Swirling Jets Undergoing Vortex Breakdown Research Articles

Uncertainty quantification analysis of Reynolds-averaged Navier–Stokes simulation of spray swirling jets undergoing vortex breakdown

The computational fluid dynamics-based design of next-generation aeronautical combustion chambers is challenging due to many geometrical and operational parameters to be optimized and several sources of uncertainty that arise from numerical modeling. The present work highlights the potential benefits of exploiting Bayesian uncertainty quantification at the preliminary design stage. A prototypical configuration of an acetone/air spray swirling jet is investigated through an Eulerian–Lagrangian method under non-reactive conditions. Two direct numerical simulations (DNSs) provide reference data, coping with different vortex breakdown states. Consequently, a set of Reynolds-averaged Navier–Stokes simulations is conducted. Polynomial chaos expansion (PCE) is adopted to propagate the uncertainty associated with the spray dispersion model and the turbulent Schmidt number, delivering confidence intervals and the sensitivity of the output variance to each uncertain input. Consequently, the most significant sources of modeling uncertainty may be identified and eventually removed via a calibration procedure, thus making it possible to carry out a combustion chamber optimization process that is no longer affected by numerical biases. The uncertainty quantification analysis in the current study demonstrates that the spray dispersion model slightly affects the fuel vapor spatial distribution under vortex breakdown flow conditions, compared with the output variance induced by the selection of the turbulent Schmidt number. As a result, additional high-fidelity experimental and numerical campaigns should exclusively address the development of an ad hoc model characterizing the spatial distribution of the latter in the presence of vortex breakdown phenomenology, discarding any effort to improve the spray dispersion formulation.

Modeling capabilities of unsteady RANS for the simulation of turbulent swirling flow in an annular bluff-body combustor geometry

In this paper, we investigate the capabilities of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for capturing the helical structures found in a three-dimensional, incompressible and isothermal annular swirling jet undergoing vortex breakdown. The flow topology is representative of a bluff-body combustor operating at a Reynolds number Re = 8500 and swirl number S = 0.39. As a turbulence model, the SSG Reynolds stress model (RSM) was chosen. The numerical simulation is validated by means of tomographic particle image velocimetry measurements of the same flow configuration. To detect the coherent structures in the flow field, the recently introduced spectral proper orthogonal decomposition technique is adopted, which gives both temporal and spatial information on the large scale coherent structures. The spectral analysis of the sampled velocity signals identified a precessing vortex core with a frequency of 24.3 Hz. In particular, two different large-scale helical flow structures are identified: a single and a double helix. Both of them are wound in the counter-swirl direction and wrapped around the central breakdown bubble. Those findings are quite similar to recent experimental tomographic particle image velocimetry results (Vanierschot et al., Phys. Rev. Fluids (2018) & J. Fluid Mech. (2020)). This study demonstrates that the unsteady RANS approach with RSM is able to predict the coherent structures found in an annular swirling jet undergoing vortex breakdown both temporally and spatially with reasonable accuracy and this approach can hence be used in the design of bluff-body combustors, where a multi-dimensional parameter space may require many simulations to find the optimal design.

Single- and double-helix vortex breakdown as two dominant global modes in turbulent swirling jet flow

In this paper, we study the shape and dynamics of helical coherent structures found in the flow field of an annular swirling jet undergoing vortex breakdown. The flow field is studied by means of time-resolved tomographic particle image velocimetry measurements. The obtained flow fields are analysed using both classic and spectral proper orthogonal decomposition. Despite the simple geometrical set-up of the annular jet, the flow field is very complex. Two distinct large-scale helical flow structures are identified: a single and a double helix, both co-rotating with the swirl direction, and it is revealed that these structures are not higher harmonics of each other. The structures have a relatively low energy content which makes it hard to separate them from other dynamics of the flow field, notably turbulent motions. Because of this, classic proper orthogonal decomposition fails to identify both structures properly. Spectral proper orthogonal decomposition, on the other hand, allows them to be identified accurately when the filter size is set at around eight times the precession period. The precession frequencies of the single and double helices correspond to Strouhal numbers of 0.273 and , respectively. A global stability analysis of the mean flow field shows that these structures correspond to two separate global modes. The precessing frequencies obtained by the stability analysis and the related spatial structures match very well with the experimental observations. The current work extends our knowledge on turbulent vortex breakdown and on mean field global stability theory in general. It leads to the following conclusions. Firstly, single- and double-helix vortex breakdown are both manifestations of global modes. Previous studies have shown that both and modes can coexist in swirling jets. However, the mode has been identified as a second harmonic of the first mode, while this study identifies both as two independent global modes. Secondly, this work shows that the simultaneous occurrence of multiple helical global modes is possible within a turbulent flow and their shapes and frequencies are very well predicted by mean field stability analysis. The latter finding is of general interest as it applies to a wide class of fluid problems dominated by multiple oscillatory structures.

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.

Measurement of the fluctuating temperature field in a heated swirling jet with BOS tomography

This work investigates the potential of background-oriented schlieren tomography (3D-BOS) for the temperature field reconstruction in a non-isothermal swirling jet undergoing vortex breakdown. The evaluation includes a quantitative comparison of the mean and phase-averaged temperature field with thermocouple and fast-response resistance thermometer as well as a qualitative comparison between the temperature field and the flow field obtained from particle image velocimetry (PIV). Compared to other temperature-measuring techniques, 3D-BOS enables non-invasive capturing of the entire three-dimensional temperature field. In contrast to previous 3D-BOS applications, the present investigation makes use of the special character of the flow, which provides a global instability that leads to a rotational symmetry of the jet. Additionally, the rotational motion of the jet is used to obtain a tomographic reconstruction from a single camera. The quality of 3D-BOS results with respect to the physical setup as well as the numerical procedure is analyzed and discussed. Furthermore, a new approach for the treatment of thin occluding objects in the field of view is presented.

Transient evolution of the global mode in turbulent swirling jets: Experiments and modal stability analysis

Swirling jets undergoing vortex breakdown are dominated by a strong coherent structure that is characterized by a precessing vortex core and the large-scale roll-up of the shear layers. These fully synchronized flow dynamics play an important role for the stabilization of swirl flames commonly applied in gas-turbine combustion. It is now well accepted that these flow dynamics are the manifestation of a saturated global instability triggered by a hydrodynamic feedback loop. Yet, the origin of this instability is still discussed controversially. Nonlinear wavefront theory predict the global mode to be selected in the lee of the breakdown bubble, while linear local and global stability analysis predict the region upstream of the breakdown bubble to be more influential. In this work, we intend to clarify this controversy. We consider a turbulent swirling jet undergoing a control parameter transient. The flow undergoes a transition from a globally stable non-vortex breakdown state to a state with a strong recirculation bubble and the associated global mode. High-speed Particle Image Velocimetry measurements are the basis for a local linear stability analysis of the temporarily evolving base flow. This analysis reveals that the onset of the global mode is strongly linked to the formation of the internal stagnation point. Several transition scenarios are discussed and the ability of a frequency selection criterion to predict the wavemaker location, frequency and growth rate of the global mode are evaluated. We find excellent agreement between the linear global mode frequency and the experimental results throughout the entire transient. The corresponding growth rate qualitatively conforms to experimental observations. We find no indication for a global mode that is selected in the lee of the breakdown bubble. The present study confirms that the flow upstream of the vortex breakdown bubble is most influential for the onset of the global mode. Given that the flow under investigation is fully turbulent, these results provide important guidelines for the control of this instability mechanism in real scale combustion applications.

The impact of heating the breakdown bubble on the global mode of a swirling jet: Experiments and linear stability analysis

This study investigates the dynamics of non-isothermal swirling jets undergoing vortex breakdown, with an emphasis on helical coherent structures. It is proposed that the dominant helical coherent structure can be suppressed by heating the recirculation bubble. This proposition is assessed with stereo Particle Image Velocimetry (PIV) measurements of the breakdown region of isothermal and heated swirling jets. The coherent kinetic energy of the dominant helical structure was derived from PIV snapshots via proper orthogonal decomposition. For one set of experimental parameters, mild heating is found to increase the energy content of the dominant helical mode. Strong heating leads to a reduction by 30% of the coherent structures energy. For a second set of experimental parameters, no alteration of the dominant coherent structure is detectable. Local linear stability analysis of the time-averaged velocity fields shows that the key difference between the two configurations is the density ratio at the respective wavemaker location. A density ratio of approximately 0.8 is found to correlate to a suppression of the global mode in the experiments. A parametric study with model density and velocity profiles indicates the most important parameters that govern the local absolute growth rate: the density ratio and the relative position of the density profiles and the inner shear layer.

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

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 nonisothermal swirling jet to demonstrate the use of advanced data analysis techniques. In particular, the finite time Lyapunov exponent (FTLE) and the 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.

Effect of initial vortex core size on the coherent structures in the swirling jet near field

This study investigates the sensitivity to initial conditions of swirling jets undergoing vortex breakdown. Emphasis is placed on the recirculation bubble and on the helical coherent structures that evolve in its periphery. It is proposed that the vortex core size of the incoming swirling jet is the critical parameter that determines the dynamics of these coherent structures. This proposition is assessed with Stereo Particle-Image-Velocimetry (PIV) measurements of the breakdown region of two swirling jet configurations with different vortex core sizes at very similar overall swirl intensities. The swirling jets were generated by radial vanes entering a mixing tube, and the vortex core size was adjusted by using different center-body geometries. The time-averaged flow fields in the breakdown region reveal substantial differences in the jet spreading and the size of the recirculation bubble. Proper Ortogonal Decomposition (POD) was applied to the anti-axisymmetric and axisymmetric velocity fluctuations, to reconstruct the dynamics of the helical instability and the breakdown bubble, respectively. We find that the mode shape of the helical instability is not affected by the vortex core size. The frequency is found to coincide with the vortex core rotation rate, which relates inversely to the core size. The shape and dynamics of the non-periodic breakdown bubble are significantly affected by a change in vortex core size. The POD reveals that the energy content of the dominant non-periodic structure is changed markedly with the vortex core size. The bubble dynamics are further investigated by tracking the upstream stagnation point from the PIV snapshots. It is shown that a larger vortex core promotes smooth fluctuations of the recirculation bubble, while a small initial vortex core is linked to bimodal fluctuations of the recirculation bubble. The conclusions drawn from this study are relevant for fundamental swirling jet studies, as well as for the design of swirl-stabilized combustors, where the investigated coherent structures influence combustion performance.

Effects of boundary conditions on vortex breakdown in compressible swirling jet flow simulations

We investigate the sensitivity of numerical simulation results for swirling jet flows undergoing vortex breakdown to inflow and outflow boundary conditions. The compressible regime at Mach number Ma=0.6 and Reynolds number Re=5000 is considered. The swirl velocity is approximately of the same magnitude as the streamwise centreline velocity at inflow. We perform Large-Eddy Simulations using high-order discretization schemes in space and time. A rotating nozzle with isothermal wall is included in the computational domain. Six different combinations of inflow and outflow boundary conditions are investigated. These use a Dirichlet condition at the inflow supplemented with a sponge layer imposing up to five variables and a sponge layer at the outflow acting on several combinations of variables, applied together with non-reflecting boundary conditions. The advantages and drawbacks of each setup are investigated. The qualitative features of the swirling jet undergoing vortex breakdown are robust to changes in the inflow and outflow boundary conditions, i.e., conical shear-layers, a recirculation bubble, the existence of a single-helix type instability, and the occurrence of a dominant frequency, are all captured by combinations of the boundary conditions investigated. However, significant quantitative differences are observed depending on the conditions set at inflow and outflow. In particular, the locations of the stagnation points and the spreading angle of the swirling jet are strongly influenced. The size and shape of the recirculation bubble change as well, as does the intensity of the recirculation flow and of the counter-rotating motion observed at the jet centreline. The dominant frequency in the breakdown region also depends on the setup. As a result of this study, we recommend setting the three velocity components, density, and pressure at the inflow and outflow using sponge layers supplementing non-reflecting boundary conditions as the most suitable choice.

Global modes in a swirling jet undergoing vortex breakdown

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

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.

Response of unconfined vortex breakdown to axial pulsing

The response of unconfined swirling jets undergoing vortex breakdown to axial pulsing is explored experimentally. In particular, the combination of particle visualization and particle image velocimetry has enabled the effect of axial pulsing on the development of shear-layer flow structures and vortex breakdown to be quantified, as a function of both pulsing frequency and amplitude. A range of Reynolds and swirl numbers is considered. A key result is that application of low-level forcing at the natural frequency intensifies the shear-layer vortices considerably and results in a substantial relative downstream shift of the mean breakdown position.