Low-order Model Research Articles

Brain tumor detection using proper orthogonal decomposition integrated with deep learning networks

Background and ObjectiveThe central organ of the human nervous system is the brain, which receives and sends stimuli to the various parts of the body to engage in daily activities. Uncontrolled growth of brain cells can result in tumors which affect the normal functions of healthy brain cells. An automatic reliable technique for detecting tumors is imperative to assist medical practitioners in the timely diagnosis of patients. Although machine learning models are being used, with minimal data availability to train, development of low-order based models integrated with machine learning are a tool for reliable detection. MethodsIn this study, we focus on comparing a low-order model such as proper orthogonal decomposition (POD) coupled with convolutional neural network (CNN) on 2D images from magnetic resonance imaging (MRI) scans to effectively identify brain tumors. The explainability of the coupled POD-CNN prediction output as well as the state-of-the-art pre-trained transfer learning models such as MobileNetV2, Inception-v3, ResNet101, and VGG-19 were explored. ResultsThe results showed that CNN predicted tumors with an accuracy of 99.21% whereas POD-CNN performed better with about 1/3rd of computational time at an accuracy of 95.88%. Explainable AI with SHAP showed MobileNetV2 has better prediction in identifying the tumor boundaries. ConclusionsIntegration of POD with CNN is carried for the first time to detect brain tumor detection with minimal MRI scan data. This study facilitates low-model approaches in machine learning to improve the accuracy and performance of tumor detection.

Low-order modelling of three-dimensional surface waves in liquid film flow on a rotating disk

Using low-dimensional numerical simulations, we investigate the characteristics of complex and three-dimensional surface waves in a liquid film flowing over a rotating disk, focusing on large flow rates from a nozzle. Existing integral boundary layer (IBL) models, which are based on spatially averaged variables along the direction normal to the disk surface, have primarily focused on the formation of axisymmetric waves under relatively small flow rates. In this study, an extended IBL model that accounts for both laminar and turbulent regimes is developed by considering the non-uniformity of the local flow rate in the spreading film flow and incorporating closure models dependent on the local Reynolds number. Our numerical results successfully capture the generation of concentric waves by an impinging circular liquid jet and their transition into three-dimensional solitary waves. These findings are in good agreement with visualization images and time-series data of free-surface fluctuations from a displacement sensor. The backscattering of small-scale three-dimensional turbulence into large-scale horizontal turbulence inside the film plays a critical role in determining the transition of wave modes and the nonlinear dynamics of the waves in the turbulent regime. Furthermore, the behaviour of three-dimensional waves in the downstream region, including frequent wave coalescence in the transition region and the breakup of small-scale solitons, is distinct from that of gravity-driven falling film flows. The amplitude of the three-dimensional waves is inversely related to the generalized Reynolds number defined for rotating films.

Experimental Investigation of Tip Design Effects on the Unsteady Aerodynamics and Heat Transfer of a High-Speed Turbine

Abstract While modern engine manufacturers devote significant efforts to the development of reliable and efficient machines, the introduction of novel, optimized components in the hot gas path represents a risky opportunity. Accurate experimental and numerical data are critical to assess the impact of new technologies on the harsh engine environment. The present study addresses the impact of a selection of high-performance rotor blade tips on the aerodynamic and heat flux field of a high-pressure turbine (HPT) stage. A combined numerical and experimental approach is employed to characterize the interaction of the tip leakage flow with the rotor secondary flows and the casing heat transfer mechanisms for each individual tip geometry. The turbine stage is tested at engine-scaled conditions in the rotating turbine facility of the von Karman Institute. In the present study, the turbine rotor is operated in rainbow configuration to allow the simultaneous testing of multiple blade tip geometries. Reynolds-averaged Navier–Stokes (RANS) simulations are employed to predict the aerodynamic and thermal fields of the individual profiles using test-calibrated boundary conditions. Isothermal steady computations are performed at different wall temperatures to compute the adiabatic wall temperature and the heat transfer convective coefficient. Low-order models are used to represent the over-tip thermal field and the driving heat transfer mechanisms. The time-resolved outlet flow is characterized using a vortex tracking technique and high-frequency aerodynamic measurements to identify the rotor secondary flow structures.

Modeling hydrodynamic and biomass pyrolysis effects of recycled product gases in a bubbling fluidized bed reactor

Fast pyrolysis of biomass in a fluidized bed reactor is typically conducted in a nitrogen gas environment. Recycling product gas can improve the economics of operating such a system by reducing reliance on pure process streams, but much less is known about how recycling pyrolysis product gas may affect fluidization behavior and pyrolysis kinetics. Therefore, gas effects in a fluidized bed biomass pyrolysis reactor were investigated using engineering correlations, low-order models, and CFD simulations for N2, H2, CO, CO2, and CH4 carrier gas mixtures. Our findings reveal viscosity of a gas mixture can be significantly underestimated depending on the model and correlation. Furthermore, fluidization characteristics such as Umf and gas-solid convective heat transfer can be greatly affected by the gas properties. By utilizing H2 as the fluidizing gas (instead of N2), while maintaining a constant fluidization ratio (Us/Umf), the bio-oil yields can be increased ∼5%. This is due to the lower density H2 producing similar hydrodynamics as N2 at higher gas flow rates. These higher flow rates result in shorter gas residence times, and as a result, less secondary reactions that convert bio-oil to light gases and char. Model results also suggest that bio-oil yield is not significantly affected by the type of carrier gas used, with bio-oil yield varying by ∼2% across different gas mixtures while maintaining constant flow rate. This indicates that recycled pyrolytic gas can be used as the carrier gas for biomass pyrolysis.

Aerodynamic response of a red-tailed hawk to discrete transverse gusts

A limiting factor in the design of smaller size uncrewed aerial vehicles is their inability to navigate through gust-laden environments. As a result, engineers have turned towards bio-inspired engineering approaches for gust mitigation techniques. In this study, the aerodynamics of a red-tailed hawk’s response to variable-magnitude discrete transverse gusts was investigated. The hawk was flown in an indoor flight arena instrumented by multiple high-speed cameras to quantify the 3D motion of the bird as it navigated through the gust. The hawk maintained its flapping motion across the gust in all runs; however, it encountered the gust at different points in the flapping pattern depending on the run and gust magnitude. The hawk responded with a downwards pitching motion of the wing, decreasing the wing pitch angle to between −20∘ and −5∘, and remained in this configuration until gust exit. The wing pitch data was then applied to a lower-order aerodynamic model that estimated lift coefficients across the wing. In gusts slower than the forward flight velocity (low gust ratio), the lift coefficient increases at a low-rate, to a maximum of around 2–2.5. In gusts faster than the forward flight velocity (high gust ratio), the lift coefficient initially increased rapidly, before increasing at a low-rate to a value around 4–5. In both regimes, the hawk’s observed height change due to gust interaction was similar (and small), despite larger estimated lift coefficients over the high gust regime. This suggests another mitigation factor apart from the wing response is present. One potential factor is the tail pitching response observed here, which prior work has shown serves to mitigate pitch disturbances from gusts.

Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b

Context. WASP-76 b has been a recurrent subject of study since the detection of a signature in high-resolution transit spectroscopy data indicating an asymmetry between the two limbs of the planet. The existence of this asymmetric signature has been confirmed by multiple studies, but its physical origin is still under debate. In addition, it contrasts with the absence of asymmetry reported in the infrared (IR) phase curve. Aims. We provide a more comprehensive dataset of WASP-76 b with the goal of drawing a complete view of the physical processes at work in this atmosphere. In particular, we attempt to reconcile visible high-resolution transit spectroscopy data and IR broadband phase curves. Methods. We gathered 3 phase curves, 20 occultations, and 6 transits for WASP-76 b in the visible with the CHEOPS space telescope. We also report the analysis of three unpublished sectors observed by the TESS space telescope (also in the visible), which represents 34 phase curves. Results. WASP-76 b displays an occultation of 260 ± 11 and 152 ± 10 ppm in TESS and CHEOPS bandpasses respectively. Depending on the composition assumed for the atmosphere and the data reduction used for the IR data, we derived geometric albedo estimates that range from 0.05 ± 0.023 to 0.146 ± 0.013 and from <0.13 to 0.189 ± 0.017 in the CHEOPS and TESS bandpasses, respectively. As expected from the IR phase curves, a low-order model of the phase curves does not yield any detectable asymmetry in the visible either. However, an empirical model allowing for sharper phase curve variations offers a hint of a flux excess before the occultation, with an amplitude of ~40 ppm, an orbital offset of ~ −30°, and a width of ~20º. We also constrained the orbital eccentricity of WASP-76 b to a value lower than 0.0067, with a 99.7% confidence level. This result contradicts earlier proposed scenarios aimed at explaining the asymmetry observed in high-resolution transit spectroscopy. Conclusions. In light of these findings, we hypothesise that WASP-76 b could have night-side clouds that extend predominantly towards its eastern limb. At this limb, the clouds would be associated with spherical droplets or spherically shaped aerosols of an unknown species, which would be responsible for a glory effect in the visible phase curves.

Resolvent model for aeroacoustics of trailing edge noise

This study presents a physics-based, low-order model for the trailing edge (TE) noise generated by an airfoil at low angle of attack. The approach employs incompressible resolvent analysis of the mean flow to extract relevant spanwise-coherent structures in the transitional boundary layer and near wake. These structures are integrated into Curle’s solution to Lighthill’s acoustic analogy to obtain the scattered acoustic field. The model has the advantage of predicting surface pressure fluctuations from first principles, avoiding reliance on empirical models, but with a free amplitude set by simulation data. The model is evaluated for the transitional flow (Re=5e4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {Re} = 5e4$$\\end{document}) around a NACA0012 airfoil at 3 deg angle of attack, which features TE noise with multiple tones. The mean flow is obtained from a compressible large eddy simulation, and spectral proper orthogonal decomposition (SPOD) is employed to extract the main hydrodynamic and acoustic features of the flow. Comparisons between resolvent and SPOD demonstrate that the physics-based model accurately captures the leading coherent structures at the main tones’ frequencies, resulting in a good agreement of the reconstructed acoustic power with that of the SPOD (within 4 dB). Discrepancies are observed at high frequencies, likely linked to nonlinearities that are not considered in the resolvent analysis. The model’s directivity aligns well with the data at low Helmholtz numbers, but it fails at high frequencies where the back-scattered pressure plays a significant role in directivity. This modeling approach opens the way for efficient optimization of airfoil shapes in combination with low-fidelity mean flow solvers to reduce TE noise.Graphical abstract

BOATS: Bayesian Optimization for Active control of ThermoacousticS

This investigation presents novel adaptive control algorithms specifically designed to address and mitigate thermoacoustic instabilities. Gas turbines are limited in their operational range due to thermoacoustic instability. Two control strategies are available to alleviate this issue: active and passive. Active control strategies have a wider flexibility than passive control strategies because they can adapt to the operating conditions of the gas turbine. However, optimizing the control parameters remains a challenge, especially if additional constraints have to be fulfilled, such as e.g. pollutant emission levels. To address this issue, we propose three adaptive control strategies based on Bayesian optimization. The first and foundational algorithm is the safeOpt algorithm, and the two adaptations that have been made are stageOpt and shrinkAlgo. The algorithms facilitate safe exploration within the control parameter space, ensuring compliance with the constraint function, while simultaneously optimizing the objective function. The Gaussian Process Regressor (GPR) is employed to approximate both the objective and constraint functions, with continuous updates occurring during iterations. The algorithms also enable the transfer of knowledge obtained from one operating point to another, thereby reducing the number of iterations needed to reach the optimal point. We demonstrate the effectiveness of the algorithms both numerically and through two distinct experimental validations. In the numerical demonstration, we employ a low-order thermoacoustic network model to simulate a single-stage combustor setup equipped with loudspeaker actuation and a gain-delay (n−τ) controller for active stabilization. In the first experimental validation, we optimize the control parameters of a single-stage turbulent combustor with loudspeaker actuation and a gain-delay controller. For the second experimental validation, we apply the framework to a sequential combustor configuration utilizing nanosecond repetitively pulsed discharges (NRPD) as the control actuator. This demonstrates the framework’s adaptability to various control actuation methods in turbulent combustors where control parameter optimization is required.

Flame transfer function shaping for robust thermoacoustic systems: Application to a kinematic flame model

This work presents a data-driven optimization technique for the optimization of the flame response within a low-order acoustic network model. The methodology exploits the Nyquist criterion to compute a measure of thermoacoustic robustness at targeted frequencies, which serves as an objective value for the optimized system. The method is demonstrated using a simple Rijke tube model coupled with a [Formula: see text]-equation solver to model flame dynamics. The approach is shown to efficiently increase the stability margin of the system by modifying the flame transfer function. The methodology is applied to two examples, based on which possible scenarios are discussed and the potential and limitations associated with the practical implementation of the method are analyzed.

Evaluation of the thermo-acoustic instability frequency and growth rate via input reflection coefficient measurement for central heating equipment

Experimental measurement methods and theoretical evaluations based on low-order modeling approaches for both the growth rate and frequency at the onset of thermo-acoustic combustion instability are proposed, and their performance is evaluated. The developed techniques are demonstrated through a systematic measurement of the linear growth rate and frequency of evolving oscillations in the laboratory setup and also applied for the thermo-acoustic qualification of an industrial domestic boiler and a heat cell unit (combination of a burner with a heat-exchanger). Generic measurements have been done for a burner deck with premixed surface-stabilized Bunsen-type flames. The industrial domestic boiler and the heat cell unit are equipped with burners of a similar type but differ by their perforation pattern. They have been tested at different conditions and the experimental and theoretical results are compared. Two modeling strategies are tested: 1- in Laplace domain, with estimating a rational function in the complex domain to fit the measured frequency response, 2- exclusively in frequency domain, without estimating a rational function. Both methods include measurement of the frequency response of two reflection coefficients from i) the upstream part of the system, Rup, and ii) burner with flame completed by the downstream part of the appliance, Rin. Within the first approach, a procedure for an analytic continuation of the measured frequency response to the complex domain is applied and complex eigenfrequencies are calculated by solving the corresponding dispersion equation. An alternative approach was proposed by Kopitz and Polifke and allows estimating both the frequency of oscillation and the growth rate from the analysis of the polar plot of the system's characteristic equation in the frequency domain. The comparison shows that the unstable frequencies can be predicted accurately by both tested modeling strategies. This conclusion holds also for the tested industrial applications. The prediction of the instability growth rates is closer to the measured one when the modeling method in the complex domain is used. However, the frequency domain analysis provides less accurate, but still reasonable estimates of the growth rates and frequencies. Moreover, a good overview of thermo-acoustic performance of each industrial boiler/burner at different conditions is obtained via Rin measurements.

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.

Modelling the unsteady lift of a pitching NACA 0018 aerofoil using state-space neural networks

The development of simple, low-order and accurate unsteady aerodynamic models represents a crucial challenge for the design optimisation and control of fluid dynamical systems. In this work, wind tunnel experiments of a pitching NACA 0018 aerofoil conducted at a Reynolds number $Re = 2.8 \times 10^5$ and at different free-stream turbulence intensities are used to identify data-driven nonlinear state-space models relating the time-varying angle of attack of the aerofoil to the lift coefficient. The proposed state-space neural network (SS-NN) modelling technique explores an innovative methodology, which brings the flexibility of artificial neural networks into a classical state-space representation and offers new insights into the construction of reduced-order unsteady aerodynamic models. The work demonstrates that this technique provides accurate predictions of the nonlinear unsteady aerodynamic loads of a pitching aerofoil for a wide variety of angle-of-attack ranges and frequencies of oscillation. Results are compared with a modified version of the Goman–Khrabrov dynamic stall model. It is shown that the SS-NN methodology outperforms the classical semi-empirical dynamic stall models in terms of accuracy, while retaining a fast evaluation time. Additionally, the proposed models are robust to noisy measurements and do not require any pre-processing of the data, thus involving only a limited user interaction. Overall, these features make the SS-NN technique an excellent candidate for the construction of accurate data-driven models from experimental fluid dynamics data, and pave the way for their adoption in applications entailing design optimisation and real-time control of systems involving lift.

Low-order modeling approach for the prediction of transverse combustion instabilities in multi-injector engines

This paper addresses the prediction of spontaneous self-sustained transverse combustion instabilities in multi-injector engines using a multi-dimensional non-linear low-order Eulerian model. The approach utilizes a physically aware response function that directly links pressure oscillations to fuel mass flow rate, independent of external data. This enables accurate capture of the behavior of shear coaxial injectors that have been proven to show a peculiar dynamics of cyclic fuel accumulation and release in response to acoustic waves. A NASA test case is employed as a reference, and a comprehensive analysis is conducted to investigate the behavior of the model. Firstly, a preliminary analysis is performed within a quasi-one-dimensional framework for a reduced single-injector configuration. This analysis provides insights into the influence of key parameters on the instability onset. Subsequently, the full-scale geometry is considered in a multi-dimensional framework, and the low-order solver is employed to analyze the thermo-acoustic behavior of the engine. The model successfully captures the instability dynamics, including temporal evolution, dominant frequency, and mode shapes. Sensitivity analyses are conducted to examine the impact of the model free parameters on the unstable modes. Additionally, the effect of introducing baffles as damping devices within the combustion chamber is investigated. The results highlight the model predictive capabilities and its potential for guiding the design and optimization of liquid rocket engines.

Plasticity in nonlinear elastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials have been shown to admit a variety of rich, dynamical features that can be leveraged to tailor the propagation of mechanical waves. Since these materials derive their properties from intricate, subwavelength geometries, direct numerical simulations are often prohibitively expensive at scales of interest. To overcome this limitation, reduced-order models, typically in the form of effective continua or discrete lattices that capture the essential features of the material at sufficiently long wavelengths, have been developed. While many prior studies have implemented these models successfully, the vast majority have considered only recoverable elastic deformations with linear damping and neglected history-dependent effects, such as plasticity and friction. In this presentation, we introduce an effective lattice modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history-dependent nature of plasticity, this framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than a purely elastic system of similar size. We apply the method to several examples of interest and explore means to obtain phenomenological elastic-plastic models for general material architectures.

Low-order gray-box modeling of heating buildings and the progressive dimension reduction identification of uncertain model parameters

Heating buildings have a huge heat capacity and have abilities to accept fluctuating heat supply from renewables. Creating a low-order scalable model that describes the thermal dynamics of coupled heat transfer, charge, and discharge processes among heating buildings is essential to unlocking the thermal storage potential of building mass and achieving space heating decarbonization. White-box models tend to be too complex and black-box models lack scalability. Thus, a low-order gray-box model with uncertain lumped parameters is proposed based on comprehensive heat transfer analyses and necessary assumptions. Thermal mass in heating buildings is divided into four independent heat storage units. The building envelope that can be heated directly or not is regarded as a different heat storage unit. To reduce the search space dimension of model identification, the decision variables are downsized to essential model parameters based on the sensitivity analysis. Moreover, a progressive dimension reduction method is introduced to further improve the probability that the optimization algorithm converges to a global minimum. Case studies show that the calibrated model with global optimal solutions of uncertain model parameters has a good performance on the prediction of the average temperature of indoor air, the average absolute error is only 0.1 °C.

A practical solution for multivariable control of temperature and humidity in greenhouses

This paper presents a simple and effective control solution to regulate temperature and humidity inside a greenhouse, which are the main climatic variables affecting crop growth and health. A multivariable control strategy with inverted decoupling is proposed in two schemes. The nighttime control scheme uses heating and dehumidification, and the daytime control scheme uses natural ventilation, dehumidification, and humidification. A system identification methodology is used to obtain low-order linear models from data measured in a greenhouse. This simplifies the design of proportional–integral (PI) controllers and allows the use of well-known control techniques. For instance, anti-windup is used to deal with the saturation of the actuators and for a bumpless transfer mechanism to switch between the nighttime and the daytime control schemes. Setpoint weighting is used for the humidity controllers to attenuate undesired effects on the temperature control loop when the humidity setpoint is changed. Furthermore, split range control is used for the first time to control humidity by combining a heat-pump dehumidifier and a fogging system. The control solution presented in this work allows the integral absolute error to be reduced, on average, by 88.5% for the interactions affecting the temperature control loop, and by 85.6% for the humidity control loop, compared to decentralized PI control. The control schemes have been tested in simulation with real disturbance data from a Mediterranean greenhouse and in preliminary form in a real facility to conclude that the proposed multivariable control strategy could be effective in decoupling the temperature and the humidity control loops.

Data-Driven Unsteady Aerodynamic Modeling for Fluid–Structure Interaction

The piston theory class of simplified aerodynamic models that link body deformation to localized pressure fluctuation with respect to a mean steady state is attractive for modeling purposes as they constitute a computationally efficient model to calculate the unsteady pressure response on deforming bodies. However, as piston theories are valid for flow regimes where M>1.5, they are inaccurate for modeling the aerodynamic response associated with aeroelastic phenomena in subsonic or low-supersonic flow regimes. Unsteady computational fluid dynamics (CFD) simulations are used to learn the unsteady pressure response, and dynamic mode decomposition (DMD) is applied to the error between the CFD-computed pressure fluctuation and the piston-theory-predicted pressure fluctuation. This process is performed on two-dimensional and three-dimensional flow domains over various flow regimes. For both scenarios, the DMD analysis learns dominant spatial modes in the error that constitute low-order models, which may be used to improve the pressure response and are confirmed to be physically relevant. A method for computing aeroelastic stability with these leading modes is discussed and applied to fluid–structural beam and panel configurations. The results are compared against prior numerical and experimental investigations to quantify the improvement in prediction obtained by the DMD-augmented piston theory.

Genetic Algorithm-Based Optimisation of a Double-Wall Effusion Cooling System for a High-Pressure Turbine Nozzle Guide Vane

Double-Wall Effusion Cooling schemes present an opportunity for aeroengine designers to achieve high overall cooling effectiveness and convective cooling efficiency in High-Pressure Turbine blades with reduced coolant usage compared to conventional cooling technologies. This is accomplished by combining impingement, pin-fin and effusion cooling. Optimising these cooling schemes is crucial to ensuring that cooling is achieved sufficiently at high-heat-flux regions and not overused at low-heat-flux ones. Due to the high number of design variables employed in these systems, optimisation through the use of Computational Fluid Dynamics (CFD) simulations can be a computationally costly and time-consuming process. This study makes use of a Low-Order Flow Network Model (LOM), developed, validated and presented previously, which quickly assesses the pressure, temperature, mass flow and heat flow distributions through a Double-Wall Effusion Cooling scheme. Results generated by the LOM are used to rapidly produce an ideal cooling system design through the use of an Evolutionary Genetic Algorithm (GA) optimisation process. The objective is to minimise the coolant mass flow whilst maintaining acceptable metal cooling effectiveness around the external surface of the blade and ensuring that the Backflow Margin for all film holes is above a selected threshold. For comparison, a Genetic Aggregation model-based optimisation using CFD simulations in ANSYS Workbench is also conducted. Results for both the reduction of coolant mass flow and the total optimisation runtime are analysed alongside those from the LOM, demonstrating the benefit of rapid low-order solving techniques.

A Low-Order Steady-State Model of Electric Springs for Conservation Voltage Reduction in Active Distribution Networks With Renewables

Electric spring (ES), as a new type of power electronic device, can flexibly regulate the voltage of noncritical load (NL) and improve the voltage quality of critical load (CL). It can further increase the energy savings of conservation voltage reduction (CVR) in active distribution networks (ADNs). However, the high-order nonlinearity of ESs steady-state model brings the difficulty of solving the CVR optimization problem Therefore, this paper proposes a low-order steady-state model of ESs for CVR in ADNs. The operation modes of ESs are extended based on analysis of voltage regulation characteristics, firstly. The equivalent circuit of the bus with an ES is also derived, and a steady-state model with low-order nonlinearity is further proposed. Then, considering significant difference in response speeds among ESs, distributed generation (DGs) and discrete control devices (DCDs), a two-stage coordinated operation model of ESs, DGs and DCDs is established. By means of convex envelope and linearization, the nonconvex nonlinear constraints are transformed into linear constraints, which can improve the convergence and solving efficiency of the optimization model. Finally, the case studies demonstrate that ESs can increase the CVR energy savings, and the proposed low-order steady-state model can improve the solving efficiency of this CVR optimization problem.

On the rotation of a Savonius turbine at low Reynolds numbers subject to Kolmogorov cascade of turbulence

With an increasing demand for small energy generation in urban areas, small-scale Savonius wind turbines are growing their share rapidly. In such an environment, Savonius turbines are exposed to low mean velocity with highly turbulent flows made by complex geographies. Here, we report the flow-induced rotation of a Savonius turbine in a highly turbulent flow (18% turbulence intensity). The high turbulence is realized by using the far-field of an open-jet. Compared to low turbulence inflow (1% turbulence intensity), the turbine rotates 4% faster in high turbulence since the torque/power increases with turbulence intensity. The wake measurement by hot-wire anemometry and particle image velocimetry reveals the suppression of vortex shedding in high turbulence. In addition, a newly developed semi-empirical low-order model, which can include the effect of turbulence intensity and integral length scale, also confirms high turbulence intensity contributes to the rotation of the turbine. These results will boost more installation of small Savonius turbines in urban areas in the future.