Stochastic modelling of a noise-driven global instability in a turbulent swirling jet

Sieber, Moritz; Paschereit, Christian Oliver; Oberleithner, Kilian

doi:10.1017/jfm.2021.133

Cited by 16 publications

(20 citation statements)

References 70 publications

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“…More recently, this framework was further developed and used for the analysis of global hydrodynamic instabilities in turbulent flows (e.g. Lee et al 2019;Callaham et al 2021;Sieber, Paschereit & Oberleithner 2021).…”

Section: Langevin Equation For the State Variablesmentioning

confidence: 99%

Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries

et al. 2022

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This article deals with the symmetry breaking of azimuthal thermoacoustic modes in annular combustors. Using a nominally symmetric annular combustor, we present experimental evidence of a predicted spontaneous reflectional symmetry breaking, and also an unexpected explicit rotational symmetry breaking in the neighbourhood of the Hopf bifurcation which separates linearly stable azimuthal thermoacoustic modes from self-oscillating modes. We derive and solve a multidimensional Fokker–Planck equation to unravel a unified picture of the phase space topology. We demonstrate that symmetric probability density functions of the thermoacoustic state vector are elusive, because the effect of asymmetries, even imperceptible ones, is magnified close to the bifurcation. This conclusion implies that the thermoacoustic oscillations of azimuthal modes in real combustors will systematically exhibit a statistically dominant orientation of the mode in the vicinity of the Hopf bifurcation.

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Section: Langevin Equation For the State Variablesmentioning

confidence: 99%

Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries

et al. 2022

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“…Hence, the stochastic characteristics of the turbulence make an accurate long-term prediction with a deterministic model impossible. The deviations from constant amplitude (limit-cycle) oscillations are similarly observed for an isolated global instability in a turbulent flow [ 17 , 36 ]. There, the deviations from the limit-cycle are explained by turbulent perturbations and related to the turbulence intensity.…”

Section: Application To Experimental Datamentioning

confidence: 82%

“…This approach does not improve the predictive capabilities of the model since it only adds random perturbations. However, it allows better reproduction of the average statistics [ 36 ]. In this context, it should be noted that, although the perturbations can be considered as additive random forcing for modelling purposes, in the experimental data they are not filtered out by the decomposition.…”

Section: Application To Experimental Datamentioning

confidence: 99%

“…This work presents a generic approach, which uses a two-stage cross-validation procedure for identifying a low-dimensional system to represent deterministic flow dynamics, to obtain a robust and accurate ROM. This is different form related investigations that use a statistical approach to separate the deterministic and stochastic dynamics in the data [ 17 , 36 ]. The latter relies on the evaluation of probability density functions of the state variables to infer a stochastic state space model.…”

Section: Introductionmentioning

confidence: 95%

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Towards robust data-driven reduced-order modelling for turbulent flows: application to vortex-induced vibrations

Schubert

Sieber

Oberleithner

et al. 2022

Theor. Comput. Fluid Dyn.

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This work presents a robust method that minimises the impact of user-selected parameter on the identification of generic models to study the coherent dynamics in turbulent flows. The objective is to gain insight into the flow dynamics from a data-driven reduced order model (ROM) that is developed from measurement data of the respective flow. For an efficient separation of the coherent dynamics, spectral proper orthogonal decomposition (SPOD) is used, projecting the flow field onto a low-dimensional subspace, so that the dominating dynamics can be represented with a minimal number of modes. A function library is defined using polynomial combinations of the temporal modal coefficients to describe the flow dynamics with a system of nonlinear ordinary differential equations. The most important library functions are identified in a two-stage cross-validation procedure (conservative and restrictive sparsification) and combined in the final model. In the first stage, the process uses a simple approximation of the derivative to match the model with the data. This stage delivers a reduced set of possible library function candidates for the model. In the second, more complex stage, the model of the entire flow is integrated over a short time and compared with the progression of the measured data. This restrictive stage allows a robust identification of nonlinearities and modal interactions in the data and their representation in the model. The method is demonstrated using data from particle image velocimetry (PIV) measurements of a circular cylinder undergoing vortex-induced vibration (VIV) at $$\mathrm{Re}=4000$$ Re = 4000 . It delivers a reduced order model that reproduces the average dynamics of the flow and reveals the interaction of coexisting flow dynamics by the model structure.

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“…This is a straightforward extension of the 1-dimensional SLE which involves memory effects. It has also been discussed in, e.g., references [6,25,26,27,10,28,29,30,31], which include applications in various fields. In many of these works, the noise component is an Ornstein-Uhlenbeck (OU) process which means that the drift function is linear and the diffusion function is constant (additive noise).…”

Section: Introductionmentioning

confidence: 99%

Efficient Bayesian estimation of a non-Markovian Langevin model driven by correlated noise

Willers¹,

Kamps²

2022

Preprint

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Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin equation, memory effects can be implemented through an additional hidden component which functions as correlated noise, thus resulting in a non-Markovian model. It can

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Stochastic modelling of a noise-driven global instability in a turbulent swirling jet

Abstract: Abstract

Cited by 16 publications

References 70 publications

Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries

Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries

Towards robust data-driven reduced-order modelling for turbulent flows: application to vortex-induced vibrations

Efficient Bayesian estimation of a non-Markovian Langevin model driven by correlated noise

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