Alberto Soria

DSG Under Two-Phase and Stratified Flow in a Steel Receiver of a Parabolic Trough Collector

The bending of a receiver tube in two-phase flow under stratified conditions when water is first introduced to the hot steel receiver of a 14.5-m long parabolic trough concentrator is presented in this paper Thermal gradients were observed on the absorber wall at the inlet of the receiver tube during the boiling of water, at low mass flow of 1.6 ×10 -5 m 3 /sec (I liter/min), and low pressure (4 ×10 2 kPa). It should be noted that the solar concentrator was focused on the receiver tube, which contained static air before the water was introduced. The introduction of the water produced a change in the temperature difference between the upper and lower sides of the receiver from 40-60 K to much lower temperatures, in about 45 seconds. The bending of the steel receiver tube occurred when the two-phase flow began. Maximum deflection was observed when the thermal gradient reached a minimum value. We conclude that, when the flow of steam, water, and air exist in a stratified pattern, the combination of these three elements produces the bending phenomenon. The theoretical model, developed to evaluate the experimental data, confirms that the change in temperature gradient produces the bending of the steel receiver tube during this transient stage.

HYDRODYNAMIC INTERACTION OF TWO SPHERICAL BUBBLES RISING IN-LINE: A SEMI-ANALYTICAL APPROACH

A model is proposed to relate the flow structure in the wake behind a leading bubble with the hydrodynamic force acting on the trailing bubble rising in-line. The model is valid at separation distances between bubbles (s) within the same order of magnitude as their diameters (dB) (2.5 ≤ s/dB ≤ 14.5) and moderate-to-large particle Reynolds numbers (50 ≤ Re1 ≤ 300). An equation for the axial velocity profile in the wake of a spherical bubble was proposed in the form of an analytical approximation, but incorporating a theoretically reasoned artificial origin, which was fitted to numerical data. This equation, once substituted in a general hydrodynamic force model, resulted in a predictive equation explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. Moreover, the force experienced by the leading bubble due to the trailing bubble presence was obtained, and the theoretical equilibrium distances between the bubbles were calculated; good agreement with known behavior was achieved.

Modelo Hidrodinámico para la Velocidad de un Par de Burbujas Ascendiendo en Línea

Resumen Se presenta un analisis hidrodinamico de la interaccion de dos burbujas esfericas del mismo tamano alineadas en la direccion de un flujo uniforme, laminar, newtoniano e incompresible. La burbuja puntera se considera aislada y la burbuja acarreada (segunda burbuja) esta sujeta a la accion de cuatro fuerzas: flotacion, arrastre cuasiestacionario, impulso del fluido y masa agregada. Aplicando un balance de fuerzas sobre cada burbuja se obtuvo una nueva expresion para la velocidad de ascenso de la burbuja acarreada. La expresion se comparo con mediciones experimentales, realizadas por otros autores citados en la literatura, para numeros de Reynolds de 3.06, 21.5 y 35.4 y se obtuvo un error relativo promedio entre 1.2% y 2.1%. Se discuten dos alternativas para aproximar la reduccion del arrastre sobre la burbuja acarreada. Se encontro que el arrastre cuasiestacionario no puede incorporar el efecto total de la estela sobre la burbuja acarreada. Palabras clave: modelo hidrodinamico, velocidad de burbujas, e

Effect of Surface Contamination on the Drag of a Bubble Rising in a Line

The presence of surfactants critically increases the drag on bubbles rising in contaminated water compared with bubbles rising in pure water. This is explained by the Marangoni effect, occurring when the surface tension forces existing on the surface generate tangential shear stresses on the surface bubble. This mechanism has been studied by considering stagnant cap hypothesis to simulate the increase in the drag as a function of surface contamination. In this work, the steady drag for contaminated spherical bubbles was obtained numerically for \(0.1\le Re\le 200\) by using Comsol \({\text {Multiphysics}}^{\circledR }\) 3.5a assuming the stagnant cap hypothesis. The numerical values of the vorticity, flow velocity and pressure fields as function of the angle of superficial contamination and Re were examined. The agreement of the numerical results with reported drag values for clean and partially contaminated bubbles, as well as rigid spheres was proved. By using an appropriate normalization of the numerical data, a simple drag correlation for contaminated bubbles as a function of the spherical angle of the stiff surface zone was obtained.

Assessing Significant Phenomena in 1D Linear Perturbation Multiphase Flows

A procedure based on small perturbations linearization is developed for the assessment of relevant physical effects in fast fluidized beds. The fluid compressibility and wall interaction effects onto a main incompressible behavior are appreciated. A model by contributions is developed and the coefficients of all terms are evaluated in order to assess their significance. The process to get a lumped model is performed and the equivalence of lumped terms and variables under asymptotic conditions is developed. It is shown how wall effects are able to change a parabolic to a hyperbolic structure and how a third order waving structure collapses to a first order one onto a diffusive operator, under the limit of the incompressibility assumption.

Hydrodynamic Force and Rise Velocity of an Interactive Bubble due to a Laminar Wake Effect

The interaction between two spherical bubbles rising in-line in a stagnant Newtonian liquid was studied. A model was proposed to relate the flow structure in the wake of a leading bubble with the hydrodynamic force and the rise velocity of a trailing bubble, at separation distances of the order of its diameter (2 ? s/d B ? 14) and moderate particle Reynolds numbers (20 ? Re 1 ? 200). To this end, a force balance on the trailing bubble was used as a starting point. The flow character in the axisymmetric laminar wake of a spherical bubble was analyzed, and an equation for the axial velocity profile was proposed in the modified form of an analytical approximation, which was fitted to numerical data. This equation, once substituted in the force balance, allowed obtaining a predictive model explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. The predictions of the proposed models show a good agreement with numerical and experimental data for the hydrodynamic force and the rise velocity of a trailing bubble, respectively.

Multiphase Phenomena Identification by Spectral Analysis: Electrical Impedance Sensor Signals in a Bubble Column

Multiphase phenomena identification in frequency domain through an electrical impedance sensor (EIS) in air–water pipes were analyzed experimentally. The electrical properties between the components were used to settle on the relative volumes of both phases. The selection of the appropriate a.c. frequency is well known to eliminate the capacitive impedance. The EIS is a device whose variable size electrodes were used to measure void fraction and its fluctuations. Measurements were carried out with six electrodes, when air was flowed into a standing water column, producing a bubble chain. Analysis in frequency domain of the electrical impedance signals allowed the spectral power density. This analysis was correlated with observed phenomena through video recording, in order to show that low frequency peaks can be associated to dynamic phenomena, while high frequency peaks could not be clearly correlated to flow particularities.