The structural sensitivity of open shear flows calculated with a local stability analysis

Juniper, Matthew P.; Pier, Benoı̂t

doi:10.1016/j.euromechflu.2014.05.011

Cited by 33 publications

(62 citation statements)

References 30 publications

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“…To reduce the numerical effort, the stability problem (3) is first solved locally and the global stability properties are thereafter deduced from the local stability properties. The same approach has recently been adopted in several related studies dealing with swirling and non-swirling wake flows [34,36,[40][41][42]61,62]. A local eigenvalue problem is posed by adopting a quasi parallel, axially symmetric velocity profile…”

Section: Determining the Global Instabilitymentioning

confidence: 99%

Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: Experiments and linear stability analysis

Oberleithner

Stöhr

et al. 2015

Combustion and Flame

198

164

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a b s t r a c tThe precessing vortex core (PVC) is a coherent flow structure that is often encountered in swirling flows in gas turbine (GT) combustors. In some swirl combustors, it has been observed that a PVC is present under non-reacting conditions but disappears in the corresponding reacting cases. Since numerous studies have shown that a PVC has strong effects on the flame stabilization, it is desirable to understand the formation and suppression of PVCs in GT combustors. The present work experimentally studies the flow field in a GT model combustor at atmospheric pressure. Whereas all non-reacting conditions and detached M-shaped flames exhibit a PVC, the PVC is suppressed for attached V-shaped flames. A local linear stability analysis is then applied to the measured time-averaged velocity and density fields. For the cases where a PVC appeared in the experiment, the analysis shows a global hydrodynamic instability that manifests in a single-helical mode with its wavemaker located at the combustor inlet. The frequency of the global mode is in excellent agreement with the measured oscillation frequency and the growth rate is approximately zero, indicating the marginally stable limit-cycle. For the attached V-flame without PVC, strong radial density/temperature gradients are present at the inlet, which are shown to suppress the global instability. The interplay between the PVC and the flame is further investigated by considering a bi-stable case with intermittent transitions between V-and M-flame. The flame and flow transients are investigated experimentally via simultaneous highspeed PIV and OH-PLIF. The experiments reveal a sequence of events wherein the PVC forms prior to the transition of the flame shape. The results demonstrate the essential role of the PVC in the flame stabilization, and thereby the importance of a hydrodynamic stability analysis in the design of a swirl combustor.

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Section: Determining the Global Instabilitymentioning

confidence: 99%

Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: Experiments and linear stability analysis

Oberleithner

Stöhr

et al. 2015

Combustion and Flame

198

164

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“…A formal link between the two concepts was established in Juniper & Pier (2014). Here, we have shown that the global mode wavemaker of the Turbomeca flow lies inside the nozzle.…”

Section: Relation To Local Stability Analyses In Swirling Jets and Inmentioning

confidence: 99%

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

2016

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The large-scale coherent motions in a realistic swirl fuel injector geometry are analysed by direct numerical simulations (DNS), proper orthogonal decomposition (POD), and linear global modes. The aim is to identify the origin of instability in this turbulent flow in a complex internal geometry.The flow field in the nonlinear simulation is highly turbulent, but with a distinguishable coherent structure: the precessing vortex core (a spiraling mode).The most energetic POD mode pair is identified as the precessing vortex core. By analysing the FFT of the time coefficients of the POD modes, we conclude that the first four POD modes contain the coherent fluctuations. The remaining POD modes (incoherent fluctuations) are used to form a turbulent viscosity field, using the Newtonian eddy model.The turbulence sets in from convective shear layer instabilities even before the nonlinear flow reaches the other end of the domain, indicating that equilibrium solutions of the Navier-Stokes are never observed. Linear global modes are computed around the mean flow from DNS, applying the turbulent viscosity extracted from POD modes. A slightly stable discrete m = 1 eigenmode is found, well separated from the continuous spectrum, in very good agreement with the POD mode shape and frequency. The structural sensitivity of the precessing vortex core is located upstream of the central recirculation zone, identifying it as a spiral vortex breakdown instability in the nozzle. Furthermore, the structural sensitivity indicates that the dominant instability mechanism is the KelvinHelmholtz instability at the inflection point forming near vortex breakdown. Adjoint modes are strong in the shear layer along the whole extent of the nozzle, showing that the optimal initial condition for the global mode is localized in the shear layer.We analyse the qualitative influence of turbulent dissipation in the stability problem (eddy viscosity) on the eigenmodes by comparing them to eigenmodes computed without eddy viscosity. The results show that the eddy viscosity improves the complex frequency and shape of global modes around the fuel injector mean flow, while a qualitative wavemaker position can be obtained with or without turbulent dissipation, in agreement with previous studies.This study shows how sensitivity analysis can identify which parts of the flow in a complex geometry need to be altered in order to change its hydrodynamic stability characteristics.Key Words: † Email address for correspondence: outi-leena.tammisola@nottingham.ac.uk , and the exit velocity from the swirler (U E ). The coordinate system is also defined: the origin is at the centerline at the swirler exit location. The relative dimensions of the geometry are the same as in the numerical simulation, except that the numerical domain is longer in the downstream direction.

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“…Figure 8(b) shows the structural sensitivity based on the local stability analysis where the global adjoint modes were reconstructed from the local analysis data according to Ref. [13]. Like in the global analysis, the region of highest structural sensitivity is located at the exit of the primary injector.…”

Section: Resultsmentioning

confidence: 99%

“…Adjoint methods based on global stability analysis give valuable insight into the internal feedback of hydrodynamic instability mechanisms. Juniper and Pier [13], for example, used structural sensitivity analysis to find the location of highest sensitivity to changes in the internal feedback mechanism of a confined co-flow wake and a cylinder wake, using both local and global stability analysis. Recently, Tammisola and Juniper [14] used global stability analysis on the mean flow in the interior of a fuel injector.…”

Section: Introductionmentioning

confidence: 99%

Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

Kaiser

Poinsot

Oberleithner

2017

Volume 4A: Combustion, Fuels and Emissions

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The structural sensitivity of open shear flows calculated with a local stability analysis

Cited by 33 publications

References 30 publications

Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: Experiments and linear stability analysis

Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: Experiments and linear stability analysis

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

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