Prediction of frequencies in thermosolutal convection from mean flows

Turton, Sam E.; Tuckerman, Laurette S.; Barkley, Dwight

doi:10.1103/physreve.91.043009

Cited by 76 publications

(165 citation statements)

References 26 publications

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“…A similar argument based on the relative amplitude of the second harmonic has been emphasized by several authors, for example Sipp & Lebedev (2007). In the present study, we have verified a posteriori that the second harmonic is invisible among the broadband turbulent spectrum, and hence we conclude similarly to Turton et al (2015) that N 1 O( 2 ) in this flow. Now, for mean flow stability to reproduce the fundamental limit cycle, the broadband turbulent motions still need to satisfy Au m,1 = u u .…”

Section: Interpretation Of Stability Analysis Around a Turbulent Meansupporting

confidence: 71%

“…As noted by Turton et al (2015), we observe that the fundamental mode m is then an exact eigenmode of the Navier-Stokes operator linearised around the mean flow:…”

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

“…Neverthless, a qualitative mathematical and physical interpretation of mean flow stability results and qualitative criteria for their validity can be found. The argument below follows the main lines presented in Turton et al (2015). In the present study, a triple decomposition of the flow field is introduced following Reynolds & Hussain (1972):…”

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

“…(The first option is actually a special case of the second one, obtained where A = 0.) To relate the above constraints into qualitative properties of a flow model, we proceed similarly to Turton et al (2015), who pointed out that if the amplitude of the fundamental mode is ||u m,1 || = , the harmonics often decay as u m,n ∝ O( n ). If this is the case, then …”

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

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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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Section: Interpretation Of Stability Analysis Around a Turbulent Meansupporting

confidence: 71%

“…As noted by Turton et al (2015), we observe that the fundamental mode m is then an exact eigenmode of the Navier-Stokes operator linearised around the mean flow:…”

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

Section: Interpretation Of Stability Analysis Around a Turbulent Meanmentioning

confidence: 99%

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

2016

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“…In the present study, we reformulate the self-consistent model in the frequency domain to account for the stochastic nonlinear response to a band-limited δ-correlated white noise. The results aim at clarifying whether the nonlinear stochastic response can be well approximated linearly in the frequency domain and the role of the Reynolds stress and the mean flow distortion in the saturation mechanism, as discussed in the literature [29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

Mantič-Lugo

Gallaire

2016

Phys. Rev. Fluids

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Selective noise amplifiers are characterized by large linear amplification to external perturbations in a particular frequency range despite their global linear stability. Applying a stochastic forcing with increasing amplitude, the response undergoes a strong nonlinear saturation when compared to the linear estimation. Building upon our previous work, we introduce a predictive model that describes this nonlinear dynamics, and we apply it to a canonical example of selective noise amplifiers: the backward-facing step flow. Rewriting conveniently the stochastic forcing and response in the frequency domain, the model consists in a mean flow equation coupled to the linear response to forcing at each frequency. This coupling is attained by the Reynolds stress, which is constructed by the integral in frequency of the independent responses. We generalize the model for a response to a white noise forcing δ-correlated in space and time restricting the flow dynamics to its most energetic patterns calculated from the optimal harmonic forcing and response of the flow. The model estimates accurately the response saturation when compared to direct numerical simulations, and it correctly approximates the structure of the response and the mean flow modification. It also shows that the response undergoes a selective process governed by the nonlinear gain, which promotes a response structure with an approximately single frequency and wavelength in the whole domain. These results suggest that the mean flow modification by the Reynolds stress is the key nonlinearity in the saturation process of the response to white noise.

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Special issue on global flow instability and control

Theofilis

Colonius

2017

Theor. Comput. Fluid Dyn.

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This special issue is the second on the topic of "Global Flow Instability and Control," following the first in 2011. As with the previous special issue, the participants of the last two symposia on Global Flow Instability and Control, held in Crete, Greece, were invited to submit publications. These papers were peer reviewed according to the standards of the journal, and this issue represents a snapshot of the progress since 2011. In this preface, a sampling of important developments in the field since the first issue is discussed. A synopsis of the papers in this issue is given in that context.

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Prediction of frequencies in thermosolutal convection from mean flows

Cited by 76 publications

References 26 publications

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

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

Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

Special issue on global flow instability and control

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