Basics
01
According Betz's law, the maximum achievable extraction of wind power by a wind turbine is 16⁄27 or 59.3% (Also called power coefficient or Cp). Most wind turbines extract around 35% for small and medium scale wind turbines and can reach up to 43% (within narrow band of wind speeds) for industrial scale wind turbines.
The existence of the Betz limit is due to the presence of a region of stagnant flow behind the plane of the windmill, formed as a result of the extraction of kinetic energy by the wind turbine. Thus the whole wind turbine is treated as an obstacle (in very simple terms) thus some part of the wind is simply going around it instead of interacting (creating lift) with the blades.
*Pictured is the scheme of the air flow through the rotor of the wind generator according to the Betz law.
02
Invention
The purpose of this research work is to test the hypothesis, according to which, introducing a higher speed air stream through the stagnant flow area behind the rotor plane of a wind generator, can direct more flow over the main blades thus resulting in increased efficiency of wind energy extraction.
To carry out the study, we preformed simulation modeling in 2018, based on the finite element
method. Later in 2019-2022, real test prototypes were created to compare against the classical wind
turbine model under the same conditions.
*Pictured is part of the CFD model testing results.
In order to explain the difference between the classical wind turbine and proposed improved one, let us drop all the complexities of wind interacting with the blades of wind turbine for a moment and treat the “wind turbine” as a whole, an object in the flow of wind that has a property of being either totally non obstructive at 0 percent efficiency or on a contrary being a total obstruction to the wind at 100% (a solid disk or a dish that blocks any air from passing through it).
The Betz law (Zhukowsky/Lanchester) states that if “the wind stopped moving at the exit of the turbine, then no more fresh wind could get in; it would be blocked. In order to keep the wind moving through the turbine, there has to be some wind movement, however small, on the other side with some wind speed greater than zero. Betz's law shows that as air flows through a certain area, and as wind speed slows from losing energy to extraction from a turbine, the airflow must distribute to a wider area. As a result, geometry limits the maximum efficiency of any turbine”. Thus the maximum energy that can be extracted from an ideal wind turbine is limited to 59.3%.
If you place a solid object in the flow of gas it creates pressure gradient before and after that object and the air is sped up around it in order to compensate for that (separation). If we represent it in simplified 2D drawing = all air that comes in 100% diameter of an object has to flow around it with higher speed.
Lets assume for a moment that we have a classical wind turbine with maximum 59.3% efficiency at its peak performance (ideal conditions of wind speed and aerodynamic qualities of the blades and wind turbine) – in simple terms it not only means efficiency , but also a blockage of 59% in the diameter of wind turbine. The wind treats it as an obstacle and the remaining air in the diameter of a wind turbine, in simplified terms, has to go around the blockage area with stagnant flow with slightly higher speed that acts as a balancer, entrapping some of the stagnant higher pressure flow in a wake of a wind turbine – giving it additional momentum to gradually purge that area and return the wind to laminar flow after the wake of the wind turbine.
Now lets treat the air going around the "obstacle" as a 100% force that has to do some work (in order to keep the 59% efficiency) of speeding up the stagnant air flow behind the wind turbine. If we represent it in 2D (pictured bellow) there are two streams of higher speed air around the object upper and lower one (in reality in 3D space its just one layer around the diameter of a wind turbine). If we assume, for the x that both upper and lower stream exert the same amount of force entrapping air from the wind flow and from the stagnant area equally (simplification) than 50% of that force will be wasted or slowed down to prevailing wind speed and only remaining 50% will do positive the work to the stagnant flow in the wake of wind turbine equalizing the wind flow behind the wind turbine.
If we take a look at proposed method (Improved on a picture bellow) of purging stagnant air through the center of wind turbine, again oversimplifying the scheme with air going around the "obstacle" as a 100% force that has to do some work (in order to keep the 59% efficiency) of speeding up the stagnant air flow behind the wind turbine. In 2D representation we will see that no energy of that force is wasted – almost all of it gives an additional impulse to the stagnant area in wake of wind turbine! Some of the flow around that “obstacle” still exist, but the different pressure gradient, now diverts the flow not around the blades, but through them! That's what rises the efficiency! When fan is used – some of the extracted wind energy has to be converted to the higher speed flow produced by the fan in center, but due to smaller diameter of the fan as compared to the main wind turbine (blades) diameter, the balance still stands positive.
One more point that has to be mentioned is how the blades do the work with 50% of the outer diameter (upper blade section) doing 90% of the work due to the higher speed of the blade moving through the air – so the center (lower) section of the blades don't contribute much due to lower speed in rotational plane.
See the Video bellow to better understand the difference
03
Research and Testing
Based on the theoretical calculations set forth in the patent application, as well as previously performed results of mathematical modeling, placing the working area of the wind turbine blades, due to the difference in rotational speed across the blade length, to the outer radius, allows for the incoming air stream to pass through at speed close to the incoming wind or accelerating it through the inner part in order to speed up the stagnant flow behind the wind turbine blades, as a result obtaining more flow around the main blades of the wind turbine rotor, achieving higher efficiency. Experimental test prototype was created, using available materials and parts, to test its performance and compare the efficiency of the proposed wind generator design with the classical wind generator.
In 2019, tests were carried out using a) a permanently fixed wind turbine, b) mounted on a car, in order to achieve a constant wind speed. The results of these tests showed increased efficiency, despite the sub optimal design of the wind turbine.
In order to verify the reliability of the results obtained, in a hangar near Moscow, a blower module was created using 16 jet fans mounted on a 4x4 rack, with a total of electrical power input of 12.8 kW. Size of the module is 2.84m by 2.84m. The mount for the wind turbine is installed at a distance of 2.74 meters from the blower module.
In order for the results to be representative, a wind generator of classical design SMARAAD SS-400 (a horizontal 3-blade 400W, 48V with a diameter of 1.34m), as well as 3 other wind generators of classical design were purchased to test and compare their efficiency against an experimental wind generator, using similar type and speed of airflow.
Note the test was aimed at comparing efficiency of different types of wind generators and not the absolute numbers.
The blockage ratio of the blower module is far from optimal (less than 7%), so the flow velocity varies from 7.5 m/s in the middle to 5 m/s towards the edges. The average speed in the plane of the blades is about 6.4 m/s for the experimental wind generator and about 6.9 m/s for the classic one due to the smaller diameter. It is also worth considering that the resulting air flow in the blowing plane turned out to be highly turbulent, and not laminar.
In the diagram, the classical wind generator is marked in red, the experimental one is marked in green, the flow velocity at different points and the average speed in the plane of the wind turbine blades are also marked.
Despite the fact that wind generators of various diameters were tested - an indicator of relative efficiency in percentages, calculated through the formula - is a generally accepted measure of comparison.
Even though the design of the tested experimental wind turbine was not optimal, as most parts were used on the principle of "availability/cost" rather than tailored for maximum efficiency, due to the lack of capacity to create our own wind turbine components. As a result angle of attack of the blades were not optimal at a given arrangement, they should be different (in terms of angle of attack, twist and width). Three blades from a classic wind turbine were used, 70 cm in length each (75 cm including holders). The blades are fixed on the wheel rim. The total diameter of the experimental wind turbine is 2.14 meters.
The jet fan design used in our experimental wind turbine is also not optimal, consisting of 3 to 9 improvised blades (59 cm in diameter, each blade is about 20 cm), which at a given wind flow speed does not allow to fully use the effect of blowing out the stalled airflow area behind the wind generator rotor plane, so static blowing/purging in this case is sometimes as effective as dynamic.
Also, the choice of other components was not optimal at this stage in terms of the interaction between them. Generator, revs, voltage, blades, we used mostly available components in our experiments. Namely: a bicycle electric motor, 3-phase, alternating current, on permanent neodymium magnets, phase angle 120 °, maximum efficiency 87.6%, 1000 W, 48 V, diameter 245 mm (used as a generator). Note that type of generator used, blocks off part of the flow, thus decreasing the effect of blowing through the stalled airflow area behind the wind turbine. For experimental wind generator, a direct-drive rim generator would be far more optimal.
Turbine Power output can be expressed as follows:
3 P=½·ρ·S·V ·Cp·(ηg·ηt·ηe), Watt
where
ρ= 1.22 is the air density (standard at +15°C and 720mm pc), kg/m3
V is the wind speed, m/s;
ηg·ηm·ηe are the efficiency of the generator, the mechanical transmission between the wind wheel and the generator, the losses for the transmission of electricity;
Cp is the wind energy Power Coefficient, the max limit value of which is 0.593;
S is the area of the wind turbine, which, in the case of a propeller turbine, is calculated by the formula:
S=¼π·D2, where D is the rotor diameter.
The swept area of the wind generator rotors we tested is calculated below:
Sc= (3,14·1,34 )/4 = 1,4 m2 – classic wind generator
Se= (3,14·2,14 )/4 = 3,6 m2 – experimental wind generator
As a result of the tests, the following values of the charging current and voltage supplied to the battery (48V, Li) were recorded:
Classic wind generator:
Pc = ½·1,22·1,4·6,9 ·25%·0,883=63 Watt, (U=51,5V, I=1,23A)
Pc = ½·1,22·1,4·6,4 ·30%·0,883=63 Watt (U=51,5V, I=1,23A)
Experimental wind generator:
Pe = ½·1,22·3,6·6,4 ·46%·0,883=230 Watt, (U=53,3V, I=4,3A)
Pe = ½·1,22·3,6·6,4 ·48%·0,883=240 Watt, (U=53,3V, I=4.5A)
Pe = ½·1,22·3,6·6,4 ·57%·0,740=230 Watt (U=53,3V, I=4,3A)*
*Pe - efficiency recalculated with real loss measurements
You can re-calculate the results on this website: https://www.omnicalculator.com/ecology/wind-turbine
Even without taking into account the non-optimal use of components for the experimental wind generator in comparison with the factory designed classical wind generator, the experimental wind generator shows an efficiency increase that exceeds the classical model!
Optimal model of the experimental wind generator in laminar wind flow, should approach the efficiency close to the maximum possible of 59.3% in wider ranges of wind speeds!
Economic efficiency is also an important consideration and is worth paying attention to. After all, over the past 100 years, it was all about increase in the diameter of classical wind turbines, that was economically feasible to obtain a greater return than any technological improvements in efficiency, since this was usually associated with an increase in the cost of the structure.
As a small example, our prototype, having a generator of 1000 W against 400 W on the classics and a rotor diameter of 2.14m against a diameter of 1.34m on a classic generator are comparable in costs, if not cheaper, than a classical wind generator!
First Patent in Jan 2024
The Patent
04
The Patent for the Invention "Advanced wind turbine with dynamic entrainment and scavenging of wind flow" has already been granted by the Eurasian Patent Organization for Russia and CIS countries.
We are also expecting to receive patents in the USA, China, the European Patent Organization (30 countries), India, Brazil, Japan, Canada and Australia.
Who may be interested in our offer?
Investors
Whose with patience, funds and acquaintances that can make this invention production ready and can sell it to the second group.
Wind Turbines Manufacturers
Even the slightest improvement in efficiency can be a game changer in the wind turbine market. Our patent is something to consider.
For questions about acquiring patent rights, please contact:
Vorobiev Valerii, valmes@yandex.com, +7 902 940 33 04
*Using an invention without a patent will be prosecuted by law.