Sonic anemometry of planetary atmospheres

The application of a recently developed model of sonic anemometers measuring process has revealed that these sensors cannot be considered as absolute ones when measuring spectral characteristics of turbulent wind speed since it is demonstrated that the ratios of measured to real spectral density functions depend on the composition and temperature of the considered planetary atmosphere. The new model of the measuring process of sonic anemometers is applied to describe the measuring characteristics of these sensors as fluid/flow dependent (against the traditional hypothesis of fluid/flow independence) and hence dependent on the considered planetary atmosphere. The influence of fluid and flow characteristics (quantified via the Mach number of the flow) and the influence of the design parameters of sonic anemometers (mainly represented by time delay between pulses shots and geometry) on turbulence measurement are quantified for the atmospheres of Mars, Jupiter, and Earth. Important differences between the behavior of these sensors for the same averaged wind speed in the three considered atmospheres are detected in terms of characteristics of turbulence measurement as well as in terms of optimum values of anemometer design parameters for application on the different considered planetary atmospheres. These differences cannot be detected by traditional models of sonic anemometer measuring process based on line averaging along the sonic acoustic paths.

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k W1=1/l (where k W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k W1=C l /l, where C l is usually lesser than unity and depends on all the new parameters taken into account by the present model.

On sonic anemometer measurement theory

In this paper a model for the measuring process of sonic anemometers (ultrasound pulse based) is presented. The differential equations that describe the travel of ultrasound pulses are solved in the general case of non-steady, non-uniform atmospheric flow field. The concepts of instantaneous line-average and travelling pulse-referenced average are established and employed to explain and calculate the differences between the measured turbulent speed (travelling pulse-referenced average) and the line-averaged one. The limit k1l=1 established by Kaimal in 1968, as the maximum value which permits the neglect of the influence of the sonic measuring process on the measurement of turbulent components is reviewed here. Three particular measurement cases are analysed: A non-steady, uniform flow speed field, a steady, non-uniform flow speed field and finally an atmospheric flow speed field. In the first case, for a harmonic time-dependent flow field, Mach number, M (flow speed to sound speed ratio) and time delay between pulses have revealed themselves to be important parameters in the behaviour of sonic anemometers, within the range of operation. The second case demonstrates how the spatial non-uniformity of the flow speed field leads to an influence of the finite transit time of the pulses (M≠0) even in the absence of non-steady behaviour of the wind speed. In the last case, a model of the influence of the sonic anemometer processes on the measurement of wind speed spectral characteristics is presented. The new solution is compared to the line-averaging models existing in the literature. Mach number and time delay significantly distort the measurement in the normal operational range. Classical line averaging solutions are recovered when Mach number and time delay between pulses go to zero in the new proposed model. The results obtained from the mathematical model have been applied to the calculation of errors in different configurations of practical interest, such as an anemometer located on a meteorological mast and the transfer function of a sensor in an atmospheric wind. The expressions obtained can be also applied to determine the quality requirements of the flow in a wind tunnel used for ultrasonic anemometer calibrations.

Deviations of cup anemometer rotational speed measurements due to steady state harmonic accelerations of the rotor

The measurement deviations of cup anemometers are studied by analyzing the rotational speed of the rotor at steady state (constant wind speed). The differences of the measured rotational speed with respect to the averaged one based on complete turns of the rotor are produced by the harmonic terms of the rotational speed. Cup anemometer sampling periods include a certain number of complete turns of the rotor, plus one incomplete turn, the residuals from the harmonic terms integration within that incomplete turn (as part of the averaging process) being responsible for the mentioned deviations. The errors on the rotational speed due to the harmonic terms are studied analytically and then experimentally, with data from more than 500 calibrations performed on commercial anemometers.