A theoretical study of cup and vane anemometers

Abstract

SUMMARYThe predictions of a simplified theory of anemometers are compared with observation. The theoretical response of cup and vane anemometers to steady and varying flows are derived analytically It is found that the mean indicated windspeed can be overestimated by as much as 20 per cent and that and by using an analogue computer.the form of fluctuations is distorted and their amplitude considerably reduced.

Improved analytical method to study the cup anemometer performance

“…From equation (5) and averaging its value along one turn, which is equal to zero [4,8,9,12,20], it is possible to derive the following expression:…”

“…This model gives information based on the aerodynamic forces on a single cup, considering its angle in relation to the incoming wind flow but not any rotational effect. The 3-cup analytical model [8,9] represents an improvement, not only in relation to the results [4], but also in relation to the possibilities of the model. The effects of rotor asymmetries (rotor damaged, or one cup missing) have been successfully studied with the 3-cup analytical model [4,10,11].…”

Aerodynamic Analysis of Cup Anemometers Performance: The Stationary Harmonic Response

“…In tune with this effect, it should also be said that other experimental results have already demonstrated the direct relationship between the slope of the anemometer transfer function, A , and the front area of the cups [44]: $\begin{array}{c}A=\frac{\mathrm{1}}{N_p}{A}_r=\frac{\mathrm{1}}{N_p}\left(\frac{\text{d}{A}_r}{\text{d}{R}_{rc}}{R}_{rc}+A_{r\mathrm{0}}\right),\end{array}$ where d A r /d R rc depends on the aerodynamic forces on the cups (for rotors equipped with the same conical cups tested in the present work, it was found that this coefficient has constant value with very little or no correlation to the cups' size) and A r 0 strongly depends on the cups' front area, S c . Finally, it should also be said that as far as the authors know, this particular effect of the cups' size has not been included in the different analytical models developed to study cup anemometer behavior [30, 31, 33, 38, 40]. These models are based on wind speed, cup aerodynamic coefficients, and cup and rotor geometries and take as starting point that the behavior of cup anemometers is mainly driven by aerodynamic forces, the frictional torque being much lower in comparison [37, 49].…”

“…The aerodynamic forces on a single cup have been correlated with the aforementioned anemometer performance in two different ways, by means of analytical models correlated with experimental testing [30, 31, 33, 38] and by means of a direct comparison based on experimental calibration [48]. In Figure 8, the anemometer constant at 16 m/s wind speed with regard to the calibrations performed on the anemometer equipped with elliptical and porous cups rotors, has been included, respectively, as a function of the eccentricity, $e=\sqrt{\mathrm{1}-{false(b/afalse)}^{\mathrm{2}}}$, and the ratio of the hole diameter to the cup diameter, h /2 R c .…”

“…The transfer function can be rewritten in terms of the anemometer's rotation frequency, f r , instead of the output frequency, f , introducing in the expression the number of pulses per revolution given by the anemometer, N p : $\begin{array}{c}V=A·N_p·f_r+B=A_r·f_r+B.\end{array}$ The expression above is preferable than the preceding one, as it has a clearer physical meaning. Expression (2) also allows a direct comparison between anemometers [29] and between experimental results and analytical models [30, 31]. The number of pulses, N p , is different depending on the anemometer's inner system for translating the rotation into electric pulses.…”