Cup Anemometer Behavior in Turbulent Environments

Leif Kristensen Risø National Laboratory, Roskilde, Denmark

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Abstract

The behavior of the cup anemometer rotor in turbulent atmospheric flow is discussed in terms of a general equation of motion. This equates the rate of change s̃̇ of the rotation rate of the rotor to a forcing F(s̃, , w̃), which is proportional to the torque and a function of and of the total horizontal and the vertical wind velocity components, , and w̃, respectively. To determine the so-called overspeeding, it is necessary to carry out first-and second-order perturbation calculations around the response curve obtained in a laminar flow. From this curve, which for the purpose of this paper can be considered linear, five constraints are derived between the first and second partial derivatives of F. These constraints provide sufficient information for deriving an expression for the overspeeding to which four distinctly different biases contribute—one for each of the velocity components and one from the covariance between streamwise velocity components ũ and w̃. A phenomenological model of F in terms of the response distance ℓ, the distance constant L, a third instrument length scale Λ, and two dimensionless constants μ1 and μ2, defining the angular response, makes it possible to quantify the four terms in the overspeeding expression. It turns out that the most significant bias in the mean wind speed is due to lateral velocity fluctuations. Under certain conditions it may be larger than 10%. It is shown how it is possible to reduce all the other biases to acceptable levels. The bias from the lateral velocity fluctuations can also be suppressed significantly by combining the cup anemometer with a wind vane and using a signal processing technique called the vector wind-run method.

Corresponding author address: Dr. Leif Kristensen, The Pennsylvania State University, Dept. of Meteorology, 503 Walker Building, University Park, PA 16802.

Email: leif.kristensen@risoe.dk

Abstract

The behavior of the cup anemometer rotor in turbulent atmospheric flow is discussed in terms of a general equation of motion. This equates the rate of change s̃̇ of the rotation rate of the rotor to a forcing F(s̃, , w̃), which is proportional to the torque and a function of and of the total horizontal and the vertical wind velocity components, , and w̃, respectively. To determine the so-called overspeeding, it is necessary to carry out first-and second-order perturbation calculations around the response curve obtained in a laminar flow. From this curve, which for the purpose of this paper can be considered linear, five constraints are derived between the first and second partial derivatives of F. These constraints provide sufficient information for deriving an expression for the overspeeding to which four distinctly different biases contribute—one for each of the velocity components and one from the covariance between streamwise velocity components ũ and w̃. A phenomenological model of F in terms of the response distance ℓ, the distance constant L, a third instrument length scale Λ, and two dimensionless constants μ1 and μ2, defining the angular response, makes it possible to quantify the four terms in the overspeeding expression. It turns out that the most significant bias in the mean wind speed is due to lateral velocity fluctuations. Under certain conditions it may be larger than 10%. It is shown how it is possible to reduce all the other biases to acceptable levels. The bias from the lateral velocity fluctuations can also be suppressed significantly by combining the cup anemometer with a wind vane and using a signal processing technique called the vector wind-run method.

Corresponding author address: Dr. Leif Kristensen, The Pennsylvania State University, Dept. of Meteorology, 503 Walker Building, University Park, PA 16802.

Email: leif.kristensen@risoe.dk

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