Double Multiple Streamtube Model Research Articles

Numerical Investigation of a Vertical Axis Wind Turbine Performance Characterization Using New Variable Pitch Control Scheme

Abstract A double multiple streamtube model coupled with variable pitch methodology is used to analyze the performance characteristics of a small-scale straight-bladed Darrieus type vertical axis wind turbine (SB-VAWT). The numerical study revealed that a fixed pitch of −2.5 deg could greatly enhance the performance of the wind turbine. However, no improvement is observed in the starting torque capacity. Furthermore, the performance of upwind and downwind zones has been investigated, and it is found that the VAWT starting capacity is improved by increasing/decreasing the pitch angle upwind/downwind of the turbine. To optimize the performance, four cases of variable pitch angle schemes of sinusoidal nature were examined. The parameters of the sinusoidal functions were optimized using differential evolution (DE) algorithm with different cost functions. The results showed improvement in the power coefficient, yet with low starting capacity enhancement. Among the objective functions used in DE algorithm, the negative of the average power coefficient is found to lead to the best starting capacity with moderate peak power coefficient.

Parametric Study and Comparison of Aerodynamics Momentum-Based Models for Straight-Bladed Vertical Axis Wind Turbines

In this study, different momentum models for vertical axis wind turbines (VAWTs) are investigated and compared for different operating parameters. The performance over different rotor solidities and aspect ratios is studied to find the best configuration of the turbine. By comparing different models, the merit of double multiple streamtube model is established. Three different airfoils were investigated using the parameters of reference turbines from the literature. NACA0015 is found to be advantageous among NACA0012 and NACA0021. Also, the effect of different number of blades is studied and it is found that two-bladed rotor with NACA0015 airfoil provides excellent performance. By studying the turbine aspect ratio, it is found that a VAWT of 5.1 m height and 4.25 m diameter will generate a maximum power coefficient of 36.13% at TSR of 5.51 with good starting behavior.

Effect of blade pitching on power coefficient of small-scale vertical axis wind turbine at different tip speed ratios

This article analyses the effect of best blade pitching positions on the power coefficient of vertical axis wind turbine at different tip speed ratios. Analysis of the power coefficient of the vertical axis wind turbine is carried out for optimized six blade pitching curves. The first three pitching curves are designed for the tip speed ratios below 1.5 (0 < λ < 1.5) and other three are for the tip speed ratios in the range of 0 < λ < 3. The double multiple stream tube model is used for the present analysis. The results are compared between the optimized and sinusoidal pitching curves. It is concluded that the best optimized pitch position blade method improves the power coefficient than the typical sinusoidal blade pitching in the range of tip speed ratios 0 < λ < 3.

Performance of SB-VAWT using a modified double multiple streamtube model

The present study introduces a new relation to evaluate the equilibrium induced air velocity in the mid plane between the upstream and downstream rotor zones to give a good improvement in prediction of the maximum power coefficient. The relation is derived as a function of both interference factor in upwind and downwind rotor zones determined using classical DMST model. The root-finding algorithm is used to obtain the interference factor both in upwind and downwind zones of the turbine at each streamtube. The comparison between the numerical results and the experimental data of 5-m, 17-m, and 34-m Darrieus VAWTs shows that the use of the introduced relation gives a sensible improvement in the prediction of maximum value for turbine power coefficient. A theoretical study is presented based on the use of well documented symmetrical NACA0012 turbine blade profile. The effect of wind speed and rotor solidity on maximum power coefficient and corresponding optimal speed ratio on the turbine rotor is evaluated in order to determine an improved aerodynamic configuration for a given application.

Performance Evaluation of Small-Scale Vertical Axis Wind Turbine by Optimized Best Position Blade Pitching at Different Tip Speed Ratios

This paper analyzes and evaluates the effect of various design and operating parameters in the view of their influence on the starting turbine by itself, power coefficient and overall performance of the vertical axis wind turbine. Best pitch position of each blade in the rotation of turbine at different azimuth angles has been calculated at different tip speed ratios (TSRs) by using the aerodynamic analysis. Best pitch position of the blade is fixed at specific azimuth angle to produce the maximum tangential force in order to start turbine by itself and improve the power coefficient of the turbine. The double-multiple streamtube model is used for the present analysis. The results indicate that the best pitch position blade method improves the self-starting capacity and power coefficient. The best position blade pitching curve-1 with 45° pitch angle gives maximum power coefficient for TSRs of 1.0, and the best position blade pitching curve-5 with 15° pitch angle gives maximum coefficient of power about 0.53 for TSRs at 2.3. The results indicate that the optimized blade pitching with pitch variations from 45° to 10° improves performance of the turbine for TSRs 0 < λ < 3.

Hydrodynamic modeling and experimental validation of a cycloidal propeller

In this paper, a lower-order unsteady hydrodynamic model of a cycloidal propeller along with in-house experiments to validate the model is presented. Towards this, the hydrodynamics of a cycloidal propeller is investigated thoroughly and various underlying physical phenomena such as dynamic virtual camber, effects of near and shed wake, leading-edge vortices are rigorously modeled. It is shown that the chord-wise variation of incidence velocity angle on cycloidal propeller blade is manifested as dynamic virtual camber, which depends on curvilinear flow geometry, pitch angle, pitch rate and inflow distribution. By including all these effects together, a generalized expression of additional lift due to virtual camber effect is developed. To capture the effects of near wake, a nonlinear lifting line model is incorporated. Rapid pitching of rotor blades produces unsteady phenomena such as strong leading-edge vortices and shed wakes. Polhamus leading-edge-suction analogy is applied to model leading-edge vortex. To capture the effects of shed wake, a method based on Theodorsen's approach is developed. A modified Double Multiple Streamtube (D-MS) model is used for modeling the complex inflow characteristics of a cycloidal propeller. The present hydrodynamic model is validated with measured time-history of forces obtained from in-house experiments at low Reynolds numbers.

Uticaj najboljeg položaja lopatice na koeficijent snage vetroturbine sa vertikalnom osom obrtanja pri različitom odnosu koeficijenta rada rotora kod SST i DMST modela

This paper analyses the effect of best position blade pitching on the power coefficient of vertical axis wind turbine (VAWT) at different tip speed ratios (TSRs). Single Stream Tube (SST) and Double Multiple Stream Tube (DMST) models are used for present analysis. The results indicate that the best pitch position blade method improves the self-starting capacity and power coefficient of turbine. The best position blade pitching curve-1 with 45° pitch angles gives maximum power coefficient for TSRs of 0.5 and the best position blade pitching curve-5 with 15° pitch angle gives maximum coefficient of power about 0.49 for TSR 2.5. The results of SST model are compared with DMST model and presented at the end of this paper.

Aerodynamic Performance of Straight-Bladed Vertical Axis Wind Turbines: A Practical Open Source Implementation

This study presents a practical open source implementation that uses double-multiple streamtube model for the aerodynamic performance prediction of straight-bladed vertical axis wind turbines, particularly, the power coefficient ( C p ) and tip speed ratio ( λ ) relationship. To improve the analytical capability of the proposed implementation, important aspects of performance such as dynamics stall and, fixed/variable pitch blade were added. In addition, a fast convergence method for finding the axial induction factor was adopted, giving simplicity to the implementation. Simulated C p ( λ ) curves were compared with the experimental data (wind tunnel and field) reported in the literature. The mean absolute error of the simulated C p ( λ ) curves, in terms of efficiency, was 0.06, with a mean maximum of 0.078 and a mean minimum of 0.047. The good agreement in combination with the low computing time, suggests that the proposed implementation provides a useful tool for predicting aerodynamic properties of the straight-bladed vertical axis wind turbines and, therefore, for its design. The implementation can be carried out successfully by using GNU-Octave.

Double multiple stream tube analysis of non-uniform wind stream of exhaust air energy recovery turbine generator

The novel exhaust air energy recovery turbine generator is designed to recover part of energy from a fan-powered exhaust air system which represented by a cooling tower. The discharge wind from the cooling tower varies throughout the radius makes it a non-uniform profile. A vertical axis wind turbine (VAWT) is placed at the outlet of a cooling tower to recover the energy. The VAWT behavior in the non-uniform wind stream from the exhaust air system is studied by experiment and double multiple stream tube (DMST) theory. A novel application of the DMST model is applied for non-uniform wind stream. The experimental results show that best horizontal position of the VAWT is at a distance of about 2/3 of the outlet radius with respect to turbine rotation. Theoretical analysis explains the wind turbine behavior in the non-uniform wind stream as acquired from the experiment. For the selected wind turbine, it is the best to match the highest wind velocity region to the wind turbine at the range of 45° to 115° azimuth angle. This innovative system has a huge potential due to wide application of exhaust air system globally.

Comparison of low-order aerodynamic models and RANS CFD for full scale 3D vertical axis wind turbines

A Double Multiple Streamtube model, a free-wake vortex model (both widely used for vertical axis wind turbine design) and RANS CFD simulations are used in this work to predict the performance of the 17 m Vertical Axis Wind Turbine, field tested by Sandia National Laboratories. The three-dimensional, full scale calculations are compared with the experiments in terms of power coefficient, power and instantaneous turbine torque to assess the validity of each model. Additionally, the two aerodynamic models and RANS CFD are compared to each other in terms of thrust and lateral force. The two models and CFD agree well with the experiments at the turbine optimal tip speed ratio. However, away from the optimal tip speed ratio, the streamtube model significantly deviates from the experimental data and from the other numerical models. RANS CFD gives a good agreement with the experiments, slightly underestimating the power coefficient at every tip speed ratio tested. The vortex model proves to be a useful tool with a better accuracy than the streamtube model and a much lower computational cost compared to RANS CFD.

Study on approach of performance improvement of VAWT employing double multiple stream tubes model

On the circular blade path of a Darrieus-type vertical axis wind turbine (VAWT), there are two azimuth positions where torques are small or even negative. These two azimuths have the lowest aerodynamic performance and greatly weaken the overall performance of the VAWT. An approach is proposed to rebuild the flow field of the turbine blades by applying two additional airflows at the two azimuths to enhance the local performance. The aim is to improve the overall power coefficient of the VAWT. A Φ-type VAWT with a diameter of 2 m and a height of 2 m is studied to evaluate the effectiveness of the proposed approach. The effect of additional airflow on the aerodynamic performance of the blade and the turbine is researched using the double multiple streamtube model. The simulation results suggest that the additional airflows are effective in promoting the performance of the rotor blades and the overall rotor; the increase in maximum power coefficient achieved was 6% at an optimum tip speed ratio. Some rules of the effect on the performances of the rotor are obtained in this paper.

Wind Tunnel Validation of Double Multiple Streamtube Model for Vertical Axis Wind Turbine

The performance and annual energy output have to be predicted to maximize the economic benefits from a wind turbine. Mathematically predicting the performance of Darrieus type lift based turbines are challenging due to the inconsistent angle of attack, blade wake interaction and local induced velocities giving rise to complex flow physics. A reliable and validated mathematical model is therefore essential to optimize the various design parameters prior to manufacture. The objective of the current study is to evaluate widely employed aerodynamic models based on their prediction accuracy, limitations, and computational requirements. Double multiple stream tube models have been discussed in detail and the predictions are experimentally validated through the wind tunnel test of three-bladed H-Darrieus rotor in terms of torque and power coefficient. The possible sources for the deviation between the predicted and measured values have been discussed and concluded with potential solutions.

Predicted and measured performance of a vertical axis wind turbine with passive variable pitch compared to fixed pitch

The performance of a 5-m diameter Darrieus vertical axis wind turbine was predicted using both a double multiple streamtube model and a two-dimensional unsteady Reynolds-averaged Navier–Stokes computational fluid dynamics simulation with constant rotational speed for a series of operational points. The actual performance was measured in both fixed and variable pitch modes. The aims were (1) to compare starting torque and peak efficiency in fixed and variable pitch modes and (2) to test an overspeed control mechanism. Starting torque was approximately three times higher in variable pitch mode and the maximum efficiency on some runs was significantly higher. The overspeed control mechanism functioned consistently as designed. Thus, variable pitch was shown to overcome two major disadvantages of normal fixed pitch vertical axis wind turbines, self-starting and overspeed control. Discrepancies between the predicted and measured results showed the importance of accurately assessing parasitic drag losses and the need for three-dimensional simulation to give reliable performance predictions.

Electric Circuit Model for the Aerodynamic Performance Analysis of a Three-Blade Darrieus-Type Vertical Axis Wind Turbine: The Tchakoua Model

The complex and unsteady aerodynamics of vertical axis wind turbines (VAWTs) pose significant challenges for simulation tools. Recently, significant research efforts have focused on the development of new methods for analysing and optimising the aerodynamic performance of VAWTs. This paper presents an electric circuit model for Darrieus-type vertical axis wind turbine (DT-VAWT) rotors. The novel Tchakoua model is based on the mechanical description given by the Paraschivoiu double-multiple streamtube model using a mechanical‑electrical analogy. Model simulations were conducted using MATLAB for a three-bladed rotor architecture, characterized by a NACA0012 profile, an average Reynolds number of 40,000 for the blade and a tip speed ratio of 5. The results obtained show strong agreement with findings from both aerodynamic and computational fluid dynamics (CFD) models in the literature.

Energy-based iteration scheme of the double-multiple streamtube model in vertical-axis wind turbines

Due to their simplicity, blade element momentum models, such as the double-multiple streamtube (DMS) model, are among the most common models to predict the performance of Darrieus vertical-axis wind turbines (VAWTs). A two-dimensional energy-based iteration scheme of the DMS model (EB-DMSM) is shown in the present work. Its purpose is to improve predictions of power performance and flow expansion. This new approach is compared with a momentum-based iteration scheme (MB-DMSM) and the results of a two-dimensional computational simulation of a 12-kW straight-bladed VAWT. The mathematical representation of streamlines used for modeling the flow expansion is in good agreement with the simulations. Convergence of both schemes is achieved for tip-speed ratios (TSRs) up to 4. Failure of the models to convergence at higher TSRs is attributed to their inability to adequately represent the aerodynamic forces acting on the blades, due to the simplicity of their formulation. Relative to computational simulations, the maximum differences in the peak power coefficient predictions are 16 and 32 % and in the flow expansion predictions are 53 and 5 % for the MB-DMSM and EB-DMSM, respectively. Corrections are required to improve predictions of power performance and flow expansion of turbines with different geometric and operational parameters.

A New Approach for Modeling Darrieus-Type Vertical Axis Wind Turbine Rotors Using Electrical Equivalent Circuit Analogy: Basis of Theoretical Formulations and Model Development

Models are crucial in the engineering design process because they can be used for both the optimization of design parameters and the prediction of performance. Thus, models can significantly reduce design, development and optimization costs. This paper proposes a novel equivalent electrical model for Darrieus-type vertical axis wind turbines (DTVAWTs). The proposed model was built from the mechanical description given by the Paraschivoiu double-multiple streamtube model and is based on the analogy between mechanical and electrical circuits. This work addresses the physical concepts and theoretical formulations underpinning the development of the model. After highlighting the working principle of the DTVAWT, the step-by-step development of the model is presented. For assessment purposes, simulations of aerodynamic characteristics and those of corresponding electrical components are performed and compared.

Multi-objective design optimization strategies for small-scale vertical-axis wind turbines

Extracting energy from wind has been an interesting and serious topic over the last few decades and a lot of work has been done on the subject. This paper discusses in detail possible approaches to optimization of a somewhat less known type of wind turbines, particularly suitable for small consumers. In order to perform full aerodynamic and structural shape optimization of a small-scale vertical-axis wind turbine, a Double-multiple streamtube model code, known to provide good results in stationary working regimes, was complemented by a finite element analysis and implemented into a multi-objective particle swarm algorithm. For the purpose of shortening the total time needed for aerodynamic computation, the performed numerical simulations were two-dimensional and experimentally measured static airfoil data were used. The used aerodynamic model was validated against the available experimental data of similar wind turbines. The subsequent structural analyses of the composite turbine blades were performed by applying computed maximal aerodynamic forces together with gravitational and inertial loads. By employing various input and output parameters different multi-objective optimization strategies were analyzed and compared and their applicability was demonstrated. Investigated input parameters included: wind turbine rotor diameter, blade length, chord and airfoil, composite shell thickness, laminate lay-up and ply orientations, while optimization goal functions and constraints comprised rated power, cut-in and optimal wind speed, blade mass, tip deflection, failure index and blade natural frequencies. The fidelity and accuracy of proposed methodologies can be increased by employing more complex numerical models which can easily be implemented into the code.

Simulating Dynamic Stall Effects for Vertical Axis Wind Turbines Applying a Double Multiple Streamtube Model

The complex unsteady aerodynamics of vertical axis wind turbines (VAWT) poses significant challenges to the simulation tools. Dynamic stall is one of the phenomena associated with the unsteady conditions for VAWTs, and it is in the focus of the study. Two dynamic stall models are compared: the widely-used Gormont model and a Leishman–Beddoes-type model. The models are included in a double multiple streamtube model. The effects of flow curvature and flow expansion are also considered. The model results are assessed against the measured data on a Darrieus turbine with curved blades. To study the dynamic stall effects, the comparison of force coefficients between the simulations and experiments is done at low tip speed ratios. Simulations show that the Leishman–Beddoes model outperforms the Gormont model for all tested conditions.

Comparison of aerodynamic models for Vertical Axis Wind Turbines

Multi-megawatt Vertical Axis Wind Turbines (VAWTs) are experiencing an increased interest for floating offshore applications. However, VAWT development is hindered by the lack of fast, accurate and validated simulation models. This work compares six different numerical models for VAWTS: a multiple streamtube model, a double-multiple streamtube model, the actuator cylinder model, a 2D potential flow panel model, a 3D unsteady lifting line model, and a 2D conformal mapping unsteady vortex model. The comparison covers rotor configurations with two NACA0015 blades, for several tip speed ratios, rotor solidity and fixed pitch angle, included heavily loaded rotors, in inviscid flow. The results show that the streamtube models are inaccurate, and that correct predictions of rotor power and rotor thrust are an effect of error cancellation which only occurs at specific configurations. The other four models, which explicitly model the wake as a system of vorticity, show mostly differences due to the instantaneous or time averaged formulation of the loading and flow, for which further research is needed.

Model improvements for evaluating the effect of tower tilting on the aerodynamics of a vertical axis wind turbine

ABSTRACTIf a vertical axis wind turbine is mounted offshore on a semi‐submersible, the pitch motion of the platform will dominate the static pitch and dynamic motion of the platform and wind turbine such that the effect of tower tilting on the aerodynamics of the vertical axis wind turbine should be investigated to more accurately predict the aerodynamic loads. This paper proposes certain modifications to the double multiple‐streamtube (DMS) model to include the component of wind speed parallel to the rotating shaft. The model is validated against experimental data collected on an H‐Darrieus wind turbine in skewed flow conditions. Three different dynamic stall models are also integrated into the DMS model: Gormont's model with the adaptation of Strickland, Gormont's model with the modification of Berg and the Beddoes–Leishman dynamic stall model. Both the small Sandia 17 m wind turbine and the large DeepWind 5 MW are modelled. According to the experimental data, the DMS model with the inclusion of the dynamic stall model is also well validated. On the basis of the assumption that the velocity component parallel to the rotor shaft is small in the downstream part of the rotor, the effect of tower tilting is quantified with respect to power, rotor torque, thrust force and the normal force and tangential force coefficients on the blades. Additionally, applications of Glauert momentum theory and pure axial momentum theory are compared to evaluate the effect of the velocity component parallel to the rotor shaft on the accuracy of the model. Copyright © 2013 John Wiley &amp; Sons, Ltd.