Ensemble-LES analysis of perturbation response of turbulent partially-premixed flames

Hassanaly, Malik; Raman, Venkat

doi:10.1016/j.proci.2018.06.209

Cited by 28 publications

(13 citation statements)

References 38 publications

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“…The interplay between these contrasting features leads to significant spatio-temporal complexity [4,5,16,17], from intermittent disorder, through to chaos and turbulence: "turbulence" in the Kuramoto-Sivashinsky PDE is typically described as weak, incipient or localized, rather than fully turbulent; however, this regime provides mathematical insights into the transition from dynamical chaos to true turbulence [17,24]. Lyapunov exponents characterize this chaos and turbulence [8,27,34], and are increasingly used to analyse such spatio-temporal complexity in various applications such as turbulent Poiseuille flow [19], turbulence in flames [14] and Rayleigh-Bérnard fluid convection [2,36].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov Exponents of the Kuramoto–sivashinsky Pde

Edson¹,

Bunder²,

Mattner³

et al. 2019

ANZIAM J.

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The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan–Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto–Sivashinsky PDE, and the transition to its one-dimensional turbulence.

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Section: Introductionmentioning

confidence: 99%

Lyapunov Exponents of the Kuramoto–sivashinsky Pde

Edson¹,

Bunder²,

Mattner³

et al. 2019

ANZIAM J.

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“…Chaotic systems naturally appear in many branches of science and engineering, from turbulent flows [e.g., 1, 2, 3], through vibrations [4], electronics and telecommunications [5], quantum mechanics [6], reacting flows [7,8], to epidemic modelling [9], to name only a few. The time-accurate computation of chaotic systems is hindered by the "butterfly effect" [10]: an error in the system's knowledge-e.g, initial conditions and parameters-grows exponentially until nonlinear saturation.…”

Section: Introductionmentioning

confidence: 99%

Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics

Racca¹,

Magri²

2021

Preprint

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The time-accurate prediction of a chaotic system is challenging because its evolution becomes unpredictable after the predictability time. This is because infinitesimal errors in a chaotic system increase exponentially, i.e., two nearby time series diverge from each other. An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the predictability time. Existing studies, however, also showed that small changes in the hyperparameters may markedly affect the network's performance. The overarching aim of this paper is to assess and improve the robustness of Echo State Networks for the time-accurate prediction of chaotic solutions. The goal is three-fold. First, we investigate the robustness of routinely used validation strategies. Second, we propose the Recycle Validation, and the chaotic versions of existing validation strategies, to specifically tackle the forecasting of chaotic systems. Third, we compare Bayesian optimization with the traditional Grid Search for optimal hyperparameter selection. Numerical tests are performed on two prototypical nonlinear systems that have both chaotic and quasiperiodic solutions. Both model-free and model-informed Echo State Networks are analysed. By comparing the network's robustness in learning chaotic (unpredictable) versus quasiperiodic (predictable) solutions, we highlight fundamental challenges in learning chaotic solutions.The proposed validation strategies, which are based on the dynamical systems properties of chaotic time series, are shown to outperform the state-of-the-art validation strategies. Because the strategies are principled-they are based on chaos theory such as the Lyapunov time-they can be applied to other Recurrent Neural Networks architectures with little modification. This work opens up new possibilities for the robust design and application of Echo State Networks, and Recurrent Neural Networks, to the time-accurate prediction of chaotic systems.

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“…In statistically stationary flows, it is hypothesized that the trajectory followed by the flow in this high-dimensional state space is confined to a low-dimensional subspace. There have been many attempts to characterize the size of this subspace [35][36][37]39,40 . While theoretical scaling suggests that the manifold dimension will increase as Re n , where n > 2, in statistically stationary turbulence 38 , more recent numerical studies have concluded that the manifold may be lower dimensional.…”

Section: Introductionmentioning

confidence: 99%

“…While theoretical scaling suggests that the manifold dimension will increase as Re n , where n > 2, in statistically stationary turbulence 38 , more recent numerical studies have concluded that the manifold may be lower dimensional. For instance, application to the Sandia flame series 40 showed that the dimension is much smaller than the degrees of freedom generated by discretization.…”

Section: Introductionmentioning

confidence: 99%

Using approximate inertial manifold approach to model turbulent non-premixed combustion

Akram,

Raman

2021

Preprint

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The theory of inertial manifolds (IM) is used to develop reduced-order models of turbulent combustion. In this approach, the dynamics of the system are tracked in a low-dimensional manifold determined in-situ without invoking laminar flame structures or statistical assumptions about the underlying turbulent flow. The primary concept in approximate IM (AIM) is that slow dominant dynamical behavior of the system is confined to a low-dimension manifold, and fast dynamics respond to the dynamics on the IM instantaneously. Decomposition of slow/fast dynamics and formulation of an AIM is accomplished by only exploiting the governing equations.Direct numerical simulations (DNS) of initially non-premixed fuel-air mixtures developing in forced isotropic turbulence have been carried out to investigate the proposed model. Reaction rate parameters are varied to allow for varying levels of extinction and reignition. The AIM performance in capturing different flame behaviors is assessed both a priori and a posteriori. It is shown that AIM captures the dynamics of the flames including extinction and reignition. Moreover, AIM provides scalar dissipation rate, mixing time for reactive scalars, and closures for nonlinear terms without any additional modeling. The AIM formulation is found promising, and provides a new approach to modeling turbulent combustion.

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Ensemble-LES analysis of perturbation response of turbulent partially-premixed flames

Cited by 28 publications

References 38 publications

Lyapunov Exponents of the Kuramoto–sivashinsky Pde

Lyapunov Exponents of the Kuramoto–sivashinsky Pde

Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics

Using approximate inertial manifold approach to model turbulent non-premixed combustion

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