Theoretical and Empirical Limits: Reexamining Betz’s Upper Limit towards a Practical Power Coefficients in Wind Turbines*

The aspiration of all wind turbine designers is to attain Betz’s upper limit, which represents the highest efficiency in wind energy extraction. Majority of working turbines operate slightly below this limit with an exception of a few operating in wind tunnels. This study proposes for a comprehensive reevaluation of Betz’s derivation, aiming to establish the gap between a theoretical power limit and a practical limit for realization. There are two common expressions for power coefficient giving the same optimal value of 59%, but they generate different power-coefficient curves when plotted against velocity ratios. This paper presents a new method being referred as “Direct Multiplication Fractional Change” (DMFC) for deriving power-coefficient curves in wind energy, and compares its generated curve with established models. Discrepancies in power-coefficient expressions are identified and harmonized. Three approaches, namely EVAM, LVM, and DMFCM, were used for the numerical derivation of cp in the study, with their evaluation summarized in a table. The study collaborates its findings with a formulated velocity-distance curve, commonly presented as a hypothetical velocity profile in some publications. The results from DMFCM indicate two distinct maxima for the power coefficient. On the front side of the disc, a maximum of 0.5 is achievable in practice, although it is not the highest theoretically. On the rear side, a theoretical maximum of 0.59 is observed, but this value is not attainable in practice. These maxima are separated by their positions along the line of flow relative to the disc. However, this approximation is limited to a streamlined flow model of the rotor disc.

Numerical investigation on the flow and power of small-sized multi-bladed straight Darrieus wind turbine

Straight Darrieus wind turbine has attractive characteristics such as the ability to accept wind from random direction and easy installation and maintenance. But its aerodynamic performance is very complicated,especially for the existence of dynamic stall. How to get better aerodynamic performance arouses lots of interests in the design procedure of a straight Darrieus wind turbine. In this paper,mainly the effects of number of blades and tip speed ratio are discussed. Based on the numerical investigation,an assumed asymmetric straight Darrieus wind turbine is proposed to improve the averaged power coefficient. As to the numerical method,the flow around the turbine is simulated by solving the 2D unsteady Navier-Stokes equation combined with continuous equation. The time marching method on a body-fitted coordinate system based on MAC (Marker-and-Cell) method is used. O-type grid is generated for the whole calculation domain. The characteristics of tangential and normal force are discussed related with dynamic stall of the blade. Averaged power coefficient per period of rotating is calculated to evaluate the eligibility of the turbine.

STUDY ON POWER SPARE COEFFICIENT OF ELECTRICAL MOTOR IN LARGE PUMP STATION BASED ON RELIABILITY

Characters of head of low head pump station and the pump shaft power areanalyzed. Influence of each single factor on pump shaft power is expressed as change of specificshaft power. (non-dimensional) and the probability density function is determined. Influences ofmultiple factors on pump shaft power are analyzed. Method of calculating none over-loadedprobability of motor by integration by successive reductions is put forward and then relationbetween power spare coefficient and none over-loaded reliability of electric motor is established.Influences of all factors on pump shaft power being considered completely; power spare coefficientsof motor are calculated in three kinds of heads (changing and unchanging), two kinds of dirty-outconditions. Electrical motor power spare coefficients should be chosen as 1.20 approx 1.44, 1.11approx 1.19, 1.09 approx.14 respectively when pump heads are 4, 7, 9.5 m. The results mean much toreasonable choose of electrical motors in large pump stations, increasing reliability of pump unitsand saving equipment investment.

Regulation of Power Conversion in Fuel Cells

Here we report a regulation about power conversion in fuel cells. This regulation is expressed as that total power produced by fuel cells is always proportional to the square of the potential difference between the \{equilibrium\} potential and work potential. With this regulation we deduced fuel cell performance equation which can describe the potential vs.the current performance curves, namely, polarization curves of fuel cells with three power source parameters: equilibrium potential E_0; internal resistance R; and power conversion coefficient K. The concept of the power conversion coefficient is a new criterion to evaluate and compare the characteristics and capacity of different fuel cells. The calculated values obtained with this equation agree with practical performance of different types of fuel cells.

Study on Purchasing Power Conversion Coefficient at Par

The basic theory of the purchasing power at par refers to the rate of one country＇s currency to U.S. dollar while purchasing ＂a basket＂ goods and services in the same quantity and quality respectively in this country and U.S.A. This paper gives out calculation method of purchasing power conversion coefficient at par and how to calculate the non-base year purchasing power at par.

Simulation of pavement roughness based on time domain model

In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pavement roughness is denoted as the sum of numerous sines or cosines with stochastic phases, and uses the discrete spectrum to approach the target stochastic process. It is a discrete numerical method used to simulate pavement roughness. According to a given pavement power spectral density （PSD） coefficient, under the condition that the character of displacement frequency based on the time domain model is in accordance with the given pavement surface spectrum, the pavement roughness is optimized to stochastic equivalent vibrations by computer simulation, and the curves that describe pavement roughness under each grade are obtained. The results show that the stochastic sinusoidal wave is suitable for simulation of measured pavement surface spectra based on the time domain model. The method of the stochastic sinusoidal wave is important to the research on vehicle ride comfort due to its rigorous mathematical derivation, extensive application range and intuitive simulation curve. Finally, a roughness index defined as the nominal roughness index （NRI） is introduced, and it has correlation with the PSD coefficient.

Effect of blade pitch angle on aerodynamic performance of straight-bladed vertical axis wind turbine

Wind energy is one of the most promising renewable energy sources, straight-bladed vertical axis wind turbine(S-VAWT) appears to be particularly promising for the shortage of fossil fuel reserves owing to its distinct advantages, but suffers from poor self-starting and low power coefficient. Variable-pitch method was recognized as an attractive solution to performance improvement, thus majority efforts had been devoted into blade pitch angle effect on aerodynamic performance. Taken into account the local flow field of S-VAWT, mathematical model was built to analyze the relationship between power outputs and pitch angle. Numerical simulations on static and dynamic performances of blade were carried out and optimized pitch angle along the rotor were presented. Comparative analyses of fixed pitch and variable-pitch S-VAWT were conducted, and a considerable improvement of the performance was obtained by the optimized blade pitch angle, in particular, a relative increase of the power coefficient by more than 19.3%. It is further demonstrated that the self-starting is greatly improved with the optimized blade pitch angle.

CATIA AIDED RADOME ANALYSIS USING GEOMETRIC OPTICS METHOD

In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.

Influence of a Deflector or a Wall on Savonius Rotor Efficiency

The Savonius rotor is a vertical axis-wind machine composed of two half cylindrical blades presenting a central gap. It is a slow velocity machine compared with horizontal wind machines. Its efficiency is about twenty per cent. In this work experimental tests are presented using two kind of deflectors placed in front of the resistive blade. Such disposition allows to hide the resistant blade and to guide the flow toward the motrice blade. Two deflectors have been used： a short one and a long one. The results obtained in wind tunnel have shown that the long deflector is the more efficient, essentially for high values of the tip speed ratio. One has been interested, using a numerical approach, in the study of the influence of a wall on the aerodynamical field near the rotor.

Study and innovation of a flexible blade turbine,a new type of tidal current generating device

Utilization of tidal current is becoming a focus of marine energy research and development field. In this paper, a new type of tidal current power generating device which was called flexible blade turbine was put forward. A scale model testing was carried out, and results show that the models performed as expected with good hydrodynamic characteristics. Based on analysis of the results, a scale model turbine with a rated power of 5 kW was constructed, which was an optimal scheme of the flexible blade turbine having higher coefficient of power and power generation capacity. Sea trials were carried out in the Zhaitang Island Channel to evaluate the performance of the turbine. Results show that the turbine performed well, generating the power predicted.

Simulation of radiation losses using non-coronal model on HL-2A

In this paper, the radiation losses of impurity on HL-2A have been simulated by assuming the profiles electron temperature and density and solving ionization rate equation under conditions of non-coronal radiation. The time required for an impurity species to establish equilibrium is proved to be sensitively dependent on the plasma electron temperature, and it is strongly correlated with the ionization state distribution during equilibrium establishment of impurity species, It is found from simulation results that the residence parameter plays an important role in the enhancement of radiation losses of plasma.

Criterion of aerodynamic performance of large-scale offshore horizontal axis wind turbines

With the background of offshore wind energy projects, this paper studies aerodynamic performance and geometric characteristics of large capacity wind turbine rotors （1 to 10 MW）, and the main characteristic parameters such as the rated wind speed, blade tip speed, and rotor solidity. We show that the essential criterion of a high- performance wind turbine is a highest possible annual usable energy pattern factor and a smallest possible dimension, capturing the maximum wind energy and producing the maximum annual power. The influence of the above-mentioned three parameters on the pattern factor and rotor geometry of wind turbine operated in China＇s offshore meteoro- logical environment is investigated. The variation patterns of aerodynamic and geometric parameters are obtained, analyzed, and compared with each other. The present method for aerodynamic analysis and its results can form a basis for evaluating aerodynamic performance of large-scale offshore wind turbine rotors.

Application of 2D Numerical Model to Unsteady Performance Evaluation of Vertical-Axis Tidal Current Turbine

Abstract Tidal current energy is renewable and sustainable, which is a promising altemative energy resource for the future elec- tricity supply. The straight-bladed vertical-axis turbine is regarded as a useful tool to capture the tidal current energy especially under low-speed conditions. A 2D unsteady numerical model based on Ansys-Fluent 12.0 is established to conduct the numerical simulation, which is validated by the corresponding experimental data. For the unsteady calculations, the SST model, 2x 105 and 0.01 s are se- lected as the proper turbulence model, mesh number, and time step, respectively. Detailed contours of the velocity distributions around the rotor blade foils have been provided for a flow field analysis. The tip speed ratio （TSR） determines the azimuth angle of the appearance of the torque peak, which occurs once for a blade in a single revolution. It is also found that simply increasing the incident flow velocity could not improve the turbine performance accordingly. The peaks of the averaged power and torque coeffi- cients appear at TSRs of 2.1 and 1.8, respectively. Furthermore, several shapes of the duct augmentation are proposed to improve the turbine performance by contracting the flow path gradually from the open mouth of the duct to the rotor. The duct augmentation can significantly enhance the power and torque output. Furthermore, the elliptic shape enables the best performance of the turbine. The numerical results prove the capability of the present 2D model for the unsteady hydrodynamics and an operating performance analy- sis of the vertical tidal stream turbine.

An Efficient Approach for Segmentation, Feature Extraction and Classification of Audio Signals

Due to the presence of non-stationarities and discontinuities in the audio signal, segmentation and classification of audio signal is a really challenging task. Automatic music classification and annotation is still considered as a challenging task due to the difficulty of extracting and selecting the optimal audio features. Hence, this paper proposes an efficient approach for segmentation, feature extraction and classification of audio signals. Enhanced Mel Frequency Cepstral Coefficient (EMFCC)-Enhanced Power Normalized Cepstral Coefficients (EPNCC) based feature extraction is applied for the extraction of features from the audio signal. Then, multi-level classification is done to classify the audio signal as a musical or non-musical signal. The proposed approach achieves better performance in terms of precision, Normalized Mutual Information (NMI), F-score and entropy. The PNN classifier shows high False Rejection Rate (FRR), False Acceptance Rate (FAR), Genuine Acceptance rate (GAR), sensitivity, specificity and accuracy with respect to the number of classes.

Effect of rotation curvature correction and inviscid spatial discretization scheme on the aerodynamics of vertical axis wind turbine

The effect of rotation-curvature correction and inviscid spatial discretization scheme on the aerodynamic performance and flow characteristics of Darrieus H-type vertical axis wind turbine(VAWT)are investigated based on an in-house solver.This solver is developed on an in-house platform HRAPIF based on the finite volume method(FVM)with the elemental velocity vector transformation(EVVT)approach.The present solver adopts the density-based method with a low Mach preconditioning technique.The turbulence models are the Spalart-Allmaras(SA)model and the k-ωshear stress transport(SST)model.The inviscid spatial discretization schemes are the third-order monotone upstream-centered schemes for conservation laws(MUSCL)scheme and the fifth-order modified weighted essentially non-oscillatory(WENO-Z)scheme.The power coefficient,instantaneous torque of blades,blade wake,and turbine wake are compared and analyzed at different tip speed ratios.The extensive analysis reveals that the density-based method can be applied in VAWT numerical simulation;the SST models perform better than the SA models in power coefficient prediction;the rotation-curvature correction is not necessary and the third-order MUSCL is enough for power coefficient prediction,the high-order WENO-Z scheme can capture more flow field details,the rotation-curvature correction and high-order WENO-Z scheme reduce the length of the velocity deficit region in the turbine wake.

Effect of additional cylinders on power-extraction performance of a Savonius vertical-axis wind turbine

To improve the power-extraction performance of the Savonius vertical-axis wind turbine(S-VAWT),additional cylinders,which are used to control the fluid flow around the wind turbine blade,were introduced into the blade design.In contrast to the traditional numerical method,a mathematical model in the form of a dynamical system was used in this study.A numerical calculation program that could effectively solve the equations of wind-induced rotation of S-VAWT was developed,and combined with the Taguchi experimental method to investigate the influence of additional cylinders on the power-extraction characteristics of the S-VAWT.The results showed that the additional cylinders have a significant impact on the power-extraction performance of the S-VAWT.At 4-m/s wind speed,the average power coefficient of the S-VAWT with additional cylinders is 15%higher than that of the conventional S-VAWT.After construction of the wind turbine prototype and power-extraction tests,the results showed that compared with a conventional S-VAWT,the output power was 29%higher for the S-VAWT with additional cylinders under the same particular conditions.

Wind Tunnel Experiments and Numerical Study on Performance Characteristics of an H-type Vertical Axis Wind Turbine in the Spanwise Direction

The aerodynamic forces and vortex characteristics of an H-type Vertical Axis Wind Turbine(VAWT)become complicated because of dynamic stall,particularly in the three-dimensional impact on the blade spanwise direction.This study focused on the evaluation of the aerodynamic performance and vortex characteristics of an H-type VAWT in the spanwise direction by numerical simulations and wind tunnel experiments.Pressure acting on the blade surface was obtained from multiport pressure measurement devices by wind tunnel.Meanwhile,the vortex field around different blade sections was investigated through numerical simulations.The stall behavior was analysed by comparing the results of numerical simulations and experiments.As a result,the tangential force of single blade was mainly contributed at the chordwise position of x/c≤0.4 c and the power of single blade was mainly contributed at the azimuthal angle range of 60°≤θ≤150°in the blade section position region of 0≤z/(H/2)≤0.7.At the section position of z/(H/2)=0.5,the initial flow separation was found at the suction side and progressed forward to the leading edge.With the increase of the tip speed ratios,the decreasing position of the averaged local power coefficient of each section was closer to the middle section of z/(H/2)=0,and the attenuation speed became faster.The power coefficient reductions at the blade section position of z/(H/2)=0.9 were 38.29%,46.78%and 56.42%when the tip speed ratios were 1.38,2.19 and 2.58,respectively.The results of this study provided a better understanding of the development of the performance characteristics and vortex characteristics of H-type VAWT.

Novel high-PSRR high-order curvature-compensated bandgap voltage reference

This paper proposes a novel high-power supply rejection ratio（high-PSRR） high-order curvature-compensated CMOS bandgap voltage reference（BGR） in SMIC 0.18 μm CMOS process. Three kinds of current are added to a conventional BGR in order to improve the temperature drift within wider temperature range, which include a piecewise-curvaturecorrected current in high temperature range, a piecewise-curvature-corrected current in low temperature range and a proportional-to-absolute-temperature T^（1.5） current. The high-PSRR characteristic of the proposed BGR is achieved by adopting the technique of pre-regulator. Simulation results shows that the temperature coefficient of the proposed BGR with pre-regulator is 8.42x10^（-6）′ /℃ from - 55 ℃ to 125 ℃ with a 1.8 V power supply voltage. The proposed BGR with pre-regulator achieves PSRR of - 123.51 dB, - 123.52 dB, - 88.5 dB and - 50.23 dB at 1 Hz, 100 Hz, 100 kHz and 1 MHz respectively.

Experimental study on the optimum design of diffuser-augmented horizontal-axis tidal turbine

Ocean current energy is a promising and reliable resource that offers sustainability and predictability in realizing green future needs.A diffuser-augmented horizontal-axis turbine is utilized to generate ocean current energy.A numerical study on the impact of diffuser angle variations on the power coefficient has been carried out in the previous research.To elucidate the fluid dynamics aspects and further validation of previous computational results,the experimental investigation on the optimal design of tidal turbine with 20.04°diffuser augmentation is presented in this study.The study was conducted in a flowing tank with a current velocity of 0.7 m/s.The maximum power coefficient of 20.04°is 0.436 experimentally,which is a little smaller than the numerical value.Moreover,to reinforce the 20.04°result,a diffuser with an angle of 10.43°was also manufactured and tested experimentally.The maximum power coefficient of 10.43°is 0.303 experimentally,which is 3%smaller than the numerical value.It was concluded that the numerical approach might be considered satisfactory and represent similar phenomena to the experimental investigation in an application for modelling of multi-objective optimization.