Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

2011 ◽  
Vol 679 ◽  
pp. 383-414 ◽  
Author(s):  
K. OBERLEITHNER ◽  
M. SIEBER ◽  
C. N. NAYERI ◽  
C. O. PASCHEREIT ◽  
C. PETZ ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Coherent Structures ◽  
Vortex Breakdown ◽  
Particle Image Velocimetry Data ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Helical Structures ◽  
Global Mode ◽  
Swirling Jet ◽  
Time Periodic

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

scholarly journals On the impact of swirl on the growth of coherent structures

2014 ◽  
Vol 741 ◽  
pp. 156-199 ◽  
Author(s):  
K. Oberleithner ◽  
C. O. Paschereit ◽  
I. Wygnanski
Keyword(s):  
Stability Analysis ◽  
Coherent Structures ◽  
Large Scale ◽  
Vortex Breakdown ◽  
Shear Mode ◽  
Mean Flow ◽  
Swirling Jet ◽  
The Mean ◽  
The Impact ◽  
Helical Mode

AbstractSpatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co- and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time- and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities.

Structural sensitivity of spiral vortex breakdown

2013 ◽  
Vol 720 ◽  
pp. 558-581 ◽  
Author(s):  
Ubaid Ali Qadri ◽  
Dhiren Mistry ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Passive Control ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Axial Component ◽  
Azimuthal Mode ◽  
Global Mode ◽  
Structural Sensitivity ◽  
Spiral Vortex

AbstractPrevious numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier–Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the $m= - 1$ azimuthal mode is the most unstable and that the wavemaker regions of the $m= - 1$ mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown.

A swirling jet with vortex breakdown: three-dimensional coherent structures

2016 ◽  
Vol 23 (2) ◽  
pp. 301-304 ◽  
Author(s):  
S. V. Alekseenko ◽  
V. M. Dulin ◽  
M. P. Tokarev ◽  
D. M. Markovich
Keyword(s):  
Coherent Structures ◽  
Vortex Breakdown ◽  
Three Dimensional ◽  
Swirling Jet

Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

2015 ◽  
Author(s):  
Pedro Paredes ◽  
Vassilis Theofilis ◽  
Steffen Terhaar ◽  
Kilian Oberleithner ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Prediction Models ◽  
Global Analysis ◽  
Local Analysis ◽  
Reacting Flow ◽  
Dynamics Modeling ◽  
Mean Flow ◽  
Global Mode ◽  
Precessing Vortex Core

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures is thereby highly wanted for thermo-acoustic prediction models. In this work we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work biglobal and local stability analysis is applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analysis accurately predicts the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analysis agree very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.

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

Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Pedro Paredes ◽  
Steffen Terhaar ◽  
Kilian Oberleithner ◽  
Vassilis Theofilis ◽  
Christian Oliver Paschereit
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Prediction Models ◽  
Global Analysis ◽  
Local Analysis ◽  
Reacting Flow ◽  
Dynamics Modeling ◽  
Mean Flow ◽  
Global Mode ◽  
Precessing Vortex Core

Coherent flow structures in shear flows are generated by instabilities intrinsic to the hydrodynamic field. In a combustion environment, these structures may interact with the flame and cause unsteady heat release rate fluctuations. Prediction and modeling of these structures are thereby highly wanted for thermo-acoustic prediction models. In this work, we apply hydrodynamic linear stability analysis to the time-averaged flow field of swirl-stabilized combustors obtained from experiments. Recent fundamental investigations have shown that the linear eigenmodes of the mean flow accurately represent the growth and saturation of the coherent structures. In this work, biglobal and local stability analyses are applied to the reacting flow in an industry-relevant combustion system. Both the local and the biglobal analyses accurately predict the onset and structure of a self-excited global instability that is known in the combustion community as a precessing vortex core (PVC). However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis wrongly predicts an unstable global growth rate. The predicted spatial distribution of the amplitude functions using both analyses agrees very well to the experimentally identified global mode. The presented tools are considered as very promising for the understanding of the PVC and physics based flow control.

A numerical study of global frequency selection in the time-mean wake of a circular cylinder

2010 ◽  
Vol 645 ◽  
pp. 435-446 ◽  
Author(s):  
J. S. LEONTINI ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Saddle Point ◽  
Numerical Study ◽  
Streamwise Velocity ◽  
Three Dimensions ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Global Mode ◽  
The Mean

A series of direct numerical simulations, both in two- and three-dimensions, of the flow past a circular cylinder for Reynolds numbers Re ≤ 600 has been conducted. From these simulations, the time-mean (and, for the three-dimensional simulations, the spanwise spatial-mean) flow has been calculated. A global linear stability analysis has been conducted on these mean flows, showing that the mean cylinder wake for Re ≤ 600 is marginally stable and the eigenfrequency of the leading global mode closely predicts the eventual saturated vortex shedding frequency. A local stability analysis has also been conducted. For this, a series of streamwise velocity profiles has been extracted from the mean wake and the stability of these profiles has been analysed using the Rayleigh stability equation. The real and imaginary instability frequencies gained from these profiles have then been used to find the global frequency selected by the flow using a saddle-point criterion. The results confirm the success of the saddle-point criterion when the mean flow is quasi-parallel in the vicinity of the saddle point; however, the limitations of the method when the mean flow exhibits higher curvature are also elucidated.

Sign in / Sign up

Export Citation Format

Share Document