Dynamics and Control of Energy Systems

Increasing demands for energy, dwindling reserves of fossil fuel and growing concern for environmental impacts of energy generation call for a multidisciplinary and concerted effort towards energy sustainability. Optimized energy conversion method must consider the dynamic behaviour of the systems, which are mostly complex and nonlinear in nature. Hence a unified framework, based on dynamical systems analysis and time series analysis, needs to be adopted and applied for a wide spectrum of energy systems, ranging from combustion systems, which account for the bulk of energy generation to multiphase systems like natural circulation loops and multicomponent systems like batteries. With increasing contributions from renewable sources like wind and solar energy, nonlinear dynamics associated with aeroelastic and fluid dynamics effects and heat transfer effects also demand serious attention. Energy systems, whose dynamics, need to be studies also span several orders of length scale starting from large thermal and nuclear power plants to microscale devices.

Many of the real world systems are highly complex with little or no apriori information about the underlying dynamics. We have to depend mostly on measurements or observations of their average responses to study them. These measured or observational data come as a sequence of values at intervals, called time series. A few typical examples are sunspot data, variable star data, x-ray variability of black holes, climate or rainfall data, earth quake data, combustion data, thermoacoustic data, physiological data like EEG, ECG and fMRI, financial market data, output of agricultural crops, gene expression data etc. We present an overview of the techniques used for nonlinear time series analysis, to detect nontrivial structures in such time series data that will indicate the nature of underlying dynamics that produce the data. We start with the method of time delay embedding that can be used to re-construct the dynamics in higher dimension. The geometry and intricate structure of the re-constructed dynamics can then be characterized using two powerful techniques. The first one aims at computing the measures of the fractal geometry of the structure and its scaling properties. The resultant multi-fractal spectrum is uniquely characterized by four parameters that can be computed for each time series or data. The second method involves generating a complex network from the recreated phase space using its recurrence properties. The measures of the recurrence network then helps to identify the dynamical states of the system and their possible transitions. The applications of these techniques to several different types of real data are also included as illustrations.

The success of dynamic characterization of a system mostly depends on how far the nonlinear structure of the data is identified. In most of the practical systems, the dynamic behaviour is to some extent dominated by stochastic processes. In such a scenario, unfolding the hidden determinism and nonlinearity from the real world data which is acquired from a complex physical phenomenon is a challenging task. The tools from nonlinear time series analysis facilitate a systematic investigation of complex dynamics mostly observed in real life phenomena. The present chapter proposes a survey on different such tools which are used for the dynamic characterization of experimental time series. To take the first step in this course, detecting noise contamination in the time series data is discussed, highlighting the tests for determinism such as local flow test (Kaplan-Glass test), translation error, correlation dimension, and correlation entropy. Once the determinism of a time series is identified, figuring out the nonlinear nature is the next concern. There are a few direct tests such as Lyapunov exponent, correlation dimension to confirm chaos, however, they have their inherent limitations while analysing experimental data contaminated with noise. In such a situation, a statistical test popularly known as surrogate test is adopted. The test is based on different (null) hypotheses and examining their validity through any discriminating statistics such as translation error, permutation entropy. Permutation spectrum can further be used to characterize the dynamic nature of the time series. Other aspects which help further understanding of the data sets in hand are the fractal features and the predictability. The fractal features of a time series are identified by using singularity spectrum. Finally, the role of local predictor such as Sugihara-May algorithm for forecasting the dynamics of a deterministic system is discussed.

This chapter addresses the stability behavior of closed diabatic loops. The focus is on the prediction of stability boundaries for both single-phase and two-phase systems with minimum numerical distortion. As a means to check the performance of numerical schemes, several analytical solutions using method of characteristics have been evolved. These are then used to demonstrate the superiority of the characteristics based numerical method that is evolved systematically. Once the power is demonstrated, stability boundary is evolved for both single phase and two phase natural circulation in a closed rectangular loop. The method is demonstrated to satisfactorily predict the linear stability results obtained in single phase and experimental data generated in a two phase system.

The concept of supercritical natural circulation loops (scNCLs) is only a recent one, with the pioneering research being publicized only in 2001. But the favorable heat transport properties and large volumetric expansion of the supercritical fluids make them ideal for natural circulation based cooling applications, and hence is gaining increased popularity in several applications, particularly for reactor core cooling. The unique nature of the supercritical fluid ensures distinct thermal hydraulic and stability characteristics of scNCLs, widely different than other fluid-driven loops. Only a small temperature variation is sufficient to induce drastic changes in the density of the supercritical fluid, leading to substantial local buoyancy and radial motion. Therefore, a thorough understanding of both thermal hydraulic and stability behavior of an scNCL is mandatory before full-scale industrial applications. However, the knowledge base is reasonably thin and some of the reported observations are also not in consensus, making it difficult for the beginners to grasp the initial concepts, particularly with the contrasting standards adopted by various research groups around the world. That prepares the backdrop of the present chapter, with the basic aim being to introduce a reader with basic engineering knowledge into the field of scNCL and primarily into the dynamics of such systems. Starting with a brief state-of-the-art review of the technology, both experimental and theoretical studies are discussed, in order to summarize the stability responses of such loops. Considering the increasing popularity, the comprehensive discussion present in this chapter will definitely help in consolidating the concerned knowledge for the future researchers.

Intermittent renewable energy sources such as solar and wind are still in their early stages of market penetration. However, fraction of electricity coming from these sources continues to increase, putting pressure on the stability of the new grid, which is best characterized as a hybrid energy system (HES). Generation II nuclear power plants (NPPs) were designed to supply base load to the grid, making it necessary for the new generation of NPPs to have some level of load following capability to respond to the needs of the new grid with varying load and frequency needs. NPPs that can follow load need new kind of hardware and control strategy. One of the newer reactors, AP1000, is designed to load follow, thus permitting its easy integration into a modern HES electricity grid. The advanced Mechanical Shim (MSHIM) control system is used in the AP1000 reactor design to regulate power. This control system consists of two separate rod controllers that control the core reactivity and axial power distribution using the “gray and black M control banks” (M-banks) and the “axial offset control bank” (AO-bank), respectively. In this chapter, past works on the development of the modeling of AP1000 will be reviewed first. This will include nodal model for reactor, pressurizer and UTSG dynamics, and corresponding models for their control. This will be followed by a discussion of load following capability of AP1000 with original MSHIM strategy and a revised one.

Control of a nuclear reactor poses a challenge to a control-system designer due to the inherent nonlinear and a time varying nature of the associated dynamics which changes with the power level and the depletion level of the radio-active fuel in the reactor core. A constraint on the rate of rise of reactor power poses an additional challenge restricting the operation of a Nuclear Power Plant (NPP) mostly as a base load station. Conventional reactor control approaches aim to achieve a stable reactor period around a designated reactor power level—which is usually 100% Full Power (FP), with refinements like flux-tilt control and zonal power level variations within a narrow range using reactivity devices distributed across the reactor core. A bulk power controller is invoked either to raise the reactor power to a steady operational level or during a sharp reduction, known as a step-back and seldom in a demand following mode.

This chapter focuses on investigating the phenomenon of intermittency in the dynamical behavior of aeroelastic systems. To that end, a classical two degree-of freedom pitch plunge aeroelastic system is considered as the representative aeroelastic model. Investigations are first carried out on the route to aeroelastic flutter in fluctuating flow conditions through wind tunnel experiments. The recurring nature of intermittent periodic bursts observed in the pre-flutter response are subsequently utilized to develop quantitative measures using time series based tools, that can serve as precursors to flutter instability. To gain further insights into the experimental observations, numerical investigations are carried out using a well known two degree-of-freedom pitch plunge mathematical model for the aeroelastic system. A stochastic bifurcation analysis is also carried out that provide insights into the noise induced dynamical stability characteristics. Finally, a detailed study is undertaken to investigate the physical mechanisms that lead to the appearance of intermittency. Particularly, the effect of time scales of the flow fluctuations are investigated.

Vortex induced vibrations (VIV) is a widely explored fluid-structure interaction problem with immense applications ranging from heat exchanger tube arrays, power transmission lines to offshore structures. VIV of circular cylinders stands as one of the classical problems in this area, wherein the cylinder undergoes high amplitude vibrations due to the ‘lock-in’ phenomenon. The dynamics of the structure and flow field are well studied in the literature for a varied range of flow and structural parameters. However, real-life situations can be characterized by the presence of ‘noise’, which are fluctuations or uncertainties associated with the incoming flow or geometrical parameters of the system. The dynamical characteristics of the VIV system in the presence of such stochastic fluctuations are a relatively lesser-explored domain of research and not much documentation on this subject is available. In this chapter, we aim to present a comprehensive review of stochastic dynamics of VIV systems, especially we will highlight the presence of novel dynamical states and its implication on the coupled system behaviour that have been reported recently by us. It is known from experimental studies that free-stream noise can increase the response amplitudes of the structure and thus acts as a source of negative aerodynamic damping. Analytical works which model turbulence in experiments as stochastic processes use asymptotic expressions of Lyapunov exponents to determine the stability boundaries of VIV systems. Studies based on mathematical models investigating stochastic dynamics have modelled noise as additive and parametric, in the equations governing the VIV system. The current chapter mainly reviews the literature on stochastic VIV studies based on mathematical models that include wake oscillator models, single degree of freedom and force decomposition models, from a nonlinear dynamics perspective. Brief reviews on previous numerical studies using uncertainty quantification techniques in high fidelity solvers and key experimental results emphasizing the role of free-stream noise are also presented.

Ambient energy harvesting for power supply to low power hardware, like sensors in inaccessible environments, has garnered sustained interest over the last two decades. Common sources of ambient energy include vehicle vibrations and natural fluid flow. The latter is also proposed as a possible quiet alternative to conventional renewable energy systems like horizontal and vertical axis wind turbines. Various forms of flexible structures have been proposed and tested over years and found to be comparable to conventional systems on an energy density basis. These harvesters often rely on instability of the fluid-structure coupled system at increasing flow velocities. Thus, the design of these harvesters requires an understanding of the complex fluid-structure interaction inherent in them, which may include nonlinear effects. The inclusion of an electric circuit to scavenge the vibratory energy further transforms it into a three-way coupling problem. Despite laboratory scale verification of the potential of these systems, practical deployment has been deterred by the fluctuating nature of the natural fluid flows. Recent researches have sought to develop adaptive harvesters for such scenarios. Some progress has also been made in exploiting the spatio-temporal flow fluctuations beneficially for enhancing harvested power. This chapter summarizes the state-of-the-art in this regard and classifies the various approaches to tackling flow fluctuations.

Future energy needs that are supplemented by combustion require alternate fuel sources derived from both fossil and non-fossil sources. In this regard, syngas provides a relatively clean and large-scale resource. However, contrasted to conventional gaseous fuels, syngas poses challenges along both static and dynamic stability of flames owing to source dependent composition changes. These often result in altered global flame stabilization and dynamics when compared to its constituents being individually combusted. The present chapter deals with dynamic challenges is syngas combustion, when its static component, i.e., flame stabilization, is taken to be sufficiently addressed by resorting to non-premixed combustion. The chapter is descriptive of the combustion dynamics of syngas combustion across varying compositions in a turbulent bluff-body combustor, with focus on numerous aspects that need to be accounted to explain the vastly different behavior that syngas combustion dynamics display. The differences in the dynamic behavior of syngas compared to fuels that have been sought to “mimic” syngas like hydrogen-enriched hydrocarbon include-1. Excitation of higher modes across similar parameter change and most significantly 2. Presence of two heat release rate zones as a result of differing diffusion and chemical time-scales. Time-resolved pressure, velocity and OH* and CO₂* imaging reveal that peculiarities arising in syngas combustion dynamics are a result of various steady and unsteady processes viz. fuel to air momentum ratio, the effect of the same on mean flame stabilization, baroclinic torque, shear layer stabilization and the offset between peak OH* and CO₂* concentrations. The foresaid processes are aided by the time-lag between acoustic quantities that result in excitation of various modes as seen from a simple theoretical model. The chapter thus explains the unique nature of syngas combustion from a multitude of well-established combustion theories that are required to understand and control the dynamic challenges of syngas combustion.

Practical combustion systems such as gas turbine combustors, rocket engines, industrial furnaces, and boilers are essentially thermoacoustic oscillators involving acoustic energy amplification through feedback interaction among fluctuations in the aerodynamic field, acoustic field, and the combustion process. Such systems are also noisy, in the sense that there inherently exists noise within the system. Noise may be associated with various sources–noise in fuel/air supply systems, fluctuations in the flow field, acoustic fluctuations, fluctuations in the heat release. Additionally, such noise may be correlated or uncorrelated, may have a specific spectral characteristic; but often noise will interact with/influence the feedback process. Since the importance of noise in determining the stability of the system discussed by Culick et al. (Combustion noise and combustion instabilities in propulsion systems, 1992) and group at Caltech, there have been several recent contributions to the theory of noise-induced phenomena in thermoacoustic systems–further advancements in the determination of system stability through noise-induced behaviour in the system prior to bifurcation as well as during the self-excited state, noise-induced effects in the presence of nonlinear interactions, noise-induced transitions (incl. dynamics in the bistable regime in the case of transition to self-excited oscillations via a subcritical Hopf bifurcation), as well as recent identification of interesting behaviour such as noise-induced coherence and stochastic bifurcations (stochastic P-bifurcations). The latter effects are based on new findings in the theory of dynamical systems and since reports on their influence in thermoacoustic systems are also being investigated in other aero/hydrodynamic systems such as in jets. The review will focus on the influence of developments in the theory of random noise (such as the Fokker-Plank equations), the theory of oscillators and dynamical systems on noise induced behaviour in thermoacoustic systems; experiments, modelling, and predictions on noisy thermoacoustic systems; and the implications of these findings on practical systems.

Combustion instabilities are prevalent in a variety of systems including gas turbine engines. In this regard, the introduction of active control opens the potential for new paradigms in combustor design and optimization. However, the limited ability to detect the onset of instabilities can lead to difficulty in implementing active control approaches. Machine learning—specifically deep learning tools—may be employed to detect instabilities from various measurement and sensor data related to the combustion process. Deep learning models have recently shown remarkable potential for extraction of meaningful features from data without the need to hand-craft. As one of the early studies of deep learning for combustion instability detection, we extract sequential image frames from high-speed images of a premixed, bluff-body stabilized flame which exhibits varying levels of combustion instability. Using an efficient detection framework (based on 2-D convolutional neural networks) to detect the growth of an unstable mode can lead to effective control schemes. In addition, we apply a second deep learning framework to capture the temporal correlations in the data with corresponding learned spatial features.

Real-time condition monitoring of complex dynamical systems is of critical importance for predictive maintenance. This chapter focuses on data-driven techniques of fault diagnostics with an emphasis on real-time detection of anomalous behavior in combustion systems. It presents the applications of well-known statistical learning techniques such as D-Markov modeling and hidden Markov modeling (HMM) as possible data-driven solutions for anomaly detection in combustion systems. From the perspective of real-time monitoring and diagnostics, such statistical tools are applicable to stochastic dynamical systems in general. Both D-Markov and HMM algorithms have been validated on experimental data from a laboratory apparatus, which is an electrically heated Rijke tube.

The progress in manufacturing techniques in last few decades has accelerated the application of micro-structured devices in a range of industrial sectors such as healthcare, pharmaceuticals, electronics, environment, chemical processing and energy. Many of these applications stem from the advantages of high surface area to volume ratio, small diffusion paths and ability to operate safely at high temperatures and pressures in micro-devices. The applications of these devices in the energy sector often involve convective heat transfer, condensation, evaporation and boiling in microchannels. Extensive experimental studies on flow boiling in microchannels in the last twenty five years suggest the boiling at the microscale to be significantly different from that in the large channels and the critical heat flux above which the boiling heat transfer becomes ineffective and catastrophic is scale-dependent. The studies also indicate that several dynamic instabilities occur during two-phase boiling in microchannels and these can be different from those that occur in large channels. Therefore, it is imperative to understand the mechanisms of boiling stabilities in microchannels and develop techniques to control them to design efficient and safe micro-structured devices. The boiling instabilities in microchannels can be categorized in two groups- one, those caused by interaction between upstream compressibility and bubble generation and second, those caused by parallel channel instability. This chapter reviews the current status of the understanding of these instabilities and the techniques to avoid or minimize them.

In recent years, electromagnetohydrodynamically modulated control and hydroelectric energy conversion through narrow fluidic devices have emerged as promising means for controlling and manipulating liquid flows in diverse applications. Such processes include development of smart sensors, micrototal analysis systems (μTAS), capillary electrophoresis, electrochromatography, mixing, flow cytometry, DNA hybridization and analysis, cell manipulation, cell patterning, immunoassay, enzymatic reactions, and molecular detection, etc. Accordingly, in the present chapter, we discuss the fundamental theories and elucidate the semi analytical and numerical approaches for analysis of the electromagnetohydrodynamic forces and their effect on thermofluidic control and energy transfer characteristics in narrow fluidic confinements. The consequences of electromagnetohydrodynamic forces and interfacial slip on the streaming potential development has been discussed in detail for pressure driven flows in a narrow fluidic confinement. It has been inferred that wall slip activated electro-magnetohydrodynamic transport can enhance the induced streaming potential and intensifies the convective heat transfer rate. Furthermore, we have also shown an analysis for combined electroosmotic and pressure-driven flows through narrow confinements, subjected to spatially varying non-uniform magnetic field. It is revealed that one can augment heat transfer rate for such a situation by judiciously choosing the spatially varying magnetic field strength. Next, we highlight the collective interaction of the fluid rheology, kinematics, volumetric effects of ionic species (steric effect), and the electrodynamics leading to giant augmentations in the energy conversion efficiency. For all the studies reported above, exergy analysis can indicate the route for optimal designs of process and the reduction in the thermodynamic irreversibility. Finally, the specific points emerging out from the research are concluded and relevant application areas have been discussed.

Rayleigh-Bénard convection (RBC), where a horizontal layer of fluid is kept between two conducting plates and the system is heated from below, provides a simplified model of convection. RBC is a classical extended dissipative system which displays a plethora of instabilities and patterns very close to the onset of convection for wide range of fluids. The study of these instabilities is an important topic of research and several approaches are available for the investigation. This chapter deals with the low dimensional modeling technique for investigating instabilities and the associated pattern dynamics in RBC.

Hydrogen is a potential alternative energy carrier to embrace the global need of a clean and efficient energy resource. It minimizes dependence on fossil fuels as well as is an effective measure towards increasing global warming. Hydrogen based fuel cells are an attractive solution for producing clean electrical energy by emitting only water as a by-product. However, storage and distribution of hydrogen is a major issue for stationary fuel cells as well as mobile power generators. To avert the risks of any hydrogen leaks, membrane reactor (MR) technology enables to deliver only the desirable release of hydrogen using a fine control between on-site hydrogen generation and separation. Moreover, in contrast to traditional and bulky integration methodologies, MR allows single unit ‘compact’ integration that also eliminates additional downstream of products by producing hydrogen of >99% purity. These factors motivate MR to be explored widely and demonstrate its commercial feasibility in the coming years.

The current chapter focuses on the broad overview on membrane reactors for ultra pure hydrogen production, its technological challenges and case studies to illustrate the critical role played by dense palladium membranes in the successful viability of this technology. Further, recent developments within the scope of membrane reactors for hydrogen generation will also be briefly discussed. Special focus will be given for hydrogen generation by using methanol as a feed to membrane reformer.

Batteries of the future are envisioned to have high energy density, power density and cycle efficiency with low production cost and long life. Among the most promising ones is the rechargeable lithium-oxygen (Li–O₂) battery. Li–O₂ batteries operate with a Li anode, a porous cathode with ambient oxygen as the oxidizer in an organic electrolyte environment. In Li–O₂ battery, Li ions, formed via oxidization of Li at the anode reach the cathode and react with O₂ to form Li₂O₂ as the primary reaction product. The use of Li-based anode material has been quite popular in the recent past due to its high energy density and abundance. With Li as the anode material and oxidizer derived from the ambient air, Li–O₂ battery provides superior energy density, comparable to that of the internal combustion engines. Further, the fast reaction kinetics of Li and O₂ to form Li₂O₂, without the breaking the O–O bond, facilitates the use of cheaper catalysts. Despite the above advantages, the Li–O₂ battery suffers from significant challenges limiting its application at a commercial scale. First, the Li–O₂ battery suffers from electrode passivation, i.e., the clogging of the pores of the electrode and the stresses due to volume expansion caused by the insoluble reaction products. Second, the slow O₂ transport, in the electrode, limits the specific capacity and output power density. Finally, the battery endures electrolyte degradation and formation of undesirable products from secondary reactions. The present chapter discusses the above challenges of transport and electrochemical phenomena, occurring in the electrodes and electrolytes, during the discharge-charge cycling of the battery. We emphasize the battery operation, material selection and design variables affecting the performance, degradation characteristics and efficiency of Li–O₂ battery. The chapter presents detail mathematical modelling and simulation results at both cell- as well as pore-scale and concludes with specific design recommendation of futuristic Li–O₂ batteries.

Infrared thermal imaging technique is a tool that is utilized for sensing two-dimensional thermal images of various applications. The present chapter reports the working principle of Infrared thermal imaging technique and application of this technique to measure surface temperature in various engineering applications. Also, the research work carried out by the authors by using this technique has been summarized in this chapter.

Carbon nanofibers (CNFs) are a very promising material of carbon family and gained a severe concern by researchers since the last decades. There are numerous existed technologies for the synthesis of CNF or CNF/composites, but the focus of this book chapter is limited to catalytic chemical vapor deposition (CVD) grown CNFs and their different applications. Owing to the high specific surface area, significant porosity with uniform pores, high electrical conductivity, corrosion resistance, electrochemical stability, biocompatible, less cytotoxic and mechanically stable, they are employed in several biochemical and electrochemical applications such as bioenergy generation, electrode materials for batteries, fuel cell, and supercapacitors and as sensors. They are being used keenly in different catalytic reactions for refining the atmosphere from different types of pollutants such as VOPs, POPs, etc. This paper summarizes the role/effect of various parameters which are actively or passively liable for the growth of CVD grown CNF such as metal catalysts, carbon sources, temperatures, and carbon source decomposition timing.