Hysteresis and turbulent vortex breakdown in transitional swirling jets

Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter $S$ (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl ($S=1$) a helical mode of azimuthal wavenumber $m=-2$ (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at $S=1.38$, and a steady bubble breakdown at $S=1.4$. On further increase to $S=1.5$, a helical, self-excited global mode ($m=+1$, counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl ($S=1.55$), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.

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A weakly nonlinear mechanism for mode selection in swirling jets

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.93 ◽

2012 ◽

Vol 699 ◽

pp. 216-262 ◽

Cited By ~ 52

Author(s):

Philippe Meliga ◽

François Gallaire ◽

Jean-Marc Chomaz

Keyword(s):

Normal Form ◽

Numerical Simulations ◽

Vortex Breakdown ◽

Double Helix ◽

Mode Selection ◽

Direct Numerical Simulations ◽

Swirling Jets ◽

Graphic Mode ◽

Stable Solutions ◽

Single Helix

AbstractGlobal linear and nonlinear bifurcation analysis is used to revisit the spiral vortex breakdown of nominally axisymmetric swirling jets. For the parameters considered herein, stability analyses single out two unstable linear modes of azimuthal wavenumber $m= \ensuremath{-} 1$ and $m= \ensuremath{-} 2$, bifurcating from the axisymmetric breakdown solution. These modes are interpreted in terms of spiral perturbations wrapped around and behind the axisymmetric bubble, rotating in time in the same direction as the swirling flow but winding in space in the opposite direction. Issues are addressed regarding the role of these modes with respect to the existence, mode selection and internal structure of vortex breakdown, as assessed from the three-dimensional direct numerical simulations of Ruith et al. (J. Fluid Mech., vol. 486, 2003, pp. 331–378). The normal form describing the leading-order nonlinear interaction between modes is computed and analysed. It admits two stable solutions corresponding to pure single and double helices. At large swirl, the axisymmetric solution bifurcates to the double helix which remains the only stable solution. At low and moderate swirl, it bifurcates first to the single helix, and subsequently to the double helix through a series of subcritical bifurcations yielding hysteresis over a finite range of Reynolds numbers, the estimated bifurcation threshold being in good agreement with that observed in the direct numerical simulations. Evidence is provided that this selection is not to be ascribed to classical mean flow corrections induced by the existence of the unstable modes, but to a non-trivial competition between harmonics. Because the frequencies of the leading modes approach a strong $2$:$1$ resonance, an alternative normal form allowing interactions between the $m= \ensuremath{-} 2$ mode and the first harmonics of the $m= \ensuremath{-} 1$ mode is computed and analysed. It admits two stable solutions, the double helix already identified in the non-resonant case, and a single helix differing from that observed in the non-resonant case only by the presence of a slaved, phase-locked harmonic deformation. On behalf of the finite departure from the $2$:$1$ resonance, the amplitude of the slaved harmonic is however low, and the effect of the resonance on the bifurcation structure is merely limited to a reduction of the hysteresis range.

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Formation of Turbulent Vortex Breakdown: Intermittency, Criticality, and Global Instability

AIAA Journal ◽

10.2514/1.j050642 ◽

2012 ◽

Vol 50 (7) ◽

pp. 1437-1452 ◽

Cited By ~ 69

Author(s):

K. Oberleithner ◽

C. O. Paschereit ◽

R. Seele ◽

I. Wygnanski

Keyword(s):

Vortex Breakdown ◽

Global Instability ◽

Turbulent Vortex

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Turbulent Vortex Breakdown at High Reynolds Numbers

AIAA Journal ◽

10.2514/2.1036 ◽

2000 ◽

Vol 38 (5) ◽

pp. 825-834 ◽

Cited By ~ 27

Author(s):

F. Novak ◽

T. Sarpkaya

Keyword(s):

Vortex Breakdown ◽

Reynolds Numbers ◽

Turbulent Vortex ◽

High Reynolds Numbers ◽

High Reynolds

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Shaping Air Flow Characteristics of a High-Speed Rotary-Bell Sprayer for Automotive Painting Processes

Journal of Fluids Engineering ◽

10.1115/1.4030703 ◽

2015 ◽

Vol 137 (11) ◽

Cited By ~ 7

Author(s):

Ch. Stevenin ◽

Y. Béreaux ◽

J.-Y. Charmeau ◽

J. Balcaen

Keyword(s):

High Speed ◽

Vortex Breakdown ◽

Flow Behavior ◽

Air Flow ◽

Flow Characteristics ◽

Rotation Frequency ◽

Zone Length ◽

Swirling Jets ◽

Automotive Parts

Electrostatic rotary bell sprayers (ERBS) are widely used in automotive painting applications. These processes involve complex airflows to shape paint sprays and transport droplets toward automotive parts to be coated. Despite the importance of shaping airflow on global spray characteristics, a detailed characterization of this aerodynamic flow is still missing. For this purpose, an experimental study was conducted on the influence of some ERBS operating parameters on the development and characteristics of shaping airflow. Results show that, for low swirl numbers, the flow behavior is close to that of annular swirling jets and a good agreement is found between ERBS flow characteristics and data available in literature. When rotational speed of the bell cup is sufficiently fast, a change of regime is observed with a shift in the longitudinal flow development and an increase of recirculation zone length. This change of regime is attributed to vortex breakdown instability, known to occur when high swirl strength is beyond a critical value. Experimental results obtained in this study put forward a clear link between the shaping air flow rate and the rotation frequency on the aerodynamics and also provide valuable leads to design shaping air flow in modern ERBS.

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Instabilities and Vortex Breakdown in Swirling Jets and Wakes

IUTAM Symposium on Dynamics of Slender Vortices - Fluid Mechanics and Its Applications ◽

10.1007/978-94-011-5042-2_23 ◽

1998 ◽

pp. 267-286 ◽

Cited By ~ 2

Author(s):

Paul Billant ◽

Jean-Marc Chomaz ◽

Ivan Delbende ◽

Patrick Huerre ◽

Thomas Loiseleux ◽

...

Keyword(s):

Vortex Breakdown ◽

Swirling Jets

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Methods for the Extraction and Analysis of the Global Mode in Swirling Jets Undergoing Vortex Breakdown

Volume 4A: Combustion, Fuels and Emissions ◽

10.1115/gt2016-56588 ◽

2016 ◽

Cited By ~ 1

Author(s):

Lothar Rukes ◽

Moritz Sieber ◽

C. Oliver Paschereit ◽

Kilian Oberleithner

Keyword(s):

Vortex Breakdown ◽

Control Strategies ◽

Combustion Process ◽

Flame Stabilization ◽

Global Mode ◽

Swirling Jets ◽

Precessing Vortex Core ◽

Finite Time Lyapunov Exponent ◽

Image Velocimetry ◽

The Impact

Swirling jets undergoing vortex breakdown are widely used in combustion applications, due to their ability to provide aerodynamic flame stabilization. It is well known that vortex breakdown is accompanied by a dominant coherent structure, the so called precessing vortex core (PVC). Reports on the impact of the PVC on the combustion process range from beneficial to detrimental. In any event, efficient methods for the analysis of the PVC help to increase the benefit or reduce the penalty resulting from it. This study uses Particle Image Velocimetry (PIV) measurements of a generic non-isothermal swirling jet to demonstrate the use of advanced data analysis techniques. In particular, the Finite Time Lyapunov Exponent (FTLE) and local linear stability analysis (LSA) are shown to reveal deep insight into the physical mechanisms that drive the PVC. Particularly, it is demonstrated that the PVC amplitude is strongly reduced, if heating is applied at the wavemaker of the flow. These techniques are complemented by the traditionally used Proper Orthogonal Decomposition (POD) and spatial correlation techniques. It is demonstrated how these methods complement each other and lead to a comprehensive understanding of the PVC that lays out the path to efficient control strategies.

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The Role of the Centerbody Wake on the Precessing Vortex Core Dynamics of a Swirl Nozzle

Volume 4B: Combustion, Fuels, and Emissions ◽

10.1115/gt2020-15777 ◽

2020 ◽

Author(s):

Arnab Mukherjee ◽

Nishanth Muthichur ◽

Chaitali More ◽

Saarthak Gupta ◽

Santosh Hemchandra

Keyword(s):

Stability Analysis ◽

Nozzle Exit ◽

Vortex Core ◽

Vortex Breakdown ◽

Spatial Separation ◽

Reynolds Numbers ◽

Swirling Jets ◽

Precessing Vortex Core ◽

Swirl Flows ◽

Structural Sensitivity Analysis

Abstract The precessing vortex core (PVC) phenomenon in swirling jets is a helical instability in the flow driven by the coherent precession of the vortex breakdown bubble (VBB) around the flow axis, resulting in the helical rollup of the shear layer. This instabilitty is driven mainly by flow processes in the region upstream of the VBB. Centerbodies, commonly employed in combustor nozzles create a central wake recirculation zone (CWRZ) that can interfere with VBB precession and hence suppress the PVC. We study this phenomenon in a swirl nozzle with a centerbody whose end face is flush with the nozzle exit plane, using large eddy simulations (LES) and linear hydrodynamic stability analysis for flow Reynolds numbers Re = 48,767 and 82,751, based on nozzle exit diameter and bulk flow velocity. For one of the Re = 82,751 cases the centerbody end face diameter is halved resulting in the onset of coherent VBB precession. Linear stability analysis reveals a marginally unstable mode in this case. The same mode is found to be stable in the nominal cases. Structural sensitivity analysis for these two cases, shows that the VBB precession eigenmode is sensitive to changes in the time averaged flow in the VBB-CWRZ merger region. This suggests that the reduction in CWRZ length due to halving the centerbody end face diameter is the reason for the onset of VBB precession. These results suggest that in general, spatial separation between the CWRZ and VBB can result in the onset of VBB precession and the emergence of PVC oscillations in swirl flows.

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The Role of the Centerbody Wake on the Precessing Vortex Core Dynamics of a Swirl Nozzle

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4050155 ◽

2021 ◽

Vol 143 (5) ◽

Author(s):

Arnab Mukherjee ◽

Nishanth Muthichur ◽

Chaitali More ◽

Saarthak Gupta ◽

Santosh Hemchandra

Keyword(s):

Stability Analysis ◽

Nozzle Exit ◽

Vortex Core ◽

Vortex Breakdown ◽

Spatial Separation ◽

Reynolds Numbers ◽

Swirling Jets ◽

Precessing Vortex Core ◽

Large Eddy ◽

Structural Sensitivity Analysis

Abstract The precessing vortex core (PVC) phenomenon in swirling jets is a helical instability in the flow driven by the coherent precession of the vortex breakdown bubble (VBB) around the flow axis, resulting in the helical rollup of the shear layer. This instability is driven by flow processes in the region upstream of the VBB. Centerbodies, commonly employed in combustor nozzles, create a centerbody wake recirculation zone (CWRZ) that can interfere with VBB precession and hence suppress the PVC. We study this phenomenon in a swirl nozzle with a centerbody whose end face is flush with the nozzle exit plane, using large eddy simulations (LES) and linear hydrodynamic stability analysis for flow Reynolds numbers Re = 48,767 and 82,751, based on nozzle exit diameter and bulk flow velocity. For one of the Re = 82,751 cases, the centerbody end face diameter is halved, resulting in the onset of coherent VBB precession. Linear stability analysis reveals a marginally unstable mode in this case. The same mode is found to be stable in the nominal cases. Structural sensitivity analysis shows that the VBB precession eigenmode is sensitive to changes in the time-averaged flow in the VBB-CWRZ merger region. This suggests that the reduction in CWRZ length due to halving the centerbody end face diameter is the reason for the onset of VBB precession. These results suggest that in general, spatial separation between the CWRZ and VBB can result in the onset of VBB precession and the emergence of PVC oscillations in flows with swirl.

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