1,721,065 research outputs found
Stability, sensitivity and optimisation of chaotic acoustic oscillations
Full text linkIn an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic oscillations, also known as thermoacoustic instabilities, can cause large vibrations up to structural failure. Numerical and experimental studies showed that thermoacoustic oscillations can be chaotic. It is not yet known, however, how to minimise such chaotic oscillations. We propose a strategy to analyse and minimise chaotic acoustic oscillations, for which traditional stability and sensitivity methods break down. We investigate the acoustics of a nonlinear heat source in an acoustic resonator. First, we propose covariant Lyapunov analysis as a tool to calculate the stability of chaotic acoustics, making connections with eigenvalue and Floquet analyses. We show that covariant Lyapunov analysis is the most general flow stability tool. Second, covariant Lyapunov vector analysis is applied to a chaotic system. The time-averaged acoustic energy is investigated by varying the heat-source parameters. Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as well as discontinuities in the time-averaged acoustic energy. Third, we embed sensitivities of the time-averaged acoustic energy in an optimisation routine. This procedure achieves a significant reduction in acoustic energy and identifies the bifurcations to chaos. The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. The techniques presented can be used in other unsteady fluid-dynamics problems with virtually no modification
Convolutional Autoencoder for the Spatiotemporal Latent Representation of Turbulence
No full textTurbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices or large-scale modes, which can help obtain a latent description of turbulent flows. However, current approaches are often limited by either the need to use some form of thresholding on quantities defining the isosurfaces to which the flow structures are associated or the linearity of traditional modal flow decomposition approaches, such as those based on proper orthogonal decomposition. This problem is exacerbated in flows that exhibit extreme events, which are rare and sudden changes in a turbulent state. The goal of this paper is to obtain an efficient and accurate reduced-order latent representation of a turbulent flow that exhibits extreme events. Specifically, we employ a three-dimensional multiscale convolutional autoencoder (CAE) to obtain such latent representation. We apply it to a three-dimensional turbulent flow. We show that the Multiscale CAE is efficient, requiring less than 10% degrees of freedom than proper orthogonal decomposition for compressing the data and is able to accurately reconstruct flow states related to extreme events. The proposed deep learning architecture opens opportunities for nonlinear reduced-order modeling of turbulent flows from data.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Aerodynamic
Data-Driven Stability Analysis of a Chaotic Time-Delayed System
Full text linkSystems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is time-delayed. The stability analysis is based only on data. We employ the echo state network (ESN), a type of recurrent neural network, and train it on timeseries of a prototypical time-delayed nonlinear thermoacoustic system. By running the trained ESN autonomously, we show that it can reproduce (i) the long-term statistics of the thermoacoustic system’s variables, (ii) the physical portion of the Lyapunov spectrum, and (iii) the statistics of the finite-time Lyapunov exponents. This work opens up the possibility to infer stability properties of time-delayed systems from experimental observations
Statistical Prediction of Extreme Events from Small Datasets
Full text linkWe propose Echo State Networks (ESNs) to predict the statistics of extreme events in a turbulent flow. We train the ESNs on small datasets that lack information about the extreme events. We asses whether the networks are able to extrapolate from the small imperfect datasets and predict the heavy-tail statistics that describe the events. We find that the networks correctly predict the events and improve the statistics of the system with respect to the training data in almost all cases analysed. This opens up new possibilities for the statistical prediction of extreme events in turbulence
Sound Generation in Multicomponent Nozzle Flows With Dissipation
No full textLow emission aircraft engines burn in a lean regime, which makes the combustor susceptible to unsteady combustion. Along with improper mixing and air cooling, the unsteady combustion process gives rise to flow inhomogeneities. The acceleration of these inhomogeneities in the nozzle downstream of the combustor generates indirect combustion noise. If the acoustic waves that are reflected off the nozzle are sufficiently in phase with the heat released by the flame, thermoacoustic instabilities can occur. The generation and transmission of sound through the nozzle guide vane are typically modeled with a compact and isentropic nozzle model. Because the flow is non-isentropic due to losses from wall friction and recirculation zones, in the literature, a mismatch is observed between experimental and theoretical predictions in subsonic-choked regimes. In this work, we propose a low-order physical model to predict indirect noise in a multicomponent nozzle flow with dissipation using conservation laws whilst modeling non-isentropicity using a friction factor. The model is generalized for finite-length (non-compact) arbitrary geometry nozzles. We show that the friction factor can account for wall friction and two (or three) dimensional effects, such as flow recirculation in a cross-averaged sense. We analyze the model numerically for both subsonic and supersonic nozzles, emphasizing the importance of non-isentropic and non-compact assumptions with compositional inhomogeneities. Further, we show the effect of the nozzle geometry. The results are validated with existing experimental data from the literature
Data-driven computation of adjoint sensitivities without adjoint solvers: An application to thermoacoustics
Full text linkAdjoint methods have been the pillar of gradient-based optimization for decades. They
enable the accurate computation of a gradient (sensitivity) of a quantity of interest with
respect to all system parameters in one calculation. When the gradient is embedded in an
optimization routine, the quantity of interest can be optimized for the system to have the
desired behavior. Adjoint methods, however, require the system’s governing equations and
their Jacobian. In this paper, we propose a computational strategy to infer the adjoint sensitivities from data when the governing equations might be unknown (or partly unknown),
and noise might be present. The key component of this strategy is an echo state network,
which learns the dynamics of nonlinear regimes with varying parameters, and it evolves
dynamically via a hidden state. Although the framework does not make assumptions on
the dynamical system, we focus on thermoacoustics, which are governed by nonlinear and
time-delayed systems. First, we show that a parameter-aware echo state network (ESN)
infers the parametrized dynamics. Second, we derive the adjoint of the ESN to compute
two types of sensitivity: (i) parameter sensitivity, which is the gradient of a time-averaged
cost functional with respect to physical or design parameters of the system, and (ii) initial
condition sensitivity, which is the gradient of a cost functional of the final state with
respect to the initial condition. Third, we propose the thermoacoustic echo state network
(T-ESN), which embeds the physical knowledge in the network architecture for improved
generalization. Fourth, we apply the framework to a variety of nonlinear thermoacoustic
regimes of a prototypical system. We show that the T-ESN accurately infers the correct
adjoint sensitivities of the acoustic energy with respect to the flame parameters and initial
conditions. The results are robust to noisy data, from periodic, through quasiperiodic, to
chaotic regimes. The inferred adjoint sensitivities are employed to suppress an instability
via steepest descent. We show that a single network predicts the nonlinear bifurcations on
unseen scenarios, which allows it to converge to the minimum of the acoustic energy. This
work opens new possibilities for gradient-based data-driven design optimization
Adjoint Sensitivities of Chaotic Flows Without Adjoint Solvers: A Data-Driven Approach
No full textIn one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system’s parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which can be a cumbersome task and is code-specific. To propose an adjoint solver that is not code-specific, we develop a data-driven strategy. We demonstrate its application on the computation of gradients of long-time averages of chaotic flows. First, we deploy a parameter-aware echo state network (ESN) to accurately forecast and simulate the dynamics of a dynamical system for a range of system’s parameters. Second, we derive the adjoint of the parameter-aware ESN. Finally, we combine the parameter-aware ESN with its adjoint version to compute the sensitivities to the system parameters. We showcase the method on a prototypical chaotic system. Because adjoint sensitivities in chaotic regimes diverge for long integration times, we analyse the application of ensemble adjoint method to the ESN. We find that the adjoint sensitivities obtained from the ESN match closely with the original system. This work opens possibilities for sensitivity analysis without code-specific adjoint solvers
Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaos
Full text linkWe present the Physics-Informed Long Short-Term Memory (PI-LSTM) network to
reconstruct and predict the evolution of unmeasured variables in a chaotic
system. The training is constrained by a regularization term, which penalizes
solutions that violate the system's governing equations. The network is
showcased on the Lorenz-96 model, a prototypical chaotic dynamical system, for
a varying number of variables to reconstruct. First, we show the PI-LSTM
architecture and explain how to constrain the differential equations, which is
a non-trivial task in LSTMs. Second, the PI-LSTM is numerically evaluated in
the long-term autonomous evolution to study its ergodic properties. We show
that it correctly predicts the statistics of the unmeasured variables, which
cannot be achieved without the physical constraint. Third, we compute the
Lyapunov exponents of the network to infer the key stability properties of the
chaotic system. For reconstruction purposes, adding the physics-informed loss
qualitatively enhances the dynamical behaviour of the network, compared to a
data-driven only training. This is quantified by the agreement of the Lyapunov
exponents. This work opens up new opportunities for state reconstruction and
learning of the dynamics of nonlinear systems
Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach
Full text linkIn chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks.
Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult.
By learning the dynamics from observables (data), reservoir computers can time accurately predict extreme
events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by
exploiting quantum-computer ansätze and entanglement, we design reservoir computers with compact reservoirs
and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RFQRC) architecture. By developing ad hoc quantum feature maps and removing recurrent connections, the RFQRC has quantum circuits with smaller depths. This allows the RF-QRC to scale well with higher-dimensional
chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic
dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RFQRC requires smaller reservoirs than classical reservoir computers for higher-dimensional systems and the same
predictability. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent
shear flow with turbulent bursts. We find that the RF-QRC has longer predictability than the classical reservoir
computer for extreme events forecasting. The results and analyses indicate that quantum-computer ansätze offers
nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and
extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum
computers
A Hybrid Adjoint Network Model for Thermoacoustic Optimization
No full textA method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoint equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved while maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor
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