Search results for: blade aerodynamics

Authors: Blaga Alexandra Cristina, Kloetzer Lenuta, Bompa Amalia Stela, Galaction Anca Irina, Cascaval Dan

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Vitamin B9 is an important member of vitamins B group, being a growth factor, important for making genetic material as DNA and RNA, red blood cells, for building muscle tissues, especially during periods of infancy, adolescence and pregnancy. Its production by biosynthesis is based on the high metabolic potential of mutant Bacillus subtilis, due to a superior biodisponibility compared to that obtained by chemical pathways. Pertraction, defined as the extraction and transport through liquid membranes consists in the transfer of a solute between two aqueous phases of different pH-values, phases that are separated by a solvent layer of various sizes. The pertraction efficiency and selectivity could be significantly enhanced by adding a carrier in the liquid membrane, such as organophosphoric compounds, long chain amines or crown-ethers etc., the separation process being called facilitated pertraction. The aim of the work is to determine the impact of the presence of two extractants/carriers in the bulk liquid membrane, i.e. di(2-ethylhexyl) phosphoric acid (D2EHPA) and lauryltrialkylmetilamine (Amberlite LA2) on the transport kinetics of vitamin B9. The experiments have been carried out using two pertraction equipments for a free liquid membrane or bulk liquid membrane. One pertraction cell consists on a U-shaped glass pipe (used for the dichloromethane membrane) and the second one is an H-shaped glass pipe (used for h-heptane), having 45 mm inner diameter of the total volume of 450 mL, the volume of each compartment being of 150 mL. The aqueous solutions are independently mixed by means of double blade stirrers with 6 mm diameter and 3 mm height, having the rotation speed of 500 rpm. In order to reach high diffusional rates through the solvent layer, the organic phase has been mixed with a similar stirrer, at a similar rotation speed (500 rpm). The area of mass transfer surface, both for extraction and for reextraction, was of 1.59x10-³ m2. The study on facilitated pertraction with the mixture of two carriers, namely D2EHPA and Amberlite LA-2, dissolved in two solvents with different polarities: n-heptane and dichloromethane, indicated the possibility to obtain the synergic effect. The synergism has been analyzed by considering the vitamin initial and final mass flows, as well as the permeability factors through liquid membrane. The synergic effect has been observed at low D2EHPA concentrations and high Amberlite LA-2 concentrations, being more important for the low-polar solvent (n-heptane). The results suggest that the mechanism of synergic pertraction consists on the reaction between the organophosphoric carrier and vitamin B9 at the interface between the feed and membrane phases, while the aminic carrier enhances the hydrophobicity of this compound by solvation. However, the formation of this complex reduced the reextraction rate and, consequently, affects the synergism related to the final mass flows and permeability factor. For describing the influences of carriers concentrations on the synergistic coefficients, some equations have been proposed by taking into account the vitamin mass flows or permeability factors, with an average deviations between 4.85% and 10.73%.

Keywords: pertraction, synergism, vitamin B9, Amberlite LA-2, di(2-ethylhexyl) phosphoric acid

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Authors: Desmond Appiah, Fan Zhang, Shouqi Yuan, Wei Xueyuan, Stephen N. Asomani

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The side channel pump has distinctive hydraulic performance characteristics over other vane pumps because of its generation of high pressure heads in only one impeller revolution. Hence, there is soaring utilization and application in the fields of petrochemical, food processing fields, automotive and aerospace fuel pumping where high heads are required at low flows. The side channel pump is characterized by unstable flow because after fluid flows into the impeller passage, it moves into the side channel and comes back to the impeller again and then moves to the next circulation. Consequently, the flow leaves the side channel pump following a helical path. However, the pressure fluctuation exhibited in the flow greatly contributes to the unwanted noise and vibration which is associated with the flow. In this paper, a side channel pump prototype was examined thoroughly through numerical calculations based on SST k-ω turbulence model to ascertain the pressure fluctuation behavior. The pressure fluctuation intensity of the 3D unstable flow dynamics were carefully investigated under different working conditions 0.8QBEP, 1.0 QBEP and 1.2QBEP. The results showed that the pressure fluctuation distribution around the pressure side of the blade is greater than the suction side at the impeller and side channel interface (z=0) for all three operating conditions. Part-load condition 0.8QBEP recorded the highest pressure fluctuation distribution because of the high circulation velocity thus causing an intense exchanged flow between the impeller and side channel. Time and frequency domains spectra of the pressure fluctuation patterns in the impeller and the side channel were also analyzed under the best efficiency point value, QBEP using the solution from the numerical calculations. It was observed from the time-domain analysis that the pressure fluctuation characteristics in the impeller flow passage increased steadily until the flow reached the interrupter which separates low-pressure at the inflow from high pressure at the outflow. The pressure fluctuation amplitudes in the frequency domain spectrum at the different monitoring points depicted a gentle decreasing trend of the pressure amplitudes which was common among the operating conditions. The frequency domain also revealed that the main excitation frequencies occurred at 600Hz, 1200Hz, and 1800Hz and continued in the integers of the rotating shaft frequency. Also, the mass flow exchange plots indicated that the side channel pump is characterized with many vortex flows. Operating conditions 0.8QBEP, 1.0 QBEP depicted less and similar vortex flow while 1.2Q recorded many vortex flows around the inflow, middle and outflow regions. The results of the numerical calculations were finally verified experimentally. The performance characteristics curves from the simulated results showed that 0.8QBEP working condition recorded a head increase of 43.03% and efficiency decrease of 6.73% compared to 1.0QBEP. It can be concluded that for industrial applications where the high heads are mostly required, the side channel pump can be designed to operate at part-load conditions. This paper can serve as a source of information in order to optimize a reliable performance and widen the applications of the side channel pumps.

Keywords: exchanged flow, pressure fluctuation, numerical simulation, side channel pump

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Authors: Madjid Karimirad

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Floating solar was not very well-known in the renewable energy field a decade ago; however, there has been tremendous growth internationally with a Compound Annual Growth Rate (CAGR) of nearly 30% in recent years. To reach the goal of global net-zero emission by 2050, all renewable energy sources including solar should be used. Considering that 40% of the world’s population lives within 100 kilometres of the coasts, floating solar in coastal waters is an obvious energy solution. However, this requires more robust floating solar solutions. This paper tries to enlighten the fundamental requirements in the design of floating solar for offshore installations from the hydrodynamic and offshore engineering points of view. In this regard, a closer look at dynamic characteristics, stochastic behaviour and nonlinear phenomena appearing in this kind of structure is a major focus of the current article. Floating solar structures are alternative and very attractive green energy installations with (a) Less strain on land usage for densely populated areas; (b) Natural cooling effect with efficiency gain; and (c) Increased irradiance from the reflectivity of water. Also, floating solar in conjunction with the hydroelectric plants can optimise energy efficiency and improve system reliability. The co-locating of floating solar units with other types such as offshore wind, wave energy, tidal turbines as well as aquaculture (fish farming) can result in better ocean space usage and increase the synergies. Floating solar technology has seen considerable developments in installed capacities in the past decade. Development of design standards and codes of practice for floating solar technologies deployed on both inland water-bodies and offshore is required to ensure robust and reliable systems that do not have detrimental impacts on the hosting water body. Floating solar will account for 17% of all PV energy produced worldwide by 2030. To enhance the development, further research in this area is needed. This paper aims to discuss the main critical design aspects in light of the load and load effects that the floating solar platforms are subjected to. The key considerations in hydrodynamics, aerodynamics and simultaneous effects from the wind and wave load actions will be discussed. The link of dynamic nonlinear loading, limit states and design space considering the environmental conditions is set to enable a better understanding of the design requirements of fast-evolving floating solar technology.

Keywords: floating solar, offshore renewable energy, wind and wave loading, design space

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Authors: Zbigniew Czyz, Krzysztof Skiba, Miroslaw Wendeker

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This paper discusses the results of aerodynamic investigation of the Tajfun gyroplane body designed by a Polish company, Aviation Artur Trendak. This gyroplane has been studied as a 1:8 scale model. Scaling objects for aerodynamic investigation is an inherent procedure in any kind of designing. If scaling, the criteria of similarity need to be satisfied. The basic criteria of similarity are geometric, kinematic and dynamic. Despite the results of aerodynamic research are often reduced to aerodynamic coefficients, one should pay attention to how values of coefficients behave if certain criteria are to be satisfied. To satisfy the dynamic criterion, for example, the Reynolds number should be focused on. This is the correlation of inertial to viscous forces. With the multiplied flow speed by the specific dimension as a numerator (with a constant kinematic viscosity coefficient), flow speed in a wind tunnel research should be increased as many times as an object is decreased. The aerodynamic coefficients specified in this research depend on the real forces that act on an object, its specific dimension, medium speed and variations in its density. Rapid prototyping with a 3D printer was applied to create the research object. The research was performed with a T-1 low-speed wind tunnel (its diameter of the measurement volume is 1.5 m) and a six-element aerodynamic internal scales, WDP1, at the Institute of Aviation in Warsaw. This T-1 wind tunnel is low-speed continuous operation with open space measurement. The research covered a number of the selected speeds of undisturbed flow, i.e. V = 20, 30 and 40 m/s, corresponding to the Reynolds numbers (as referred to 1 m) Re = 1.31∙106, 1.96∙106, 2.62∙106 for the angles of attack ranging -15° ≤ α ≤ 20°. Our research resulted in basic aerodynamic characteristics and observing the impact of undisturbed flow speed on the correlation of aerodynamic coefficients as a function of the angle of attack of the gyroplane body. If the speed of undisturbed flow in the wind tunnel changes, the aerodynamic coefficients are significantly impacted. At speed from 20 m/s to 30 m/s, drag coefficient, Cx, changes by 2.4% up to 9.9%, whereas lift coefficient, Cz, changes by -25.5% up to 15.7% if the angle of attack of 0° excluded or by -25.5% up to 236.9% if the angle of attack of 0° included. Within the same speed range, the coefficient of a pitching moment, Cmy, changes by -21.1% up to 7.3% if the angles of attack -15° and -10° excluded or by -142.8% up to 618.4% if the angle of attack -15° and -10° included. These discrepancies in the coefficients of aerodynamic forces definitely need to consider while designing the aircraft. For example, if load of certain aircraft surfaces is calculated, additional correction factors definitely need to be applied. This study allows us to estimate the discrepancies in the aerodynamic forces while scaling the aircraft. This work has been financed by the Polish Ministry of Science and Higher Education.

Keywords: aerodynamics, criteria of similarity, gyroplane, research tunnel

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Authors: Maria Zulema Morquecho Vega, Fabiola CarolinaMiranda Castro, Rafael Verdugo Miranda, Ignacio Yocupicio Villegas, Ana lidia Barron Raygoza, Martin enrique MArquez Cordova, Jose Alberto Duarte Moller

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Background: Anemopsis californica, also called (tame grass) belongs to the Saururaceae family small, green plant. The blade is long and wide. Gives a white flower. The plant population is only found in humid, swampy habitats, it grows where there is water, along the banks of streams and water holes. In the winter, it dries up. The leaves, rhizomes, or roots of this plant have been used to treat a range of diseases. Some of its healing properties are used to treat wounds, cold and flu symptoms, spasmodic cough, infection, pain and inflammation, burns, swollen feet, as well as lung ailments, asthma, circulatory problems (varicose veins), rheumatoid arthritis, purifies blood, helps in urinary and digestive tract diseases, sores and healing, for headache, sore throat, diarrhea, kidney pain. The tea made from the leaves and roots is used to treat uterine cancer, womb cancer, relieves menstrual pain and stops excessive bleeding after childbirth. It is also used as a gynecological treatment for infections, hemorrhoids, candidiasis and vaginitis. Objective: To study the cytotoxicity of gels prepared with silver nanoparticles in AC extract combined with chitosan, collagen and hyaluronic acid as an alternative therapy for skin conditions. Methods: The Ag NPs were synthesized according to the following method. A 0.3 mg/mL solution is prepared in 10 ml of deionized water, adjust to pH 12 with NaOH, stirring is maintained constant magnetic and a temperature of 80 °C. Subsequently, 100 ul of a 0.1 M AgNO3 solution and kept stirring constantly for 15 min. Once the reaction is complete, measurements are performed by UV-Vis. A gel was prepared in a 5% solution of acetic acid with the respective nanoparticles and AC extract of silver in the extract of AC. Chitosan is added until the process begins to occur gel. At that time, collagen will be added in a ratio of 3 to 5 drops, and later, hyaluronic acid in 2% of the total compound formed. Finally, after resting for 24 hours, the cytotoxic effect of the gels was studied. in the presence of highly positive bacteria Staphylococcus aureus and highly negative for Escherichia coli. Cultures will be incubated for 24 hours in the presence of the compound and compared with the reference. Results: Silver nanoparticles obtained had a spherical shape and sizes among 20 and 30 nm. UV-Vis spectra confirm the presence of silver nanoparticles showing a surface plasmon around 420 nm. Finally, the test in presence of bacteria yield a good antibacterial property of this nanocompound and tests in people were successful. Conclusion: Gel prepared by biogenic synthesis shown beneficious effects in severe acne, acne vulgaris and wound healing with diabetic patients.

Keywords: anemopsis californica, nanomedicina, biotechnology, biomedicine

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Authors: Mazaher Yarmohamadi-Vasel, Ali Reza Modarresi-Alama, Sahar Shabzendedara

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Purpose/Objectives: The first purpose was synthesize Poly(N-(sulfophenyl)aniline) nanoflowers (PSANFLs) and Poly(N-(sulfophenyl)aniline) nanofibers/titanium dioxide nanoparticles ((PSANFs/TiO2NPs) by a solid-state mechano-chemical reaction and template-free method and use them in hybrid solar cell. Also, our second aim was to increase the solubility and the processability of conjugated nanomaterials in water through polar functionalized materials. poly[N-(4-sulfophenyl)aniline] is easily soluble in water because of the presence of polar groups of sulfonic acid in the polymer chain. Materials/Methods: Iron (III) chloride hexahydrate (FeCl3∙6H2O) were bought from Merck Millipore Company. Titanium oxide nanoparticles (TiO2, <20 nm, anatase) and Sodium diphenylamine-4-sulfonate (99%) were bought from Sigma-Aldrich Company. Titanium dioxide nanoparticles paste (PST-20T) was prepared from Sharifsolar Co. Conductive glasses coated with indium tin oxide (ITO) were bought from Xinyan Technology Co (China). For the first time we used the solid-state mechano-chemical reaction and template-free method to synthesize Poly(N-(sulfophenyl)aniline) nanoflowers. Moreover, for the first time we used the same technique to synthesize nanocomposite of Poly(N-(sulfophenyl)aniline) nanofibers and titanium dioxide nanoparticles (PSANFs/TiO2NPs) also for the first time this nanocomposite was synthesized. Examining the results of electrochemical calculations energy gap obtained by CV curves and UV–vis spectra demonstrate that PSANFs/TiO2NPs nanocomposite is a p-n type material that can be used in photovoltaic cells. Doctor blade method was used to creat films for three kinds of hybrid solar cells in terms of different patterns like ITO│TiO2NPs│Semiconductor sample│Al. In the following, hybrid photovoltaic cells in bilayer and bulk heterojunction structures were fabricated as ITO│TiO2NPs│PSANFLs│Al and ITO│TiO2NPs│PSANFs /TiO2NPs│Al, respectively. Fourier-transform infrared spectra, field emission scanning electron microscopy (FE-SEM), ultraviolet-visible spectra, cyclic voltammetry (CV) and electrical conductivity were the analysis that used to characterize the synthesized samples. Results and Conclusions: FE-SEM images clearly demonstrate that the morphology of the synthesized samples are nanostructured (nanoflowers and nanofibers). Electrochemical calculations of band gap from CV curves demonstrated that the forbidden band gap of the PSANFLs and PSANFs/TiO2NPs nanocomposite are 2.95 and 2.23 eV, respectively. I–V characteristics of hybrid solar cells and their power conversion efficiency (PCE) under 100 mWcm−2 irradiation (AM 1.5 global conditions) were measured that The PCE of the samples were 0.30 and 0.62%, respectively. At the end, all the results of solar cell analysis were discussed. To sum up, PSANFLs and PSANFLs/TiO2NPs were successfully synthesized by an affordable and straightforward mechanochemical reaction in solid-state under the green condition. The solubility and processability of the synthesized compounds have been improved compared to the previous work. We successfully fabricated hybrid photovoltaic cells of synthesized semiconductor nanostructured polymers and TiO2NPs as different architectures. We believe that the synthesized compounds can open inventive pathways for the development of other Poly(N-(sulfophenyl)aniline based hybrid materials (nanocomposites) proper for preparing new generation solar cells.

Keywords: mechanochemical synthesis, PSANFLs, PSANFs/TiO2NPs, solar cell

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Authors: Jhonnatan Eduardo Zamudio Palacios, Oscar Leonardo Mosquera Dussan, Daniel Guzman Perez, Daniel Alfonso Botero Rosas, Oscar Fabian Rubiano Espinosa, Jose Antonio Garcia Torres, Ivan Dario Chavarro, Ivan Ramiro Rodriguez Camacho, Jaime Orlando Rodriguez

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The training of cilsitas with some type of disability finds in the technological development an indispensable ally, generating every day advances to contribute to the quality of life allowing to maximize the capacities of the athletes. The performance of a cyclist depends on physiological and biomechanical factors, such as aerodynamic profile, bicycle measurements, connecting rod length, pedaling systems, type of competition, among others. This study particularly focuses on the description of the dynamic model of a transtibial prosthesis for Paralympic cyclists. To make the model, two points are chosen: in the radius centers of rotation of the plate and pinion of the track bicycle. The parametric scheme of the track bike represents a model of 6 degrees of freedom due to the displacement in X - Y of each of the reference points of the angles of the curve profile β, cant of the velodrome α and the angle of rotation of the connecting rod φ. The force exerted on the crank of the bicycle varies according to the angles of the curve profile β, the velodrome cant of α and the angle of rotation of the crank φ. The behavior is analyzed through the Matlab R2015a software. The average strength that a cyclist exerts on the cranks of a bicycle is 1,607.1 N, the Paralympic cyclist must perform a force on each crank about 803.6 N. Once the maximum force associated with the movement has been determined, it is continued to the dynamic modeling of the transtibial prosthesis that represents a model of 6 degrees of freedom with displacement in X - Y in relation to the angles of rotation of the hip π, knee γ and ankle λ. Subsequently, an analysis of the kinematic behavior of the prosthesis was carried out by means of SolidWorks 2017 and Matlab R2015a, which was used to model and analyze the variation of the hip angles π, knee γ and ankle of the λ prosthesis. The reaction forces generated in the prosthesis were performed on the ankle of the prosthesis, performing the summation of forces on the X and Y axes. The same analysis was then applied to the tibia of the prosthesis and the socket. The reaction force of the parts of the prosthesis varies according to the hip angles π, knee γ and ankle of the prosthesis λ. Therefore, it can be deduced that the maximum forces experienced by the ankle of the prosthesis is 933.6 N on the X axis and 2.160.5 N on the Y axis. Finally, it is calculated that the maximum forces experienced by the tibia and the socket of the transtibial prosthesis in high performance competitions is 3.266 N on the X axis and 1.357 N on the Y axis. In conclusion, it can be said that the performance of the cyclist depends on several physiological factors, linked to biomechanics of training. The influence of biomechanical factors such as aerodynamics, bicycle measurements, connecting rod length, or non-circular pedaling systems on the cyclist performance.

Keywords: biomechanics, dynamic model, paralympic cyclist, transtibial prosthesis

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Authors: Quan Wen, Tianxiao Chang, Shaolu Shi, Yushi Wang, Guangyu Wang

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As a kind of working environment of the fuze, the spin rate decaying law of projectile in exterior trajectory is of great value in the design of the rotation count fixed distance fuze. In addition, it is significant in the field of devices for simulation tests of fuze exterior ballistic environment, flight stability, and dispersion accuracy of gun projectile and opening and scattering design of submunition and illuminating cartridges. Besides, the self-destroying mechanism of the fuze in small-caliber projectile often works by utilizing the attenuation of centrifugal force. In the theory of projectile aerodynamics and fuze design, there are many formulas describing the change law of projectile angular velocity in external ballistic such as Roggla formula, exponential function formula, and power function formula. However, these formulas are mostly semi-empirical due to the poor test conditions and insufficient test data at that time. These formulas are difficult to meet the design requirements of modern fuze because they are not accurate enough and have a narrow range of applications now. In order to provide more accurate ballistic environment parameters for the design of a hemispherical head projectile fuze, the projectile’s spin rate decaying law in exterior trajectory under the effect of air resistance was studied. In the analysis, the projectile shape was simplified as hemisphere head, cylindrical part, rotating band part, and anti-truncated conical tail. The main assumptions are as follows: a) The shape and mass are symmetrical about the longitudinal axis, b) There is a smooth transition between the ball hea, c) The air flow on the outer surface is set as a flat plate flow with the same area as the expanded outer surface of the projectile, and the boundary layer is turbulent, d) The polar damping moment attributed to the wrench hole and rifling mark on the projectile is not considered, e) The groove of the rifle on the rotating band is uniform, smooth and regular. The impacts of the four parts on aerodynamic moment of the projectile rotation were obtained by aerodynamic theory. The surface friction stress of the projectile, the polar damping moment formed by the head of the projectile, the surface friction moment formed by the cylindrical part, the rotating band, and the anti-truncated conical tail were obtained by mathematical derivation. After that, the mathematical model of angular spin rate attenuation was established. In the whole trajectory with the maximum range angle (38°), the absolute error of the polar damping torque coefficient obtained by simulation and the coefficient calculated by the mathematical model established in this paper is not more than 7%. Therefore, the credibility of the mathematical model was verified. The mathematical model can be described as a first-order nonlinear differential equation, which has no analytical solution. The solution can be only gained as a numerical solution by connecting the model with projectile mass motion equations in exterior ballistics.

Keywords: ammunition engineering, fuze technology, spin rate, numerical simulation

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Authors: Kimberley Adamek

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According to the Council on Tall Buildings, there has been a rapid increase in the construction of tall or “megatall” buildings over the past two decades. Simultaneously, the New England Journal of Medicine has reported that there has been a steady increase in climate related natural disasters since the 1970s; the eastern expansion of the USA's infamous Tornado Alley being just one of many current issues. In the future, this could mean that tall buildings, which already guide high speed winds down to pedestrian levels would have to withstand stronger forces and protect pedestrians in more extreme ways. Although many projects are required to be verified within wind tunnels and a handful of cities such as San Francisco have included wind testing within building code standards, there are still many examples where wind is only considered for basic loading. This typically results in and an increase of structural expense and unwanted mitigation strategies that are proposed late within a project. When building cities, architects rarely consider how each building alters the invisible patterns of wind and how these alterations effect other areas in different ways later on. It is not until these forces move, overpower and even destroy cities that people take notice. For example, towers have caused winds to blow objects into people (Walkie-Talkie Tower, Leeds, England), cause building parts to vibrate and produce loud humming noises (Beetham Tower, Manchester), caused wind tunnels in streets as well as many other issues. Alternatively, there exist towers which have used their form to naturally draw in air and ventilate entire facilities in order to eliminate the needs for costly HVAC systems (The Met, Thailand) and used their form to increase wind speeds to generate electricity (Bahrain Tower, Dubai). Wind and weather exist and effect all parts of the world in ways such as: Science, health, war, infrastructure, catastrophes, tourism, shopping, media and materials. Working in partnership with a leading wind engineering company RWDI, a series of tests, images and animations documenting discovered interactions of different building forms with wind will be collected to emphasize the possibilities for wind use to architects. A site within San Francisco (due to its increasing tower development, consistently wind conditions and existing strict wind comfort criteria) will host a final design. Iterations of this design will be tested within the wind tunnel and computational fluid dynamic systems which will expose, utilize and manipulate wind flows to create new forms, technologies and experiences. Ultimately, this thesis aims to question the amount which the environment is allowed to permeate building enclosures, uncover new programmatic possibilities for wind in buildings, and push the boundaries of working with the wind to ensure the development and safety of future cities. This investigation will improve and expand upon the traditional understanding of wind in order to give architects, wind engineers as well as the general public the ability to broaden their scope in order to productively utilize this living phenomenon that everyone constantly feels but cannot see.

Keywords: wind engineering, climate, visualization, architectural aerodynamics

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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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