Desenvolvimento de um método para correção de curvas de desempenho em bombas centrífugas submersas operando com fluidos viscosos

Electrical Submersible Pump (ESP) is used as an artificial lift technique. However, pumping viscous oil is generally associated with low Reynolds number flows. This condition leads to a performance degradation respect to the performance expected from the regular operation with water that most of the centrifugal pumps are originally designed for. These issues are considered in this investigation through a numerical study of the flow in two different multistage, semi-axial type ESPs. This investigation is carried out numerically using a Computational Fluid Dynamics (CFD) package, where the transient RANS equations are solved numerically. The turbulence is modeled using the SST model. Head curves for several operating conditions are compared with manufacturer’s curves and experimental data for a three-stage ESP, showing good agreement for a wide range of fluid viscosities and rotational speeds. Dimensionless numbers (n, n, n e Re) are used to investigate performance degradation of the ESPs. In addition, flow phenomena through the impellers of the ESPs are investigated using flow field from numerical results. Results show that performance degradation is directly related to rotational Reynolds number, Re. In addition, it was verified that performance degradation occurs for constant normalized specific speedn, which shows that performance degradation occurs similarly for different centrifugal pumps. Moreover, experimental data and numerical results agreed with a correlation from literature between head and flow correction factors proposed by Stepanoff (1967). A definition of modified Reynolds number was proposed and relates the head correction factor to viscosity. A correlation between head correction factor and the modified Reynolds number was proposed, which agreed well with numerical and experimental data. Then, a method to predict performance degradation based on the previous correlations was proposed. This method was compared with others from literature. In general, results and conclusions from this work can also be useful to bring more information about the flow of highly viscous fluids in pumps, especially in semi-axial, multistage ESPs.

Studies of turbulent flows in continuous casting of steel with and without magnetic field

This thesis develops and tests various transient and steady-state computational models such as direct numerical simulation (DNS), large eddy simulation (LES), filtered unsteady Reynolds-averaged Navier-Stokes (URANS) and steady Reynolds-averaged Navier-Stokes (RANS) with and without magnetic field to investigate turbulent flows in canonical as well as in the nozzle and mold geometries of the continuous casting process. The direct numerical simulations are first performed in channel, square and 2:1 aspect rectangular ducts to investigate the effect of magnetic field on turbulent flows. The rectangular duct is a more practical geometry for continuous casting nozzle and mold and has the option of applying magnetic field either perpendicular to broader side or shorter side. This work forms the part of a graphic processing unit (GPU) based CFD code (CU-FLOW) development for magnetohydrodynamic (MHD) turbulent flows. The DNS results revealed interesting effects of the magnetic field and its orientation on primary, secondary flows (instantaneous and mean), Reynolds stresses, turbulent kinetic energy (TKE) budgets, momentum budgets and frictional losses, besides providing DNS database for two-wall bounded square and rectangular duct MHD turbulent flows. Further, the low- and high-Reynolds number RANS models (k-ε and Reynolds stress models) are developed and tested with DNS databases for channel and square duct flows with and without magnetic field. The MHD sink terms in k- and ε-equations are implemented as proposed by Kenjereš and Hanjalić using a user defined function (UDF) in FLUENT. This work revealed varying accuracies of different RANS models at different levels. This work is useful for industry to understand the accuracies of these models, including continuous casting. After realizing the accuracy and computational cost of RANS models, the steady-state k-ε model is then combined with the particle image velocimetry (PIV) and impeller probe velocity measurements in a 1/3rd scale water model to study the flow quality coming out of the well- and mountain-bottom nozzles and the effect of stopper-rod misalignment on fluid flow. The mountain-bottom nozzle was found more prone to the longtime asymmetries and higher surface velocities. The left misalignment of stopper gave higher surface velocity on the right leading to significantly large number of vortices forming behind the nozzle on the left. Later, the transient and steady-state models such as LES, filtered URANS and steady RANS models are combined with ultrasonic Doppler velocimetry (UDV) measurements in a GaInSn model of typical continuous casting process. LES-CU-LOW is the fastest and the most accurate model owing to much finer mesh and a smaller timestep. This work provided a good understanding on the performance of these models. The behavior of instantaneous flows, Reynolds stresses and proper orthogonal decomposition (POD) analysis quantified the nozzle bottom swirl and its importance on the turbulent flow in the mold. Afterwards, the aforementioned work in GaInSn model is extended with electromagnetic braking (EMBr) to help optimize a ruler-type brake and its location for the continuous casting process. The magnetic field suppressed turbulence and promoted vortical structures with their axis aligned with the magnetic field suggesting tendency towards 2-d turbulence. The stronger magnetic field at the nozzle well and around the jet region created large scale and lower frequency flow behavior by suppressing nozzle bottom swirl and its front-back alternation. Based on this work, it is advised to avoid stronger magnetic field around jet and nozzle bottom to get more stable and less defect prone flow.

Sloshing and slamming oscillations in collapsible channel flow

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to an external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes contribute increasingly to the global instability and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.

A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Mixing, Chemical Reactions, and Combustion in Supersonic Flows

Experiments were conducted at the GALCIT supersonic shear-layer facility to investigate aspects of reacting transverse jets in supersonic crossflow using chemiluminescence and schlieren image-correlation velocimetry. In particular, experiments were designed to examine mixing-delay length dependencies on jet-fluid molar mass, jet diameter, and jet inclination.

The experimental results show that mixing-delay length depends on jet Reynolds number, when appropriately normalized, up to a jet Reynolds number of 500,000. Jet inclination increases the mixing-delay length, but causes less disturbance to the crossflow when compared to normal jet injection. This can be explained, in part, in terms of a control-volume analysis that relates jet inclination to flow conditions downstream of injection.

In the second part of this thesis, a combustion-modeling framework is proposed and developed that is tailored to large-eddy simulations of turbulent combustion in high-speed flows. Scaling arguments place supersonic hydrocarbon combustion in a regime of autoignition-dominated distributed reaction zones (DRZ). The proposed evolution-variable manifold (EVM) framework incorporates an ignition-delay data-driven induction model with a post-ignition manifold that uses a Lagrangian convected 'balloon' reactor model for chemistry tabulation. A large-eddy simulation incorporating the EVM framework captures several important reacting-flow features of a transverse hydrogen jet in heated-air crossflow experiment.

Experimental and analytical methodologies for predicting peak loads on building envelopes and roofing systems

The performance of building envelopes and roofing systems significantly depends on accurate knowledge of wind loads and the response of envelope components under realistic wind conditions. Wind tunnel testing is a well-established practice to determine wind loads on structures. For small structures much larger model scales are needed than for large structures, to maintain modeling accuracy and minimize Reynolds number effects. In these circumstances the ability to obtain a large enough turbulence integral scale is usually compromised by the limited dimensions of the wind tunnel meaning that it is not possible to simulate the low frequency end of the turbulence spectrum. Such flows are called flows with Partial Turbulence Simulation.^ In this dissertation, the test procedure and scaling requirements for tests in partial turbulence simulation are discussed. A theoretical method is proposed for including the effects of low-frequency turbulences in the post-test analysis. In this theory the turbulence spectrum is divided into two distinct statistical processes, one at high frequencies which can be simulated in the wind tunnel, and one at low frequencies which can be treated in a quasi-steady manner. The joint probability of load resulting from the two processes is derived from which full-scale equivalent peak pressure coefficients can be obtained. The efficacy of the method is proved by comparing predicted data derived from tests on large-scale models of the Silsoe Cube and Texas-Tech University buildings in Wall of Wind facility at Florida International University with the available full-scale data.^ For multi-layer building envelopes such as rain-screen walls, roof pavers, and vented energy efficient walls not only peak wind loads but also their spatial gradients are important. Wind permeable roof claddings like roof pavers are not well dealt with in many existing building codes and standards. Large-scale experiments were carried out to investigate the wind loading on concrete pavers including wind blow-off tests and pressure measurements. Simplified guidelines were developed for design of loose-laid roof pavers against wind uplift. The guidelines are formatted so that use can be made of the existing information in codes and standards such as ASCE 7-10 on pressure coefficients on components and cladding.^

Lattice Boltzmann Modeling and Specialized Laboratory Techniques to Determine the Permeability of Megaporous Karst Rock

The Pleistocene carbonate rock Biscayne Aquifer of south Florida contains laterally-extensive bioturbated ooltic zones characterized by interconnected touching-vug megapores that channelize most flow and make the aquifer extremely permeable. Standard petrophysical laboratory techniques may not be capable of accurately measuring such high permeabilities. Instead, innovative procedures that can measure high permeabilities were applied. These fragile rocks cannot easily be cored or cut to shapes convenient for conducting permeability measurements. For the laboratory measurement, a 3D epoxy-resin printed rock core was produced from computed tomography data obtained from an outcrop sample. Permeability measurements were conducted using a viscous fluid to permit easily observable head gradients (~2 cm over 1 m) simultaneously with low Reynolds number flow. For a second permeability measurement, Lattice Boltzmann Method flow simulations were computed on the 3D core renderings. Agreement between the two estimates indicates an accurate permeability was obtained that can be applied to future studies.

Vortex evolution in the wake of accelerating low-aspect-ratio plates and three-dimensional bodies of revolution

To find examples of effecient locomotion and manoeuvrability, one need only turn to the elegant solutions natural flyers and swimmers have converged upon. This dissertation is specifically motivated by processes of evolutionary convergence, which have led to the propulsors and body shapes in nature that exhibit strong geometric collapse over diverse scales. These body features are abstracted in the studies presented herein using low-aspect-ratio at plates and a three-dimensional body of revolution (a sphere). The highly-separated vortical wakes that develop during accelerations are systematically characterized as a function of planform shape, aspect ratio, Reynolds number, and initial boundary conditions. To this end, force measurements and time-resolved (planar) particle image velocimetry have been used throughout to quantify the instantaneous forces and vortex evolution in the wake of the bluff bodies. During rectilinear motions, the wake development for the flat plates is primarily dependent on plate aspect ratio, with edge discontinuities and curvature playing only a secondary role. Furthermore, the axisymmetric case, i.e. the circular plate, shows strong sensitivity to Reynolds number, while this sensitivity quickly diminishes with increasing aspect ratio. For rotational motions, global insensitivity to plate aspect ratio has been observed. For the sphere, it has been shown that accelerations play an important role in the mitigation of flow separation. These results - expounded upon in this dissertation - have begun to shed light on the specific vortex dynamics that may be coopted by flying and swimming species of all shapes and sizes towards efficient locomotion.

Turbulent Pipe Flow - High Resolution Measurements in CICLoPE

The thesis deals with the experimental investigation of turbulent pipe flow at high Reynolds number. Wall-bounded turbulence is an extremely relevant topic for engineering and natural science applications and yet many aspects of the physics are not clear due to the difficulty in performing high Re experiments. To overcome these difficulties the CICLoPE Laboratory was developed, the main element of which is the Long Pipe wind tunnel. The facility is unique in its kind, as thanks to its large scale it delivers a flow quality and resolution that can not be achieved elsewhere at these Reynolds number. Reported here are the results from the first experimental campaign performed in the facility. A first part of the results presented concerns the characterization of this new facility. Flow quality and stability are assessed, particular attention is given to the characterization of pressure drop. The scaling of velocity fluctuations is analysed. The magnitude of the inner peak of the streamwise normal stress shows an increasing trend up to the highest Reynolds number examined, while no outer peak was clearly distinguishable from present measurements. Scaling of coherent motions is investigated via spectral analysis. An inner and outer spectral peaks are identified, with the former scaling in inner units while the latter neither following inner nor outer scaling, and increasing in magnitude with Re. Analysis of the spectra at y+ ≈ 15 shows how the increase of Reynolds normal stress is related to the influence of large scales in the inner wall region. Quadrant analysis was carried out on streamwise and wall-normal velocity fluctuations. The results show the important role in contribution to Reynolds shear stress of highly intermittent and strong events like ejections, that assume an even more intermittent and dominant role with the increase of Reynolds number.

Experimental characterization of a planar jet by hot-wire anemometry

The study of turbulence is also nowadays a problem that does not have solution from the mathematical point of view due to the lack of solution to link the mean part of the flow with the fluctuating one. To solve this problem, in the CICLoPE laboratory of Predappio, experiments on different type of jets are performed in order to derive a closure model able to close our mathematical model. One of the most interesting type of jet that could be studied is the planar turbulent free jet which is a two dimensional canonical jet characterized by the self-similarity condition of the velocity profiles. To study this particular jet, a new facility was built. The aim of this project is to characterize the jet at different distances from the nozzle exit, for different values of Reynolds number, to demonstrate that the self-similarity condition is respected. To do that, the evaluation of quantities such as spreading rate, centerline velocity decay and relation between fluctuations and mean part of the flow has to be obtain. All these parameters could be detected thanks to the use of single and X hot-wire anemometry with which it is possible to analyzed the fluctuating behaviour of the flow by associating to an electric signal a physical variable expressed in terms of velocity. To justify the data obtain by the measures, a comparison with results coming from the literature has to be shown.

Temperature measurements in turbulent pipe flow with cold wire anemometry

Passive scalars measurements in turbulent pipe flows are difficult to perform and only few experimental data are available in literature. The present thesis deals with the experimental acquisition and study of the first turbulent temperature profile inside the CICLoPE wind tunnel through cold wire anemometry technique at Reτ = 6000 and Reτ = 9500. This type of measurements provides not only useful data on temperature (and passive scalars) behaviour and statistics in turbulent pipe flows, but could be used also for temperature correction of turbulent velocity profiles. In the present work, subsequent acquisitions of temperature and velocity profiles has been performed at the same Reynolds number and in the same points, through cold wire and hot wire techniques respectively. Taking as reference data from both DNS and experimental campaigns, the activity has been carried out obtaining satisfactory results. We have verified the presence of turbulent temperature profile inside the CICLoPE wind tunnel and then studied its statistical and spectral behaviours obtaining results in agreement with existing data from Hishida, Nagano, and Ferro. Cold wire temperature data were then used to correct hot wire velocity data, obtaining a slightly improvement in the near wall region.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Estimating uncertainty in terrestrial critical loads and their exceedances at four sites in the UK

Critical loads are the basis for policies controlling emissions of acidic substances in Europe and elsewhere. They are assessed by several elaborate and ingenious models, each of which requires many parameters, and have to be applied on a spatially-distributed basis. Often the values of the input parameters are poorly known, calling into question the validity of the calculated critical loads. This paper attempts to quantify the uncertainty in the critical loads due to this "parameter uncertainty", using examples from the UK. Models used for calculating critical loads for deposition of acidity and nitrogen in forest and heathland ecosystems were tested at four contrasting sites. Uncertainty was assessed by Monte Carlo methods. Each input parameter or variable was assigned a value, range and distribution in an objective a fashion as possible. Each model was run 5000 times at each site using parameters sampled from these input distributions. Output distributions of various critical load parameters were calculated. The results were surprising. Confidence limits of the calculated critical loads were typically considerably narrower than those of most of the input parameters. This may be due to a "compensation of errors" mechanism. The range of possible critical load values at a given site is however rather wide, and the tails of the distributions are typically long. The deposition reductions required for a high level of confidence that the critical load is not exceeded are thus likely to be large. The implication for pollutant regulation is that requiring a high probability of non-exceedance is likely to carry high costs. The relative contribution of the input variables to critical load uncertainty varied from site to site: any input variable could be important, and thus it was not possible to identify variables as likely targets for research into narrowing uncertainties. Sites where a number of good measurements of input parameters were available had lower uncertainties, so use of in situ measurement could be a valuable way of reducing critical load uncertainty at particularly valuable or disputed sites. From a restricted number of samples, uncertainties in heathland critical loads appear comparable to those of coniferous forest, and nutrient nitrogen critical loads to those of acidity. It was important to include correlations between input variables in the Monte Carlo analysis, but choice of statistical distribution type was of lesser importance. Overall, the analysis provided objective support for the continued use of critical loads in policy development. (c) 2007 Elsevier B.V. All rights reserved.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.