Nonlinear thermoacoustic oscillations of a ducted laminar premixed flame

This thesis was awarded the Leonardo da Vinci prize in 2013 for outstanding doctoral research in fluid mechanics, turbulence, combustion and acoustics (a Europe wide award). This thesis was also awarded the silver award of the ERCOFTAC (European research community on flow, turbulence and combustion) 10th Osborne Reynolds Award in 2013.Finding limit cycles and their stability is one of the central problems of nonlinear thermoacoustics. However, a limit cycle is not the only type of self-excited oscillation in a nonlinear system. Nonlinear systems can have quasi-periodic and chaotic oscillations. This thesis examines the different types of oscillation in a numerical model of a ducted premixed flame, the bifurcations that lead to these oscillations and the influence of external forcing on these oscillations. Criteria for the existence and stability of limit cycles in single mode thermoacoustic systems are derived analytically. These criteria, along with the flame describing function, are used to find the types of bifurcation and minimum triggering amplitudes. The choice of model for the velocity perturbation field around the flame is shown to have a strong influence on the types of bifurcation in the system. Therefore, a reduced order model of the velocity perturbation field in a forced laminar premixed flame is obtained from Direct Numerical Simulation. It is shown that the model currently used in the literature precludes subcritical bifurcations and multi-stability. The self-excited thermoacoustic system is simulated in the time domain with many modes in the acoustics and analysed using methods from nonlinear dynamical systems theory. The transitions to the periodic, quasiperiodic and chaotic oscillations are via sub/supercritical Hopf, Neimark-Sacker and period-doubling bifurcations. Routes to chaos are established in this system. It is shown that the single mode system, which gives the same results as a describing function approach, fails to capture the period-$2$, period-$k$, quasi-periodic and chaotic oscillations or the bifurcations and multi-stability seen in the multi-modal case, and underpredicts the amplitude. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and chaotic oscillations. Cusp formation, their destruction by flame propagation normal to itself, and pinch-off and rapid burning of pockets of reactants are shown to be responsible for generating a heat release rate that is a highly nonlinear function of the velocity perturbations. It is also shown that for a given acoustic model of the duct, many discretization modes are required to capture the rich dynamics and nonlinear feedback between heat release and acoustics seen in experiments. The influence of external harmonic forcing on self-excited periodic, quasi-periodic and chaotic oscillations are examined. The transition to lock-in, the forcing amplitude required for lock-in and the system response at lock-in are characterized. At certain frequencies, even low-amplitude forcing is sufficient to suppress period-$1$ oscillations to amplitudes that are 90$\%$ lower than that of the unforced state. Therefore, open-loop forcing can be an effective strategy for the suppression of thermoacoustic oscillations. This thesis shows that a ducted premixed flame behaves similarly to low-dimensional chaotic systems and that methods from nonlinear dynamical systems theory are superior to the describing function approach in the frequency domain and time domain analysis currently used in nonlinear thermoacoustics.University Gas Turbine Partnership, Rolls Royce Plc., EPSRC, Dorothy Hodgkin Postgraduate Award, Trinity college fellowships, Ford foundation fellowship, Rouse Ball and Eddington fellowships, American Society of Mechanical Engineers, International Gas Turbine Institute, The Combustion Institute

Unsupervised Discovery of Extreme Weather Events Using Universal Representations of Emergent Organization

Spontaneous self-organization is ubiquitous in systems far from thermodynamic equilibrium. While organized structures that emerge dominate transport properties, universal representations that identify and describe these key objects remain elusive. Here, we introduce a theoretically-grounded framework for describing emergent organization that, via data-driven algorithms, is constructive in practice. Its building blocks are spacetime lightcones that embody how information propagates across a system through local interactions. We show that predictive equivalence classes of lightcones -- local causal states -- capture organized behaviors and coherent structures in complex spatiotemporal systems. Employing an unsupervised physics-informed machine learning algorithm and a high-performance computing implementation, we demonstrate automatically discovering coherent structures in two real world domain science problems. We show that local causal states identify vortices and track their power-law decay behavior in two-dimensional fluid turbulence. We then show how to detect and track familiar extreme weather events -- hurricanes and atmospheric rivers -- and discover other novel coherent structures associated with precipitation extremes in high-resolution climate data at the grid-cell level

Forced synchronization of periodic and aperiodic thermoacoustic oscillations: lock-in, bifurcations, and open-loop control

Synchronization is a universal concept in nonlinear science but has received little attention in thermoacoustics. In this numerical study, we take a dynamical systems approach to investigating the influence of harmonic acoustic forcing on three different types of self-excited thermoacoustic oscillations: periodic, quasi-periodic and chaotic. When the periodic system is forced, we find that: (i) at low forcing amplitudes, it responds at both the forcing frequency and the natural (self-excited) frequency, as well as at their linear combinations, indicating quasi-periodicity; (ii) above a critical forcing amplitude, the system locks in to the forcing; (iii) the bifurcations leading up to lock-in and the critical forcing amplitude required for lock-in depend on the proximity of the forcing frequency to the natural frequency; (iv) the response amplitude at lock-in may be larger or smaller than that of the unforced system and the system can exhibit hysteresis and the jump phenomenon owing to a cusp catastrophe; and (v) at forcing amplitudes above lock-in, the oscillations can become unstable and transition to chaos, or switch between different stable attractors depending on the forcing amplitude. When the quasi-periodic system is forced at a frequency equal to one of the two characteristic frequencies of the torus attractor, we find that lock-in occurs via a saddle-node bifurcation with frequency pulling. When the chaotic system is forced at a frequency close to the dominant frequency of its strange attractor, we find that it is possible to destroy chaos and establish stable periodic oscillations. These results show that the open-loop application of harmonic acoustic forcing can be an effective strategy for controlling periodic or aperiodic thermoacoustic oscillations. In some cases, we find that such forcing can reduce the response amplitude by up to 90 %, making it a viable way to weaken thermoacoustic oscillations

MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder. We empirically study the performance of MeshfreeFlowNet on the task of super-resolution of turbulent flows in the Rayleigh-Benard convection problem. Across a diverse set of evaluation metrics, we show that MeshfreeFlowNet significantly outperforms existing baselines. Furthermore, we provide a large scale implementation of MeshfreeFlowNet and show that it efficiently scales across large clusters, achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of less than 4 minutes.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2