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.

Noise Figure Measurement of Differential Amplifiers Using non-Ideal Baluns

This paper analyzes the noise and gain measurement of microwave differential amplifiers using two passive baluns. A general model of the baluns is considered, including potential losses and phase/amplitude unbalances. This analysis allows de-embedding the actual gain and noise performance of the isolated amplifier by using single-ended measurements of the cascaded system and baluns. Finally, measured results from two amplifier prototypes are used to validate the theoretical principles.

Analysis and suppression of reflections in far-field antenna measurement ranges

This paper presents the analysis of the reflections in two kind of spherical far field ranges: one if the classical acquisition where the AUT is rotated and the second one corresponds to the systems where the AUT is fixed and the antenna probe is rotated. In large far field systems this is not possible, but this can be used to the measurement of small antennas, for instance, with the SATIMO StarGate system. In both cases, it is assumed that only one frequency is acquired and the results should be improved cut by cut, in order not to lose the advantages or far field measurements. Finally, some practical results are studied using measurements of one antenna in the outdoor far field facility of LIT INPE in Brazil.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Implementation of the Heated Pulsed Theory using actively heated fiber optics: measurements of soil volumetric water content and soil volumetric heat capacity

Existe una creciente necesidad de hacer el mejor uso del agua para regadío. Una alternativa eficiente consiste en la monitorización del contenido volumétrico de agua (θ), utilizando sensores de humedad. A pesar de existir una gran diversidad de sensores y tecnologías disponibles, actualmente ninguna de ellas permite obtener medidas distribuidas en perfiles verticales de un metro y en escalas laterales de 0.1-1,000 m. En este sentido, es necesario buscar tecnologías alternativas que sirvan de puente entre las medidas puntuales y las escalas intermedias. Esta tesis doctoral se basa en el uso de Fibra Óptica (FO) con sistema de medida de temperatura distribuida (DTS), una tecnología alternativa de reciente creación que ha levantado gran expectación en las últimas dos décadas. Específicamente utilizamos el método de fibra calentada, en inglés Actively Heated Fiber Optic (AHFO), en la cual los cables de Fibra Óptica se utilizan como sondas de calor mediante la aplicación de corriente eléctrica a través de la camisa de acero inoxidable, o de un conductor eléctrico simétricamente posicionado, envuelto, alrededor del haz de fibra óptica. El uso de fibra calentada se basa en la utilización de la teoría de los pulsos de calor, en inglés Heated Pulsed Theory (HPP), por la cual el conductor se aproxima a una fuente de calor lineal e infinitesimal que introduce calor en el suelo. Mediante el análisis del tiempo de ocurrencia y magnitud de la respuesta térmica ante un pulso de calor, es posible estimar algunas propiedades específicas del suelo, tales como el contenido de humedad, calor específico (C) y conductividad térmica. Estos parámetros pueden ser estimados utilizando un sensor de temperatura adyacente a la sonda de calor [método simple, en inglés single heated pulsed probes (SHPP)], ó a una distancia radial r [método doble, en inglés dual heated pulsed probes (DHPP)]. Esta tesis doctoral pretende probar la idoneidad de los sistemas de fibra óptica calentada para la aplicación de la teoría clásica de sondas calentadas. Para ello, se desarrollarán dos sistemas FO-DTS. El primero se sitúa en un campo agrícola de La Nava de Arévalo (Ávila, España), en el cual se aplica la teoría SHPP para estimar θ. El segundo sistema se desarrolla en laboratorio y emplea la teoría DHPP para medir tanto θ como C. La teoría SHPP puede ser implementada con fibra óptica calentada para obtener medidas distribuidas de θ, mediante la utilización de sistemas FO-DTS y el uso de curvas de calibración específicas para cada suelo. Sin embargo, la mayoría de aplicaciones AHFO se han desarrollado exclusivamente en laboratorio utilizando medios porosos homogéneos. En esta tesis se utiliza el programa Hydrus 2D/3D para definir tales curvas de calibración. El modelo propuesto es validado en un segmento de cable enterrado en una instalación de fibra óptica y es capaz de predecir la respuesta térmica del suelo en puntos concretos de la instalación una vez que las propiedades físicas y térmicas de éste son definidas. La exactitud de la metodología para predecir θ frente a medidas puntuales tomadas con sensores de humedad comerciales fue de 0.001 a 0.022 m3 m-3 La implementación de la teoría DHPP con AHFO para medir C y θ suponen una oportunidad sin precedentes para aplicaciones medioambientales. En esta tesis se emplean diferentes combinaciones de cables y fuentes emisoras de calor, que se colocan en paralelo y utilizan un rango variado de espaciamientos, todo ello en el laboratorio. La amplitud de la señal y el tiempo de llegada se han observado como funciones del calor específico del suelo. Medidas de C, utilizando esta metodología y ante un rango variado de contenidos de humedad, sugirieron la idoneidad del método, aunque también se observaron importantes errores en contenidos bajos de humedad de hasta un 22%. La mejora del método requerirá otros modelos más precisos que tengan en cuenta el diámetro del cable, así como la posible influencia térmica del mismo. ABSTRACT There is an increasing need to make the most efficient use of water for irrigation. A good approach to make irrigation as efficient as possible is to monitor soil water content (θ) using soil moisture sensors. Although, there is a broad range of different sensors and technologies, currently, none of them can practically and accurately provide vertical and lateral moisture profiles spanning 0-1 m depth and 0.1-1,000 m lateral scales. In this regard, further research to fulfill the intermediate scale and to bridge single-point measurement with the broaden scales is still needed. This dissertation is based on the use of Fiber Optics with Distributed Temperature Sensing (FO-DTS), a novel approach which has been receiving growing interest in the last two decades. Specifically, we employ the so called Actively Heated Fiber Optic (AHFO) method, in which FO cables are employed as heat probe conductors by applying electricity to the stainless steel armoring jacket or an added conductor symmetrically positioned (wrapped) about the FO cable. AHFO is based on the classic Heated Pulsed Theory (HPP) which usually employs a heat probe conductor that approximates to an infinite line heat source which injects heat into the soil. Observation of the timing and magnitude of the thermal response to the energy input provide enough information to derive certain specific soil thermal characteristics such as the soil heat capacity, soil thermal conductivity or soil water content. These parameters can be estimated by capturing the soil thermal response (using a thermal sensor) adjacent to the heat source (the heating and the thermal sources are mounted together in the so called single heated pulsed probe (SHPP)), or separated at a certain distance, r (dual heated pulsed method (DHPP) This dissertation aims to test the feasibility of heated fiber optics to implement the HPP theory. Specifically, we focus on measuring soil water content (θ) and soil heat capacity (C) by employing two types of FO-DTS systems. The first one is located in an agricultural field in La Nava de Arévalo (Ávila, Spain) and employ the SHPP theory to estimate θ. The second one is developed in the laboratory using the procedures described in the DHPP theory, and focuses on estimating both C and θ. The SHPP theory can be implemented with actively heated fiber optics (AHFO) to obtain distributed measurements of soil water content (θ) by using reported soil thermal responses in Distributed Temperature Sensing (DTS) and with a soil-specific calibration relationship. However, most reported AHFO applications have been calibrated under laboratory homogeneous soil conditions, while inexpensive efficient calibration procedures useful in heterogeneous soils are lacking. In this PhD thesis, we employ the Hydrus 2D/3D code to define these soil-specific calibration curves. The model is then validated at a selected FO transect of the DTS installation. The model was able to predict the soil thermal response at specific locations of the fiber optic cable once the surrounding soil hydraulic and thermal properties were known. Results using electromagnetic moisture sensors at the same specific locations demonstrate the feasibility of the model to detect θ within an accuracy of 0.001 to 0.022 m3 m-3. Implementation of the Dual Heated Pulsed Probe (DPHP) theory for measurement of volumetric heat capacity (C) and water content (θ) with Distributed Temperature Sensing (DTS) heated fiber optic (FO) systems presents an unprecedented opportunity for environmental monitoring. We test the method using different combinations of FO cables and heat sources at a range of spacings in a laboratory setting. The amplitude and phase-shift in the heat signal with distance was found to be a function of the soil volumetric heat capacity (referred, here, to as Cs). Estimations of Cs at a range of θ suggest feasibility via responsiveness to the changes in θ (we observed a linear relationship in all FO combinations), though observed bias with decreasing soil water contents (up to 22%) was also reported. Optimization will require further models to account for the finite radius and thermal influence of the FO cables, employed here as “needle probes”. Also, consideration of the range of soil conditions and cable spacing and jacket configurations, suggested here to be valuable subjects of further study and development.

Waves, analytical signals, and some postulates of quantum theory

In this paper we apply the formalism of the analytical signal theory to the Schrödinger wavefunction. Making use exclusively of the wave-particle duality and the rinciple of relativistic covariance, we actually derive the form of the quantum energy and momentum operators for a single nonrelativistic particle. Without using any more quantum postulates, and employing the formalism of the characteristic function, we also derive the quantum-mechanical prescription for the measurement probability in such cases.