Many industrial combustion systems, especially power generation gas turbines, use fuel-lean combustion to reduce NOx emissions. However, these systems are highly susceptible to combustion instability, the coupling between combustor acoustics and heat release rate oscillations of the flame. It has been shown in previous work by the authors that a precessing vortex core (PVC) can suppress shear layer receptivity to external perturbations, reducing the potential for thermoacoustic coupling. The goal of this study is to understand the effect of combustor exit boundary condition on the flow structure of a swirling jet to increase fundamental understanding of how combustor design impacts PVC dynamics. The swirling jet is generated with a radial-entry, variable-angle swirler, and a quartz cylinder is fixed on the dump plane for confinement. Combustor exit constriction plates of different diameters are used to determine the impact of exit boundary condition on the flow field. Particle image velocimetry (PIV) is used to capture the velocity field inside the combustor. Spectral proper orthogonal decomposition, a frequency-resolved eigenvalue decomposition that can identify energetic structures in the flow, is implemented to identify the PVC at each condition in both energy and frequency space. We find that exit boundary diameter affects both the structure of the flow and the dynamics of the PVC. Higher levels of constriction (smaller diameters) force the downstream stagnation point of the vortex breakdown bubble upstream, resulting in greater divergence of the swirling jet. Further, as the exit diameter decreases, the PVC becomes less energetic and less spatially defined. Despite these changes in the base flow and PVC coherence, the PVC frequency is not altered by the exit boundary constriction. These trends will help inform our understanding of the impact of boundary conditions on both static and dynamic flame stability.
more »
« less
A weakly nonlinear analysis of the precessing vortex core oscillation in a variable swirl turbulent round jet
We study the emergence of precessing vortex core (PVC) oscillations in a swirling jet experiment. We vary the swirl intensity while keeping the net mass flow rate fixed using a radial-entry swirler with movable blades upstream of the jet exit. The swirl intensity is quantified in terms of a swirl number $S$ . Time-resolved velocity measurements in a radial–axial plane anchored at the jet exit for various $S$ values are obtained using stereoscopic particle image velocimetry. Spectral proper orthogonal decomposition and spatial cross-spectral analysis reveal the simultaneous emergence of a bubble-type vortex breakdown and a strong helical limit-cycle oscillation in the flow for $S>S_{c}$ where $S_{c}=0.61$ . The oscillation frequency, $f_{PVC}$ , and the square of the flow oscillation amplitudes vary linearly with $S-S_{c}$ . A solution for the coherent unsteady field accurate up to $O(\unicode[STIX]{x1D716}^{3})$ ( $\unicode[STIX]{x1D716}\sim O((S-S_{c})^{1/2})$ ) is determined from the nonlinear Navier–Stokes equations, using the method of multiple scales. We show that onset of bubble type vortex breakdown at $S_{c}$ , results in a marginally stable, helical linear global hydrodynamic mode. This results in the stable limit-cycle precession of the breakdown bubble. The variation of $f_{LC}$ with $S-S_{c}$ is determined from the Stuart–Landau equation associated with the PVC. Reasonable agreement with the corresponding experimental result is observed, despite the highly turbulent nature of the flow in the present experiment. Further, amplitude saturation results from the time-averaged distortion imposed on the flow by the PVC, suggesting that linear stability analysis may predict PVC characteristics for $S>S_{c}$ .
more »
« less
- Award ID(s):
- 1749679
- NSF-PAR ID:
- 10166443
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 884
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Theoretical predictions and numerical simulations are used to determine the transition to bubble and conical vortex breakdown in low-Mach-number laminar axisymmetric variable-density swirling jets. A critical value of the swirl number $S$ for the onset of the bubble ( $S^*_B$ ) and the cone ( $S^*_C$ ) is determined as the jet-to-ambient density ratio $\varLambda$ is varied, with the temperature dependence of the gas density and viscosity appropriate to that of air. The criterion of failure of the slender quasi-cylindrical approximation predicts $S^*_B$ that decreases with increasing values of $\varLambda$ for a jet in solid-body rotation emerging sharply into a quiescent atmosphere. In addition, a new criterion for the onset of conical breakdown is derived from divergence of the initial value of the radial spreading rate of the jet occurring at $S^*_C$ , found to be independent of $\varLambda$ , in an asymptotic analysis for small distances from the inlet plane. To maintain stable flow in the unsteady numerical simulations, an effective Reynolds number $Re_{eff}$ , defined employing the geometric mean of the viscosity in the jet and ambient atmosphere, is fixed at $Re_{eff}=200$ for all $\varLambda$ . Similar to the theoretical predictions, numerical calculations of $S^*_B$ decrease monotonically as $\varLambda$ is increased. The critical swirl numbers for the cone, $S^*_C$ , are found to depend strongly on viscous effects; for $\varLambda =1/5$ , the low jet Reynolds number (51) at $Re_{eff}=200$ delays the transition to the cone, while for $\varLambda =5$ at $Re_{eff}=200$ , the large increase in kinematic viscosity in the external fluid produces a similar trend, significantly increasing $S^*_C$ .more » « less
-
Lifting line theory describes the cumulative effect of shed vorticity from finite span lifting surfaces. In this work, the theory is reformulated to improve the accuracy of the actuator line model (ALM). This model is a computational tool used to represent lifting surfaces, such as wind-turbine blades in computational fluid dynamics. In ALM, blade segments are represented by means of a Gaussian body force distribution with a prescribed kernel size. Prior analysis has shown that a representation of the blade using an optimal kernel width $\unicode[STIX]{x1D716}^{opt}$ of approximately one quarter of the chord size results in accurate predictions of the velocity field and loads along the blades. Also, simulations have shown that use of the optimal kernel size yields accurate representation of the tip-vortex size and the associated downwash resulting in accurate predictions of the tip losses. In this work, we address the issue of how to represent the effects of finite span wings and tip vortices when using Gaussian body forces with a kernel size larger than the optimal value. This question is relevant in the context of coarse-scale large-eddy simulations that cannot afford the fine resolutions required to resolve the optimal kernel size. For this purpose, we present a filtered lifting line theory for a Gaussian force distribution. Based on the streamwise component of the vorticity transport equation, we develop an analytical model for the induced velocity resulting from the spanwise changes in lift force for an arbitrary kernel scale. The results are used to derive a subfilter-scale velocity model that is used to correct the velocity along the blade when using kernel sizes larger than $\unicode[STIX]{x1D716}^{opt}$ . Tests are performed in large-eddy simulation of flow over fixed wings with constant and elliptic chord distributions using various kernel sizes. Results show that by using the proposed subfilter velocity model, kernel-size independent predictions of lift coefficient and total lift forces agree with those obtained with the optimal kernel size.more » « less
-
Global instabilities in swirling flows can significantly alter the flame and flow dynamics of swirl-stabilized flames, such as those in modern gas turbine engines. In this study, we characterize the interaction between the precessing vortex core (PVC), which is the consequence of a global hydrodynamic instability, and thermoacoustic instabilities, which are the result of a coupling between combustor acoustics and the unsteady heat release rate. This study is performed using experimental data obtained from a model gas turbine combustor employing two concentric swirling nozzles of air, separated by a ring of fuel injectors, operating at five bar pressure. The flow split between the two streams is systematically varied to observe the impact of flow structure variation on the system dynamics at both non-reacting and reacting conditions. High-speed stereoscopic particle image velocimetry, OH planar laser-induced fluorescence and acetone planar laser-induced fluorescence are used to obtain information about the velocity fields, flame and fuel flow behaviour, respectively. Spectral proper orthogonal decomposition and a complex network analysis are used to identify and characterize the dominant oscillation mechanisms driving the system. In the non-reacting data, a PVC is present in most cases and the amplitude of the oscillation increases with increasing flow through the centre nozzle. In the reacting data, three dominant modes are seen: two thermoacoustic modes and the PVC. Our results show that in the cases where the frequency of the PVC overlaps with either of the thermoacoustic modes, the thermoacoustic modes are suppressed. The complex network analysis coupled with a weakly nonlinear theoretical analysis suggests the mechanisms by which this coupling and suppression of the thermoacoustic mode occur.more » « less
-
Precessing vortex cores (PVC), arising from a global instability in swirling flows, can dramatically alter the dynamics of swirl-stabilized flames. Previous study of these instabilities has identified their frequencies and potential for interaction with the shear layer instabilities also present in swirling flows. In this work, we investigate the dynamics of precessing vortex cores at a range of swirl numbers and the impact that turbulence, which tends to increase with swirl number due to the increase in mean shear, has on the dynamics of this instability. This is particularly interesting as stability predictions have previously incorporated turbulence effects using an eddy viscosity model, which only captures the impact of turbulence on the base flow, not on the instantaneous dynamics of the PVC itself. Time-resolved experimental measurements of the three-component velocity field at ten swirl numbers show that at lower swirl numbers, the PVC is affected by turbulence through the presence of vortex jitter. With increasing swirl number, the PVC jitter decreases as the PVC strength increases. There is a critical swirl number below which jitter of the PVC vortex monotonically increases with increasing swirl number, and beyond which the jitter decreases, indicating that the strength of the PVC dominates over turbulent fluctuations at higher swirl numbers, despite the fact that the turbulence intensities continue to rise with increasing swirl number. Further, we use a nonlinear van der Pol oscillator model to explain the competition between the random turbulent fluctuations and coherent oscillations of the PVC. The results of this work indicate that while both the strength of the PVC and magnitude of turbulence intensity increase with increasing swirl number, there are defined regimes where each of them hold a stronger influence on the large-scale, coherent dynamics of the flow field.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.903
