pp. 265-281 ◽  
Author(s):  
A. M. H. BROOKER ◽  
J. C. PATTERSON ◽  
S. W. ARMFIELD
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Navier Stokes ◽  
Parabolized Stability Equations ◽  
The Stability ◽  
Flow Quantity ◽  
Energy Equations ◽  
Made In

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

Rayleigh–Bénard instability generated by a diffusion flame

2013 ◽  
Vol 736 ◽  
pp. 464-494 ◽  
Author(s):  
P. Pearce ◽  
J. Daou
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Diffusion Flame ◽  
Damkohler Number ◽  
Benard Convection ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe investigate the Rayleigh–Bénard convection problem within the context of a diffusion flame formed in a horizontal channel where the fuel and oxidizer concentrations are prescribed at the porous walls. This problem seems to have received no attention in the literature. When formulated in the low-Mach-number approximation the model depends on two main non-dimensional parameters, the Rayleigh number and the Damköhler number, which govern gravitational strength and reaction speed respectively. In the steady state the system admits a planar diffusion flame solution; the aim is to find the critical Rayleigh number at which this solution becomes unstable to infinitesimal perturbations. In the Boussinesq approximation, a linear stability analysis reduces the system to a matrix equation with a solution comparable to that of the well-studied non-reactive case of Rayleigh–Bénard convection with a hot lower boundary. The planar Burke–Schumann diffusion flame, which has been previously considered unconditionally stable in studies disregarding gravity, is shown to become unstable when the Rayleigh number exceeds a critical value. A numerical treatment is performed to test the effects of compressibility and finite chemistry on the stability of the system. For weak values of the thermal expansion coefficient $\alpha $, the numerical results show strong agreement with those of the linear stability analysis. It is found that as $\alpha $ increases to a more realistic value the system becomes considerably more stable, and also exhibits hysteresis at the onset of instability. Finally, a reduction in the Damköhler number is found to decrease the stability of the system.

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