The Coriolis sass flowaeter is modelled using the theory of vibrating beams. Tube deformations for the fundamental mode and the next two nodes of natural (out-of-plane) vibration are worked out for many tube geometries. An improved model taking into account the effects of elastic boundary conditions and added masses of the electromagnetic drive and detectors is also discussed. A method for predicting the optimum detection positions is suggested in relation to signal-to-noise ratio. In addition, an argument for prediction of the effects of a dilute suspension of small bubbles or particles in the fluid is presented. Finally, experimental studies are conducted in order to demonstrate the validity of the theoretical models.

When an electrically conducting fluid moves through a magnetic field, fluid mechanics and electromagnetism are coupled. This interaction is the object of magnetohydrodynamics, a discipline which covers a wide range of applications, from electromagnetic processing to plasma- and astro-physics. In this dissertation, the attention is restricted to turbulent liquid metal flows, typically encountered in steel and aluminium industries. Velocity measurements in such flows are extremely challenging because liquid metals are opaque, hot and often corrosive. Therefore, non-intrusive measurement devices are essential. One of them is the Lorentz force flowmeter. Its working principle is based on the generation of a force acting on a charge, which moves in a magnetic field. Recent studies have demonstrated that this technique can measure efficiently the mean velocity of a liquid metal. In the existing devices, however, the measurement depends on the electrical conductivity of the fluid. In this work, a novel version of this technique is developed in order to obtain measurements that are independent of the electrical conductivity. This is particularly appealing for metallurgical applications, where the conductivity often fluctuates in time and space. The study is entirely numerical and uses a flexible computational method, suitable for industrial flows. In this framework, the cost of numerical simulations increases drastically with the level of turbulence and the geometry complexity. Therefore, the simulations are commonly unresolved. Large eddy simulations are then very promising, since they introduce a subgrid model to mimic the dynamics of the unresolved turbulent eddies. The first part of this dissertation focuses on the quality and reliability of unresolved numerical simulations. The attention is drawn on the ambiguity that may arise when interpretating the results. Owing to coarse resolutions, numerical errors affect the performances of the discrete model, which in turn looses its physical meaning. In this work, a novel implementation of the turbulent strain rate appearing in the models is proposed. As opposed to its usual discretisation, the present strain rate is in accordance with the discrete equations of motion. Two types of flow are considered: decaying turbulence located far from boundaries, and turbulent flows between two parallel and infinite walls. Particular attention is given to the balance of resolved kinetic energy, in order to assess the role of the model. The second part of this dissertation deals with a novel version of Lorentz force flowmeters, consisting in one or two coils placed around a circular pipe. The forces acting on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated to a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional turbulent flow. In both cases, the influence of the geometrical parameters of the coils is systematically assessed.

<div>Particle Image Velocimetry (PIV) is a non-invasive measurement technique which resolves the flow velocity by taking instantaneous snapshots of tracer particle motion in the flow and uses digital image cross-correlation to estimate the particle shift up to subpixel accuracy. The measurement chain incorporates numerous sets of parameters, such as the particle displacements, the particle image size, the flow shear rate, the out-of-plane motion for planar PIV and image noise to name a few, and these parameters are interrelated and influence the final velocity estimate in a complicated way. In the last few decades, PIV has become widely popular by virtue of developments in both the hardware capabilities and correlation algorithms, especially with the scope of 3-component (3C) and 3-dimensional (3D) velocity measurements using stereo-PIV and tomographic-PIV techniques, respectively. The velocity field measurement not only leads to other quantities of interest such as Pressure, Reynold stresses, vorticity or even diffusion coefficient, but also provides a reference field for validating numerical simulations of complex flows. However, such a comparison with CFD or applicability of the measurement to industrial design requires one to quantify the uncertainty in the PIV estimated velocity field. Even though the PIV community had a strong impetus in minimizing the measurement error over the years, the problem of uncertainty estimation in local instantaneous PIV velocity vectors have been rather unnoticed. A typical norm had been to assign an uncertainty of 0.1 pixels for the whole field irrespective of local flow features and any variation in measurement noise. The first article on this subject was published in 2012 and since then there has been a concentrated effort to address this gap. The current dissertation is motivated by such a requirement and aims to compare the existing 2D PIV uncertainty methods, propose a new method to directly estimate the planar PIV uncertainty from the correlation plane and subsequently propose the first comprehensive methods to quantify the measurement uncertainty in stereo-PIV and 3D Particle Tracking Velocimetry (PTV) measurements.</div><div>The uncertainty quantification in a PIV measurement is, however, non-trivial due to the presence of multitude of error sources and their non-linear coupling through the measurement chain transfer function. In addition, the advanced algorithms apply iterative correction process to minimize the residual which increases the complexity of the process and hence, a simple data-reduction equation for uncertainty propagation does not exist. Furthermore, the calibration or a reconstruction process in a stereo or volumetric measurement makes the uncertainty estimation more challenging. Thus, current uncertainty quantification methods develop a-posterior models utilizing the evaluated displacement information and combine it with either image information, correlation plane information or even calibration “disparity map” information to find the desired uncertainties in the velocity estimates.</div><div><br></div>

When an electrically conducting fluid moves through a magnetic field, fluid mechanics and electromagnetism are coupled.<p>This interaction is the object of magnetohydrodynamics, a discipline which covers a wide range of applications, from electromagnetic processing to plasma- and astro-physics.<p><p>In this dissertation, the attention is restricted to turbulent liquid metal flows, typically encountered in steel and aluminium industries. Velocity measurements in such flows are extremely challenging because liquid metals are opaque, hot and often corrosive. Therefore, non-intrusive measurement devices are essential. One of them is the Lorentz force flowmeter. Its working principle is based on the generation of a force acting on a charge, which moves in a magnetic field. Recent studies have demonstrated that this technique can measure efficiently the mean velocity of a liquid metal. In the existing devices, however, the measurement depends on the electrical conductivity of the fluid. <p><p>In this work, a novel version of this technique is developed in order to obtain measurements that are independent of the electrical conductivity. This is particularly appealing for metallurgical applications, where the conductivity often fluctuates in time and space. The study is entirely numerical and uses a flexible computational method, suitable for industrial flows. In this framework, the cost of numerical simulations increases drastically with the level of turbulence and the geometry complexity. Therefore, the simulations are commonly unresolved. Large eddy simulations are then very promising, since they introduce a subgrid model to mimic the dynamics of the unresolved turbulent eddies. <p><p>The first part of this dissertation focuses on the quality and reliability of unresolved numerical simulations. The attention is drawn on the ambiguity that may arise when interpretating the results. Owing to coarse resolutions, numerical errors affect the performances of the discrete model, which in turn looses its physical meaning. In this work, a novel implementation of the turbulent strain rate appearing in the models is proposed. As opposed to its usual discretisation, the present strain rate is in accordance with the discrete equations of motion. Two types of flow are considered: decaying turbulence located far from boundaries, and turbulent flows between two parallel and infinite walls. Particular attention is given to the balance of resolved kinetic energy, in order to assess the role of the model.<p><p>The second part of this dissertation deals with a novel version of Lorentz force flowmeters, consisting in one or two coils placed around a circular pipe. The forces acting on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated to a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional turbulent flow. In both cases, the influence of the geometrical parameters of the coils is systematically assessed. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Fluid dynamicists are always in need of innovative instruments for flow velocity measurements. An ideal instrument would be non-intrusive, have a very fine spatial resolution as well as a very fine temporal resolution, be able to measure three-components of velocity, and be compact. Through recent advancements, laser Doppler velocimetry can now meet all of those requirements making it an important part of aerodynamicist's research toolbox. The first paper presented in this manuscript style thesis explains the development of an advanced three-velocity component, spatially-resolving laser-Doppler velocimetry (LDV) system for highly resolved velocity measurements in situations with limited optical access. The new instrument, a next generation version of the previously developed 'comprehensive' LDV technology, enables measurements of three components of velocity and particle position in the axial direction all through a single transceiving lens. Described here is the design process and the final design for the 'compact, comprehensive' LDV (Comp²LDV). The probe was designed to achieve ± 10 micron root-mean-square uncertainties in axial particle position, which combined with the long measurement volume, allow researchers to obtain a three-velocity-component velocity statistics profiles over a span of approximately 1.5mm without the need for traversing. Results from measurements in a flat plate turbulent boundary layer very near the wall have compared favorably to data from previous studies. The second paper focuses on the motion and evolution of coherent structures in supersonic jet flows and how that relates to the intense noise the flows generate. As a preliminary study to experimentally address these relationships, novel non-intrusive measurements using two-component laser Doppler velocimetry (LDV) have been conducted at exceptionally high data rates to lend insight into the statistical behavior of noise-generating flow structures. A new heated supersonic jet facility has been constructed to provide supersonic flow at total temperatures ratios (T₀/Tₐ) up to 3. In the present work, the instrumentation is validated via comparison of LDV measurements along the centerline of a screeching cold jet with microphone and high-speed shadowgraph results. Reynolds stress spectra are presented for an over-expanded case (nozzle pressure ratio of 3.2) of a design Mach number 1.65 nozzle operated cold (T₀/Tₐ = 1). A preliminary study was then conducted in the near-nozzle shear layer, up to x/d = 4.0, at design nozzle pressure ratio (4.58) and total temperature ratio of 2.0. Results are presented for Reynolds stress time-delay correlations and power spectra at Re_d = 1.1M for this case. The stream-wise Reynolds normal stress spectra are compared with published spectral behavior reported by other researchers, indicating a similar spectral shape in the downstream stations as previously measured with LDV and hot wire anemometry for cold jets, but which differ in shape from density-based techniques. / Master of Science

An advanced laser-Doppler velocimeter is designed to acquire fully-resolved turbulence structural measurements in high Reynolds number two- and three-dimensional turbulent boundary layers. The new instrument combines, for the first time, new techniques allowing for the direct measurement of particle acceleration and sub-measurement-volume-scale position resolution so that second-order 3D particle trajectories may be measured at high repetitions. Using these measurements, several terms in the Reynolds stress transport equations may be directly estimated, giving new data for modeling and understanding the processes leading to the transport of turbulence in boundary layer flows. Due to the unique performance of the probe, many aspects of LDV instrumentation development were addressed. The LDV configuration was optimized for lowest uncertainties by considering the demanding applications of particle position and acceleration measurements. Low noise light detection and signal conditioning was specified for the three electronic channels. A high-throughput data acquisition system allows for exceptional burst rate acquisition. Signal detection and processing algorithms have been implemented which draw from previous techniques but also address distinctive problems with the current system. In short, the instrument was designed to advance the state-of-the-art in LDV systems. Measurements presented include turbulence dissipation rate and fluctuating velocity-pressure gradient correlations that have been measured in 2D and 3D turbulent boundary layers using the unique capabilities of the CompLDV--many of these measurements are the first of their kind ever acquired in high Reynolds number turbulent flows. The flat-plate turbulent boundary layer is studied at several momentum thickness Reynolds numbers up to 7500 to examine Reynolds numbers effects on terms such as the velocity-pressure gradient correlation and the dissipation rate in the Reynolds transport equations. Measurements are also presented in a pressure-driven three-dimensional turbulent boundary layer created upstream from a wing-body junction. The current results complement the extensive data from previous studies and provide even richer depth of knowledge on the most-completely-documented 3D boundary layer flow in existence. Further measurements include the wakes of three circular-cylinder protuberances submerged in a constant pressure turbulent boundary layer. / Ph. D.