J. Cataldo (1), C. López(2)

(1)Instituto de Mecánica de los Fluidos e Ingeniería Ambiental, (2) Centro de Cálculo

Facultad de Ingeniería, J.H. y Reissig 565, CP11300, Montevideo, Uruguay.

ABSTRACT

Numerical and physical modelling techniques are applied jointly to deduce the velocity wind field up to the meteorogical microscale in Uruguay. The calculated wind velocities in some points are verified against measurements taken with cup anemometers.

INTRODUCTION.

Wind climate determination is the common problem in wind power assessment programs. In Uruguay, as in other places, the sites of principal interest for wind power exploitation are over complex terrain zones where measurements of wind velocity do not exist. Between the methods to deduce the wind velocity field can be mentioned forrest indicators (Druyan,L.,1985), on site direct measuring for short periods (Barros et.al.,1983), physical modelling when some data are known near to the place of interest (Neal,D.,1979) and extrapolation of routine meteorological data by mass consistent models (Endlich, et.al., 1982 Tombrou,M.,et.al., 1990, Rato, et.al., 1994). The methodology applied to estimate the hourly wind field in Uruguay up to the meteorological microscale uses a combination of numerical and physical modelling.

NUMERICAL MODEL. METHOD DESCRPTION.

The numerical model used to solve the mean wind velocity field up to meterological mesoscale is a mass consistent code, similar to the one presented in Sherman, 1978. This model uses as data the hourly mean wind velocity time series obtained in the weather stations located in the volume to be studied. This volume (Fig. 1) has a 500kmx500km base and its height is equal to the one of the atmospheric boundary layer (500 to 1500m).

A first guess of the mean wind field is obtained by a weighting mean of the known mean velocities, where the weighting factors are proportional to the inverse of the distance between the site and the weather station. The mean velocity field is calculated as the one which makes the integral square difference minimum between the first guess and the mean velocity field and verifying the equation of continuity. The equation obtained is a Poisson equation which is solved using the finite element method. López, 1992 points out details of the methodology and compares calculation and theory for

potential flows.

The data of the velocity vectors are expressed using the principal patterns (eigenvectors of the covariance matrix of the data).

The aforementioned calculations are applied to the time mean of the velocity vectors and to each principal pattern. The results obtained applying the methodology to the three or four principal patterns with higher eigenvalues shows little difference with the results obtained for all the eigenvectors. Table 1 shows the mean velocity values calculated using the three eigenvectors with higher eigenvalues and all eigenvectors at different sites.

N^o of vectors

Site 3 10

C. del Toro 26.6 27.2

Caracoles 27.5 27.8

Animas 24.0 24.6

José Ignacio 24.0 24.6

Aigua 23.0 23.4

Table 1 - Calculated mean velocity values.

Fig. 2 shows the mean velocity field obtained at 30m over the terrain in the grid nodes with 15km mesh size.

Also, the principal pattern technique was used to study the quality of the ensambles velocity data.

PHYSICAL MODEL.

The physical modelling was used to solve the wind velocity field up to the meteorological microscale. The Atmospheric Boundary - Layer flow (ABL) was modelled for "high wind" conditions. The obtained mean velocity profile was adjusted to a logarithmic law inside the inertial sub-layer and to power law over the wake sub-layer. The intensity of turbulence profile were compared to the results reported by Harris, 1969 and E.S.D.U., 1985. The measured length scale of the turbulence profile were compared with field results presented in the last reference and Counihan, 1975. From the match between measured spectral peak and the von Karman spectral peak, the geometrical scale (1/6000) used to compare all the aforementioned magnitudes was obtained.

The characteristic roughness length in the zone to be studied is 5cm and the heigth of the boundary-layer was initially estimated in 600m.

The method reported first in Counihan, 1969 and later in Robins, 1979 for ABL physical simulation was used. The physical modelling was made in a wind tunnel with a 1.2mx1.6mx3.6m test section. The measurements of velocity were made with a TSI hot-wire anemometer. The data adquisition was made using a spectrum analyzer Hewlett-Packard 3582A and a National A/D converter. The hot-wire probes were positioned using a four freedom degrees robot. Figures 3, 4 ,5 and 6 show the mean velocity profile, intensity of turbulence profile, the longitudinal scale length of the turbulence profile and the spectrum of turbulence in a postion upstream of the model. Cataldo, 1992 gives more details about this physical simulation.

The terrain was modelled to scale 1/6000 as was deduced before. The models

were constructed following the method described in Neal, 1979 and they were located where the flow in the wind tunnel was able to be considered self-preserving. The measures were made over a set of points of the model, where the existence of a wind farm is assumed. The local speed-up and the intensity of turbulence were deduced at 30m (at the prototype scale) over each point.

FIELD MEASUREMENTS.

The field measurements used in this paper were undertaken as part of the URU/87/028 program and they were obtained from cup anemometer and vane B.A.P.T. mounted on 10m towers. The on-site measuring was made for short periods as part of the overall methodology reported in Barros,et. al., 1983. Some anemometers were located in homologous sites to the model selected points.

Applying the speed-up factors deduced from the physical model to the wind velocity time series obtained from the numerical modelling the wind velocity time series was obtained at the sites where there are field measurements. The results obtained in some of these sites were used to calibrate the calculations. Thus, several statistical parameters of these time series were obtained at the different sites, specially for the interval of time with field measurements. The same statistical parameters were calculated for the field measurements.

Table 2 shows the calculated and measured mean velocity values.

Site Mean cal. Mean meas. Dif.

vel. vel.

(m/s) (m/s) (%)

C. del Toro 24.67 24.74 -0.3

S. de Animas 25.65 25.32 1.3

S. de Caracoles 28.01 29.49 -5.0

José Ignacio 20.27 19.62 3.3

Table 2 - Mean velocities.

A maximum difference of 5% can be observed.

Fig. 7 shows the probability density function calculated and measured for a calibration site. Fig. 8 shows the same for a comparison site. In all cases a calculated function smoother than the measured one is observed, which to the elimination of experimental errors from the calculations can be assigned.

Fig. 9 shows the velocity difference between correspond components of calculated and measured time series. Fig 10 shows the difference between the wind direction for the mentioned components.

Table 3 shows the energy calculated with the wind velocity time series calculated and measured at the considered points using the perfomance curve of a real wind turbine.

Site Cal. Meas.

(kw.h/year)

C. del Toro 816020 818340

S. de Caracoles 954346 1004772

Tabla 3 - Calculated energy.

The described method provides a relatively fast and low cost tool that

provides a good estimation of the wind mean velocity and turbulence component in complex terrain regions of interest in the choice of locations for Wind farms.

After the calibration is made and experimental errors are eliminated, the mean velocity values deduced (Table 2) and the estimation of energy (Table 3) show a low difference with the measured time series. Also, it is a good method to make comparisons between different sites (compare Tables 2 and 3) where more intensive studies must to be done. The time series calculated shows a low discrepance with the measured ones (see figs. 9 and 10).

The method also allow us to deduce the turbulence characteristics of the sites necessary to find out structural problems and control system operation prior of the installation.

Two difficulties should be pointed out about this method: 1)the results are highly dependent on the data quality, but following the principal components method used in this paper the quality can be studied; and 2)the kind of terrain can limit the test directions of the models, which may imply that the speed-up factors for those directions must be assumed.

This method provides a fast and low cost tool to make a first relatively conservative estimation of the available wind power in extensive zones of complex terrain.

REFERENCES.

Barros,V. and Rodríguez Seró, J.(1983) Measurement strategies: use of short observation records for estimating the annual wind variations, Centro Nacional Patagónico, Conicet, Argentina.

Cataldo,J. and Farell,C.(1992) Comparación entre simulaciones físicas de flujos tipo Capa Límite Atmosférica a escalas 1/500 y 1/6250, XV Congreso Latinoamericano de Hidráulica, Cartagena.

Counihan, J.(1969) An improved method of simulating an atmospheric boundary-layer in a wind tunnel, Atmos. Env.,vol.3, 197-214.

Counihan, J.(1975) Adiabatic atmospheric boudary-layers: A review and analysis of data from the period 1880-1972, Atmos. Env., vol. 9, 871-905.

Druyan,L.(1985) Wind climate studies for WECS siting, J. of Climatology, vol. 5, 95-104.

Endlich,R.M., Ludwig,F.L., Bhumralkar,C.M. and Estoque,M.A.(1982) A diagnostic model for estimating winds at potential sites for wind turbines, J. Appl. Meteorol., 21, 1441-1454.

E.S.D.U. (1985) Characteristics of atmospheric turbulence near the ground. Part II: single point data for strong winds (neutral atmosphere), Item Number 85020.

Harris,I.(1969) Measurements of wind structure at heigths up to 598ft above ground level, Symposium on Wind Effects on Buildings and Structures Organized by Loughborough University of Technology National Physical Laboratory Royal Aeronautical Society.

López,C.L.(1992) Estimación del campo de velocidades a partir de un número insuficiente de datos, 1^a Reunión del Grupo de Trabajo sobre Hidromecánica, División Latinoamerica de la IAHR, Salto Grande, Marzo.

Neal,D.(1979) Wind flow and structure over Gebbies Pass, New Zealand: a comparision between wind tunnel simulation and field measurements, Ph.D. thesis, University of Canterbury, Christchurch, New Zealand.

Rato, C, Festa, R, Romeo, C, Fruento, O and Galluzzi, M.(1994) Mass-Consistent models for wind fields over complex terrain: The state of the art, Environmental Software, 9, 247-268.

Robins, A.G.(1979) The development and structure of simulated neutrally stable atmospheric boundary-layers, J. of Industrial Aerodynamics, vol. 4, 71-100.

Sherman,C.(1978) A mass-consistent model for wind fields over complex terrain, J. Appl. Meteorol., 17, 312-319.

Tombrou,M. and Lalas, D.P.(1990) A telescoping procedure for local wind energy potential assessment, European Community Wind Energy Conference, Madrid.