The only way to raise wind loading on the blade in the vertical turbine with a horizontal axis, without causing their destruction and worsening their aerodynamic quality, is increase in quantity of blades and a fastening their ends by a ring in a shape of an airfoil.

THE FUTURE OF WORLD WIND POWER

Izosimov Evgeniy

EarthToys Renewable Energy Article
The only way to raise wind loading on the blade in the vertical turbine with a horizontal axis, without causing their destruction and worsening their aerodynamic quality, is increase in quantity of blades and a fastening their ends by a ring in a shape of an airfoil.
The Future of World Wind Power

Izosimov Evgeniy, www.windrotor.info


The increase in efficiency of the wind turbine usually means expenses reduction for manufacturing, maintenance, transportation and installation either the turbine itself, or its components due to application of new technologies, the equipment or optimization of organizational actions. Besides, efficiency is influenced by life span of the turbine, quantity of orders for manufacturing and accommodation of turbines (in case of line production and delivery the cost of each one gets lower). One of the ways of increasing of efficiency is increase in size and, as consequence, power capacities of each turbine (which does not concern independent turbines of small and average capacity where the concept of efficiency pursues other purpose, namely minimization of expenses for achievement of sufficient and more stable capacity). So why not increase the size of turbines even more then? It appears, that at the present stage of development of technology rates of growth of cost of wind turbines with the further increase in their sizes start to exceed rates of growth of their capacity so, efficiency goes down and cost of each kilowatt thus grows.

Efficiency of a rotor of the wind turbine.

The basic role of a rotor of the turbine is transformation of wind energy into mechanical rotation of a shaft of the electro generator. As any converter, a rotor has the efficiency. In aerodynamics it has its own name Cp which means useful factor of a wind power. This factor has its theoretical limit. For a rotor with ideal characteristics Срi = 4е x (1-е) / (1+е). Срi has a maximum value of 0,686 (or 68,6 %) at е = 0,414. The aerodynamic parameter "e" is equal to the relation of change of speed of a wind a plane of a rotor towards the speed of a wind before rotor and refers to as factor of slowing down of a stream of air in a plane of a rotor. It depends on speed of movement of blades, their width and their quantity. Real factor Ср always less than the ideal one and depends also on the quality of an aerodynamic structure of the blade expressed in aerodynamic factors Сy, Cx and k = Сy / Cx. This quality defines, first of all, the basic component of losses of a rotor, namely loss from friction of air about the blade which, in turn, grows with increase of speed of an air stream accumulating on the blade.

In practice average Ср is within the limits of 0,35 – 0,45. The matter is that this factor is not constant; it depends on speed of a wind, speed of rotation of a rotor and varies on length of the blade. For example, in a narrow external part of the blade speed of its moving is so great, that losses of friction become comparable with useful capacity which forces to reduce speed of rotation, reducing thus parameter "e" (as well as Ср). It’s possible to increase parameter "e" in this part of the blade, without increasing speed of rotation, only either increasing the width of the blade, or increasing the number of blades. Thus, the wide edge of the blade increases so-called trailer losses. In wider part of the blade located closer to the center of a rotor, speed of an accumulating stream is small, but the big relative thickness of the blade is necessary for mechanical durability, which considerably worsens aerodynamic parameters of this site. The average part of the blade has intermediate values of speed of an air stream and thickness of the blade that also reduces Cp. Special expensive materials are applied for reduction of relative thickness of the blade at preservation of necessary durability. However powerful loadings on the blade of the big rotors do not allow us to achieve good results.

About a choice of rated power of the generator.

Speed of a wind for a rated power usually equal’s 11 - 13 m/s. The choice of this restriction is explained by the fact that at rated power the loading on the blade, a tower, other units of a design corresponding to this speed, reaches maximum values. At the further increase in speed of a wind, system of automatics of the turbine due to change of corners of turns of blades and speeds of rotation of a rotor support rated power on an output of the turbine. At the maximum speed of a wind, which is 22 - 27 m/s, the generator is switched off, the rotor is stopped, blades are established parallel to a wind, and the turbine stays in a waiting regime until the wind abates.

There is a question. Whether change of rating value at these speeds can affect the size of annual harvest of energy and at what cost? To answer this question it is necessary to know the average probable distribution of speeds of a wind for different wind areas and to take into account the power contribution of each of these speeds. An example of such calculation can be http://www.nrel.gov/wind/docs/weibull_betz5_lswt_baseline.xls

Taking into account the fact, that capacity of a wind has third-degree dependence on its speed, it is possible to assume, that at increase in rated power of the turbine annual gathering of energy will increase, as the probability of obtaining speeds higher than nominal ones is still high enough, but capacity is already limited. We shall check up this assumption calculations for the wind turbine with parameters: Diameter of a rotor – 120 m; Height of hub – 120 m; Capacity – 4,5 MW; Speeds of a wind: initial, nominal, maximum – 4, 12, 25 m/s accordingly; Ср – 0,4. Let us increase (without changing the sizes of the turbine) rated power up to 15 MW, speeds of a wind – up to 5, 18, 35 m/s accordingly and make the similar calculation. The comparative analysis we shall make for 4 basic wind classes 4, 5, 6 and 7 (for districts with mid-annual speeds 5,8; 6,2; 6,7 and 8,2 m/s) and parameters Weibull K – 1,5; 2 and 2,5 (the less K is, the more probable the disorder of speeds of a wind is and the more K is, and more probable average speed and less the disorder of speeds is. Usually in the general calculations value of K is K = 2).

Results of calculations are submitted in Tab. 1.

Tab. 1. Gross annual production of wind energy, GWh / year
K = 1,5, for classes K = 2,0, for classes K = 2,5, for classes
4 5 6 7 4 5 6 7 4 5 6 7
Prated = 4,5 MW 13,38 14,38 15,42 17,38 13,92 15,45 17,16 20,77 14,04 15,91 18,07 23,00
Prated = 15 MW 23,04 26,39 30,46 41,16 18,83 22,61 27,53 42,14 16,04 19,82 24,99 41,72
Benefit 1,722 1,836 1,975 2,368 1,352 1,464 1,604 2,029 1,143 1,246 1,383 1,814

From the table one can see, that there is a real benefit and it averages 1,5 times and more and is the more the higher the wind class of area and the less parameter Weibull K is. However, it is not as easy as it appears.

The increase in rated power of the wind turbine with 4,5 MW up to 15 MW will show in the following, loading on the blades will increase. Even in case the blades are made from the strongest and the most expensive materials, it will be necessary either to make them very wide (and also thick, heavy and expensive), reducing thus the speed of rotation, or to increase their relative thickness, thus, worsening aerodynamic quality and reducing Cp. Both will considerably reduce or kill the total benefit.

New design of wind turbines.

The only way to raise wind loading on the blade in the vertical turbine with a horizontal axis, without causing their destruction and worsening their aerodynamic quality, is increase in quantity of blades and a fastening their ends by a ring in a shape of an airfoil. In such design the wind loading onto blades does not make any bending influence to the blade, but extending (especial small conicity a rotor and its inclination providing) as the external ring will not let the blades to be bent, similarly to the spokes in a rim of a wheel of a bicycle. Besides fixing of the ends of blades stabilizes position of blades, practically, excluding probability of flutter. As it is necessary to change the angle of turn of the blade, connection of the end of the blade with a ring should be mobile and have the bearing. The most loaded part in such design will not be the blades, but an external ring.

The quantity of blades is taken out of reasons of sufficiency at uniform loading of a ring. Optimum quantity of blades will equal 8 – 9. Taking into account reduction of bending loading onto the blade, each of them can be made less wide, less thick, less heavy and, as consequence, less expensive. Also appears an opportunity of increasing rated power of a rotor, having increased rated speed of wind, and essentially increase its sizes at preservation of strength of a design.

Aerodynamic quality of a design.

At increase in quantity of blades from 2 – 3 up to 8 – 9 speed of moving of the blade, corresponding to optimum value "e", will decrease, that will lead to reduction of losses because of friction and, as consequence, to increase of Cp. Besides due to presence of an external ring so-called trailer losses will practically disappear that will allow to increase the width of the end of the blade and to choose it from the point of view of an optimality of number "e". Reduction of the blade bending force (even at increase in capacity) will allow to reduce relative thickness of the blade up to the values corresponding to high aerodynamic quality, which also will raise Cp. Additional increase of aerodynamic quality can be achieved by applying so-called laminarized airfoil the use of which in the traditional wind turbine is limited by the big relative thickness and increase of probability of flutter because of displacement of the center of rigidity in such structures.

Results of calculations confirm above mentioned reasoning about increase of aerodynamic quality. So average received Ср = 56,9 %, and with the use of laminarized airfoil and more careful optimization of the sizes of blade Cp will exceed 60 %. The external ring will not worsen aerodynamic quality, and force of pressure of a wind because of the ring onto rotor will increase insignificantly even at very strong wind. As energy of losses of a rotor is spend basically for noise, and in a new design losses are considerably reduced, also the noise level of the turbine will strongly decrease.

The general benefit in annual gathering of the wind energy.

The comparative analysis also we shall carry out for 4 basic wind classes 4, 5, 6 and 7 (for districts with mid-annual speeds 5,8; 6,2; 6,7 and 8,2 m/s) and parameters Weibull K – 1,5; 2 and 2,5.

Tab. 2. Gross annual production of wind energy, GWh / year
K = 1,5, for classes K = 2,0, for classes K = 2,5, for classes
4 5 6 7 4 5 6 7 4 5 6 7
3 blades, P = 4,5 MW 13,38 14,38 15,42 17,38 13,92 15,45 17,16 20,77 14,04 15,91 18,07 23,00
8 blades, P = 20 MW 33,37 38,00 43,59 58,07 28,01 33,38 40,26 60,25 24,26 29,79 37,21 60,45
Benefit 2,494 2,644 2,826 3,340 2,012 2,160 2,346 2,900 1,728 1,872 2,060 2,628

Results of calculations show, that annual gathering with application of the wind turbine of new type is 2 – 3 times greater, then that of traditional turbine, depending on a wind class and factor Weibull K of district of installation of the turbine. In other words, one new turbine replaces 2 – 3 traditional turbines of the same size, and it is already essential benefit and it the greater, the higher the wind class and the less parameter Weibull K of district of installation of the turbine is.

Detailed estimation of expenses for all types of turbines is difficult to carry out. It is usually made by each manufacturer of wind turbines individually, taking into account their own conditions and opportunities. However, approximately it is possible to assume, that the increase of expenses will make not more than 20 – 50 % in comparison with traditional turbines of the same size.

Thus, summing up estimations of efficiency, it is possible to draw a conclusion, that application of turbines of new type will raise general efficiency (while reducing the cost of wind energy) approximately 1,5 – 2,5 times. Besides there is an additional reserve in increase in the sizes of wind turbines up to diameters of a rotor of 250 – 300 meters at increase of rated power of each turbine up to 100 – 200 МW. The increase in the sizes of turbines will raise their efficiency in complement, at least in 1,5 - 2 times, and finally will allow to lower cost of wind energy in 3 – 5 times.

Such essential expected growth of efficiency in use of the wind turbines of new type allows considering, that the future of the big wind power will be based on application of that kind of turbines.

Answers to the majority of questions and the doubts which have arisen at reading of this reduced version of article, you will find in the full version and in the calculations applied to it. Also read page F.A.Q. at www.windrotor.info

 

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