Vortex Breakdown Modes Research Articles

Detection and analysis of coherent structures in the near-field of a turbulent annular swirling jet: an unsteady Reynolds-averaged Navier–Stokes (URANS) simulation

This paper analyses the capabilities of unsteady Reynolds-averaged Navier-Stokes (URANS) simulations to predict the coherent structures found in a swirling jet undergoing vortex breakdown. Recently, tomographic particle image velocimetry experiments of an annular swirling jet at a Reynolds number of 8500 at moderate swirl showed the presence of a double helical structure in the flow field (Vanierschot et al., Physical Review Fluids, 2018). This structure corresponds to the double helix vortex breakdown mode and is rarely observed in turbulent flows. In this study, the same flow topology is simulated using Computational Fluid Dynamics (CFD). Turbulence is modeled using the unsteady RANS methodology with a RNG k-e turbulence model. The coherent structures in the flow field were analysed using the spectral proper orthogonal decomposition technique. Despite the fact that it is known that steady-state RANS simulations using two-equation isotropic turbulence models have problems in accurately describing swirling flows which are highly anisotropic, this study shows that the unsteady variant was able to predict the large scale flow structures and their associated dynamics reasonable well. In particular, similar to the experiments, a double helical structure was found in the flow field. The structure has windings in the counter-swirl direction and it is wrapped around the central breakdown bubble. To the authors knowledge, this study is the first one to show the ability of unsteady RANS to predict not only the presence of the double helix vortex breakdown in the flow field, but also the spatial and temporal structure of it.

Insights into the dynamics of conical breakdown modes in coaxial swirling flow field

The main idea of this paper is to understand the fundamental vortex breakdown mechanisms in the coaxial swirling flow field. In particular, the interaction dynamics of the flow field is meticulously addressed with the help of high fidelity laser diagnostic tools. Time-resolved particle image velocimetry (PIV) (${\sim}1500~\text{frames}~\text{s}^{-1}$) is employed in $y{-}r$ and multiple $r{-}\unicode[STIX]{x1D703}$ planes to precisely delineate the flow dynamics. Experiments are carried out for three sets of co-annular flow Reynolds number $Re_{a}=4896$, 10 545, 17 546. Furthermore, for each $Re_{a}$ condition, the swirl number ‘$S_{G}$’ is varied independently from $0\leqslant S_{G}\leqslant 3$. The global evolution of flow field across various swirl numbers is presented using the time-averaged PIV data. Three distinct forms of vortex breakdown namely, pre-vortex breakdown (PVB), central toroidal recirculation zone (CTRZ; axisymmetric toroidal bubble type breakdown) and sudden conical breakdown are witnessed. Among these, the conical form of vortex breakdown is less explored in the literature. In this paper, much attention is therefore focused on exploring the governing mechanism of conical breakdown. It is should be interesting to note that, unlike other vortex breakdown modes, conical breakdown persists only for a very short band of $S_{G}$. For any small increase/decrease in $S_{G}$ beyond a certain threshold, the flow spontaneously reverts back to the CTRZ state. Energy ranked and frequency-resolved/ranked robust structure identification methods – proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) respectively – are implemented over instantaneous time-resolved PIV data sets to extract the dynamics of the coherent structures associated with each vortex breakdown mode. The dominant structures obtained from POD analysis suggest the dominance of the Kelvin–Helmholtz (KH) instability (axial $+$ azimuthal; accounts for ${\sim}80\,\%$ of total turbulent kinetic energy, TKE) for both PVB and CTRZ while the remaining energy is contributed by shedding modes. On the other hand, shedding modes contribute the majority of the TKE in conical breakdown. The frequency signatures quantified from POD temporal modes and DMD analysis reveal the occurrence of multiple dominant frequencies in the range of ${\sim}10{-}400~\text{Hz}$ with conical breakdown. This phenomenon may be a manifestation of high energy contribution by shedding eddies in the shear layer. Contrarily, with PVB and CTRZ, the dominant frequencies are observed in the range of ${\sim}20{-}40~\text{Hz}$ only. We have provided a detailed exposition of the mechanism through which conical breakdown occurs. In addition, the current work explores the hysteresis (path dependence) phenomena of conical breakdown as functions of the Reynolds and Rossby numbers. It has been observed that the conical mode is not reversible and highly dependent on the initial conditions.

Predictive control of spiral vortex breakdown

The predictive control of the self-sustained single spiral vortex breakdown mode is addressed in the three-dimensional flow geometry of Ruithet al.(2003) for a constant swirl number$S=1.095$. Based on adjoint optimization algorithms, two different control strategies have been designed. First, a quadratic objective function minimizing the radial velocity intensity, taking advantage of the physical mechanism underpinning spiral vortex breakdown. The second strategy focuses on the hydrodynamic instability properties using as objective function the growth rate of the most unstable global eigenmode. These minimization algorithms seek for an optimal volume force in an axisymmetric domain avoiding therefore expensive three-dimensional computations. In addition to considering eigenvalues around the base flow, we also investigate the stability around the mean flow and we find that it correctly predicts the frequency of the self-sustained single spiral vortex breakdown mode for Reynolds numbers up to$Re=500$. Close to the instability threshold, at a Reynolds value of$Re=180$, all these control strategies successfully quench the spiral vortex breakdown. The related volume force is found identical for the base and mean flow eigenvalue control even if the uncontrolled growth rates differ significantly. The control of the least unstable eigenvalue of the mean flow is not only found optimal at$Re=180$, it also stabilizes the flow at a Reynolds value as large as$Re=300$, which opens promising extensions to industrial applications.

Transitions and blowoff of unconfined non-premixed swirling flame

The present experimental work reports the first observations of primary and secondary transitions in the time-averaged flame topology in a non-premixed swirling flame as the geometric swirl number SG (a non-dimensional number used to quantify the intensity of imparted swirl) is varied from a magnitude of zero till flame blowout. First observations of two transition types viz. primary and secondary transitions are reported. The primary transition represents a transformation from yellow straight jet flame (at SG = 0) to lifted flame with blue base and finally to swirling seated (burner attached) yellow flame. Time-averaged streamline plot obtained from 2D PIV in mid-longitudinal plane shows a recirculation zone (RZ) at the immediate vicinity of burner exit. The lifted flame is stabilized along the vortex core of this RZ. Further, when SG ∼ 1.4–3, the first occurrence of vortex breakdown (VB) induced internal recirculation zone (IRZ) is witnessed. The flame now stabilizes at the upstream stagnation point of the VB-IRZ, which is attached to the burner lip. The secondary transition represents a transformation from a swirling seated flame to swirling flame with a conical tailpiece and finally to a highly-swirled near blowout oxidizer-rich flame. This transition is understood to be the result of transition in vortex breakdown modes of the swirling flow field from dual-ring VB bubble to central toroidal recirculation zone (CTRZ). The physics of transition is described on the basis of modified Rossby number (Rom). Finally, when the swirl intensity is very high i.e. SG ∼ 10, the flame blows out due to excessive straining and due to entrainment of large amount of oxidizer due to partial premixing. The present investigation involving changes in flame topology is immensely important because any change in global flame structure causes oscillatory heat release that can couple with dynamic pressure and velocity fluctuations leading to unsteady combustion. In this light, understanding mechanisms of flame stabilization is essential to tackle the problem of thermo-acoustic instability.

Acoustic response of vortex breakdown modes in a coaxial isothermal unconfined swirling jet

The present experimental work is concerned with the study of amplitude dependent acoustic response of an isothermal coaxial swirling jet. The excitation amplitude is increased in five distinct steps at the burner’s Helmholtz resonator mode (i.e., 100 Hz). Two flow states are compared, namely, sub-critical and super-critical vortex breakdown (VB) that occur before and after the critical conical sheet breakdown, respectively. The geometric swirl number is varied in the range 2.14-4.03. Under the influence of external pulsing, global response characteristics are studied based on the topological changes observed in time-averaged 2D flow field. These are obtained from high resolution 2D PIV (particle image velocimetry) in the longitudinal-mid plane. PIV results also illustrate the changes in the normalized vortex core coordinates (rvcc/(rvcc)0 Hz, yvcc/(yvcc)0 Hz) of internal recirculation zone (IRZ). A strong forced response is observed at 100 Hz (excitation frequency) in the convectively unstable region which get amplified based on the magnitude of external forcing. The radial extent of this forced response region at a given excitation amplitude is represented by the acoustic response region (b). The topological placement of the responsive convectively unstable region is a function of both the intensity of imparted swirl (characterized by swirl number) and forcing amplitude. It is observed that for sub-critical VB mode, an increase in the excitation amplitude till a critical value shifts the vortex core centre (particularly, the vortex core moves downstream and radially outwards) leading to drastic fanning-out/widening of the IRZ. This is accompanied by ∼30% reduction in the recirculation velocity of the IRZ. It is also observed that b < R (R: radial distance from central axis to outer shear layer-OSL). At super-critical amplitudes, the sub-critical IRZ topology transits back (the vortex core retracts upstream and radially inwards) and finally undergoes a transverse shrinkage (rvcc/rvcc0Hz decreases by ∼20%) when b ≥ R. In contrast, the vortex core of super-critical breakdown mode consistently spreads radially outwards and is displaced further downstream. Finally, the IRZ fans-out at the threshold excitation amplitude. However, the acoustic response region b is still less than R. This is explained based on the characteristic geometric swirl number (SG) of the flow regimes. The super-critical flow mode with higher SG (hence, higher radial pressure drop due to rotational effect which scales as ΔP ∼ ρuθ2 and acts inwards towards the center line) compared to sub-critical state imposes a greater resistance to the radial outward spread of b. As a result, the acoustic energy supplied to the super-critical flow mode increases the degree of acoustic response at the pulsing frequency and energizes its harmonics (evident from power spectra). As a disturbance amplifier, the stronger convective instability mode within the flow structure of super-critical VB causes the topology to widen/fan-out severely at threshold excitation amplitude.

Transition in vortex breakdown modes in a coaxial isothermal unconfined swirling jet

This paper reports first observations of transition in recirculation pattern from an open-bubble type axisymmetric vortex breakdown to partially open bubble mode through an intermediate, critical regime of conical sheet formation in an unconfined, co-axial isothermal swirling flow. This time-mean transition is studied for two distinct flow modes which are characterized based on the modified Rossby number (Rom), i.e., Rom ≤ 1 and Rom > 1. Flow modes with Rom ≤ 1 are observed to first undergo cone-type breakdown and then to partially open bubble state as the geometric swirl number (SG) is increased by ∼20% and ∼40%, respectively, from the baseline open-bubble state. However, the flow modes with Rom > 1 fail to undergo such sequential transition. This distinct behavior is explained based on the physical significance associated with Rom and the swirl momentum factor (ξ). In essence, ξ represents the ratio of angular momentum distributed across the flow structure to that distributed from central axis to the edge of the vortex core. It is observed that ξ increases by ∼100% in the critical swirl number band where conical breakdown occurs as compared to its magnitude in the SG regime where open bubble state is seen. This results from the fact that flow modes with Rom ≤ 1 are dominated by radial pressure gradient due to swirl/rotational effect when compared to radial pressure deficit arising from entrainment (due to the presence of co-stream). Consequently, the imparted swirl tends to penetrate easily towards the central axis causing it to spread laterally and finally undergo conical sheet breakdown. However, the flow modes with Rom > 1 are dominated by pressure deficit due to entrainment effect. This blocks the radial inward penetration of imparted angular momentum thus preventing the lateral spread of these flow modes. As such these structures fail to undergo cone mode of vortex breakdown which is substantiated by a mere 30%–40% rise in ξ in the critical swirl number range.

Dynamic-Stability Characteristics of Premixed Methane Oxy-Combustion

This work explores the dynamic stability characteristics of premixed CH4/O2/CO2 mixtures in a 50 kW swirl stabilized combustor. In all cases, the methane-oxygen mixture is stoichiometric, with different dilution levels of carbon dioxide used to control the flame temperature (Tad). For the highest Tad’s, the combustor is unstable at the first harmonic of the combustor’s natural frequency. As the temperature is reduced, the combustor jumps to fundamental mode and then to a low-frequency mode whose value is well below the combustor’s natural frequency, before eventually reaching blowoff. Similar to the case of CH4/air mixtures, the transition from one mode to another is predominantly a function of the Tad of the reactive mixture, despite significant differences in laminar burning velocity and/or strained flame consumption speed between air and oxy-fuel mixtures for a given Tad. High speed images support this finding by revealing similar vortex breakdown modes and thus similar turbulent flame geometries that change as a function of flame temperature.

Flow structures in a lean-premixed swirl-stabilized combustor with microjet air injection

The major challenge facing the development of low-emission combustors is combustion instability. By lowering flame temperatures, lean-premixed combustion has the potential to nearly eliminate emissions of thermally generated nitric oxides, but the chamber acoustics and heat release rate are highly susceptible to coupling in ways that lead to sustained, high-amplitude pressure oscillations, known as combustion instability. At different operating conditions, different modes of instability are observed, corresponding to particular flame shapes and resonant acoustic modes. Here we show that in a swirl-stabilized combustor, these instability modes also correspond to particular interactions between the flame and the inner recirculation zone. Two stable and two unstable modes are examined. At lean equivalence ratios, a stable conical flame anchors on the upstream edge of the inner recirculation zone and extends several diameters downstream along the wall. At higher equivalence ratios, with the injection of counter-swirling microjet air flow, another stable flame is observed. This flame is anchored along the upstream edge of a stronger recirculation zone, extending less than one diameter downstream along the wall. Without the microjets, a stationary instability coupled to the 1/4 wave mode of the combustor shows weak velocity oscillations and a stable configuration of the inner and outer recirculation zones. Another instability, coupled to the 3/4 wave mode of the combustor, exhibits periodic vortex breakdown in which the core flow alternates between a columnar mode and a vortex breakdown mode.

Precessing vortex breakdown mode in an enclosed cylinder flow

The flow in a cylinder driven by the rotation of one endwall for height to radius ratios around three is examined. Previous experimental observations suggest that the first mode of instability is a precession of the central vortex core, whereas a recent linear stability analysis to general three-dimensional perturbations suggests a Hopf bifurcation to a rotating wave at lower rotation rates than those where the precession mode was first detected. Here, this apparent discrepancy is resolved with the aid of fully nonlinear three-dimensional Navier–Stokes computations.

Numerical simulation and physical aspects of supersonic vortex breakdown

Existing numerical simulations and physical aspects of subsonic and supersonic vortex-breakdown modes are reviewed. The solution to the problem of supersonic vortex breakdown is emphasized in this paper and carried out with the full Navier—Stokes equations for compressible flows. Numerical simulations of vortex-breakdown modes are presented in bounded and unbounded domains. The effects of different types of downstream-exit boundary conditions are studied and discussed.

Free-Stream Turbulence and Concave Curvature Effects on Heated, Transitional Boundary Layers

An experimental investigation of transition in concave-curved boundary layers at two free-stream turbulence levels (0.6 and 8.6 percent) was performed. For the lower free-stream turbulence intensity case, Go¨rtler vortices were observed in both laminar and turbulent flows using liquid crystal visualization and spanwise velocity and temperature traverses. Transition is thought to occur via a vortex breakdown mode. The vortex locations were invariant with time but were nonuniform across the span in both the laminar and turbulent flows. The upwash regions between two vortices were more unstable than were the downwash regions, containing higher levels of u’ and u’ v’, and lower skin friction coefficients and shape factors. Turbulent Prandtl numbers, measured using a triple-wire probe, were near unity for all post-transitional profiles, indicating no gross violation of Reynolds analogy. No streamwise vortices were observed in the higher turbulence intensity case. This may be due to the high eddy viscosity, which reduces the turbulent Go¨rtler number to subcritical values, thus eliminating the vortices, or due to an unsteadiness of the vortex structure that could not be observed by the techniques used. Based upon these results, predictions that assume two-dimensional modeling of the flow over a concave wall with high free-stream turbulence levels, as on the pressure surface of a turbine blade, seem to be adequate—there is no time-average, three-dimensional structure to be resolved. High levels of free-stream turbulence superimposed on a free-stream velocity gradient (which occurs within curved channels) cause a cross-stream transport of momentum within the flow outside the boundary layer. The total pressure within this region can rise above the value measured at the inlet to the test section.