Search results for: inclined flow

Authors: Abubakar Rashid, Muhammad Saad, Faheem Ahmed

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This paper provides a comprehensive study pertaining to diagnosis of intermittent high vibrations on an industrial gas turbine using detailed vibrations analysis, followed by its rectification. Engro Polymer & Chemicals Limited, a Chlor-Vinyl complex located in Pakistan has a captive combined cycle power plant having two 28 MW gas turbines (make Hitachi) & one 15 MW steam turbine. In 2018, the organization faced an issue of high vibrations on one of the gas turbines. These high vibration peaks appeared intermittently on both compressor’s drive end (DE) & turbine’s non-drive end (NDE) bearing. The amplitude of high vibration peaks was between 150-170% on the DE bearing & 200-300% on the NDE bearing from baseline values. In one of these episodes, the gas turbine got tripped on “High Vibrations Trip” logic actuated at 155µm. Limited instrumentation is available on the machine, which is monitored with GE Bently Nevada 3300 system having two proximity probes installed at Turbine NDE, Compressor DE &at Generator DE & NDE bearings. Machine’s transient ramp-up & steady state data was collected using ADRE SXP & DSPI 408. Since only 01 key phasor is installed at Turbine high speed shaft, a derived drive key phasor was configured in ADRE to obtain low speed shaft rpm required for data analysis. By analyzing the Bode plots, Shaft center line plot, Polar plot & orbit plots; rubbing was evident on Turbine’s NDE along with increased bearing clearance of Turbine’s NDE radial bearing. The subject bearing was then inspected & heavy deposition of carbonized coke was found on the labyrinth seals of bearing housing with clear rubbing marks on shaft & housing covering at 20-25 degrees on the inner radius of labyrinth seals. The collected coke sample was tested in laboratory & found to be the residue of lube oil in the bearing housing. After detailed inspection & cleaning of shaft journal area & bearing housing, new radial bearing was installed. Before assembling the bearing housing, cleaning of bearing cooling & sealing air lines was also carried out as inadequate flow of cooling & sealing air can accelerate coke formation in bearing housing. The machine was then taken back online & data was collected again using ADRE SXP & DSPI 408 for health analysis. The vibrations were found in acceptable zone as per ISO standard 7919-3 while all other parameters were also within vendor defined range. As a learning from subject case, revised operating & maintenance regime has also been proposed to enhance machine’s reliability.

Keywords: ADRE, bearing, gas turbine, GE Bently Nevada, Hitachi, vibration.

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Authors: Mathias U. Bonet, Pericles Pilidis, Georgios Doulgeris

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A gas turbine-powered cruise Liner is scheduled to transport pilgrim passengers from Lagos-Nigeria to the Islamic port city of Jeddah in Saudi Arabia. Since the gas turbine is an air breathing machine, changes in the density and/or mass flow at the compressor inlet due to an encounter with variations in weather conditions induce negative effects on the performance of the power plant during the voyage. In practice, all deviations from the reference atmospheric conditions of 15 ^oC and 1.103 bar tend to affect the power output and other thermodynamic parameters of the gas turbine cycle. Therefore, this paper seeks to evaluate how a simple cycle marine gas turbine power plant would react under a variety of scenarios that may be encountered during a voyage as the ship sails across the Atlantic Ocean and the Mediterranean Sea before arriving at its designated port of discharge. It is also an assessment that focuses on the effect of varying aerodynamic and hydrodynamic conditions which deteriorate the efficient operation of the propulsion system due to an increase in resistance that results from some projected levels of the ship hull fouling. The investigated passenger ship is designed to run at a service speed of 22 knots and cover a distance of 5787 nautical miles. The performance evaluation consists of three separate voyages that cover a variety of weather conditions in winter, spring and summer seasons. Real-time daily temperatures and the sea states for the selected transit route were obtained and used to simulate the voyage under the aforementioned operating conditions. Changes in engine firing temperature, power output as well as the total fuel consumed per voyage including other performance variables were separately predicted under both calm and adverse weather conditions. The collated data were obtained online from the UK Meteorological Office as well as the UK Hydrographic Office websites, while adopting the Beaufort scale for determining the magnitude of sea waves resulting from rough weather situations. The simulation of the gas turbine performance and voyage analysis was effected through the use of an integrated Cranfield-University-developed computer code known as ‘Turbomatch’ and ‘Poseidon’. It is a project that is aimed at developing a method for predicting the off design behavior of the marine gas turbine when installed and operated as the main prime mover for both propulsion and powering of all other auxiliary services onboard a passenger cruise liner. Furthermore, it is a techno-economic and environmental assessment that seeks to enable the forecast of the marine gas turbine part and full load performance as it relates to the fuel requirement for a complete voyage.

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Authors: C. A. Barros, Ana P. Barroso

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Any industrial company needs to determine the amount of variation that exists within its measurement process and guarantee the reliability of their data, studying the performance of their measurement system, in terms of linearity, bias, repeatability and reproducibility and stability. This issue is critical for automotive industry suppliers, who are required to be certified by the 16949:2016 standard (replaces the ISO/TS 16949) of International Automotive Task Force, defining the requirements of a quality management system for companies in the automotive industry. Measurement System Analysis (MSA) is one of the mandatory tools. Frequently, the measurement system in companies is not connected to the equipment and do not incorporate the methods proposed by the Automotive Industry Action Group (AIAG). To address these constraints, an R&D project is in progress, whose objective is to develop a web and cloud-based MSA tool. This MSA tool incorporates Industry 4.0 concepts, such as, Internet of Things (IoT) protocols to assure the connection with the measuring equipment, cloud computing, artificial intelligence, statistical tools, and advanced mathematical algorithms. This paper presents the preliminary findings of the project. The web and cloud-based MSA tool is innovative because it implements all statistical tests proposed in the MSA-4 reference manual from AIAG as well as other emerging methods and techniques. As it is integrated with the measuring devices, it reduces the manual input of data and therefore the errors. The tool ensures traceability of all performed tests and can be used in quality laboratories and in the production lines. Besides, it monitors MSAs over time, allowing both the analysis of deviations from the variation of the measurements performed and the management of measurement equipment and calibrations. To develop the MSA tool a ten-step approach was implemented. Firstly, it was performed a benchmarking analysis of the current competitors and commercial solutions linked to MSA, concerning Industry 4.0 paradigm. Next, an analysis of the size of the target market for the MSA tool was done. Afterwards, data flow and traceability requirements were analysed in order to implement an IoT data network that interconnects with the equipment, preferably via wireless. The MSA web solution was designed under UI/UX principles and an API in python language was developed to perform the algorithms and the statistical analysis. Continuous validation of the tool by companies is being performed to assure real time management of the ‘big data’. The main results of this R&D project are: MSA Tool, web and cloud-based; Python API; New Algorithms to the market; and Style Guide of UI/UX of the tool. The MSA tool proposed adds value to the state of the art as it ensures an effective response to the new challenges of measurement systems, which are increasingly critical in production processes. Although the automotive industry has triggered the development of this innovative MSA tool, other industries would also benefit from it. Currently, companies from molds and plastics, chemical and food industry are already validating it.

Keywords: Automotive industry, Industry 4.0, internet of things, IATF 16949:2016, measurement system analysis.

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Authors: Liliia N. Butymova, Vladimir Ya Modorskii

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To ensure the gas transmittal GCU's efficient operation, leakages through the labyrinth packings (LP) should be minimized. Leakages can be minimized by decreasing the LP gap, which in turn depends on thermal processes and possible rotor vibrations and is designed to ensure absence of mechanical contact. Vibration mitigation allows to minimize the LP gap. It is advantageous to research influence of processes in the dynamic gas-structure system on LP vibrations. This paper considers influence of rotor vibrations on LP gas dynamics and influence of the latter on the rotor structure within the FSI unidirectional dynamical coupled problem. Dependences of nonstationary parameters of gas-dynamic process in LP on rotor vibrations under various gas speeds and pressures, shaft rotation speeds and vibration amplitudes, and working medium features were studied. The programmed multi-processor ANSYS CFX was chosen as a numerical computation tool. The problem was solved using PNRPU high-capacity computer complex. Deformed shaft vibrations are replaced with an unyielding profile that moves in the fixed annulus "up-and-down" according to set harmonic rule. This solves a nonstationary gas-dynamic problem and determines time dependence of total gas-dynamic force value influencing the shaft. Pressure increase from 0.1 to 10 MPa causes growth of gas-dynamic force oscillation amplitude and frequency. The phase shift angle between gas-dynamic force oscillations and those of shaft displacement decreases from 3π/4 to π/2. Damping constant has maximum value under 1 MPa pressure in the gap. Increase of shaft oscillation frequency from 50 to 150 Hz under P=10 MPa causes growth of gas-dynamic force oscillation amplitude. Damping constant has maximum value at 50 Hz equaling 1.012. Increase of shaft vibration amplitude from 20 to 80 µm under P=10 MPa causes the rise of gas-dynamic force amplitude up to 20 times. Damping constant increases from 0.092 to 0.251. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the minimum gas-dynamic force persistent oscillating amplitude under P=0.1 MPa being observed in methane, and maximum in the air. Frequency remains almost unchanged and the phase shift in the air changes from 3π/4 to π/2. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the maximum gas-dynamic force oscillating amplitude under P=10 MPa being observed in methane, and minimum in the air. Air demonstrates surging. Increase of leakage speed from 0 to 20 m/s through LP under P=0.1 MPa causes the gas-dynamic force oscillating amplitude to decrease by 3 orders and oscillation frequency and the phase shift to increase 2 times and stabilize. Increase of leakage speed from 0 to 20 m/s in LP under P=1 MPa causes gas-dynamic force oscillating amplitude to decrease by almost 4 orders. The phase shift angle increases from π/72 to π/2. Oscillations become persistent. Flow rate proved to influence greatly on pressure oscillations amplitude and a phase shift angle. Work medium influence depends on operation conditions. At pressure growth, vibrations are mostly affected in methane (of working substances list considered), and at pressure decrease, in the air at 25 ˚С.

Keywords: Aeroelasticity, labyrinth packings, oscillation phase shift, vibration.

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Authors: Douglas N. Simões, Michele Pittol, Vanda F. Ribeiro, Daiane Tomacheski, Ruth M. C. Santana

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The increasing demand of thermoplastic elastomers is related to the wide range of applications, such as automotive, footwear, wire and cable industries, adhesives and medical devices, cell phones, sporting goods, toys and others. These materials are susceptible to microbial attack. Moisture and organic matter present in some areas (such as shower area and sink), provide favorable conditions for microbial proliferation, which contributes to the spread of diseases and reduces the product life cycle. Compounds based on SEBS copolymers, poly(styrene-b-(ethylene-co-butylene)-b-styrene, are a class of thermoplastic elastomers (TPE), fully recyclable and largely used in domestic appliances like bath mats and tooth brushes (soft touch). Zinc oxide and zinc ions loaded in personal and home care products have become common in the last years due to its biocidal effect. In that sense, the aim of this study was to evaluate the effect of zinc as antimicrobial agent in compounds based on SEBS/polypropylene/oil/ calcite for use as refrigerator seals (gaskets), bath mats and sink squeegee. Two zinc oxides from different suppliers (ZnO-Pe and ZnO-WR) and one masterbatch of zinc ions (M-Zn-ion) were used in proportions of 0%, 1%, 3% and 5%. The compounds were prepared using a co-rotating double screw extruder (L/D ratio of 40/1 and 16 mm screw diameter). The extrusion parameters were kept constant for all materials. Tests specimens were prepared using the injection molding machine. A compound with no antimicrobial additive (standard) was also tested. Compounds were characterized by physical (density), mechanical (hardness and tensile properties) and rheological properties (melt flow rate - MFR). The Japan Industrial Standard (JIS) Z 2801:2010 was applied to evaluate antibacterial properties against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli). The Brazilian Association of Technical Standards (ABNT) NBR 15275:2014 were used to evaluate antifungal properties against Aspergillus niger (A. niger), Aureobasidium pullulans (A. pullulans), Candida albicans (C. albicans), and Penicillium chrysogenum (P. chrysogenum). The microbiological assay showed a reduction over 42% in E. coli and over 49% in S. aureus population. The tests with fungi showed inconclusive results because the sample without zinc also demonstrated an inhibition of fungal development when tested against A. pullulans, C. albicans and P. chrysogenum. In addition, the zinc loaded samples showed worse results than the standard sample when tested against A. niger. The zinc addition did not show significant variation in mechanical properties. However, the density values increased with the rise in ZnO additives concentration, and had a little decrease in M-Zn-ion samples. Also, there were differences in the MFR results in all compounds compared to the standard.

Keywords: Antimicrobial, home device, SEBS, zinc.

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Authors: Maria de Fátima Lambert

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Following previous studies about Writing and Seeing, this paper focuses on the aesthetic assumptions within the concept of Winter Journey (Voyage d’Hiver/Winterreise) both in Georges Perec’s Saga and the Oulipo Group vis-à-vis with the creations by William Kentridge and Michael Borremans. The aesthetic and artistic connections are widespread. Nevertheless, we can identify common poetical principles shared by these different authors, not only according to the notion of ekphrasis, but also following the procedures of contemporary creation in literature and visual arts. The analysis of the ongoing process of the French writers as individuals and as group and the visual artists’ acting might contribute for another crossed definition of contemporary conception. The same title/theme was a challenge and a goal for them. Let’s wonder how deep the concept encouraged them and which symbolic upbringings were directing their poetical achievements. The idea of an inner journey became the main point, and got “over” and “across” a shared path worth to be followed. The authors were chosen due to the resilient contents of their visual and written images, and looking for the reasons that might had driven their conceptual basis to be. In Pérec’s “Winter Journey” as for the following fictions by Jacques Roubaud, Hervé le Tellier, Jacques Jouet and Hugo Vernier (that emerges from Perec’s fiction and becomes a real author) powerful aesthetic and enigmatic reflections grow connected with a poetic (and aesthetic) understanding of Walkscapes. They might be assumed as ironic fictions and poetical drifts. Outstanding from different logics, the overwhelming impact of Winterreise Lied by Schubert after Wilhelm Müller’s poems is a major reference in present authorship creations. Both Perec and Oulipo’s author’s texts are powerfully ekphrastic, although we should not forget they follow goals, frameworks and identities. When acting as a reader, they induce powerful imageries - cinematic or cinematographic - that flow in our minds. It was well-matched with William Kentridge animated video Winter Journey (2014) and the creations (sharing the same title) of Michael Borremans (2014) for the KlaraFestival, Bozar, Cité de la musique, in Belgium. Both were taken by the foremost Schubert’s Winterreise. Several metaphors fulfil new Winter Journeys (or Travels) that were achieved in contemporary art and literature, as it once succeeded in the 19^th century. Maybe the contemporary authors and artists were compelled by the consciousness of nothingness, although outstanding different aesthetics and ontological sources. The unbearable knowledge of the road’s end, and also the urge of fulfilling the void might be a common element to all of them. As Schopenhauer once wrote, after all, Art is the only human subjective power that we can call upon in life. These newer aesthetic meanings, released from these winter journeys are surely open to wider approaches that might happen in other poetic makings to be.

Keywords: Aesthetic, Voyage d’Hiver, Georges Perec & Oulipo, Schubert's Winterreise, William Kentridge & Michael Borremans.

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Authors: M. Keshavarzi

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Grasslands of Iran are encountered with a vast desertification and destruction. Some legumes are plants of forage importance with high palatability. Studied legumes in this project are Onobrychis, Medicago sativa (alfalfa) and Trifolium repens. Seeds were cultivated in research field of Kaboutarabad (33 km East of Isfahan, Iran) with an average 80 mm. annual rainfall. Plants were cultivated in a split plot design with 3 replicate and two water treatments (weekly irrigation, and under stress with same amount per 15 days interval). Water entrance to each plots were measured by Partial flow. This project lasted 20 weeks. Destructive samplings (1m2 each time) were done weekly. At each sampling plants were gathered and weighed separately for each vegetative parts. An Area Meter (Vista) was used to measure root surface and leaf area. Total shoot and root fresh and dry weight, leaf area index and soil coverage were evaluated too. Dry weight was achieved in 750c oven after 24 hours. Statgraphic and Harvard Graphic software were used to formulate and demonstrate the parameters curves due to time. Our results show that Trifolium repens has affected 60 % and Medicago sativa 18% by water stress. Onobrychis total fresh weight was reduced 45%. Dry weight or Biomass in alfalfa is not so affected by water shortage. This means that in alfalfa fields we can decrease the irrigation amount and have some how same amount of Biomass. Onobrychis show a drastic decrease in Biomass. The increases in total dry matter due to time in studied plants are formulated. For Trifolium repens if removal or cattle entrance to meadows do not occurred at perfect time, it will decrease the palatability and water content of the shoots. Water stress in a short period could develop the root system in Trifolium repens, but if it last more than this other ecological and soil factors will affect the growth of this plant. Low level of soil water is not so important for studied legume forges. But water shortage affect palatability and water content of aerial parts. Leaf area due to time in studied legumes is formulated. In fact leaf area is decreased by shortage in available water. Higher leaf area means higher forage and biomass production. Medicago and Onobrychis reach to the maximum leaf area sooner than Trifolium and are able to produce an optimum soil cover and inhibit the transpiration of soil water of meadows. Correlation of root surface to Total biomass in studied plants is formulated. Medicago under water stress show a 40% decrease in crown cover while at optimum condition this amount reach to 100%. In order to produce forage in areas without soil erosion Medicago is the best choice even with a shortage in water resources. It is tried to represent the growth simulation of three famous Forage Legumes. By growth simulation farmers and range managers could better decide to choose best plant adapted to water availability without designing different time and labor consuming field experiments.

Keywords: Ecological parameters, Medicago, Onobrychis, Trifolium.

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Authors: Ahmad Kayvani Fard, Yehia Manawi

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Qatar’s primary source of fresh water is through seawater desalination. Amongst the major processes that are commercially available on the market, the most common large scale techniques are Multi-Stage Flash distillation (MSF), Multi Effect distillation (MED), and Reverse Osmosis (RO). Although commonly used, these three processes are highly expensive down to high energy input requirements and high operating costs allied with maintenance and stress induced on the systems in harsh alkaline media. Beside that cost, environmental footprint of these desalination techniques are significant; from damaging marine eco-system, to huge land use, to discharge of tons of GHG and huge carbon footprint. Other less energy consuming techniques based on membrane separation are being sought to reduce both the carbon footprint and operating costs is membrane distillation (MD). Emerged in 1960s, MD is an alternative technology for water desalination attracting more attention since 1980s. MD process involves the evaporation of a hot feed, typically below boiling point of brine at standard conditions, by creating a water vapor pressure difference across the porous, hydrophobic membrane. Main advantages of MD compared to other commercially available technologies (MSF and MED) and specially RO are reduction of membrane and module stress due to absence of trans-membrane pressure, less impact of contaminant fouling on distillate due to transfer of only water vapor, utilization of low grade or waste heat from oil and gas industries to heat up the feed up to required temperature difference across the membrane, superior water quality, and relatively lower capital and operating cost. To achieve the objective of this study, state of the art flat-sheet cross-flow DCMD bench scale unit was designed, commissioned, and tested. The objective of this study is to analyze the characteristics and morphology of the membrane suitable for DCMD through SEM imaging and contact angle measurement and to study the water quality of distillate produced by DCMD bench scale unit. Comparison with available literature data is undertaken where appropriate and laboratory data is used to compare a DCMD distillate quality with that of other desalination techniques and standards. Membrane SEM analysis showed that the PTFE membrane used for the study has contact angle of 127º with highly porous surface supported with less porous and bigger pore size PP membrane. Study on the effect of feed solution (salinity) and temperature on water quality of distillate produced from ICP and IC analysis showed that with any salinity and different feed temperature (up to 70ºC) the electric conductivity of distillate is less than 5 μS/cm with 99.99% salt rejection and proved to be feasible and effective process capable of consistently producing high quality distillate from very high feed salinity solution (i.e. 100000 mg/L TDS) even with substantial quality difference compared to other desalination methods such as RO and MSF.

Keywords: Membrane Distillation, Waste Heat, Seawater Desalination, Membrane, Freshwater, Direct Contact Membrane Distillation

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Authors: Kari Björn

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Introduction of games has expanded the application area of computer-aided learning tools to wide variety of age groups of learners. Serious games engage the learners into a real-world -type of simulation and potentially enrich the learning experience. Institutional background of a Bachelor’s level engineering program in Information and Communication Technology is introduced, with detailed focus on one of its majors, Health Technology. As part of a Customer Oriented Software Application thematic semester, one particular course of “eHealth Business and Solutions” is described and reflected in a gamified framework. Learning a consistent view into vast literature of business management, strategies, marketing and finance in a very limited time enforces selection of topics relevant to the industry. Health Technology is a novel and growing industry with a growing sector in consumer wearable devices and homecare applications. The business sector is attracting new entrepreneurs and impatient investor funds. From engineering education point of view the sector is driven by miniaturizing electronics, sensors and wireless applications. However, the market is highly consumer-driven and usability, safety and data integrity requirements are extremely high. When the same technology is used in analysis or treatment of patients, very strict regulatory measures are enforced. The paper introduces a course structure using gamification as a tool to learn the most essential in a new market: customer value proposition design, followed by a market entry game. Students analyze the existing market size and pricing structure of eHealth web-service market and enter the market as a steering group of their company, competing against the legacy players and with each other. The market is growing but has its rules of demand and supply balance. New products can be developed with an R&D-investment, and targeted to market with unique quality- and price-combinations. Product cost structure can be improved by investing to enhanced production capacity. Investments can be funded optionally by foreign capital. Students make management decisions and face the dynamics of the market competition in form of income statement and balance sheet after each decision cycle. The focus of the learning outcome is to understand customer value creation to be the source of cash flow. The benefit of gamification is to enrich the learning experience on structure and meaning of financial statements. The paper describes the gamification approach and discusses outcomes after two course implementations. Along the case description of learning challenges, some unexpected misconceptions are noted. Improvements of the game or the semi-gamified teaching pedagogy are discussed. The case description serves as an additional support to new game coordinator, as well as helps to improve the method. Overall, the gamified approach has helped to engage engineering student to business studies in an energizing way.

Keywords: Engineering education, integrated curriculum, learning experience, learning outcomes.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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