- The document analyzes how the aspect ratio of a vertical-axis wind turbine affects its performance.
- It finds that turbine performance is strongly influenced by the Reynolds number of the rotor blades, which is linked to the aspect ratio.
- A lower aspect ratio leads to a higher Reynolds number and improved turbine performance, as well as a lower rotational velocity.
Improving the Hydraulic Efficiency of Centrifugal Pumps through Computational...IJERA Editor
The design and optimization of turbo machine impellers such as those in pumps and turbines is a highly complicated task due to the complex three-dimensional shape of the impeller blades and surrounding devices. Small differences in geometry can lead to significant changes in the performance of these machines. We report here an efficient numerical technique that automatically optimizes the geometry of these blades for maximum performance. The technique combines, mathematical modeling of the impeller blades using non-uniform rational B-spline (NURBS), Computational fluid dynamics (CFD) with Geometry Parameterizations in turbulent flow simulation and the Globalized and bounded Nelder-Mead (GBNM) algorithm in geometry optimization.
A Wear Map for Recip Compressor PerformanceLuis Infante
Perfomance curves for recip compressor are usually, if not always, constructed in as new condition. But, what happens when seals deteriorate with time?. Can one use OEM performance curves to control unhealthy cylinders?. Surely and only for orientation purposes, as a reference point.
Updating performance maps according to accumulated wear can help field operators and analysts to estimate the recommended Variable Volume Clearance Pockets (VVCP) settings due to changing process conditions (Ps, Pd) and to match flow readings either from electronic analyzers or meters.
Accumulated wear moves (downwards) the power and flow curves thus disabling the "as new" VVCP curve.
The governing criteria for this analysis is that, as running time degrades compressor performance, the volumetric efficiencies (VEs) drop due to increasing leakages in the seals. Certainly, degraded VEs can be obtained with the electronic analyzer. On the other hand, as new VEs can be obtained either from electronic analyzers or from constant VE maps as shown in this analysis.
Here you will find a practical quasi-empirical approach to quantify wear in both engine and compressor side, and to depict a wear map with the help of an in-house compresser modeller.
At its own, engine wear appears easier to handle with the help of either a combustion pressure or static (cold) compression indicator.
Preliminary criteria for establishing alarm and trip levels is provided.
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This paper presents simplified control strategy of Space Vector Pulse Width Modulation method including over modulation region with linear transfer characteristic for cascaded H-bridge inverters. Because of large number of switching states of the cascaded H- Bridge inverter, the over modulation operation is very complex. And also requires incorporation of both under modulation and over modulation algorithms. The proposed control method is effective in terms of selecting the optimal switching states with reduced computational complexity using simplified linear calculations which makes it easier for digital implementation. The performance of the proposed method is simulated and tested experimentally through Spartan 3A FPGA processor for five level Cascaded H-bridge Inverter. The simulation results and harmonic analysis of voltage and current at various modulation indexes as are presented which are in well agreement.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Numerical Simulation of the Aerodynamic Performance of a H-type Wind Turbine ...Capvidia NV
Wind Turbine Self Starting CFD Simulation with FlowVision This is a nice example for moving bodies. Moment of inertia of turbine is defined and rotation is induced by aerodynamics forces. Simulation results of rotation speed variation during self-starting are in well agreement with the experimental results.
The formula cars need high tire grip on racing challenge by reducing rolling displacement at corner or
double change lands. In this case study, the paper clarifies some issues related to suspension system with
inerter to reduce displacement and rolling angle under impact from road disturbance on Formula SAE
Car. We propose some new designs, which have an advance for suspension system by improving dynamics.
We optimize design of model based on the minimization of cost functions for roll dynamics, by reducing the
displacement transfer and the energy consumed by the inerter. Base on a passive suspension model that we
carried out quarter-car and half-car model for different parameters which show the benefit of the inerter.
The important advantage of the proposed solution is its integration a new mechanism, the inerter, this
system can increase advance in development and have effects on the vehicle dynamics in stability vehicle.
Strategic design of aircraft wings have evolved over time for maximum fuel efficiency. One of such ideas involves winglet which has been known
to reduce turbulence at the tip of the wings. This study intends to investigate the
differences in drag and lift forces generated at aeroplane wings with and without winglet at cruising speed using FEM. Simulations were performed in the
SST turbulence model of CFD and the results are compared to that of the experimental and theoretical models. The simulation showed that the lift increased
by 26.0% and the drag decreased by 74.6% for the winglet at cruising speed.
Design and Analysis of Solar Powered RC Aircrafttheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Improving the Hydraulic Efficiency of Centrifugal Pumps through Computational...IJERA Editor
The design and optimization of turbo machine impellers such as those in pumps and turbines is a highly complicated task due to the complex three-dimensional shape of the impeller blades and surrounding devices. Small differences in geometry can lead to significant changes in the performance of these machines. We report here an efficient numerical technique that automatically optimizes the geometry of these blades for maximum performance. The technique combines, mathematical modeling of the impeller blades using non-uniform rational B-spline (NURBS), Computational fluid dynamics (CFD) with Geometry Parameterizations in turbulent flow simulation and the Globalized and bounded Nelder-Mead (GBNM) algorithm in geometry optimization.
A Wear Map for Recip Compressor PerformanceLuis Infante
Perfomance curves for recip compressor are usually, if not always, constructed in as new condition. But, what happens when seals deteriorate with time?. Can one use OEM performance curves to control unhealthy cylinders?. Surely and only for orientation purposes, as a reference point.
Updating performance maps according to accumulated wear can help field operators and analysts to estimate the recommended Variable Volume Clearance Pockets (VVCP) settings due to changing process conditions (Ps, Pd) and to match flow readings either from electronic analyzers or meters.
Accumulated wear moves (downwards) the power and flow curves thus disabling the "as new" VVCP curve.
The governing criteria for this analysis is that, as running time degrades compressor performance, the volumetric efficiencies (VEs) drop due to increasing leakages in the seals. Certainly, degraded VEs can be obtained with the electronic analyzer. On the other hand, as new VEs can be obtained either from electronic analyzers or from constant VE maps as shown in this analysis.
Here you will find a practical quasi-empirical approach to quantify wear in both engine and compressor side, and to depict a wear map with the help of an in-house compresser modeller.
At its own, engine wear appears easier to handle with the help of either a combustion pressure or static (cold) compression indicator.
Preliminary criteria for establishing alarm and trip levels is provided.
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This paper presents simplified control strategy of Space Vector Pulse Width Modulation method including over modulation region with linear transfer characteristic for cascaded H-bridge inverters. Because of large number of switching states of the cascaded H- Bridge inverter, the over modulation operation is very complex. And also requires incorporation of both under modulation and over modulation algorithms. The proposed control method is effective in terms of selecting the optimal switching states with reduced computational complexity using simplified linear calculations which makes it easier for digital implementation. The performance of the proposed method is simulated and tested experimentally through Spartan 3A FPGA processor for five level Cascaded H-bridge Inverter. The simulation results and harmonic analysis of voltage and current at various modulation indexes as are presented which are in well agreement.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Numerical Simulation of the Aerodynamic Performance of a H-type Wind Turbine ...Capvidia NV
Wind Turbine Self Starting CFD Simulation with FlowVision This is a nice example for moving bodies. Moment of inertia of turbine is defined and rotation is induced by aerodynamics forces. Simulation results of rotation speed variation during self-starting are in well agreement with the experimental results.
The formula cars need high tire grip on racing challenge by reducing rolling displacement at corner or
double change lands. In this case study, the paper clarifies some issues related to suspension system with
inerter to reduce displacement and rolling angle under impact from road disturbance on Formula SAE
Car. We propose some new designs, which have an advance for suspension system by improving dynamics.
We optimize design of model based on the minimization of cost functions for roll dynamics, by reducing the
displacement transfer and the energy consumed by the inerter. Base on a passive suspension model that we
carried out quarter-car and half-car model for different parameters which show the benefit of the inerter.
The important advantage of the proposed solution is its integration a new mechanism, the inerter, this
system can increase advance in development and have effects on the vehicle dynamics in stability vehicle.
Strategic design of aircraft wings have evolved over time for maximum fuel efficiency. One of such ideas involves winglet which has been known
to reduce turbulence at the tip of the wings. This study intends to investigate the
differences in drag and lift forces generated at aeroplane wings with and without winglet at cruising speed using FEM. Simulations were performed in the
SST turbulence model of CFD and the results are compared to that of the experimental and theoretical models. The simulation showed that the lift increased
by 26.0% and the drag decreased by 74.6% for the winglet at cruising speed.
Design and Analysis of Solar Powered RC Aircrafttheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Numerical Investigation Of Compression Performance Of Different Blade Configu...IJERA Editor
This project work is to investigate the compression efficiency of different configuration of Turbo-Prop Co-Rotor Blade System of Subsonic Axial Flow Compressor. By this method the highly compressed air can be passed over the intake of the engine to the compressor with high mass flow rate in change of low velocity and high pressure ratio. The length of the small rotor is varied in terms of large rotor length by 25,50 & 75% . Each will have three space configuration in terms of diameter of rotor and in the percentage of 5,10,15%. A total of 12 configurations will be simulated to arrive optimum blade configuration. The blades are made in the shape of an airfoil like wing of an aircraft. The engine rotates the propeller blades, which produce lift. This lift is called thrust and moves the aircraft forward. Blades are usually made of high lift airfoil which allows more rotation to generate high pressure for engine. ANSYS- Fluent is commercial software which is robust for most of the fluid dynamic problems and it is used in this project work to evaluate the different configurations of co-rotor propeller system to arrive the best.
This project work is to investigate the compression efficiency of different configuration of Turbo-Prop Co-Rotor Blade System of Subsonic Axial Flow Compressor. By this method the highly compressed air can be passed over the intake of the engine to the compressor with high mass flow rate in change of low velocity and high pressure ratio. The length of the small rotor is varied in terms of large rotor length by 25,50 & 75% . Each will have three space configuration in terms of diameter of rotor and in the percentage of 5,10,15%. A total of 12 configurations will be simulated to arrive optimum blade configuration. The blades are made in the shape of an airfoil like wing of an aircraft. The engine rotates the propeller blades, which produce lift. This lift is called thrust and moves the aircraft forward. Blades are usually made of high lift airfoil which allows more rotation to generate high pressure for engine. ANSYS- Fluent is commercial software which is robust for most of the fluid dynamic problems and it is used in this project work to evaluate the different configurations of co-rotor propeller system to arrive the best.
Simulation of gas turbine blade for enhancement of efficiency of gas turbine...IJMER
As day by day population of the world is increasing and our resources are frequently reducing
hence to meet this demand of the world of energy we have to move to a device which have a maximum
efficiency for the condition turbo-machinery are better suited machines having a good efficiency, in
which a Gas turbine is best example of turbo- machinery Turbine is the part of gas turbine which provide
the power to compressor to run or provide power to external source from where energy can be extracted
by attaching alternator in the shaft of Gas turbine. As in earlier a lot of work have been done by the
researcher to increase the efficiency and standard of Gas turbine by the method of film cooling, coating,
and curvature of blade to protect the blade from high temperature of 1200 C° inside the Gas turbine to
increase the life of blade without considering about the efficiency of the engine As in this work is to
enhancement of efficiency of Gas turbine. Gas turbine blade is very important component of engine as
they are attached to both turbine or compressor and turbine provide energy to compressor hence the
turbine blade are more important component to enhance the efficiency which will be analyzed on the
basis of blade height area of fluid flow , area of blade thickness and angles . This simulation is based on
the define value of temperature pressure density of fluid and solid used in blade construction will be
meshed in ANSYS and calculation on the basis of FEM and the result from this calculation over the
temperature and fluid flow inside the gas turbine of different number of blade is studied will be compare
to reach high efficiency point. By determent these value output is formulated on graph chart and will be
studied and result obtain
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Hybrid winding function method for inductance analysis of a line start synch...IJECEIAES
In recent years, there has been renewed interest in line-start synchronous reluctance machines (LSSRMs) due to their simple construction, magnet-free rotor, and low cost. To improve control performance, design optimization, and fault diagnostic analysis of these machines, it requires accurate estimation of their electromagnetic characteristics using detailed and time-consuming finite element analyses (FEAs). In this paper, inductances and electromagnetic torque of the LSSRM were calculated using the combination of winding function analysis and conformal mapping instead of FEA. The hybrid approach can be applied to the prediction of motor behavior, taking into account all space harmonics of the air-gap permeance without any restriction on the rotor saliencies and topologies. The influence of the core saturation, stator slots, and rotor bars were also considered. The results obtained by simulations were compared with FEA in terms of accuracy and computational time.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
In this paper, we focus on the modeling and control of a wind power system based on a double-fed induction generator DFIG. We proposed a technique of active and reactive power control to improve the performance and dynamics of variable speed wind system. The objective of the modeling is to apply the direct and indirect vector control stator flux orientation to control independently, the active and reactive power generated doubly-fed induction generator (DFIG). The simulation results are tested and compared in order to evaluate the performance of the proposed system.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
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Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Design of a vertical axis wind turbine how the aspect ratio affects
1. ORIGINAL RESEARCH
Design of a vertical-axis wind turbine: how the aspect ratio affects
the turbine’s performance
S. Brusca • R. Lanzafame • M. Messina
Received: 1 April 2014 / Accepted: 24 May 2014 / Published online: 2 August 2014
Ó The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract This work analyses the link between the aspect
ratio of a vertical-axis straight-bladed (H-Rotor) wind turbine
and its performance (power coefficient). The aspect ratio of
this particular wind turbine is defined as the ratio between
blade length and rotor radius. Since the aspect ratio variations
of a vertical-axis wind turbine cause Reynolds number varia-
tions, any changes in the power coefficient can also be studied
to derive how aspect ratio variations affect turbine perfor-
mance. Using a calculation code based on the Multiple Stream
Tube Model, symmetrical straight-bladed wind turbine per-
formance was evaluated as aspect ratio varied. This numerical
analysis highlighted how turbine performance is strongly
influenced by the Reynolds number of the rotor blade. From a
geometrical point of view, as aspect ratio falls, the Reynolds
number rises which improves wind turbine performance.
Keywords VAWT Á MSTM Á H-Rotor Á Reynolds
number Á Aspect ratio
Nomenclature
a Interference factor (–)
V0 Free stream wind speed (m/s)
R Rotor radius (m)
x Rotor angular velocity (s-1
)
h Blade length (m)
w Relative airfoil wind speed (m/s)
a Angle of attack (°)
L Lift (N)
D Drag (N)
R* Resultant force (N)
# Blade angular position (°)
P Power (W)
Nb Number of blades (–)
n Rotor rotational velocity (rpm)
Re Reynolds number (–)
q Air density (kg/m3
)
m Kinematic air viscosity (m2
/s)
cp Power coefficient (–)
k Tip speed ratio (–)
r Rotor solidity (–)
rcpmax r that maximizes cp (–)
kcpmax k that maximizes cp (–)
cpmax Maximum cp (–)
c Airfoil chord (m)
CL Lift coefficient (–)
CD Drag coefficient (–)
Abbreviations
NACA National Advisory Committee for Aeronautics
VAWT Vertical-axis wind turbine
H-Rotor VAWT with straight blades
TSR Tip speed ratio
MSTM Multiple Stream Tube Model
AR Aspect ratio
Highlights
• This paper evaluates VAWT performance;
• How Reynolds number influences rotor performance
has been studied;
S. Brusca
Department of Electronic Engineering, Chemical and Industrial
Engineering, University of Messina, Contrada Di Dio,
98166 Messina, Italy
R. Lanzafame Á M. Messina (&)
Department of Industrial Engineering, University of Catania,
Viale A. Doria, 6, 95125 Catania, Italy
e-mail: mmessina@dii.unict.it
123
Int J Energy Environ Eng (2014) 5:333–340
DOI 10.1007/s40095-014-0129-x
2. • How Reynolds number is linked to rotor aspect ratio
has been investigated;
• A new design procedure governing the rotor’s aspect
ratio has been presented;
• The new design procedure maximizes wind turbine
efficiency.
Introduction
There are two types of wind turbine which produce
electrical energy from the wind: they are horizontal-axis
wind turbines (HAWTs) and vertical-axis wind turbines
(VAWTs). The second, and in particular straight-bladed
VAWTs, have a simplified geometry with no yaw
mechanism or pitch regulation, and have neither twisted
nor tapered blades [1]. VAWTs may be utilized to
generate electricity and pump water, as well as in many
other applications [1]. Furthermore, they can handle the
wind from any direction regardless of orientation and
are inexpensive and quiet [2]. Wind turbines have
aroused the interest of both industry and the academic
community [3–15, 29–31], which have developed dif-
ferent numerical codes for designing and evaluating
wind rotor performance. Recent studies [16–20] have
highlighted that VAWTs can achieve significant
improvements in efficiency.
VAWT can work even when the wind is very unstable
making them suitable for urban and small-scale applica-
tions [21]. Their particular axial symmetry means they can
obtain energy where there is high turbulence.
Their optimum operating conditions (maximum power
coefficient) depend on rotor solidity and tip speed ratio
[22]. For a VAWT rotor solidity depends on the number of
blades, airfoil chord and rotor radius. Tip speed ratio is a
function of angular velocity, undisturbed wind speed and
rotor radius.
In the design process of a vertical-axis wind turbine
it is crucial to maximize the aerodynamic performance
[22, 26]. The aim is to maximize the annual energy
production by optimizing the curve of the power
coefficient varying with the tip speed ratio [25]. For a
fixed cross-sectional area of the turbine, to optimize the
curve of the power coefficient it is possible to use
different airfoil sections and/or rotors with different
solidity [26].
To maximize energy extraction, other authors intro-
duced guide vanes [27] and/or blade with a variable pitch
angle [28] in vertical-axis wind turbines.
In the design process of a vertical-axis wind turbine, a
wrong choice of the aspect ratio of the wind turbine may
cause a low value of the power coefficient (wind turbine
efficiency). This parameter (the aspect ratio) is often
chosen empirically on the basis of the experience of the
designer, and not on scientific considerations.
In this work, the link between the aspect ratio of a wind
turbine and its performance has been studied, and a cor-
relation between the aspect ratio and the turbine’s perfor-
mance has been found.
Designing an H-Rotor
Designing a vertical-axis wind turbine with straight
blades requires plotting power coefficient cp against
tip speed ratio k, as a function of rotor solidity r
(Fig. 1).
Figure 1 shows the behaviour of the power coefficient
for a wind turbine with straight blades and a NACA 0018
airfoil.
Figure 1 curves were obtained using a calculation code
based on MSTM theory [23].
From the graph in Fig. 1, the solidity which maximizes
power coefficient r = 0.3 can be identified, which has a
cpmax = 0.51 corresponding to k = 3.0.
Since solidity r equals:
r ¼
Nb c
R
: ð1Þ
chord c can be expressed as a function of solidity, rotor
radius and blade number Nb, as per Eq. 2:
c ¼
rcpmax
Nb
R ð2Þ
The power of a wind turbine with a vertical axis can be
expressed as per Eq. 3:
P ¼
1
2
q V0
3
2 R h cp ð3Þ
Having defined the turbine’s aspect ratio (AR) as the
ratio between blade height and rotor radius (AR = h/R),
rotor radius can be derived from Eq. 3:
Fig. 1 Power coefficient for a VAWT, straight blades and symmetric
airfoil
334 Int J Energy Environ Eng (2014) 5:333–340
123
3. R ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
q V0
3
AR cp
s
ð4Þ
(in Eq. 4 power P and wind velocity V0 are design data
and q is air volume mass).
This design approach is iterative and from time to time it
will be necessary to re-evaluate the blade’s Reynolds
number and if necessary repeat the procedure with new
power coefficient curves.
The local Reynolds number is:
Re ¼
c w
m
ð5Þ
where c is the chord from Eq. 2, m is the kinematic air
viscosity, and w is the air speed relative to the airfoil as
Fig. 2 shows.
Adopting a mathematical approximation, to evaluate the
Reynolds number, w can be substituted by xR with the
advantage of having a mean Reynolds number independent
of the angle # of rotation (see Fig. 2).
To conclude the design cycle, simply calculate xR
directly from TSR relative to cpmax identifiable in Fig. 1,
x R ¼ kcpmax V0 ð6Þ
and combining Eqs. 5 and 6:
Re ¼
c V0 kcpmax
m
ð7Þ
If the Reynolds number thus calculated is different to
the one for the power coefficient curve adopted initially
(Fig. 1), a new power coefficient curve should be plotted
for a different Reynolds number (second attempt). Usually,
the iterative design process needs only 2 or 3 iterations.
Figure 3 shows the power coefficient curves for the
wind turbine with the NACA 0018 airfoil, at high Reynolds
numbers.
Fig. 2 Wind rotor rotational
plane
Int J Energy Environ Eng (2014) 5:333–340 335
123
4. In conclusion, the Reynolds number strongly influences
the power coefficient of a vertical-axis wind turbine. Fur-
thermore, it changes as the main dimensions of the turbine
rotor change. Increasing rotor diameter rises the Reynolds
number of the blade.
The importance of aspect ratio
In Eq. 4 note how radius R increases as ratio AR decreases.
In Eq. 2 if R increases, chord c increases too, and in Eq. 7
note how increasing the chord rises the Reynolds number.
Finally, Fig. 3 shows how the power coefficient increases
as the Reynolds number rises.
Moreover, the rotational velocity x can be derived from
Eq. 6:
x ¼
kcpmaxV0
R
ð8Þ
Equation (8) shows how x is inversely proportional to
R. From the Fig. 3 graph, note how kcpmax decreases as
Reynolds number rises.
So, to maximize the power coefficient, the rotor’s
aspect ratio should be as small as possible. As aspect ratio
diminishes there are two advantages: the local Reynolds
number rises and simultaneously the rotational velocity
diminishes. The effect of the rotor’s aspect ratio on
Reynolds number and rotational velocity are shown in
Fig. 4 for a twin-bladed 1 kW turbine in a wind velocity
of 10 m/s.
Fig. 3 Characteristic curves for high Reynolds numbers
Fig. 4 Effect of aspect ratio (h/R) on VAWT performance
Fig. 5 Wind turbines with different aspect ratios
336 Int J Energy Environ Eng (2014) 5:333–340
123
5. Figure 5 shows two vertical-axis turbines with identical
design power, blade number and aerodynamic profile (NACA
0018) but with two different aspect ratios (AR1 = 2;
AR2 = 0.4). As stated above, the turbine with the lowest AR
willhavethehighestpowercoefficientandthelowestrotational
velocity. This turbine will display two further advantages:
firstly, a structural one (thicker blades are more stress resistant)
and secondly, in-service stability (greater rotor inertia).
Figure 6 shows the same graphs as Fig. 4 but parame-
terized for design power variation. Note how the turbines
with the highest power have higher Reynolds numbers and
lower rotational velocity.
To conclude, VAWT performance is directly related to the
blade’s Reynolds number. The higher this is, the better the
turbine’s performance. This is because as the Reynolds number
increases, the blade’s lift coefficient [24] rises and the drag
coefficients decrease (Fig. 7a, b) thus providing greater torque.
Application for a case study
To better explain the design procedure investigated in this
work, a case study is presented. From Fig. 4, it is possible
to notice that the lower the AR, the higher the Reynolds
number; this can improve wind turbine performance. In the
design procedure, a choice of a low value for the AR is
therefore suitable. In this case study, a comparison between
two wind rotors, designed with two different AR values
(AR = 2 and AR = 0.4), will be presented.
Suppose, for simplicity, we want to design a VAWT
with a rated power of 1 kW, with only two straight blades
with symmetrical aerodynamic profile (NACA 0018), and
that the installation site is characterized from a mean
wind speed of 10 m/s. The design procedure is showed in
the Fig. 8. In this figure a flowchart for designing the
wind turbine is adopted. In this design procedure, first of
all, a Reynolds number must be supposed. This Reynolds
number will be called: ‘‘the first attempt Reynolds num-
ber’’. Supposed a first attempt Reynolds number equal to
5 9 106
, from the graph in Fig. 3a it is possible to read
the highest performance (cpmax = 0.51) in correspondence
of a particular rotor solidity and tip speed ratio:
rcpmax = 0.3 e kcpmax = 3.0. For an aspect ratio of 2 (h/
R = 2) (square VAWT cross section), Eq. 4 will provide
the rotor radius R = 0.904 m (q = 1.2 kg/m3
). From
Eq. 2, we obtain a chord c = 0.136 m, and from Eq. 8 we
(a) (b)
Fig. 6 How aspect ratio influences Reynolds number and rotational velocity, for different design powers
Fig. 7 a Lift coefficient for NACA 0018. b Drag coefficient for NACA 0018
Int J Energy Environ Eng (2014) 5:333–340 337
123
6. obtain a rotational velocity of 317 rpm. Now a new
Reynolds number (second attempt) must be evaluated
from Eq. 7: Re = 2.8 9 105
.
Now the design procedure should be repeated with the
new value of the Reynolds number. This Reynolds number
will be called: ‘‘the second attempt Reynolds number’’.
Taking into account Fig. 3c, we will obtain the new geo-
metric values for the wind turbine. These values are
reported in Table 1. The design procedure will end when
the Reynolds number does not change in a meaningful
manner. The design procedure goes to numerical conver-
gence with only two iterations.
From the data reported in Table 1 for h/R = 2, the
design procedure gives rise to a power coefficient of 0.464.
Repeating the procedure described above for h/R = 0.4, we
will obtain an higher efficiency: cpmax = 0.475 (see
Table 2)
INPUT
END
(P, V0, Nb, AR)
i=0
Re=Re[i]=5*106
From diagrams.
Input: Re
Output: cpmax; λcpmax; σcpmax.
R=[P/(ρV0
3
ARcp)]0.5
c=σR/Nb
Re[i+1]=cV0λ/ν
Re[i+1]- Re[i]< ε
YES
NO
Re=Re[i+1]
i=i+1
Fig. 8 VAWT design flowchart
Table 1 VAWT––straight blade’s design procedure (h/R = 2)
Reference 1st attempt 2nd attempt
Power (kW) – 1 1
Airfoil – NACA 0018 NACA 0018
Wind speed (m/s) – 10 10
Air density (kg/m3
) – 1.2 1.2
Kinematic air
viscosity (m2
/s)
– 1.46 9 10-5
1.46 9 10-5
Rotor aspect ratio
(h/R)
– 2 2
Number of blades
(Nb)
– 2 2
First attempt
Reynolds
– 5 9 106
2.8 9 105
cpmax; rcpmax;
kcpmax
Fig. 3 0.51; 0.3; 3.0
(Fig. 3a)
0.464; 0.4; 2.96
(Fig. 3c)
Rotor radius (m) Eq. 3 0.904 0.947
Airfoil Chord (m) Eq. 4 0.136 0.189
Rotational speed
(rpm)
Eq. 6 317 299
Second attempt
Reynolds
Eq. 7 2.8 9 105
3.8 9 105
Next step – Go to the 2°
attempt
END
Table 2 VAWT––straight blade’s design procedure (h/R = 0.4)
Reference 1st attempt 2nd attempt
Power (kW) – 1 1
Airfoil – NACA 0018 NACA 0018
Wind speed (m/s) – 10 10
Air density (kg/m3
) – 1.2 1.2
Kinematic air
viscosity (m2
/s)
– 1.46 9 10-5
1.46 9 10-5
Rotor aspect ratio
(h/R)
– 0.4 0.4
Number of blades
(Nb)
– 2 2
First attempt
Reynolds
– 5 9 106
6.2 9 105
cpmax; rcpmax;
kcpmax
Fig. 3 0.51; 0.3; 3.0
(Fig. 3a)
0.475; 0.3; 3.01
(Fig. 3c)
Rotor radius (m) Eq. 3 2.021 2.094
Airfoil Chord (m) Eq. 4 0.303 0.314
Rotational speed
(rpm)
Eq. 6 142 137
Second attempt
Reynolds
Eq. 7 6.2 9 105
6.5 9 105
Next step – Go to the 2°
attempt
END
338 Int J Energy Environ Eng (2014) 5:333–340
123
7. Conclusion
This work looks at designing a vertical-axis wind turbine to
maximize its power coefficient. It has been seen that the
power coefficient of a wind turbine increases as the blade’s
Reynolds number rises. Using a calculation code based on
the Multiple Stream Tube Model, it was highlighted that
the power coefficient is influenced by both rotor solidity
and Reynolds number.
By analysing the factors which influence the Reynolds
number, it was found that the ratio between blade height
and rotor radius (aspect ratio) influences the Reynolds
number and as a consequence the power coefficient.
It has been highlighted that a turbine with a lower aspect
ratio has several advantages over one with a higher value.
The advantages of a turbine with a lower aspect ratio
are: higher power coefficients, a structural advantage by
having a thicker blade (less height and greater chord),
greater in-service stability from the greater inertia moment
of the turbine rotor.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution, and reproduction in any medium, provided the original
author(s) and the source are credited.
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