Search results for: Epsilon Near-Zero

Authors: Vatasta Koul, Vaibhav Sharma, Ayush Gupta, Rajesh Yadav

Abstract:

Exploratory missions to Mars and Titan have increased recently with various endeavors to find an alternate home to humankind. The use of surface rovers has its limitations due to rugged and uneven surfaces of these planetary bodies. The use of aerial robots requires the complete aerodynamic characterization of these vehicles in the atmospheric conditions of these planetary bodies. The dynamic stall phenomenon is extremely important for rotary wings performance under low Reynolds number that can be encountered in Martian and Titan’s atmosphere. The current research focuses on the aerodynamic characterization and exploration of the dynamic stall phenomenon of two different airfoils viz. E387 and Selig-Donovan7003 in Martian and Titan’s atmosphere at low Reynolds numbers of 10000 and 50000. The two-dimensional numerical simulations are conducted using commercially available finite volume solver with multi-species non-reacting mixture of gases as the working fluid. The k-epsilon (k-ε) turbulence model is used to capture the unsteady flow separation and the effect of turbulence. The dynamic characteristics are studied at a fixed different constant rotational extreme of angles of attack. This study of airfoils at different low Reynolds number and atmospheric conditions on Mars and Titan will be resulting in defining the aerodynamic characteristics of these airfoils for unmanned aerial missions for outer space exploration.

Keywords: Aerodynamic, dynamic stall, low Reynolds, Mars, Titan.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 591

Authors: Jerin John, Subanesh Shyam R., Aravind Kumar T. R., Naveen N., Vignesh R., Krishna Ganesh B, Sanal Kumar V. R.

Abstract:

Numerical studies have been carried out using a validated two-dimensional RNG k-epsilon turbulence model for the design optimization of a thrust vector control system using shock induced supersonic secondary jet. Parametric analytical studies have been carried out with various secondary jets at different divergent locations, jet interaction angles, jet pressures. The results from the parametric studies of the case on hand reveal that the primary nozzle with a small divergence angle, downstream injections with a distance of 2.5 times the primary nozzle throat diameter from the primary nozzle throat location warrant higher efficiency over a certain range of jet pressures and jet angles. We observed that the supersonic secondary jet opposing the core flow with jets interaction angle of 40o to the axis far downstream of the nozzle throat facilitates better thrust vectoring than the secondary jet with same direction as that of core flow with various interaction angles. We concluded that fixing of the supersonic secondary jet nozzle pointing towards the throat direction with suitable angle at a distance 2 to 4 times of the primary nozzle throat diameter, as the case may be, from the primary nozzle throat location could facilitate better thrust vectoring for the supersonic aerospace vehicles.

Keywords: Fluidic thrust vectoring, rocket steering, supersonic secondary jet location, TVC in spacecraft.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3615

Authors: Sayed Ahmed E. Sayed Ahmed, Emad Z. Ibrahiem, Osama M. Mesalhy, Mohamed A. Abdelatief

Abstract:

An experimental and numerical study has been conducted to clarify heat transfer characteristics and effectiveness of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Rew and the air-side Rea were at 5 x 102 and at from 1.8 x 103 to 9.7 x 103, respectively. The tubes arrangements were employed with various angles of attack θ1,2,3 from 0° to 330° at the considered Rea range. Correlation of Nu, St, as well as the heat transfer per unit pumping power (ε) in terms of Rea, design parameters for the studied bundle were presented. The temperature fields around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the heat transfer was increased by increasing the angle of attack from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. The best thermal performance and hence η of studied bundle was occurred at the lowest Rea and/or zero angle of attack. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.

Keywords: Wing-shaped tubes, Cross-flow cooling, Staggered arrangement, and CFD.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2026

Authors: R. Bansal, A. Jain, M. Kumar, R. S. Meena

Abstract:

Present wireless communication demands compact and intelligent devices with multitasking capabilities at affordable cost. The focus in the presented paper is on a dual band antenna for wireless communication with the capability of operating at two frequency bands with same structure. Two resonance frequencies are observed with the second operation band at 4.2GHz approximately three times the first resonance frequency at 1.5GHz. Structure is simple loop of microstrip line with characteristic impedance 50 ohms. The proposed antenna is designed using defective ground structure (DGS) and shows the nearly one third reductions in size as compared to without DGS. This antenna was simulated on electromagnetic (EM) simulation software and fabricated using microwave integrated circuit technique on RT-Duroid dielectric substrate (ε_r= 2.22) of thickness (H=15 mils). The designed antenna was tested on automatic network analyzer and shows the good agreement with simulated results. The proposed structure is modeled into an equivalent electrical circuit and simulated on circuit simulator. Subsequently, theoretical analysis was carried out and simulated. The simulated, measured, equivalent circuit response, and theoretical results shows good resemblance. The bands of operation draw many potential applications in today’s wireless communication.

Keywords: Defective Ground plane, Dual band, Loop Antenna, Microstrip antenna, Resonance frequency.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3724

Authors: Suresh Sahu, Abhijeet M. Vaidya, Naresh K. Maheshwari

Abstract:

The efforts to understand the heat transfer behavior of supercritical water in supercritical water cooled reactor (SCWR) are ongoing worldwide to fulfill the future energy demand. The higher thermal efficiency of these reactors compared to a conventional nuclear reactor is one of the driving forces for attracting the attention of nuclear scientists. In this work, a solution procedure has been described for solving supercritical fluid flow problems in complex geometries. The solution procedure is based on non-staggered grid. All governing equations are discretized by finite volume method (FVM) in curvilinear coordinate system. Convective terms are discretized by first-order upwind scheme and central difference approximation has been used to discretize the diffusive parts. k-ε turbulence model with standard wall function has been employed. SIMPLE solution procedure has been implemented for the curvilinear coordinate system. Based on this solution method, 3-D Computational Fluid Dynamics (CFD) code has been developed. In order to demonstrate the capability of this CFD code in supercritical fluid flows, heat transfer to supercritical water in circular tubes has been considered as a test problem. Results obtained by code have been compared with experimental results reported in literature.

Keywords: Curvilinear coordinate, body-fitted mesh, momentum interpolation, non-staggered grid, supercritical fluids.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 615

Authors: Azadeh Yazdi, Mohammadreza Nezamirad, Sepideh Amirahmadian, Nasim Sabetpour, Amirmasoud Hamedi

Abstract:

Cavitation inside diesel injector nozzle is investigated using Reynolds-Stress-Navier stokes equations. Schnerr-Sauer cavitation model is used for modeling cavitation inside diesel injector nozzle. The carrying fluid utilized in the current study is diesel fuel. The flow is verified at the beginning by comparing with the previous experimental data and it was found that K-Epsilon turbulent model could lead to a better accuracy comparing to K-Omega turbulent model. Moreover, mass flow rate obtained numerically is compared with the experimental value and discrepancy was found to be less than 5% - which shows the accuracy of the current results. Finally, a real-size four-hole nozzle is investigated and the flow inside it is visualized based on velocity profile, discharge coefficient and cavitation number. It was found that the mesh density could be reduced significantly by utilizing periodic boundary condition. Velocity contour at the mid nozzle showed that maximum value of velocity occurs at the end of the needle before entering the orifice area. Last but not least, at the same boundary conditions, when different needle heights were utilized, it was found that as needle height increases with an increase in cavitation number, discharge coefficient increases, while the mentioned increases is more tangible at smaller values of needle heights.

Keywords: cavitation, diesel fuel, CFD, real size nozzle, mass flow rate

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 462

Authors: Chongtham Jiten, Radhapiyari Laishram, K. Chandramani Singh

Abstract:

Alkaline niobate (Na_0.5K_0.5)NbO₃ ceramic system has attracted major attention in view of its potential for replacing the highly toxic but superior lead zirconate titanate (PZT) system for piezoelectric applications. Recently, a more detailed study of this system reveals that the ferroelectric and piezoelectric properties are optimized in the Li- and V-modified system having the composition (K_0.485Na_0.5Li_0.015)(Nb_0.98V_0.02)O₃. In the present work, we further study the pyroelectric behaviour of this composition along with another doped with Mn⁴⁺. So, (K_0.485Na_0.5Li_0.015)(Nb_0.98V_0.02)O₃ + x MnO₂ (x = 0, and 0.01 wt. %) ceramic compositions were synthesized by conventional ceramic processing route. X-ray diffraction study reveals that both the undoped and Mn⁴⁺-doped ceramic samples prepared crystallize into a perovskite structure having orthorhombic symmetry. Dielectric study indicates that Mn⁴⁺ doping has little effect on both the Curie temperature (T_c) and tetragonal-orthorhombic phase transition temperature (T_ot). The bulk density, room-temperature dielectric constant (ε_RT), and room-c The room-temperature coercive field (E_c) is observed to be lower in Mn⁴⁺ doped sample. The detailed analysis of the P-E hysteresis loops over the range of temperature from about room temperature to T_ot points out that enhanced ferroelectric properties exist in this temperature range with better thermal stability for the Mn⁴⁺ doped ceramic. The study reveals that small traces of Mn⁴⁺ can modify (K_0.485Na_0.5Li_0.015)(Nb_0.98V_0.02)O₃ system so as to improve its ferroelectric properties with good thermal stability over a wide range of temperature.

Keywords: Ceramics, dielectric properties, ferroelectric properties, lead-free, sintering, thermal stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 960

Authors: J. P. Panda, K. Sasmal, H. V. Warrior

Abstract:

Eddy viscosity models in turbulence modeling can be mainly classified as linear and nonlinear models. Linear formulations are simple and require less computational resources but have the disadvantage that they cannot predict actual flow pattern in complex geophysical flows where streamline curvature and swirling motion are predominant. A constitutive equation of Reynolds stress anisotropy is adopted for the formulation of eddy viscosity including all the possible higher order terms quadratic in the mean velocity gradients, and a simplified model is developed for actual oceanic flows where only the vertical velocity gradients are important. The new model is incorporated into the one dimensional General Ocean Turbulence Model (GOTM). Two realistic oceanic test cases (OWS Papa and FLEX' 76) have been investigated. The new model predictions match well with the observational data and are better in comparison to the predictions of the two equation k-epsilon model. The proposed model can be easily incorporated in the three dimensional Princeton Ocean Model (POM) to simulate a wide range of oceanic processes. Practically, this model can be implemented in the coastal regions where trasverse shear induces higher vorticity, and for prediction of flow in estuaries and lakes, where depth is comparatively less. The model predictions of marine turbulence and other related data (e.g. Sea surface temperature, Surface heat flux and vertical temperature profile) can be utilized in short term ocean and climate forecasting and warning systems.

Keywords: Eddy viscosity, turbulence modeling, GOTM, CFD.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 901

Authors: Z. Adnan, M. M. Habib

Abstract:

The laboratory tests for measuring the effects of small strain to the shear strength and maximum stiffness development of post-cyclic degradation of hemic peat are reviewed in this paper. A series of laboratory testing has been conducted to fulfil the objective of this research to study the post-cyclic behaviour of peat soil and focuses on the small strain characteristics. For this purpose, a number of strain-controlled static, cyclic and post-cyclic triaxial tests were carried out in undrained condition on hemic peat soil. The shear strength and maximum stiffness of hemic peat are evaluated immediately after post-cyclic monotonic testing. There are two soil samples taken from West Johor and East Malaysia peat soil. Based on these laboratories and field testing data, it was found that the shear strength and maximum stiffness of peat soil decreased in post-cyclic monotonic loading than its initial shear strength and stiffness. In particular, degradation in shear strength and stiffness is more sensitive for peat soil due to fragile and uniform fibre structures. Shear strength of peat soil, τ_max = 12.53 kPa (Beaufort peat, BFpt) and 36.61 kPa (Parit Nipah peat, PNpt) decreased than its initial 58.46 kPa and 91.67 kPa. The maximum stiffness, G_max = 0.23 and 0.25 decreased markedly with post-cyclic, G_max = 0.04 and 0.09. Simple correlations between the G_max and the τ_max effects due to small strain, ε = 0.1, the G_max values for post-cyclic are relatively low compared to its initial G_max. As a consequence, the reported values and patterns of both the West Johor and East Malaysia peat soil are generally the same.

Keywords: Post-cyclic, strain, shear strength, maximum stiffness.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1034

Authors: Praveen Kumar, Nitin Kumar, Hemant Kumar

Abstract:

The modernization of computer technology and commercial computational fluid dynamic (CFD) simulation has given better detailed results as compared to experimental investigation techniques. CFD techniques are widely used in different field due to its flexibility and performance. Evaluation of pipeline erosion is complex phenomenon to solve by numerical arithmetic technique, whereas CFD simulation is an easy tool to resolve that type of problem. Erosion wear behaviour due to solid–liquid mixture in the slurry pipeline has been investigated using commercial CFD code in FLUENT. Multi-phase Euler-Lagrange model was adopted to predict the solid particle erosion wear in 22.5° pipe bend for the flow of bottom ash-water suspension. The present study addresses erosion prediction in three dimensional 22.5° pipe bend for two-phase (solid and liquid) flow using finite volume method with standard k-ε turbulence, discrete phase model and evaluation of erosion wear rate with varying velocity 2-4 m/s. The result shows that velocity of solid-liquid mixture found to be highly dominating parameter as compared to solid concentration, density, and particle size. At low velocity, settling takes place in the pipe bend due to low inertia and gravitational effect on solid particulate which leads to high erosion at bottom side of pipeline.

Keywords: Computational fluid dynamics, erosion, slurry transportation, k-ε Model.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1863

Authors: Li Xu, Huanbao Jiang, Zhenfei Huang, Lailai Zhang

Abstract:

In recent years, as global warming, the sea-ice extent of North Arctic undergoes an evident decrease and Arctic channel has attracted the attention of shipping industry. Ice crystals existing in the seawater of Arctic channel which enter the seawater system of the ship with the seawater were found blocking the seawater pipe. The appearance of cooler paralysis, auxiliary machine error and even ship power system paralysis may be happened if seriously. In order to reduce the effect of high temperature in auxiliary equipment, seawater system will use external ice-water to participate in the cooling cycle and achieve the state of its flow. The distribution of ice crystals in seawater pipe can be achieved. As the ice slurry system is solid liquid two-phase system, the flow process of ice-water mixture is very complex and diverse. In this paper, the flow process in seawater pipe of ice slurry is simulated with fluid dynamics simulation software based on k-ε turbulence model. As the ice packing fraction is a key factor effecting the distribution of ice crystals, the influence of ice packing fraction on the flowing process of ice slurry is analyzed. In this work, the simulation results show that as the ice packing fraction is relatively large, the distribution of ice crystals is uneven in the flowing process of the seawater which has such disadvantage as increase the possibility of blocking, that will provide scientific forecasting methods for the forming of ice block in seawater piping system. It has important significance for the reliability of the operating of polar ships in the future.

Keywords: Ice slurry, seawater pipe, ice packing fraction, numerical simulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1335

Authors: F. A. Gdhaidh, K. Hussain, H. S. Qi

Abstract:

A numerical study of natural convection heat transfer in water filled cavity has been examined in 3-Dfor single phase liquid cooling system by using an array of parallel plate fins mounted to one wall of a cavity. The heat generated by a heat source represents a computer CPU with dimensions of 37.5∗37.5mm mounted on substrate. A cold plate is used as a heat sink installed on the opposite vertical end of the enclosure. The air flow inside the computer case is created by an exhaust fan. A turbulent air flow is assumed and k-ε model is applied. The fins are installed on the substrate to enhance the heat transfer. The applied power energy range used is between 15 - 40W. In order to determine the thermal behaviour of the cooling system, the effect of the heat input and the number of the parallel plate fins are investigated. The results illustrate that as the fin number increases the maximum heat source temperature decreases. However, when the fin number increases to critical value the temperature start to increase due to the fins are too closely spaced and that cause the obstruction of water flow. The introduction of parallel plate fins reduces the maximum heat source temperature by 10% compared to the case without fins. The cooling system maintains the maximum chip temperature at 64.68°C when the heat input was at 40W that is much lower than the recommended computer chips limit temperature of no more than 85°C and hence the performance of the CPU is enhanced.

Keywords: Chips limit temperature, closed enclosure, natural convection, parallel plate, single phase liquid.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2919

Authors: Pakawhat Khumkhreung, Yottana Khunatorn

Abstract:

The flow pattern inside rectangular intake air duct of 300 MW lignite coal-fired power plant is investigated in order to analyze and reduce overall inlet system pressure drop. The system consists of the 45-degree inlet elbow, the flow instrument, the 90-degree mitered elbow and fans, respectively. The energy loss in each section can be determined by Bernoulli’s equation and ASHRAE standard table. Hence, computational fluid dynamics (CFD) is used in this study based on Navier-Stroke equation and the standard k-epsilon turbulence modeling. Input boundary condition is 175 kg/s mass flow rate inside the 11-m² cross sectional duct. According to the inlet air flow rate, the Reynolds number of airstream is 2.7x10⁶ (based on the hydraulic duct diameter), thus the flow behavior is turbulence. The numerical results are validated with the real operation data. It is found that the numerical result agrees well with the operating data, and dominant loss occurs at the flow rate measurement device. Normally, the air flow rate is measured by the airfoil and it gets high pressure drop inside the duct. To overcome this problem, the airfoil is planned to be replaced with the other type measuring instrument, such as the average pitot tube which generates low pressure drop of airstream. The numerical result in case of average pitot tube shows that the pressure drop inside the inlet airstream duct is decreased significantly. It should be noted that the energy consumption of inlet air system is reduced too.

Keywords: Airfoil, average pitot tube, combustion air, CFD, pressure drop, rectangular duct.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1036

Authors: Funda Erdem Şahnali, Ş. Özgür Atayılmaz, Tolga N. Aynur

Abstract:

Almost all of the domestic refrigerators operate on the principle of the vapor compression refrigeration cycle and removal of heat from the refrigerator cabinets is done via one of the two methods: natural convection or forced convection. In this study, airflow and temperature distributions inside a 375L no-frost type larder cabinet, in which cooling is provided by forced convection, are evaluated both experimentally and numerically. Airflow rate, compressor capacity and temperature distribution in the cooling chamber are known to be some of the most important factors that affect the cooling performance and energy consumption of a refrigerator. The objective of this study is to evaluate the original temperature distribution in the larder cabinet, and investigate for better temperature distribution solutions throughout the refrigerator domain via system optimizations that could provide uniform temperature distribution. The flow visualization and airflow velocity measurements inside the original refrigerator are performed via Stereoscopic Particle Image Velocimetry (SPIV). In addition, airflow and temperature distributions are investigated numerically with Ansys Fluent. In order to study the heat transfer inside the aforementioned refrigerator, forced convection theories covering the following cases are applied: closed rectangular cavity representing heat transfer inside the refrigerating compartment. The cavity volume has been represented with finite volume elements and is solved computationally with appropriate momentum and energy equations (Navier-Stokes equations). The 3D model is analyzed as transient, with k-ε turbulence model and SIMPLE pressure-velocity coupling for turbulent flow situation. The results obtained with the 3D numerical simulations are in quite good agreement with the experimental airflow measurements using the SPIV technique. After Computational Fluid Dynamics (CFD) analysis of the baseline case, the effects of three parameters: compressor capacity, fan rotational speed and type of shelf (glass or wire) are studied on the energy consumption; pull down time, temperature distributions in the cabinet. For each case, energy consumption based on experimental results is calculated. After the analysis, the main effective parameters for temperature distribution inside a cabin and energy consumption based on CFD simulation are determined and simulation results are supplied for Design of Experiments (DOE) as input data for optimization. The best configuration with minimum energy consumption that provides minimum temperature difference between the shelves inside the cabinet is determined.

Keywords: Air distribution, CFD, DOE, energy consumption, larder cabinet, refrigeration, uniform temperature.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 532

Authors: M. Shiva Prasad, S. R. Atchuta, T. Vijayaraghavan, S. Sakthivel

Abstract:

The world is in need of efficient energy conversion technologies which are affordable, accessible, and sustainable with eco-friendly nature. Solar energy is one of the cornerstones for the world’s economic growth because of its abundancy with zero carbon pollution. Among the various solar energy conversion technologies, solar thermal technology has attracted a substantial renewed interest due to its diversity and compatibility in various applications. Solar thermal systems employ concentrators, tracking systems and heat engines for electricity generation which lead to high cost and complexity in comparison with photovoltaics; however, it is compatible with distinct thermal energy storage capability and dispatchable electricity which creates a tremendous attraction. Apart from that, employing cost-effective solar selective receiver tube in a concentrating solar thermal (CST) system improves the energy conversion efficiency and directly reduces the cost of technology. In addition, the development of solar receiver tubes by low cost methods which can offer high optical properties and corrosion resistance in an open-air atmosphere would be beneficial for low and medium temperature applications. In this regard, our work opens up an approach which has the potential to achieve cost-effective energy conversion. We have developed a highly selective tandem absorber coating through a facile wet chemical route by a combination of chemical oxidation, sol-gel, and nanoparticle coating methods. The developed tandem absorber coating has gradient refractive index nature on stainless steel (SS 304) and exhibited high optical properties (α ≤ 0.95 & ε ≤ 0.14). The first absorber layer (Cr-Mn-Fe oxides) developed by controlled oxidation of SS 304 in a chemical bath reactor. A second composite layer of ZrO₂-SiO₂ has been applied on the chemically oxidized substrate by So-gel dip coating method to serve as optical enhancing and corrosion resistant layer. Finally, an antireflective layer (MgF₂) has been deposited on the second layer, to achieve > 95% of absorption. The developed tandem layer exhibited good thermal stability up to 250 °C in open air atmospheric condition and superior corrosion resistance (withstands for > 200h in salt spray test (ASTM B117)). After the successful development of a coating with targeted properties at a laboratory scale, a prototype of the 1 m tube has been demonstrated with excellent uniformity and reproducibility. Moreover, it has been validated under standard laboratory test condition as well as in field condition with a comparison of the commercial receiver tube. The presented strategy can be widely adapted to develop highly selective coatings for a variety of CST applications ranging from hot water, solar desalination, and industrial process heat and power generation. The high-performance, cost-effective medium temperature receiver tube technology has attracted many industries, and recently the technology has been transferred to Indian industry.

Keywords: Concentrated solar thermal system, solar selective coating, tandem absorber, ultralow refractive index.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 686

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

Abstract:

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.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1233