Search results for: Convection-diffusion equation.

Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

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Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: Henok Hailemariam, Frank Wuttke

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Collapsible soils are weak soils that appear to be stable in their natural state, normally dry condition, but rapidly deform under saturation (wetting), thus generating large and unexpected settlements which often yield disastrous consequences for structures unwittingly built on such deposits. In this study, a prediction model for the relative subsidence of stressed collapsible soils based on dielectric permittivity measurement is presented. Unlike most existing methods for soil subsidence prediction, this model does not require moisture content as an input parameter, thus providing the opportunity to obtain accurate estimation of the relative subsidence of collapsible soils using dielectric measurement only. The prediction model is developed based on an existing relative subsidence prediction model (which is dependent on soil moisture condition) and an advanced theoretical frequency and temperature-dependent electromagnetic mixing equation (which effectively removes the moisture content dependence of the original relative subsidence prediction model). For large scale sub-surface soil exploration purposes, the spatial sub-surface soil dielectric data over wide areas and high depths of weak (collapsible) soil deposits can be obtained using non-destructive high frequency electromagnetic (HF-EM) measurement techniques such as ground penetrating radar (GPR). For laboratory or small scale in-situ measurements, techniques such as an open-ended coaxial line with widely applicable time domain reflectometry (TDR) or vector network analysers (VNAs) are usually employed to obtain the soil dielectric data. By using soil dielectric data obtained from small or large scale non-destructive HF-EM investigations, the new model can effectively predict the relative subsidence of weak soils without the need to extract samples for moisture content measurement. Some of the resulting benefits are the preservation of the undisturbed nature of the soil as well as a reduction in the investigation costs and analysis time in the identification of weak (problematic) soils. The accuracy of prediction of the presented model is assessed by conducting relative subsidence tests on a collapsible soil at various initial soil conditions and a good match between the model prediction and experimental results is obtained.

Keywords: Collapsible soil, relative subsidence, dielectric permittivity, moisture content.

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Authors: M. D. Haneef, R. B. Randall, Z. Peng

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Journal bearings used in IC engines are prone to premature failures and are likely to fail earlier than the rated life due to highly impulsive and unstable operating conditions and frequent starts/stops. Vibration signature extraction and wear debris analysis techniques are prevalent in industry for condition monitoring of rotary machinery. However, both techniques involve a great deal of technical expertise, time, and cost. Limited literature is available on the application of these techniques for fault detection in reciprocating machinery, due to the complex nature of impact forces that confounds the extraction of fault signals for vibration-based analysis and wear prediction. In present study, a simulation model was developed to investigate the bearing wear behaviour, resulting because of different operating conditions, to complement the vibration analysis. In current simulation, the dynamics of the engine was established first, based on which the hydrodynamic journal bearing forces were evaluated by numerical solution of the Reynold’s equation. In addition, the essential outputs of interest in this study, critical to determine wear rates are the tangential velocity and oil film thickness between the journals and bearing sleeve, which if not maintained appropriately, have a detrimental effect on the bearing performance. Archard’s wear prediction model was used in the simulation to calculate the wear rate of bearings with specific location information as all determinative parameters were obtained with reference to crank rotation. Oil film thickness obtained from the model was used as a criterion to determine if the lubrication is sufficient to prevent contact between the journal and bearing thus causing accelerated wear. A limiting value of 1 μm was used as the minimum oil film thickness needed to prevent contact. The increased wear rate with growing severity of operating conditions is analogous and comparable to the rise in amplitude of the squared envelope of the referenced vibration signals. Thus on one hand, the developed model demonstrated its capability to explain wear behaviour and on the other hand it also helps to establish a co-relation between wear based and vibration based analysis. Therefore, the model provides a cost effective and quick approach to predict the impending wear in IC engine bearings under various operating conditions.

Keywords: Condition monitoring, IC engine, journal bearings, vibration analysis, wear prediction.

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Authors: Roya Bakhtiar, Alireza Abdolmohammadi, Hadi Hajarian, Zahra Nikousefat, Davood, Kalantar-Neyestanaki

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The objective of the present study was to determine the polymorphism in the leptin (332G>A) and its association with biometric traits in Sanjabi sheep. For this purpose, blood samples from 96 rams were taken, and tail length, width tail, circumference tail, body length, body width, and height were simultaneously recorded. PCR was performed using specific primer to amplify 463 bp fragment including exon 3 of leptin gene, and PCR products were digested by Cail restriction enzymes. The 332G>A (at 332th nucleotide of exon 3 leptin gene) that caused an amino acid change from Arg to Gln was detected by Cail (CAGNNNCTG) endonuclease, as the endonuclease cannot cut this region if G nucleotide is located in this position. Three genotypes including GG (463), GA (463, 360and 103 bp) and GG (360 bp and 103 bp) were identified after digestion by enzyme. The estimated frequencies of three genotypes including GG, GA, and AA for 332G>A locus were 0.68, 0.29 and 0.03 and those were 0.18 and 0.82 for A and G alleles, respectively. In the current study, chi-square test indicated that 332G>A positions did not deviate from the Hardy–Weinberg (HW) equilibrium. The most important reason to show HW equation was that samples used in this study belong to three large local herds with a traditional breeding system having random mating and without selection. Shannon index amount was calculated which represent an average genetic variation in Sanjabi rams. Also, heterozygosity estimated by Nei index indicated that genetic diversity of mutation in the leptin gene is moderate. Leptin gene polymorphism in the 332G>A had significant effect on body length (P<0.05) trait, and individuals with GA genotype had significantly the higher body length compared to other individuals. Although animals with GA genotype had higher body width, this difference was not statistically significant (P>0.05). This non-synonymous SNP resulted in different amino acid changes at codon positions111(R/Q). As leptin activity is localized, at least in part, in domains between amino acid residues 106-1406, it is speculated that the detected SNP at position 332 may affect the activity of leptin and may lead to different biological functions. Based to our results, due to significant effect of leptin gene polymorphism on body size traits, this gene may be used a candidate gene for improving these traits.

Keywords: Body size, Leptin gene, PCR-RFLP, Sanjabi sheep.

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Authors: Mustafa M. Donma

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Metabolic syndrome (MetS) components are noteworthy among children with obesity and morbid obesity, because they point out the cases with MetS, which have the great tendency to severe health problems such as cardiovascular diseases both in childhood and adulthood. In clinical practice, considerable efforts are being observed to bring into the open the striking differences between morbid obese cases and those with MetS findings. The most privileged aspect is concerning cardiometabolic features. The aim of this study was to derive an index, which behaves different in children with and without MetS from the cardiac point of view. For the purpose, aspartate transaminase (AST), a cardiac enzyme still being used independently to predict cardiac-related problems was used. 124 children were recruited from the outpatient clinic of Department of Pediatrics in Tekirdag Namik Kemal University, Faculty of Medicine. 43 children with normal body mass index, 41 and 40 morbid obese (MO) children with MetS and without the characteristic features of MetS, respectively, were included in the study. Weight, height, waist circumference (WC), hip circumference (HC), head circumference (HdC), neck circumference (NC), systolic and diastolic blood pressure values were measured and recorded. Body mass index and anthropometric ratios were calculated. Fasting blood glucose (FBG), insulin (INS), triglycerides (TRG), high density lipoprotein cholesterol (HDL-C) analyses were performed. The values for AST, alanine transaminase (ALT) and AST/ALT were obtained. Advanced Donma cardiac index (ADCI) values were calculated. Statistical evaluations including correlation analysis were done by a statistical package program. The statistical significance degree was accepted as p < 0.05. The index, ADCI, was developed from both anthropometric and biochemical parameters. All anthropometric measurements except weight were included in the equation. Besides all biochemical parameters concerning MetS components were also added. This index was tested in each of three groups. Its performance was compared with the performance of cardiometabolic index (CMI). It was also checked whether it was compatible with AST activity. The performance of ADCI was better than that of CMI. Instead of double increase, the increase of three times was observed in children with MetS compared to MO children. The index was correlated with AST in MO group and with AST/ALT in MetS group. In conclusion, this index was superior in discovering cardiac problems in MO and in diagnosing MetS in MetS groups. It was also arbiter to point out cardiovascular and MetS aspects among the groups.

Keywords: Aspartate transaminase, cardiac index, metabolic syndrome, obesity.

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Authors: Orkide Donma, Mustafa M. Donma

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Basal metabolic rate (BMR) is widely used and an accepted measure of energy expenditure. Its principal determinant is body mass. However, this parameter is also correlated with a variety of other factors. The objective of this study is to measure BMR and compare it with the values obtained from predictive equations in adults classified according to their body mass index (BMI) values. 276 adults were included into the scope of this study. Their age, height and weight values were recorded. Five groups were designed based on their BMI values. First group (n = 85) was composed of individuals with BMI values varying between 18.5 and 24.9 kg/m². Those with BMI values varying from 25.0 to 29.9 kg/m² constituted Group 2 (n = 90). Individuals with 30.0-34.9 kg/m², 35.0-39.9 kg/m², > 40.0 kg/m² were included in Group 3 (n = 53), 4 (n = 28) and 5 (n = 20), respectively. The most commonly used equations to be compared with the measured BMR values were selected. For this purpose, the values were calculated by the use of four equations to predict BMR values, by name, introduced by Food and Agriculture Organization (FAO)/World Health Organization (WHO)/United Nations University (UNU), Harris and Benedict, Owen and Mifflin. Descriptive statistics, ANOVA, post-Hoc Tukey and Pearson’s correlation tests were performed by a statistical program designed for Windows (SPSS, version 16.0). p values smaller than 0.05 were accepted as statistically significant. Mean ± SD of groups 1, 2, 3, 4 and 5 for measured BMR in kcal were 1440.3 ± 210.0, 1618.8 ± 268.6, 1741.1 ± 345.2, 1853.1 ± 351.2 and 2028.0 ± 412.1, respectively. Upon evaluation of the comparison of means among groups, differences were highly significant between Group 1 and each of the remaining four groups. The values were increasing from Group 2 to Group 5. However, differences between Group 2 and Group 3, Group 3 and Group 4, Group 4 and Group 5 were not statistically significant. These insignificances were lost in predictive equations proposed by Harris and Benedict, FAO/WHO/UNU and Owen. For Mifflin, the insignificance was limited only to Group 4 and Group 5. Upon evaluation of the correlations of measured BMR and the estimated values computed from prediction equations, the lowest correlations between measured BMR and estimated BMR values were observed among the individuals within normal BMI range. The highest correlations were detected in individuals with BMI values varying between 30.0 and 34.9 kg/m². Correlations between measured BMR values and BMR values calculated by FAO/WHO/UNU as well as Owen were the same and the highest. In all groups, the highest correlations were observed between BMR values calculated from Mifflin and Harris and Benedict equations using age as an additional parameter. In conclusion, the unique resemblance of the FAO/WHO/UNU and Owen equations were pointed out. However, mean values obtained from FAO/WHO/UNU were much closer to the measured BMR values. Besides, the highest correlations were found between BMR calculated from FAO/WHO/UNU and measured BMR. These findings suggested that FAO/WHO/UNU was the most reliable equation, which may be used in conditions when the measured BMR values are not available.

Keywords: Adult, basal metabolic rate, FAO/WHO/UNU, obesity, prediction equations.

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Authors: Markus Rütten, Olaf Wünsch

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Non-Newtonian fluid properties can change the flow behaviour significantly, its prediction is more difficult when thermal effects come into play. Hence, the focal point of this work is the wake flow behind a heated circular cylinder in the laminar vortex shedding regime for thermo-viscous shear thinning fluids. In the case of isothermal flows of Newtonian fluids the vortex shedding regime is characterised by a distinct Reynolds number and an associated Strouhal number. In the case of thermo-viscous shear thinning fluids the flow regime can significantly change in dependence of the temperature of the viscous wall of the cylinder. The Reynolds number alters locally and, consequentially, the Strouhal number globally. In the present CFD study the temperature dependence of the Reynolds and Strouhal number is investigated for the flow of a Carreau fluid around a heated cylinder. The temperature dependence of the fluid viscosity has been modelled by applying the standard Williams-Landel-Ferry (WLF) equation. In the present simulation campaign thermal boundary conditions have been varied over a wide range in order to derive a relation between dimensionless heat transfer, Reynolds and Strouhal number. Together with the shear thinning due to the high shear rates close to the cylinder wall this leads to a significant decrease of viscosity of three orders of magnitude in the nearfield of the cylinder and a reduction of two orders of magnitude in the wake field. Yet the shear thinning effect is able to change the flow topology: a complex K´arm´an vortex street occurs, also revealing distinct characteristic frequencies associated with the dominant and sub-dominant vortices. Heating up the cylinder wall leads to a delayed flow separation and narrower wake flow, giving lesser space for the sequence of counter-rotating vortices. This spatial limitation does not only reduce the amplitude of the oscillating wake flow it also shifts the dominant frequency to higher frequencies, furthermore it damps higher harmonics. Eventually the locally heated wake flow smears out. Eventually, the CFD simulation results of the systematically varied thermal flow parameter study have been used to describe a relation for the main characteristic order parameters.

Keywords: Heat transfer, thermo-viscous fluids, shear thinning, vortex shedding.

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: Artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations.

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Authors: R. Abdulrahman, A. Eardley, A. Soliman

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The proliferation in the development of mobile learning (m-learning) has played a vital role in the rapidly growing electronic learning market. This relatively new technology can help to encourage the development of in learning and to aid knowledge transfer a number of areas, by familiarizing students with innovative information and communications technologies (ICT). M-learning plays a substantial role in the deployment of learning methods for nursing students by using the Internet and portable devices to access learning resources ‘anytime and anywhere’. However, acceptance of m-learning by students is critical to the successful use of m-learning systems. Thus, there is a need to study the factors that influence student’s intention to use m-learning. This paper addresses this issue. It outlines the outcomes of a study that evaluates the unified theory of acceptance and use of technology (UTAUT) model as applied to the subject of user acceptance in relation to m-learning activity in nurse education. The model integrates the significant components across eight prominent user acceptance models. Therefore, a standard measure is introduced with core determinants of user behavioural intention. The research model extends the UTAUT in the context of m-learning acceptance by modifying and adding individual innovativeness (II) and quality of service (QoS) to the original structure of UTAUT. The paper goes on to add the factors of previous experience (of using mobile devices in similar applications) and the nursing students’ readiness (to use the technology) to influence their behavioural intentions to use m-learning. This study uses a technique called ‘convenience sampling’ which involves student volunteers as participants in order to collect numerical data. A quantitative method of data collection was selected and involves an online survey using a questionnaire form. This form contains 33 questions to measure the six constructs, using a 5-point Likert scale. A total of 42 respondents participated, all from the Nursing Institute at the Armed Forces Hospital in Saudi Arabia. The gathered data were then tested using a research model that employs the structural equation modelling (SEM), including confirmatory factor analysis (CFA). The results of the CFA show that the UTAUT model has the ability to predict student behavioural intention and to adapt m-learning activity to the specific learning activities. It also demonstrates satisfactory, dependable and valid scales of the model constructs. This suggests further analysis to confirm the model as a valuable instrument in order to evaluate the user acceptance of m-learning activity.

Keywords: Mobile learning, nursing institute, unified theory of acceptance and use of technology model.

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Authors: Andrew Cummings, Rhianne Boag, Sarah Bryson, Gordon Turner

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Packages designed for transport of radioactive material must satisfy rigorous safety regulations specified by the International Atomic Energy Agency (IAEA). Higher Activity Waste (HAW) transport packages have to maintain containment of their contents during normal and accident conditions of transport (NCT and ACT). To ensure containment criteria is satisfied these packages are required to be leak-tight in all transport conditions to meet allowable activity release rates. Package design safety reports are the safety cases that provide the claims, evidence and arguments to demonstrate that packages meet the regulations and once approved by the competent authority (in the UK this is the Office for Nuclear Regulation) a licence to transport radioactive material is issued for the package(s). The standard approach to demonstrating containment in the RWM transport safety case is set out in BS EN ISO 12807. In this document a method for measuring a leak rate from the package is explained by way of a small interspace test volume situated between two O-ring seals on the underside of the package lid. The interspace volume is pressurised and a pressure drop measured. A small interspace test volume makes the method more sensitive enabling the measurement of smaller leak rates. By ascertaining the activity of the contents, identifying a releasable fraction of material and by treating that fraction of material as a gas, allowable leak rates for NCT and ACT are calculated. The adherence to basic safety principles in ISO12807 is very pessimistic and current practice in the demonstration of transport safety, which is accepted by the UK regulator. It is UK government policy that management of HAW will be through geological disposal. It is proposed that the intermediate level waste be transported to the geological disposal facility (GDF) in large cuboid packages. This poses a challenge for containment demonstration because such packages will have long seals and therefore large interspace test volumes. There is also uncertainty on the releasable fraction of material within the package ullage space. This is because the waste may be in many different forms which makes it difficult to define the fraction of material released by the waste package. Additionally because of the large interspace test volume, measuring the calculated leak rates may not be achievable. For this reason a justification for a lower releasable fraction of material is sought. This paper considers the use of aerosol processes to reduce the releasable fraction for both NCT and ACT. It reviews the basic coagulation and removal processes and applies the dynamic aerosol balance equation. The proposed solution includes only the most well understood physical processes namely; Brownian coagulation and gravitational settling. Other processes have been eliminated either on the basis that they would serve to reduce the release to the environment further (pessimistically in keeping with the essence of nuclear transport safety cases) or that they are not credible in the conditions of transport considered.

Keywords: Aerosol processes, Brownian coagulation, gravitational settling, transport regulations.

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Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

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The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: Computing experiment, hydroelasticity, physical experiment, vibration.

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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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