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We present an improved dynamic model to predict the time-varying characteristics of the far-wake flow behind a wind turbine. Our model, based on the FAST.Farm engineering model, is novel in that it estimates the turbulence generated by convective instabilities, which selectively amplifies the inflow velocity fluctuations. Our model also incorporates scale dependence when calculating the wake meandering induced by the passive wake meandering mechanism. For validation, our model is compared with FAST.Farm and large-eddy simulation (LES). For the mean flow, our model agrees well with LES in terms of the wake deficit and wake width, but the FAST.Farm model underestimates the former and overestimates the latter. For the instantaneous flow, our model predicts well the wake-center deflection and turbulent kinetic energy, reducing the discrepancies in the spectral characteristics by more than a factor of two relative to LES, depending on the Strouhal number. By incorporating two key mechanisms governing the far-wake dynamics, our model can predict more accurately the dynamic wake evolution, making it suitable for real-time calculations of wind farm performance. © 2023 Elsevier Ltd

In this experimental study, we use a data-driven machine learning framework based on genetic programing (GP) to discover model-free control laws (individuals) for suppressing self-excited thermoacoustic oscillations in a prototypical laminar combustor. This GP framework relies on an evolutionary algorithm to make decisions based on natural selection. Starting from an initial generation of individuals, we rank their performance based on a cost function that accounts for the trade-off between the state cost (thermoacoustic amplitude) and the input cost (actuator power). We then breed subsequent generations of individuals via a tournament in which the direct forwarding of elite individuals occurs alongside genetic operations such as mutation, replication, and crossover. We implement this GP control framework in both closed-loop and open-loop forms, followed by benchmarking against conventional open-loop control based on time-periodic forcing. We find that while all three control strategies can achieve similarly large reductions in thermoacoustic amplitude, GP closed-loop control consumes the least actuator power, making it the most efficient. It achieves this efficiency by learning an actuation mechanism that exploits the strong heat-release-rate amplification of the open flame at its preferred mode, even though the GP algorithm has never seen the open flame itself. This study demonstrates the feasibility of using GP to discover new and more efficient model-free individuals for suppressing self-excited thermoacoustic oscillations, providing a promising approach to data-driven feedback control of combustion devices.

The development of digital twins for wind farms often involves the use of large-eddy simulation (LES) to model atmospheric boundary layers. Existing LES solvers primarily focus on accurately capturing streamwise fluctuations. They, however, overlook the less energetic cross-stream fluctuations, which play a crucial role in wind turbine wake evolution. In this study, we conduct a systematic parametric study and incorporate changes in an open-source LES solver. The improved solver is able to predict all three components of velocity fluctuations in alignment with the scaling laws derived from the attached-eddy hypothesis. In particular, we examine the impact of (i) the subgrid-scale model, (ii) the wall model, (iii) the von Kármán constant, and (iv) the grid-cell aspect ratio. We find that although all these factors influence the prediction of velocity fluctuations, the grid-cell aspect ratio has the greatest effect on the spanwise and vertical velocity components. Notably, utilizing nearly isotropic grid cells leads to the best alignment of all three velocity component fluctuations with the scaling laws. Spectral analysis further demonstrates that the present LES solver accurately predicts the characteristic length scales for all velocity fluctuation components, making it a reliable tool for obtaining turbulent inflow conditions for wind farm modeling.

We present output-only system identification of the self-sustained low-frequency flow oscillations over an LRN (1)-1007 airfoil at a chord-based Reynolds number of Rec = 105 near stall conditions. We model the lift force fluctuations with a Van der Pol oscillator subjected to stochastic white noise, which represents the effect of intrinsic turbulence. The parameters of this low-order model are identified from the time series of the lift force acquired by a load cell. We extract the drift and diffusion coefficients of the resulting Fokker-Planck equation and optimize them with an adjoint-based algorithm. Based on these coefficients, the linear growth rate, non-linear saturation coefficient and noise intensity are identified, enabling reconstruction of the probability density functions of the oscillation amplitude. Moreover, by extrapolating the parameters found in the pre-bifurcation regime, we are able to predict the location of the Hopf point as well as the post-bifurcation behaviour. This framework can thus provide early warning indicators of low-frequency flow oscillations, facilitating the design of new control strategies. © 2023 Proceedings of the International Congress on Sound and Vibration. All rights reserved.

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in a globally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for peak multifractality produce a complex network whose node degree distribution obeys an inverse power-law scaling with an exponent of 2 < ? < 3, indicating scale-free topology and (iii) the Hurst exponent and the global clustering coefficient can serve as early warning indicators of global instability under specific operating and forcing conditions. By characterising the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics commonly observed in turbulent flows can also be observed in laminar flows under certain stochastic forcing conditions.

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle high-dimensional systems. Its implementation, however, often requires full state-vector measurements and knowledge of the system nonlinearities. We use nonlinear projector functions to expand the system measurements to a high dimensional space and then feed them to a reservoir to obtain forecasts. We demonstrate the application of such reservoir computing networks on spatiotemporally chaotic systems, which model several features of turbulence. We show that using radial basis functions as nonlinear projectors enables complex system nonlinearities to be captured robustly even with only partial observations and without knowing the governing equations. Finally, we show that when measurements are sparse or incomplete and noisy, such that even the governing equations become inaccurate, our networks can still produce reasonably accurate forecasts, thus paving the way towards model-free forecasting of practical turbulent systems. © 2023 Elsevier Ltd

We numerically explore the quenching and amplification of self-excited thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. On applying either type of coupling separately, we find that the presence of nonidentical heater powers can shrink the regions of amplitude death in both oscillators, while producing new regions of amplitude amplification in the weaker oscillator. We find that the magnitude of amplitude amplification grows with the heater power mismatch and with the total power input. These effects are also present when both types of coupling are applied simultaneously. This study highlights the critical role that nonidentical thermal loads can play in determining the amplitude response of coupled thermoacoustic systems, facilitating the design of control strategies for coupled oscillatorlike devices such as gas turbines.

We use genetic programming (GP) to discover data-driven control laws for the suppression of quasiperiodic oscillations in a prototypical thermoacoustic system. We rank the control laws based on a predefined cost function that accounts for the pressure amplitude and the actuation effort. We then breed subsequent generations of control laws via a tournament process. We find that GP closed-loop control is more effective than GP open-loop control and conventional periodic forcing, producing a similarly high degree of amplitude suppression but with the lowest actuation effort. We also find that GP closed-loop control can identify unforeseen actuation mechanisms, providing new insight into the physical coupling between the heat release rate and pressure fields. © 2022 Internoise 2022 - 51st International Congress and Exposition on Noise Control Engineering. All rights reserved.

We numerically explore the effect of non-identical heater powers on the quenching and amplification of self-excited thermoacoustic oscillations in two Rijke tubes interacting via time-delay or dissipative coupling. On applying either type of coupling separately, we find that the presence of non-identical heater powers can shrink the regions of amplitude death in both oscillators, while producing new regions of amplitude amplification in the weaker oscillator. We find that the magnitude of amplitude amplification increases with the heater power mismatch and with the total power input. This study highlights the critical role that non-identical thermal loads can play in determining the amplitude response of coupled thermoacoustic systems, facilitating the design of control strategies for coupled oscillator-like devices such as gas turbines. © 2022 Internoise 2022 - 51st International Congress and Exposition on Noise Control Engineering. All rights reserved.

Wake meandering and turbulent kinetic energy (TKE) generation in the far-wake region of wind turbines significantly affect the power production and aerodynamic loads of wind farms. This work thus aims at understanding the componentwise influence of upstream turbulence and roles of different mechanisms on the far-wake dynamics to guide the development of wind-farm wake models. We find that the wake meandering is mainly caused by the upstream spanwise (v′) and vertical (w′) velocity fluctuations, supporting the passive wake meandering mechanism. However, our results also show a scale-dependence of the wake meandering that should be accounted in wake models. We find that v′ and w′ cause greater TKE generation than the streamwise velocity fluctuations (u′). We then use simulation- and resolvent-based componentwise input–output analyses to explain that this is because the shear instability in turbine wakes is more receptive to the transverse forcing relative to the streamwise forcing. This highlights the importance of implementing the shear instability mechanism in wake models for accurate TKE estimations. Finally, we find that u′ cause the thrust fluctuations, which can lead to near-wake corrections and hence influence the far-wake evolution.

We experimentally study the hydrodynamic instability of a lean-premixed flame stabilized behind a circular cylinder. On reducing the equivalence ratio (ϕ) at a fixed Reynolds number (ReD), we find that the flame transitions from a steady mode to a varicose mode and then to a sinuous mode. By examining time-resolved CH* chemiluminescence images and analyzing how the Strouhal number scales with ReD, we determine that the varicose mode is convectively unstable, maintained by the amplification of disturbances in the turbulent base flow, whereas the sinuous mode is globally unstable as a result of the constructive interaction between the two diametrically opposite shear layers (Bénard–von Kármán instability). We attribute the emergence of the sinuous global mode to the flame moving sufficiently far downstream with decreasing ϕ that it is out of the wavemaker region. Finally, we investigate the lean blowoff dynamics and find that local flame pinch-off, which occurs at the end of the recirculation zone, is a reliable precursor of global flame blowoff.

In this numerical study, we use two-dimensional scale-adaptive simulations to investigate the lift characteristics of two tandem airfoils in the globally unstable wake of a cylinder at a Reynolds number of 104, with and without cylinder heating. Both airfoils have NACA 0012 profiles and are at the same angle of attack (α = 10°), implying zero decalage. We find that the lift characteristics of both airfoils depend strongly on the streamwise distance (X) between the trailing point of the cylinder and the leading edge of the fore airfoil. At the conditions of this study (1 ≤ X/D ≤ 5, where D is the cylinder diameter), both airfoils experience periodic limit-cycle oscillations in their lift coefficients (Cl) at the same frequency. However, when X/D < 3, abrupt decreases occur in both the Cl amplitude of the fore airfoil and the Cl oscillation frequency of both airfoils. We attribute these decreases to the fore airfoil entering the wavemaker region of the self-excited cylinder wake and altering its global instability properties. Heating the cylinder to a temperature above that of the free-stream leads to monotonic decreases in the oscillation frequency and amplitude of Cl for both airfoils. For the purpose of harvesting the maximum energy from two tandem airfoils behind a cylinder, our findings suggest that (i) the airfoils should be positioned as close as possible to the cylinder without disrupting the wavemaker of the globally unstable wake and (ii) the cylinder should be prevented from heating up. © 2020, Akadémiai Kiadó, Budapest, Hungary.

When the density of a jet is sufficiently below that of its surroundings, it can become globally unstable, transitioning from a steady state to a self-excited state characterized by axisymmetric limit-cycle oscillations. We present experiments on the closed-loop control of such oscillations using an unsupervised data-driven model-free framework based on genetic programming (GP). Our implementation of this GP-based control framework relies on a hot-wire probe for sensing and a loudspeaker for actuation. We first initialize a generation of candidate control laws and evaluate their individual performance on the basis of a cost function that accounts for the amplitude of the global mode in a low-density jet and the actuation effort. We then breed further generations of control laws by enrolling them in a tournament and by executing genetic operations such as mutation, crossover, replication and elitism. By benchmarking the best GP-based control law against the best periodic forcing strategy found via conventional open-loop mapping, we show that GP-based control can provide a more efficient means of global mode suppression, offering new insight into the physics of hydrodynamically self-excited jets.

Genetic programming (GP) is a powerful tool for unsupervised data-driven discovery of closed-loop control laws. In fluid mechanics, it has been used for various purposes, such as to enhance mixing in a turbulent shear layer and to delay flow separation. This model-free control framework is well suited for such complex tasks as it exploits an evolutionary mechanism to propagate the genetics of high-performing control laws from one generation to the next. Here we combine automated experiments with GP to discover model-free control laws for the suppression of self-excited thermoacoustic oscillations in a Rijke tube. Using a GP-based controller linked to a single sensor (a microphone) and a single actuator (a loudspeaker), we rank the performance of all the control laws in a given generation based on a cost function that accounts for the pressure amplitude and the actuation effort. We use a tournament process to breed further generations of control laws, and then benchmark them against conventional periodic forcing optimized via open-loop mapping. We find that, with only minimal input from the user, this GP-based control framework can identify new feedback actuation mechanisms, providing improved control laws for the suppression of self-excited thermoacoustic oscillations.

The Ginzburg–Landau equation (GLE) can phenomenologically model several key features of non-equilibrium systems including those in fluid mechanics. Its validity in real flows, however, remains questionable. Here, we show that the linear GLE can be formulated such that it has the same Wentzel–Kramers–Brillouin (WKB) approximation as for the linear global stability problem in open shear flows. We use the GLE to model the linear global modes of three different wakes and find that it can accurately capture the linear growth rate and frequency to first order in the WKB approximation. Furthermore, we find that it can also provide the shapes of the direct and adjoint eigenvectors and the regions of maximal structural sensitivity. The proposed model requires only the basic flow as input, but gives robust predictions and is computationally inexpensive. As well as opening up new possibilities for GLE-based control strategies, the proposed model makes accurate stability calculations possible, even for some computationally intractable open shear flows.

In nonlinear dynamics, there are three classic routes to chaos, namely the period-doubling route, the Ruelle-Takens-Newhouse route and the intermittency route. The first two routes have previously been observed in self-excited thermoacoustic systems, but the third has not. In this experimental study, we present evidence of the intermittency route to chaos in the self-excited regime of a prototypical thermoacoustic system- A laminar flame-driven Rijke tube. We identify the intermittency to be of type II from the Pomeau-Manneville scenario through an analysis of (i) the probability distribution of the quiescent epochs between successive bursts of chaos, (ii) the first return map, and (iii) the recurrence plot. By establishing the last of the three classic routes to chaos, this study strengthens the universality of how strange attractors arise in self-excited thermoacoustic systems, paving the way for the application of generic suppression strategies based on chaos control. © The Author(s), 2020. Published by Cambridge University Press.

We present a framework for performing input-output system identification near a Hopf bifurcation using data from only the fixed-point branch, prior to the Hopf point itself. The framework models the system with a van der Pol-type equation perturbed by additive noise, and identifies the system parameters via the corresponding Fokker-Planck equation. We demonstrate the framework on a prototypical thermoacoustic oscillator (a flame-driven Rijke tube) undergoing a supercritical Hopf bifurcation. We find that the framework can accurately predict the properties of the Hopf bifurcation and the limit cycle beyond it. This study constitutes an experimental demonstration of system identification on a reacting flow using only prebifurcation data, opening up pathways to the development of early warning indicators for nonlinear dynamical systems near a Hopf bifurcation.

When the density of a jet is sufficiently below that of its surroundings, it can become globally unstable, transitioning from a steady state to a self-excited state characterized by axisymmetric limit-cycle oscillations. We present experiments on the closed-loop control of such oscillations using an unsupervised data-driven model-free framework based on genetic programming (GP). Our implementation of this GP-based control framework relies on a hot-wire probe for sensing and a loudspeaker for actuation. We first initialize a generation of candidate control laws and evaluate their individual performance on the basis of a cost function that accounts for the amplitude of the global mode in a low-density jet and the actuation effort. We then breed further generations of control laws by enrolling them in a tournament and by executing genetic operations such as mutation, crossover, replication and elitism. By benchmarking the best GP-based control law against the best periodic forcing strategy found via conventional open-loop mapping, we show that GP-based control can provide a more efficient means of global mode suppression, offering new insight into the physics of hydrodynamically self-excited jets.