The overall cost of a hydropower plant is mainly due to the expenses for civil works, mechanical equipment (turbine and control units) and electrical components. The goal of a new draft tube design is to obtain a geometry that reduces investment costs, especially the excavation ones, but the primary driver is to increase the overall machine efficiency allowing for reduced payback time. In the present study, an optimization study of the elbow-draft tube assembly of a Kaplan turbine was conducted. A CFD model for the complete turbine has been developed and validated; next, an optimization of the draft tube alone was performed using a Design of Experiments technique; finally, several optimum solutions for the draft tube were obtained using a Response Surface technique aiming at maximizing pressure recovery and minimizing flow losses. A selection of optimized geometries was subsequently post-checked using the validated model of the entire turbine and a detailed flow analysis on the obtained results could make it possible to provide insight into the improved designs. It was observed that efficiency could be improved by 1% (in relative terms), and the mechanical power increased by 1,8% (in relative terms) with respect to the baseline turbine.

Production of electricity using hydro-kinetic tidal turbines has many challenges that must to be overcome to ensure reliable, economic and practical solutions. Energy from flowing water is converted by a system comprising: the turbine rotor blades, a gearbox, an electrical generator, control systems, power electronics, export cables, and a connection to the electricity grid. To date these have often been modelled using simulations of independent systems, lacking bi-directional, real-time, coupling. This approach leads to critical effects being missed. Turbulence in the flow, results in large velocity fluctuations around the blades, causing rapid variation in the shaft torque and generator speed, and consequently in the voltage seen by the power electronics and consequently the export power quality. The resulting poor quality power may be unacceptable to the grid. Conversely, grid frequency and voltage changes can also cause the generator speed to change, resulting in changes to the shaft speed and torque and consequently changes to the lift and drag forces acting on the blades. Clearly, fully integrated, bi-directional, models are needed. Here we present two fully coupled models which use different approaches to model the hydrodynamics of rotor blades. The first model uses Blade Element Momentum Theory (BEMT), resulting in an efficient tool for turbine designers. The second model also uses BEMT combines this with an actuator line model of the blades coupled to an unsteady computational fluid dynamics (CFD) simulation. This simulation, implemented in OpenFOAM, uses an energy balance to compute the shaft speed. Both the BEMT and CFD models are coupled to an Open Modellica model of the electro-mechanical system. Both models have been used to simulate the performance of a 1.2m diameter, scale model, of a three bladed horizontal axis tidal turbine tested in the University of Edinburgh FloWave Ocean Energy Research Facility. The turbulent flow around the blades and the mechanical-electrical variables during the stable period of operation are analysed. Time series and tabulated average values of mechanical thrust, power, torque, and rotational speed as well as electrical variables of generator power, electromagnetic torque, voltage and current are presented for the coupled system simulation. The relationship between the mechanical and electrical variables and the results from both tidal turbine approaches are discussed. Our comparison shows that while the BEMT model provides an effective design tool (leading to slightly more conservative designs), the CFD/BEMT simulations provide more accurate predictions of the blade loads which can be especially important in assessing fatigue on the blades (though at an increased computational cost).

The use of wind energy has been developing fast over the last years. The global cumulative wind power capacity increased by 10.5% in 2019, most of which comes from onshore wind farms. One of the consequences of this continuous increase is the use of land for onshore wind farms. There are already cases worldwide where lack of well-established plans and strategies have caused delays in projects. The need for efficiently using land for wind farms will be mandatory in the short term. In this work, we present a numerical analysis to evaluate wind farm land-use. By defining the ratio between mechanical output power over an area as a parameter called land-use ratio, this work focused on comparing several cases of aligned and staggered layouts. Mechanical output power was estimated using a validated code based on Blade Element Momentum code, and the wake velocities and wake interaction effects were estimated using a validated wind turbine CFD model. In terms of output power, staggered designs are more efficient than aligned designs. However, the results showed that even though staggered designs produced higher output power, aligned farms with tight lateral spacing could be as efficient as staggered ones in terms of land-use but using fewer turbines. In summary, tightly aligned designs should be a tendency in the future towards efficient use of land in wind farms.

Turbine generator operates with complex cooling system due to the challenge in controlling the peak temperature of the stator bar caused by ohm loss, which is unavoidable. Therefore, it is important to characterise and quantifies the thermal performance of the cooling system. The focus of the present research is to investigate the heat transfer and pressure loss characteristics of typical cooling system, so-called stator ventilation duct. A real scale model was built at its operating conditions for the present study. The direction of cooling air is varied to consider its operation condition, so that there are (1) outward flow and (2) inward flow cases. In addition, the effect of (3) cross flow (inward with cross flow case) is also studied. The transient heat transfer method using thermochromic liquid crystals is implemented to measure full surface heat transfer distribution. A series of Computational Fluid Dynamics analysis is also conducted to support the observation from the experiment. For the inward flow case, the results suggest that the average Nusselt number of the 2nd duct is about 30% higher than the 3rd duct. The trend is similar with the effect of cross flow. The CFD results are in good agreement with the experimental data.

Tidal stream energy, due to its high level of consistency and predictability, is one of the feasible and promising type of renewable energy for future development and investment. Applicability of Blade Element Momentum (BEM) method for modeling the interaction of turbines in tidal arrays has been proven in many studies. Apart from its well-known capabilities, yet there is scarcity of research using BEM for the modeling of tidal stream energy farms considering full scale rotors. In this paper, a real geographical site for developing a tidal farm in the southern coasts of Iran is selected. Then, a numerical methodology is validated and calibrated for the selected farm by analyzing array of turbines. A linear equation is proposed to calculate tidal power of marine hydrokinetic turbines. This methodology narrows down the wide range of turbine array configurations, reduces the cost of optimization and focuses on estimating best turbine arrangements in a limited number of positions.

Wind power output is highly dependent on the wind speed at the selected site, therefore wind-speed distribution modeling is the most important step in the assessment of wind energy potential. This study aims at accurate evaluation of onshore wind energy potential in seven coastal cities in the south of Iran. Six Probability Distribution Functions (PDFs) were examined over representative stations. It has been deduced that the Weibull function, which was the most used PDF in similar studies, was only applicable to one station. Here, Gamma offered the best fit for three stations and for the other ones, Generalized Extreme Value (GEV) performed better. Considering the ranking of six examined PDFs and the simplicity of Gamma, it was identified as the effective function in the southern coasts of Iran bearing in mind the geographic distribution of stations. Besides, six turbine power curve functions were contributed to investigate the capacity factor. That was very important, as using only one function could cause under- or over-estimation. Then, stations were classified based on the National Renewable Energy Laboratory system. Last but not least, examining a range of wind turbines enabled scholars to extend this study into the practice and prioritize development of stations considering budget limits.

Climate change impacts and adaptations is subject to ongoing issues that attract the attention of many researchers. Insight into the wind power potential in an area and its probable variation due to climate change impacts can provide useful information for energy policymakers and strategists for sustainable development and management of the energy. In this study, spatial variation of wind power density at the turbine hub-height and its variability under future climatic scenarios are taken under consideration. An ANFIS based post-processing technique was employed to match the power outputs of the regional climate model with those obtained from the reference data. The near-surface wind data obtained from a regional climate model are employed to investigate climate change impacts on the wind power resources in the Caspian Sea. Subsequent to converting near-surface wind speed to turbine hub-height speed and computation of wind power density, the results have been investigated to reveal mean annual power, seasonal, and monthly variability for a 20-year period in the present (1981-2000) and in the future (2081-2100). The results of this study revealed that climate change does not affect the wind climate over the study area, remarkably. However, a small decrease was projected for future simulation revealing a slightly decrease in mean annual wind power in the future compared to historical simulations. Moreover, the results demonstrated strong variation in wind power in terms of temporal and spatial distribution when winter and summer have the highest values of power. The findings of this study indicated that the middle and northern parts of the Caspian Sea are placed with the highest values of wind power. However, the results of the post-processing technique using adaptive neuro-fuzzy inference system (ANFIS) model showed that the real potential of the wind power in the area is lower than those of projected from the regional climate model.

Gas Path Analysis and matching turbine engine models to experimental data are inverse problems of mathematical modelling which are characterized by parametric uncertainty. This results from the fact that the number of measured parameters is significantly lower than the number of components’ performance parameters needed to describe the real engine. In these conditions, even small measurement errors can result in a high variation of results, and obtained efficiency, loss factors etc. can appear out of the physical range. The current methods of engine model identification have developed considerably to provide stable, precise and physically adequate solutions. Presented in this work is an estimation method of engine components’ parameters based on multi-criteria identification which provides stable estimations of parameters and their confidence intervals with the known measurement errors. A priori information about the engine, its parameters and performance is used directly in the regularised identification procedure. The mathematical basis for this approach is the fuzzy sets theory. Forming objective functions and scalar convolutions synthesis of these functions is used to estimate gas-path components’ parameters. A comparison of the proposed approach with traditional methods showed that its main advantage is high stability of estimation in the parametric uncertainty conditions. Regularization reduces scattering, excludes incorrect solutions which do not correspond to a priori assumptions, and also helps to implement the Gas Path Analysis at the limited number of measured parameters. The method can be used for matching thermodynamic models to experimental data, Gas Path Analysis and also adapting dynamic models for the needs of the engine control system.

In April 2019, a team of Keio University and Bucknell University students was assembled to participate in Ericsson Innovation Awards with a novel concept for generating renewable energy. This conceptual system consists of a vertical axis wind turbine, a crossflow marine hydrokinetic turbine, a floating platform integrated with a quadcopter system, and three to four temporary mooring lines with ship-type anchors. The proposed designed aims to offer solutions to two current problems of floating offshore wind energy: high construction cost of floating platforms and difficulties in maintenance of mooring lines. The combination of two vertical-axis turbines into a single floating platform would enable the system, namely ESwift, to extract energy from both wind and current resources. Additionally, due to the utilization of vertical axis turbines, the center of gravity of the proposed concept is significantly lower with respect to water level, compared to that of existing floating horizontal axis wind turbines, which would potentially reduce the floater's size and construction cost. Lastly, the integrated quadcopter mechanism would assist the floater in terms of stability and mobility, and enables an array of ESwifts to automatically rearrange for maximal energy generation. The authors hope that readers would find the idea described in this open access letter worth pursuing and would further develop and commercialize the ESwift concept.

This paper analyses the health and performance of 12-stage axial compressor of the TV3-117VM/VMA turboshaft operated in a desert environment. The results of the dimensional control of 4,800 worn blades are analysed to model the wear process. Operational experience and numerical simulations are used to assess the effectiveness of an Inlet Particle Separator. Numerical modal analysis is performed to generate the Campbell diagram of worn blades and identify resonant blade vibration which can lead to high cycle fatigue (HCF). It is shown that the gradual loss of the stall margin over time determines the serviceability limits of compressor blades. Recommendations setting out go / no-go criteria are made to maintenance and repair organisations.

The basic equation for estimating the aerodynamic power captured by an Anderson Vertical Axis Wind Turbine (AVAWT) is a solution of the Navier-Stokes(N-S) equations for a baroclinic, inviscid flow. In a nutshell, the pressure difference across the AVAWT is derived from Bernoulli’s equation; an upshot of the integration of the N-S momentum equation for a baroclinic inviscid flow, Euler’s momentum equation. The resulting expression for the pressure difference across the AVAWT rotor is plotted as a function of freestream speed. Experimentally determined airstream speeds at the AVAWT inlet and outlet, coupled with corresponding freestream speeds are used in estimating the aerodynamic power captured. The aerodynamic power is subsequently used in calculating the aerodynamic power coefficient of the AVAWT. The actual power coefficient is calculated from the power generated by the AVAWT at various free stream speeds and plotted as a function of the latter. Experimental results show that, at all free stream speeds and tip speed ratios, the aerodynamic power coefficient is higher than the actual power coefficient of the AVAWT. Consequently, the power generated by the AVAWT prototype is lower than the aerodynamic power captured, given the same inflow wind condition.

Instead of simplified steady-state models, with modern computers, one can solve the complete aero-thermodynamics happening in gas turbine engines. In the present article, we describe a mathematical model and numerical procedure to represent the transient response of a PT6A gas turbine engine operating at off-design conditions. The aero-thermal model consists of a set of algebraic and ordinary differential equations that arise from the application of the mass, linear momentum, angular momentum, and energy balances in each engine's component. The solution code has been developed in Matlab-Simulink using a block-oriented approach. Transient simulations of the PT6A engine start-up have been carried out by changing the original Jet-A1 fuel with biodiesel blends. Time plots of the main thermodynamic variables are shown, especially those regarding the structural integrity of the burner. Numerical results have been validated against reported experimental measurements and GasTurb simulations. The computer model has been capable to predict acceptable fuel blends, such that the real PT6A engine can be substituted to avoid the risk of damaging it.

Monin-Obukhov similarity theory (MOST) overestimates wind shear in some atmospheric stable conditions, i.e. Richardson number $R_f<0.25$. The overestimated wind shear that leads to an under-predicted friction wind speed and a lower ambient turbulence intensity for a given hub-height reference wind speed and a given roughness length, could influence wake modeling of a wind turbine. This work investigates the side effects of the breakdown of MOST on wake modeling under stable conditions and makes some modifications to the flow similarity functions to eliminate these side effects. Based on a field measurement in a wind farm, we firstly show that MOST predicts a larger wind shear for the atmospheric stability parameter $\zeta>0.1$ and proposes new flow similarity functions without constraining $R_f$ to limit the overestimated wind shear by MOST. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier–Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in larger wake deficits and slower wake recovery rate with a square root of the mean-squared-error (RSME) of wake deficit in the range of 0.07-0.18. This overestimated wake effect is improved by applying the new similarity functions and the RSME of wake deficit is averagely reduced by 0.05. Finally, we check the role of the under-predicted turbulence intensity playing in the larger wake deficit predicted by models based MOST. Additional numerical simulations using the modified turbulence model are carried out, in which the roughness length is reduced to impose a hub-height ambient turbulence intensity equivalent to the MOST case. Simulation results show that reducing turbulence intensity enhances wake effects, however, it cannot reproduce the large wake deficit predicted by models based on MOST, which suggests that the overestimated wake effect by MOST could be also related to the overestimated wind shear.

A modified free-wake vortex ring model is proposed to compute the dynamics of a floating horizontal-axis wind turbine. The model is divided into two parts. The near wake model uses a blade bound vortex model and trailed vortex model, which is developed based on vortex filament method. By contrast, the far wake model is based on the vortex ring method. The proposed model is a good compromise between accuracy and computational cost, for example when compared with more complex vortex methods. The present model is used to assess the influence of floating platform motions on the performance of a horizontal-axis wind turbine rotor. The results are validated on the 5MW NREL rotor and compared with other aerodynamic models for the same rotor subjected to different platform motions. It was found that the results from the proposed method are more reliable than the results from BEM theory especially at small angles of attack in the region of low wind speeds, on the one hand, and high wind speeds with blade pitch motions, on the other hand. And also the proposed method is less time consuming and has similar accuracy when comparing with more advanced vortex based methods.

Atmospheric stability affects wind turbine wakes significantly. High-fidelity approaches such as large eddy simulations (LES) with the actuator line (AL) model which predicts detailed wake structures, fail to be applied in wind farm engineering applications due to its expensive cost. In order to make wind farm simulations computationally affordable, this paper proposes a new actuator disk model (AD) based on the blade element method (BEM) and combined with Reynolds-averaged Navier–Stokes equations (RANS) to model turbine wakes under different atmospheric stability conditions. In the proposed model, the upstream reference velocity is firstly estimated from the disk averaged velocity based on the one-dimensional momentum theory, and then is used to evaluate the rotor speed to calculate blade element forces. Flow similarity functions based on field measurement are applied to limit wind shear under strongly stable conditions, and turbulence source terms are added to take the buoyant-driven effects into consideration. Results from the new AD model are compared with field measurements and results from the AD model based on the thrust coefficient, the BEM-AD model with classical similarity functions and a high-fidelity LES approach. The results show that the proposed method is better in simulating wakes under various atmospheric stability conditions than the other AD models and has a similar performance to the high-fidelity LES approach however in much lower computational cost.

Modern gas turbines firing temperatures (1500-2000K) are well beyond the maximum allowable blade material temperatures. Continuous safe operation is made possible by cooling the HP turbine first stages -nozzle vanes and rotor blades- with a portion of the compressor discharge air, a practice that induces a penalty on the cycle thermal efficiency. Therefore, a current issue is to investigate the real advantage, technical and economical, of raising maximum temperatures much further beyond current values. In this paper, process simulations of a gas turbine are performed to assess HP turbine first-stage cooling effects on cycle performance. A new simplified and properly streamlined model is proposed for the non-adiabatic expansion of the hot gas mixed with the cooling air within the blade passage, which allows for a comparison of several cycle configurations at different TIT (turbine inlet temperature) and max (total turbine expansion ratio) with a realistically acceptable degree of approximation.. The calculations suggest that, at a given max, the TIT can be increased in order to reach higher cycle efficiency up to a limit imposed by the required amount and temperature of the cooling air. Beyond this limit, no significant gains in thermal efficiency are obtained by adopting higher max and/or increasing the TIT, so that it is convenient in terms of cycle performance to design at lower rather than higher max. The small penalty on cycle efficiency is compensated by lower plant cost. The results of our model agree with those of some previous much more complex and computationally expensive studies, so that the novelty of this paper lies in the original method adopted on which the proposed model is based, and in the fast, accurate and low resource intensity of the corresponding numerical procedure: all advantages that can be crucial for industry needs. The presented analysis is purely thermodynamic, with no investigation on the effects of the different configurations on plant costs, so that future work addressing a thermo-economic analysis of the air-cooled gas turbine power plant is the next logical step.

This paper presents findings of a study on continuous feed-in management and continuous synthetic inertia contribution with wind turbines. A realistic case study, based on real measurements, is outlined. A wind turbine feeds into a weak feeder, such that its power has to be adapted to the permissible loading of this feeder. At the same time the wind turbine is to provide inertia to the grid by applying the previously published variable inertia constant controller. It is discussed that optimal grid utilisation and simultaneous inertia contribution are mandatory for the frequency control in power systems that are heavily penetrated with renewable energies. The study shows that continuous feed-in management can be combined well with continuous inertia provision. There are hardly any negative consequences for the wind turbine. The benefits for the grid are convincing, both in terms of increased system utilisation and in terms of provided inertia. It is concluded that wind turbines can enhance angular stability in a power system to a larger extent than conventional power plants.

Although many devices have recently been proposed for pressure regulation and energy harvesting in water distribution and transport networks, very few applications are still documented in the scientific literature. A new in-line Banki turbine with positive outflow pressure and a mobile regulating flap, named PRS, was installed and tested in a real water transport network for pressure and discharge regulation. The PRS turbine was directly connected to a 55 kW asynchronous generator with variable rotational velocity, coupled to an inverter. The start-up tests showed how automatic adjustment of the flap position and the impeller velocity variation are able to change the characteristic curve of the PRS according to the flow delivered by the water manager or to the pressure set-point assigned downstream or upstream of the system, still keeping good efficiency values in hydropower production.

Knowledge about laminar-turbulent transition on operating multi-megawatt wind turbine blades needs sophisticated equipment like hot-films or microphone arrays. Contrarily thermographic pictures can easily be taken from the ground and temperature differences indicate different states of the boundary layer. The accuracy however, still is an open question, so that an aerodynamic glove known from experimental research on aero-planes was used to classify the boundary-layer state of a 2 megawatt wind turbine blade operating in the orthern part of Schleswig-Holstein, Germany. State-of-the-art equipment for measurering static surface pressure was used for monitoring the lift distribution. To distinguish laminar and turbulent parts of the boundary layer (suction side only) 48 microphones were applied together with ground-based thermographic cameras from two teams. Additionally, an optical camera mounted on the hub was used to survey vibrations. During start-up (from 0 to 9 rpm) extended, but irregularly shaped regions of a laminar boundary layer were observed which had the same extension measured both with microphones and Thermography. When an approximately constant rotor rotation (9 rpm corresponding to approximately 6 m/s wind-speed) was achieved, a flow transition was visible at the expected position of 40 % chord length on the rotor blade, which was fouled with dense turbulent wedges and an almost complete turbulent state on the glove was detected. In all observations, quantitative determination of the flow transition positions from thermography and microphones agree well within their accuracy.

The recent growing attention to energy saving and environmental protection issues has brought to attention the possibility of exploiting syngas from gasification of biomass and coal for the firing of industrial plants included the so called Integrated Gasification Combined Cycle ones. In order to improve the knowledge about the employ of syngas in lean premixed turbulent flames, a large scale swirl stabilized gas-turbine burner has been operated with a simplified model of H₂ enriched syngas from coal gasification. The experimental campaign has been performed at atmospheric pressure with operating conditions derived from scaling the real gas turbines ones. The results are here reported and consist of OH-PLIF measurements carried out at decreasing air equivalence ratio conditions and are analysed together with the mean aerodynamic characterisation of the burner flowfield in isothermal condition. The OH concentration distributions have been analysed statistically in order to obtain information about the location of the most reactive zones and an algorithm has been applied to the data in order to identify the flame fronts. In addition, the flame front locations have been successively interpreted statistically in order to obtain information about their main features and about their dependence on the air to fuel ratio behaviour.

Renewable energy sources will play a central role in the sustainable energy systems of the future. Scenario analyses of such hypothesized energy systems require sound knowledge of the techno-economic potential of renewable energy technologies. Although there have been various studies concerning the potential of offshore wind energy, higher spatial resolution, as well as the future design concepts of offshore wind turbines, has not yet been addressed in sufficient detail. Here, we aim to overcome this gap by applying a high spatial resolution to the three main aspects of offshore wind potential analysis, namely ocean suitability, the simulation of wind turbines and cost estimation. A set of constraints is determined that reveal the available areas for turbine placement across Europe’s maritime boundaries. Then, turbine designs specific to each location are selected by identifying turbines with the cheapest levelized cost of electricity (LCOE), restricted to capacities, hub heights and rotor diameters of between 3-20 MW, 80-200 m and 80-280 m, respectively. Ocean eligibility and turbine design are then combined to distribute turbines across the available areas. Finally, LCOE trends are calculated from the individual turbine costs, as well as the corresponding capacity factor obtained by hourly simulation with wind speeds from 1980 to 2017. The results of cost-optimal turbine design reveal that the overall potential for offshore wind energy across Europe will constitute nearly 8.6 TW and 40.0 PWh at roughly 7 €_ct kWh^-1 average LCOE by 2050. Averaged design parameters at national level are provided in an appendix.

The development and application of marine current energy are attracting more and more attention around the world. Due to the hardness of its working environment, it is important and difficult to study the fault diagnosis of a marine current generation system. In this paper, an underwater image is chosen as the fault-diagnosing signal, after different sensors are compared. This paper proposes a diagnosis method based on the sparse autoencoder (SA) and softmax regression (SR). The SA is used to extract the features and SR is used to classify them. Images are used to monitor whether the blade is attached by benthos and to determine its corresponding degree of attachment. Compared with other methods, the experiment results show that the proposed method can diagnose the blade attachment with higher accuracy.

Timely detection of surface damages on wind turbine blades is imperative for minimising downtime and avoiding possible catastrophic structural failures. With recent advances in drone technology, a large number of high-resolution images of wind turbines are routinely acquired and subsequently analysed by experts to identify imminent damages. Automated analysis of these inspection images with the help of machine learning algorithms can reduce the inspection cost, thereby reducing the overall maintenance cost arising from the manual labour involved. In this work, we develop a deep learning based automated damage suggestion system for subsequent analysis of drone inspection images. Experimental results demonstrate that the proposed approach could achieve almost human level precision in terms of suggested damage location and types on wind turbine blades. We further demonstrate that for relatively small training sets advanced data augmentation during deep learning training can better generalise the trained model providing a significant gain in precision.

The interest on the use of renewable energy resources is increasing, especially towards wind and hydro powers, which should be efficiently converted into electric energy via suitable technology tools. To this aim, data--driven control techniques represent viable strategies that can be employed for this purpose, due to the features of these nonlinear dynamic processes working over a wide range of operating conditions, driven by stochastic inputs, excitations and disturbances. Some of the considered methods, such as fuzzy and adaptive self--tuning controllers, were already verified on wind turbine systems, and similar advantages may thus derive from their appropriate implementation and application to hydroelectric plants. These issues represent the key features of the work, which provides some guidelines on the design and the application of these control strategies to these energy conversion systems. The working conditions of these systems will be also taken into account in order to highlight the reliability and robustness characteristics of the developed control strategies, especially interesting for remote and relatively inaccessible location of many installations.

The fault diagnosis of wind turbine systems represent a challenging issue, especially for offshore installations, thus justifying the research topics developed in this work. Therefore, this paper addresses the problem of the fault diagnosis of wind turbines, and it present viable solutions of fault detection and isolation techniques. The design of the so--called fault indicator consists of its estimate, which involves data--driven methods, as they result effective tools for managing partial analytical knowledge of the system dynamics, together with noise and disturbance effects. In particular, the suggested data--driven strategies exploit fuzzy systems and neural networks that are employed to determine nonlinear links between measurements and faults. The selected architectures are based on nonlinear autoregressive with exogenous input prototypes, as they approximate the dynamic evolution of the system along time. The designed fault diagnosis schemes are verified via a high--fidelity simulator, which describes the normal and the faulty behaviour of an offshore wind turbine plant. Finally, by taking into account the presence of uncertainty and disturbance implemented in the wind turbine simulator, the robustness and the reliability features of the proposed methods are also assessed. This aspect is fundamental when the proposed fault diagnosis methods have to be applied to offshore installations.

Abstract: The recent growing attention to energy saving and environmental protection issues has brought to attention the possibility of exploiting syngas from gasification of biomass and coal for the firing of industrial plants included the so called Integrated Gasification Combined Cycle ones. In order to acquire a detailed knowledge about the behaviour of lean turbulent premixed flames, the present work resent the results of an experimental characterisation of a prototypical gas turbine burner operated at atmospheric pressure at condition scaled from real gas turbines ones. The results here presented derive from OH-PLIF measurements carried out at decreasing air equivalence ratio conditions and are analysed together with a mean aerodynamic characterisation of the burner operating in isothermal condition. The OH concentration distributions have been analysed statistically in order to obtain information about the location of the most reactive zones and an algorithm has been applied to the data sets in order to identify the flame fronts. In addition, the flame front locations have been successively interpreted statistically in order to obtain information about their main features and about their dependence on the air to fuel ratio behaviour.

In this study, the on-going research into the improvement of micro-gas turbine propulsion system performance and the suitability for application as propulsion systems for small tactical UAVs (<600 kg) is investigated. The study is focused around the concept of converting existing micro turbojet engines to turbofan with the use of a continuously variable gearbox, thus maintaining a single spool configuration and relative design simplicity. This is an effort to reduce the initial engine development cost, whilst improving propulsive performance. The BMT 120 KS micro turbojet engine is selected for performance evaluation of the conversion process using gas turbine performance software, GasTurb13. The preliminary design of a matched low-pressure compressor (LPC) for the proposed engine is then performed using meanline calculation methods. According to the analysis carried out, an improvement in the converted micro gas turbine engine performance in terms of thrust and specific fuel consumption is achieved. Furthermore, with the introduction of a CVT gearbox, fan speed operation may be adjusted independently of the core, allowing increased thrust generation or better fuel consumption. Therefore, enabling a wider gamut of operating conditions and enhances the performance and scope of tactical UAV.

The interest on the use of renewable energy resources is increasing, especially towards wind and hydro powers, which should be efficiently converted into electric energy via suitable technology tools. To this aim, self--tuning control techniques represent viable strategies that can be employed for this purpose, due to the features of these nonlinear dynamic processes working over a wide range of operating conditions, driven by stochastic inputs, excitations and disturbances. Some of the considered methods were already verified on wind turbine systems, and important advantages may thus derive from the appropriate implementation of the same control schemes for hydroelectric plants. This represents the key point of the work, which provides some guidelines on the design and the application of these control strategies to these energy conversion systems. In fact, it seems that investigations related with both wind and hydraulic energies present a reduced number of common aspects, thus leading to little exchange and share of possible common points. This consideration is particularly valid with reference to the more established wind area when compared to hydroelectric systems. In this way, this work recalls the models of wind turbine and hydroelectric system, and investigates the application of different control solutions. The scope is to analyse common points in the control objectives and the achievable results from the application of different solutions. Another important point of this investigation regards the analysis of the exploited benchmark models, their control objectives, and the development of the control solutions. The working conditions of these energy conversion systems will be also taken into account in order to highlight the reliability and robustness characteristics of the developed control strategies, especially interesting for remote and relatively inaccessible location of many installations.

The present studies deliver the computational investigations of a 10 MW turbine with a diameter of 205.8 m developed within the framework of the AVATAR (Advanced Aerodynamic Tools for Large Rotors) project. The simulations were carried out using two methods with different fidelity levels, namely the computational fluid dynamics (CFD) and blade element and momentum (BEM) approaches. For this purpose, a new BEM code namely B-GO was developed employing several correction terms and three different polar and spatial interpolation options. Several flow conditions were considered in the simulations, ranging from the design condition to the off-design condition where massive flow separation takes place, challenging the validity of the BEM approach. An excellent agreement is obtained between the BEM computations and the 3D CFD results for all blade regions, even when massive flow separation occurs on the blade inboard area. The results demonstrate that the selection of the polar data can influence the accuracy of the BEM results significantly, where the 3D polar datasets extracted from the CFD simulations are considered the best. The BEM prediction depends on the interpolation order and the blade segment discretization.

The Doubly-Fed Induction Generator (DFIG) has significant features in comparison with Fixed Speed Wind Turbine (FSWT), which has popularized its application in power system. Due to partial rated back-to-back converters in the DFIG, Fault Ride-Through (FRT) capability improvement is one of the great subjects regarding new grid code requirements. To enhance the FRT capability of the DFIG, many studies have been carried out. Fault current limiting devices as one of the techniques are utilized to limit the current level and protect switches of the back-to-back converter from over-current damage. In this paper, a review is done based on fault current limiting characteristic of the proposed fault current limiting devices Therefore, Fault Current Limiters (FCLs) and Series Dynamic Braking Resistors (SDBRs) are mainly taken into account. Operation of all configurations including their advantages and disadvantages is explained. Impedance type and the fault current limiting devices’ location are two important factors, which significantly affect the DFIG behaviour in the fault condition. These two factors are basically studied by the simulation and their effects on the key parameters of the DFIG are investigated. Finally, future works in respect to the FCL application in the FRT improvement of the DFIG have also been discussed.

In this paper, the active front-end (AFE) converter topology for the total harmonic distortion (THD) reduction in a wind energy system (WES) is used. A higher THD results in serious pulsations in the wind turbine (WT) output power and in several power losses at the WES. The AFE converter topology improves capability, efficiency and reliability in the energy conversion devices; by modifying a conventional back-to-back converter, from using a single voltage source converter (VSC) to use pVSC connected in parallel the AFE converter is generated. The THD reduction is done by applying a different phase shift angle at the carrier of digital sinusoidal pulse width modulation (DSPWM) switching signals of each VSC. To verify the functionality of the proposed methodology, the WES simulation in Matlab-Simulink® is analyzed, and the experimental laboratory tests using the concept of rapid control prototyping and the real-time simulator Opal-RT® Technologies is achieved. The obtained results show a type-4 WT with total output power of 6MVA, generating a THD reduction up to 5.5 times at the WES.

Aerodynamic performance of a floating offshore wind turbine (FOWT) is significantly influenced by platform surging motions. Accurate prediction of the unsteady aerodynamic loads is imperative for determining the fatigue life, ultimate loads on key components such as FOWT rotor blades, gearbox and power converter. The current study examines the predictions of numerical codes by comparing with unsteady experimental results of a scaled floating wind turbine rotor. The influence of platform surge amplitude together with the tip speed ratio on the unsteady aerodynamic loading has been simulated through unsteady CFD. It is shown that the unsteady aerodynamic loads of FOWT are highly sensitive to the changes in frequency and amplitude of the platform motion. Also, the surging motion significantly influences the windmill operating state due to strong flow interaction between the rotating blades and generated blade-tip vortices. Almost in all frequencies and amplitudes, CFD, LR-BEM and LR-uBEM predictions of mean thrust shows a good correlation with experimental results.

The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.

The wind industry is looking for ways to accurately predict the reliability and availability of newly installed wind turbines. Failure modes, effects and criticality analysis (FMECA) is a technique utilized for determining the critical subsystems of wind turbines. There are several studies which applied FMECA for wind turbines in the literature, but no studies so far have considered different weather conditions or climatic regions. Furthermore, various design types of wind turbines have been analyzed applying FMECA but no study so far has applied FMECA to compare the reliability of geared and direct-drive wind turbines. We propose to fill these gaps by using Koppen-Geiger climatic regions and two different turbine models of direct-drive and geared-drive concepts. A case study is applied on German wind farms utilizing the WMEP database which contains wind turbine failure data from 1989 to 2008. This proposed methodology increases the accuracy of reliability and availability predictions and compares different wind turbine design types and eliminates underestimation of impacts of different weather conditions.

Full-order state-space models represent the starting point for the development of advanced control methods for wind turbine systems (WTSs). Regarding existing control-oriented WTS models, two research gaps must be noted: (i) There exists no full-order WTS model in form of one overall ordinary differential equation that considers all dynamical effects which significantly influence the electrical power output; (ii) all existing reduced-order WTS models are subject to rather arbitrary simplifications and are not validated against a full-order model. Therefore, in this paper, two full-order nonlinear state-space models (of 11th and 9th-order in the (a, b, c)- and (d, q)-reference frame, resp.) for variable-speed variable-pitch permanent magnet synchronous generator WTSs are derived. The full-order models cover all relevant dynamical effects with significant impact on the system’s power output, including the switching behavior of the power electronic devices. Based on the full-order models, by a step-by-step model reduction procedure, two reduced-order WTS models are deduced: A non-switching (averaging) 7th-order WTS model and a non-switching 3rd-order WTS model. Comparative simulation results reveal that all models capture the dominant system dynamics properly. The full-order models allow for a detailed analysis covering the high frequency oscillations in the instantaneous power output due to the switching in the power converters. The reduced-order models provide a time-averaged instantaneous power output (which still correctly reflects the energy produced by the WTS) and come with a drastically reduced complexity making those models appropriate for large-scale power grid controller design.

The crack in the blade is the most common type of fatigue damage for Francis turbines. However, the crack sometimes is difficult to be detected in time using the current monitoring system even when the crack is very large. To better monitor the crack, it is imperative to research the effect of a crack on the dynamic behavior of a Francis turbine. In this paper, the dynamic behavior of a Francis turbine runner model with a crack was researched numerically. The intact numerical model was first validated by the experimental data available. Then, a crack was created at the intersection line between one blade and the crown. The change in dynamic behavior with increasing crack length was investigated. Crack-induced vibration localization theory was used to explain the dynamic behavior changes due to the crack. Modal analysis showed that the adopted theory could basically explain the modal behavior change due to the crack. The FFT results of the modal shapes and the localization factors (LF) were used to explain the forced response changes due to the crack. Based on the above analysis, the challenge of crack monitoring was analyzed. This research can also provide some references for more advanced monitoring technologies.

The main objective of this paper is to continue the development of activities of basic and applied research related to wind energy and to develop methods of optimal control to improve the performance and production of electrical energy from wind. A new control technique of Double fed induction generator for wind turbine is undertaken through a robust approach tagged nonlinear sliding mode control (SMC) with exponential reaching law control (ERL). The SMC with ERL proves to be capable of reducing the system chattering phenomenon as well as accelerating the approaching process. A nonlinear case numerical simulation test is employed to verify the superior performance of the ERL method over traditional power rate reaching strategy. Results obtained in Matlab/Simulink environment show that the SMC with ERL is more robust, prove excellent performance for the control unit by improving power quality and stability of wind turbine.

A numerical study of the flow over a NACA aerofoil is presented in this paper. The numerical simulations are achieved with the computer code CFX and the computational domain is created by the computer tool ANSYS ICEM CFD. The CFX code is based on the finite volume method to solve the equations of mass, momentum and energy. The purpose of this paper is to determine the pressure distribution, flow patterns and the forces acting on the airfoil. Effects of the attack angle and Reynolds number on the velocity and pressure distribution, on the lift and drag coefficients are also explored.

This paper is concerned with bump-less transfer of parametrized disturbance observer based controller (DOBC) with Individual Pitch Control (IPC) strategy for full load operation of wind turbine. Aerodynamic cyclic loads are reduced by tuning multivariable DOBC with the objective to reduce output power fluctuation, tower oscillation and drive-train torsion. Furthermore tower shadow and wind shear effect are also mitigated using parametrized controller. A scheduling mechanism between two DOBC is developed and tested on Fatigue, Aerodynamics, Structures, and Turbulence ( FAST) code model of National Renewable Energy Laboratory (NREL)’s 5 MW wind turbine. The closed-loop system performance is assessed by comparing the simulation results of proposed controller with a fixed gain and Linear Parameter Varying (LPV) DOBC with Collective Pitch Control (CPC) for full load operation. It is tested with step changing wind to see the behavior of the system under step change with wind shear and tower shadow (cyclic load) effects. Also turbulent wind is applied to see the smooth transition of the controllers. It can be concluded from the results that the proposed parametrized control DOBC with IPC shows smooth transition from one controller to another by interpolation. Moreover fatigue of the gear and tower due to wind shear and tower shadow effects are reduced considerably by the proposed controller as compared to collective pitch control.

Wind turbine plants are complex dynamic and uncertain processes driven by stochastic inputs and disturbances, as well as different loads represented by gyroscopic, centrifugal, and gravitational forces. Moreover, as their aerodynamic models are nonlinear, both modelling and control become challenging problems. On one hand, high-fidelity simulators should contain different parameters and variables in order to accurately describe the main dynamic system behaviour. Therefore, the development of modelling and control for wind turbine systems should consider these complexity aspects. On the other hand, these control solutions have to include the main wind turbine dynamic characteristics without becoming too complicated. The main point of this paper is thus to provide two practical examples of development of robust control strategies when applied to a simulated wind turbine plant. Experiments with the wind turbine simulator and the Monte–Carlo tools represent the instruments for assessing the robustness and reliability aspects of the developed control methodologies when the model-reality mismatch and measurement errors are also considered. Advantages and drawbacks of these regulation methods are also highlighted with respect to different control strategies via proper performance metrics.

A turbomachinery is essential part in the power generation cycle. But, it is main noise source to annoy workers and users and to make environmental problem. Thus it is important to reduce this noise for operating the power generation cycle. This noise is created by flow instability on rotor blade trailing edge. An airfoil that becomes a section of a rotor blade of a rotating machine is manufactured as a blunt trailing edge (TE) with a round or flatback shape rather than the ideal sharp TE shape for the purposes of producibility and durability. This increases the tonal noise and flow-induced vibration at low frequency owing to vortex shedding behind TE when compared with a sharp TE. In order to overcome this problem, this study investigates the oblique TE shape using numerical simulation. In order to do so, the flow was simulated using large eddy simulation (LES) and the noise was analysed by acoustic analogy coupled with LES result. Once the simulation results were verified using the flatback airfoil measurements of Sandia National Laboratories, numerical prediction was performed for airfoils modified to have oblique trailing edge angles of 60°, 45°, and 30° to analyse the flow and noise characteristics. From the simulation results for an airfoil having an oblique TE, it could be seen that the vortex shedding frequency moves in accordance with the oblique angle and that the vortex shedding noise characteristics change according to this angle when compared to the flatback TE airfoil. Therefore, it is considered that modifying the flatback TE airfoil to have an appropriate oblique angle can reduce noise and change the tonal frequency to a bandwidth that is suitable for mechanical systems.

In order to improve the performance of the draft tube in hydraulic turbine, a multi–objective optimization method for the draft tube is developed by combining the design of experiment (DOE), the radial basis function (RBF) and the non–dominated sorting genetic algorithm (NSGA–II) in this paper. The geometrical design variables of the median section in the draft tube and the cross section in its exit diffuser are considered as design parameters in this optimization, which objective function is to maximize the pressure recovery factor (Cp) and minimize the energy loss coefficient (ζ). The limited numbers of design matrix required for the shape optimization of the draft tube is generated by optimal Latin hypercube (OLH) method of the DOE technique, of which performances are evaluated through computational fluid dynamic (CFD) numerical simulation. For reducing of the computational consumption, the approximate model is used based on the RBF. The Pareto optimal solutions are finally performed using the NSGA–II for obtaining the best geometrical parameters of the draft tube. The optimization result of the draft tube shows a marked performance improvement over the original, which verifies the theoretical validity and feasibility of the proposed method in this paper.

Anomaly detection plays a significant role in helping gas turbines run reliably and economically. Considering collective anomalous data and both sensitivity and robustness of the anomaly detection model, a sequential symbolic anomaly detection method is proposed and applied to the gas turbine fuel system. A structural Finite State Machine is to evaluate posterior probabilities of observing symbolic sequences and most probable state sequences they may locate. Hence an estimating based model and a decoding based model are used to identify anomalies in two different ways. Experimental results indicates that these two models have both ideal performance overall, and estimating based model has a strong ability in robustness, while decoding based model has a strong ability in accuracy, particularly in a certain range of length of sequence. Therefore, the proposed method can well facilitate existing symbolic dynamic analysis based anomaly detection methods especially in gas turbine domain.

Computational fluid dynamics is used to study the impact of the support structure of a tidal turbine on performance and the downstream wake characteristics. A high-fidelity computational model of a dual rotor, contra-rotating tidal turbine in a large channel domain is presented, with turbulence modelled using large eddy simulation. Actuator lines represent the turbine blades, permitting the analysis of transient flow features and turbine diagnostics. The following four cases are considered: the flow in an unexploited, empty channel; flow in a channel containing the rotors; flow in a channel containing the support structure; and flow in a channel with both rotors and support structure. The results indicate that the support structure contributes significantly to the behaviour of the turbine and to turbulence levels downstream, even when the rotors are upstream. This implies that inclusion of the turbine structure, or some parametrisation thereof, is a prerequisite for the realistic prediction of turbine performance and reliability, particularly for array layouts where wake effects become significant.

Tidal stream energy is a low carbon energy source. Tidal stream turbines operate in a turbulent environment, and the effect of the structure between the turbine and seabed on this environment is not fully understood. An experimental study using 1:72 scale models based on a commercial turbine design was carried out to study the support structure influence on turbulence intensity around turbine blades. The study was conducted using the wave-current tank at LABIMA, University of Florence. A realistic flow environment (ambient turbulent intensity = 11%) was established. Turbulence intensity was measured upstream and downstream of a turbine mounted on two different support structures (one resembling a commercial design, the other the same with an additional vertical element), in order to quantify any variation in turbulence and performance between the support structures. Turbine drive power was used to calculate power generation. Acoustic Doppler Velocimetry was used to record and calculate upstream and downstream turbulence intensity. In otherwise identical conditions, performance variation of only 4% was observed between two support structures. Turbulent intensity at 1, 3 and 5 blade diameters, both upstream and downstream, showed variation up to 21% between the two cases. The additional turbulent structures generated by the additional element of the second support structure appears to cause this effect, and the upstream propagation of turbulent intensity is believed to be permitted by surface waves. This result is significant for the prediction of turbine array performance.

More and more works are using machine learning techniques while adopting supervisory control and data acquisition (SCADA) system for wind turbine anomaly or failure detection. While parameter selection is important for modelling a wind turbine’s health condition, only a few papers have been published focusing on this issue and in those papers interconnections among sub-components in a wind turbine are used to address this problem. However, merely the interconnections for decision making sometimes is too general to provide a parameter list considering the differences of each SCADA dataset. In this paper, a method is proposed to provide more detailed suggestions on parameter selection based on mutual information. Moreover, after proving that Copula, a multivariate probability distribution for which the marginal probability distribution of each variable is uniform is capable of simplifying the estimation of mutual information, an empirical copula based mutual information estimation method (ECMI) is introduced for an application. After that, a real SCADA dataset is adopted to test the method, and the results show the effectiveness of the ECMI in providing parameter selection suggestions when physical knowledge is not accurate enough.

Nacelle-based Doppler wind lidars have shown promising capabilities to assess power performance, detect yaw misalignment or perform feed-forward control. The power curve application requires uncertainty assessment. Traceable measurements and uncertainties of nacelle-based wind lidars can be obtained through a methodology applicable to any type of existing and upcoming nacelle lidar technology. The generic methodology consists in calibrating all the inputs of the wind field reconstruction algorithms of a lidar. These inputs are the line-of-sight velocity and the beam position, provided by the geometry of the scanning trajectory and the lidar inclination. The line-of-sight velocity is calibrated in atmospheric conditions by comparing it to a reference quantity based on classic instrumentation such as cup anemometers and wind vanes. The generic methodology was tested on two commercially developed lidars, one continuous wave and one pulsed systems, and provides consistent calibration results: linear regressions show a difference of ∼ 0.5 % between the lidar-measured and reference line-of-sight velocities. A comprehensive uncertainty procedure propagates the reference uncertainty to the lidar measurements. At a coverage factor of two, the estimated line-of-sight velocity uncertainty ranges from 3.2 % at 3 m s⁻¹ to 1.9 % at 16 m s⁻¹. Most of the line-of-sight velocity uncertainty originates from the reference: the cup anemometer uncertainty accounts for ∼ 90 % of the total uncertainty. The propagation of uncertainties to lidar-reconstructed wind characteristics can use analytical methods in simple cases, which we demonstrate through the example of a two-beam system. The newly developed calibration methodology allows robust evaluation of a nacelle lidar’s performance and uncertainties to be established in order to further be used for various wind turbines’ applications in confidence.

Optimizing the NACA0015 airfoil which is widely applied in small-scale vertical axis wind turbine to make it has a better aerodynamic performance. In the optimization process, using CST parameterization method to perturb the airfoil geometry, the thickness and camber of the airfoil are selected as the constraint, and the value of the maximum tangential force coefficient is chosen as the objective function, the genetic algorithm based on non-dominated sorting (NSGA-II)is selected as an optimization method, calculates the aerodynamic performance of the airfoil by applying the approach of combining XFOIL program and Viterna-Corrigan post-stall mode ,and establishes the optimizing process by the optimization software modefrontier for NACA0015 airfoil’s muti-point optimization, validate the airfoil’s performance with CFD finally. The result illustrates that, by comparing with the NACA0015 airfoil, the optimized airfoil’s lift to drag ratio is improved over a wide range of attack angles, the stall performance is more gentle. The maximum lift coefficient, the maximum lift-drag ratio and the maximum tangential force coefficient are increased by 7.5%,9 and 8.87%, respectively. The optimized airfoil has a wide variable condition performance, more suitable for the operating conditions of a vertical axis wind turbine. Finally, predict the rotor efficiency with optimized airfoil and NACA0015 airfoil for different tip speed ratios and different solidities with multiple streamtube model, the result shows the rotor with optimized airfoil has a higher efficiency.

The hump feature is one of the major instabilities in pump-turbines. When pump-turbines operate in the hump region, strong noise and serious fluctuations can be observed, which are harmful to their safe and stable operation and can even destroy the whole unit as well as water conveyance system. In this paper, a low specific speed (n_q = 36.1 min⁻¹) pump-turbine model was experimentally investigated. Firstly, the hump characteristic was obtained under 19 mm guide vane opening conditions. More interestingly, when the hump characteristic was measured in two directions (increasing and decreasing the discharge), characteristic hysteresis was found in the hump region. The analysis of performance characteristics reveals that the hump instability is the result of Euler momentum and hydraulic losses, and different Euler momentum and hydraulic losses in the two development processes lead to the hysteresis phenomenon. Then, 12 pressure sensors were mounted in the different parts of the pump-turbine model to obtain the time and frequency characteristics. The analysis of the corresponding fast Fourier transform confirms that the hump characteristic is related to low-frequency (0.04–0.15 times rotational frequency) vortices. The occurrence and cessation of vortices depend on the operating condition and measurement direction, which contribute to the hysteresis feature. Finally, the type of the low-frequency vortices was analyzed through the cross power spectrum.

This paper numerically investigates a 3D mesh independency study of a straight blade horizontal axis tidal turbine modelled using Computational Fluid Dynamics (CFD). The solution was produced by employing two turbulence models, the standard k-ε model and Shear Stress Transport (SST) in ANSYS CFX. Three parameters were investigated: mesh resolution, turbulence model, and power coefficient in the initial CFD, analysis. It was found that the mesh resolution and the turbulence model affect the power coefficient results. The power coefficients obtained from the standard k-ε model are 15% to 20% lower than the accuracy of the SST model. It can also be demonstrated that the torque coefficient increases with the increasing Tip Speed Ratio (TSR), but drops drastically after TSR = 5 and k-ε model failing to capture the non-linearity in the torque coefficient with the increasing TSR.