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Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.

As part of the implementation of wind energy evaluation and application in Mexico, at the University of Quintana Roo, division of Science Engineering Energy Systems Laboratory, is developing a methodology for preliminary evaluation of the wind energy potential, the section is trying to use computer programming in order to obtain a standard methodology that can be applied to rural areas in which the wind energy is considered a potential source to generate mechanical energy to use in pumping systems or electricity generation.

It is necessary to know the wind characteristics to predict the amount of energy that can be extracted by any wind energy converter system as well as proving the feasibility of the system in order to use the wind potential. Monthly and Annual wind distributions can be calculated and plotted from the wind speed data, since they depend on knowing how much energy can be extracted and in what period of time due to the wind aleatory characteristics. It is also necessary to analyze the aerodynamic theories of wind rotors and the pumping machines performances to match them to a wind powered pumping system and achieve to extract the maximum power from the wind in a particular place.

The energy yield of a wind turbine can be predicted with statistically validated values of mean wind speed, wind speed distribution and the vertical wind profile. Statistically reliable values required measurements at long periods of time. It is necessary the specification of a reliable value for the long-term mean annual wind speed, for this is required the mean value taken over at least ten years. Measurements taken by oneself over a period of only a few months with simple equipment are not suitable for this purpose.

Wind measurement over a relatively short period of time, for instance one year, offers the possibility of comparing these values with the long-term data measured within the same period of time at the closest location at which the long-term mean value is known. This permits the verification of whether and to what extent the local value deviates from the value ascertained for the larger area.

The wind speed is plotted against time, indications as to the turbulence intensity can be derived from the wind variations. From the point of view of the prudently planning operator, wind measurements having this objective make sense and may even be necessary.

The measurements of wind velocity requires of transducers to convert an electric signal in a velocity reading. These devices are mounted on top of or on side arms of a mast or a tower (

In the past, mechanical anemographs were used which plotted wind speed and direction on a paper strip. Mean values were determined with the help of a plotting rule. Nowadays, electronic recorders are used almost exclusively where the measured data is stored on tape or in a chip. This provides for immediate data evaluation by computer.

The manufacturers offer an almost endless variety of suitable storage devices and analyzers. Figures 2-6 show the wind data acquisition for a period of 5 months with a period of acquisition of 10 minutes. During the period of time was done a mean of the total data in 10 minutes with 10 reading per second. The data meaning was saved in a memory which include temperature, wind velocity, humidity and density.

It is quite logical to look for mathematical functions that approach the frequency and duration curves as closely as possible, as a tool to predict the output of windmills later on. In this respect much attention has been given to the Weibull distribution [

The Probability Density Function, represented in this case by the velocity frequency curve given by Equation (2).

The average wind speed can be expressed as a function of c and k or vice versa; c is a function of and k. The integral found cannot be solved, however, it can be reduced to a standard integral, the so-called gamma function.

With

F(V) and f(V) yields Equation (5) and Equation (6).

Calling

The Weibull distribution shows its usefulness when the wind data of one reference place are being used to predict the wind regime in the surrounding of that place. There are some methods to extract the Weibull parameters k and c from a given set of data [

Weibull Paper

Standard Deviation Analysis

Energy Pattern Factor

Empirical Method

Maximum Likelihood Method.

The Maximum Likelihood Method can be programmed, which is very useful to have an automatic process while obtaining the Weibull parameters. The other methods are considered with less accurate than this, one because of their graphical and empirical characteristics. Although they are used as a reference to evaluate the results of the maximum likelihood method gives.

culating the Weibull distribution Parameters. The F(X) curve (

The f(X) curve (

The fraction of extracted power that is called power coefficient Cp, in practice seldom exceeds 40% if measured as the mechanical power of a wind rotor. The subsequent conversion into electrical power or pumping power gives a reduction in available power, depending on the efficiency h of the transmission and pump or generator. A further reduction of the available power is caused by the fluctuations in speed and directions, which an actual windmill experiences in the field.

The design of the rotor consists in reach the next parameters:

Radius

The design tip speed ratio

Number of blades

It is also important to select an adequate airfoil based on a design lift coefficient and the corresponding angle of attack.

The radius of the rotor must be calculated with the required energy output E in a year (or in a critical month) given the average local wind speed and its distribution. An approximation for water pumping windmills is given by:

In that way, the energy output E and the radius for a month or for a year can be estimated. The choices of l_{d} and B are more or less related as the guidelines in

The type of load determine l_{d}: water pumping windmills driving piston pumps have 1 < l_{d} < 2 and electricity generating wind turbines usually have 4 < l_{d} < 10.

Accordingly, if one wishes to use wind rotors for water pumping which are easy to manufacture and cheap, one might be confined to using simple airfoils shape such as curved plate or flat plates, whose aerodynamics characteristics, this is to say L/D ratio, are low (CL/CD = 10 - 30).

Traditionally single-acting lift pumps have been used in wind powered pumping systems and its characteristics have to be chosen based on the water output requirements at the site.

The design wind speed (V_{d}) of the system is the wind speed at which the overall efficiency reaches a maximum. This speed can be calculated by realizing that at each wind speed, the net power supplied by the rotor-pump combination must be equal to the hydraulic power to pump the water.

l_{d } | B |
---|---|

1 | 6 - 20 |

2 | 4 - 12 |

3 | 3 - 6 |

4 | 2 - 4 |

5 - 6 | 2 - 3 |

6 - 7 | 1 - 2 |

The expression given by Equation (10) means that the design wind speed can be modified by changing the stroke of the pump or by installing another size pump. A change in water lifting head also changes the design wind speed. For a first estimation the average local wind speed can be selected as the design wind speed.

The availability of wind energy is highly variable and is likely to be intermittent. As a rule-of thumb, expect an average of 6 to 8 hours per day of water pumping at a rate specified for a wind velocity of 25 km/h. Hand pumping can be done on some windmill pumps in emergencies, but wind-powered pumping units should be used in conjunction with storage facilities capable of meeting three or four days water demand as a back-up supply during periods of low wind.

If the windmill is used to generate electricity to power an electrically-powered pump, it will probably be necessary to store the electricity in batteries due to the variability in generation. Therefore, a pump powered by an electrical motor for use in conjunction with a windmill that generates electricity should have a Direct Current motor. For such systems, it is important to use good-quality deep-cycle batteries and to incorporate electrical controls such as blocking diodes and charge regulators to protect the batteries.

The positive-displacement cylinder pump is the most common type of pump used in pumping systems using wind turbines. These pumps are connected to a gear box before the wind turbine shaft,

The air-lift pump is an alternative to use the wind energy in pumping systems. The air-lift pump is a type of deep-well pump. This pump is used in dirty water and high viscosity fluids. This pump has no moving parts, other than an air compressor driven by the windmill, and the efficiency of the air compressor is an important factor in determining the overall efficiency of the pump. Compressed air is sent to the well to this boost water to a discharge pipe. It is possible to make water flow calculations for different wind speeds using Equation (11), which includes the volumetric efficiency.

The water flow calculations can be plotted (

This expression can be reduced to Equation (13).

If a pump is coupled to a wind rotor at a given wind speed such that the mechanical power of the rotor is equal to the mechanical power exerted by the pump. This working point can be found by intersection of the rotor curve and the pump curve. Other expression to calculate the water output per day in a month or in a year period for a given average local wind speed and knowing the rotor diameter, the head and the pump-rotor system efficiency [

It is possible to use Equation (14) to calculate the water output per day by varying the rotor diameter and using the average wind speed. The rotor-pump system efficiency value can be 12%, which is used for first estimations in wind powered pumping windmills [

To facilitate the judgment to what extent a given location might be suitable for the utilization of wind energy it is necessary to know the daily, monthly, annual wind pattern, as well as energy produced per month, per year. It is often important to know the number of hours that a windmill will run, then a velocity frequency histogram is obtained for the month of May (

If the histogram is approximated by a smooth curve through the value at the middle of each interval then a Duration Curve results (

By applying Equations (11) - (14) the average water flow in (litter/hr) is obtained and it is possible to compare the results in order to have different first estimation methods to know if a place has potential for the application of wind powered water pumping systems.

from Equations (11) - (14) for a 2.2 m rotor diameter and a 10 m water lifting head.

The efficient extraction of power from the wind is governed not only by the performance of the wind rotor but also the wind behaviour and the response of the entire system [

From Equations (11) - (14) and the duration distribution, it is possible to calculate the rate of water that a pump can rise in a height of 10 m, considering that the diameter of the windmill was 2 m.

^{3} per day.

V (m/s) | t (hr) | Cp | P (W) | Q (m^{3}) |
---|---|---|---|---|

3.5 | 225 | 0.1 | 8.22 | 20.37 |

4.5 | 200 | 0.18 | 31.43 | 69.28 |

5.5 | 150 | 0.23 | 73.33 | 121.22 |

6.5 | 75 | 0.28 | 147.36 | 121.80 |

7.5 | 38 | 0.27 | 218.29 | 91.41 |

8.5 | 5 | 0.28 | 329.53 | 18.16 |

9.5 | 1 | 0.27 | 443.62 | 4.89 |

The methodology used to analyze the wind data allows establishing a preliminary evaluation over the whole country. However, it depends on availability of wind data. It is therefore possible to know the possibility of eolian utilization performing a previous technical study in order to know the resource potential. With the results obtained, it is possible to compare the rotor geometric characteristics obtained for specific water con- sumption with other machines existing in the market in order to determine its feasibility.

The theoretical approach for the description of the performance of water pumping windmills could be a powerful tool for the selection and design of equipment, together with its use for making realistic estimates of a wind powered lift pump when coupled to a particular wind regime. Another advantage of this work is that it is possible to develop economic feasibility studies about the technology for aerial machine implementation in a given location. These studies must be based on exhaustive resource measurements, necessary to consolidate an eolian project.

Velázquez, M.T., Rodríguez, J.H., Carmen, M.V.D., Murrieta, F.E.F. and Eslava, G.T. (2016) Application of the Weibull Distribution to Estimate the Volume of Water Pumping by a Windmill. Journal of Power and Energy Engineering, 4, 36-51. http://dx.doi.org/10.4236/jpee.2016.49004

F(V) Cumulative Distribution Function [--]

f(V) Probability Density Function [s/m]

G(x) Gamma Function [--]

k Weibull Shape Factor [--]

c Weibull Scale Factor [m/s]

V Wind Speed [m/s]

V_{d} Design Wind Speed [m/s]

F(X) Reduced Cumulative Distribution Function [--]

f(X) Reduced Probability Density Function [--]

X Reduced Wind Velocity [--]

P_{hyd} Hydraulic Power [W]

P_{mech} Mechanical Power [W]

A Rotor Area [m^{2}]

r_{a} Air Density = 1.225 [kg/m^{3}]

r_{w} Water Density = 1000 [kg/m^{3}]

s Stroke (pump) [m]

D_{p} Pump Diameter [m]

Cp_{max} Maximum Power Coefficient [--]

Q Water Flow [m^{3}/s]

Q_{pd} Water Output per Day [m^{3}/day]

g Gravitational Acceleration = 9.81 [m/s^{2}]

H Total Dynamic Load (Head) [m]

R Rotor Radius [m]

l Tip Speed Ratio [--]

l_{d} Design Tip Speed Ratio [--]

B Number of Blades [--]

E Energy Output [W-hr]

T Period Length [hr]

h_{rp} Rotor-Pump System Efficiency [--]

h_{vol} Volumetric Efficiency [--]

h_{mech} Mechanical Efficiency [--]

D Rotor Diameter [m]