Induction heating is commonly used in laboratory-scale facilities to replicate the heating conditions of the receiver tubes of concentrated solar power plants. This work aims at shedding light at the ...induction heating characteristics for such applications through the development of a multiphysics numerical model capable of replicating the experimental conditions of a molten salt loop locally heated by an induction heater. In the experiments, a stainless steel pipe is heated on its external surface by the induction heater, which is switched on and off during the experimental data acquisition while molten salts are continuously circulating in its interior. These conditions are replicated, for the first time, in a two-dimensional numerical domain fully coupling the electromagnetic and thermal physics, including thermally dependent material properties of the heated pipe. Once validated against the experiments, the numerical results revealed that the volumetric nature of the induction heating shall be considered for an accurate representation of the temperature profile inside the tube. As a novelty, different equivalent surface boundary conditions are presented and, despite the Gaussian-like behavior of the induction heating on the surface of the tube, the results indicate that there exists no equivalent wall boundary condition to fully replicate the temperature profile obtained with the induction heater. The effect of independently varying experimental parameters such as the geometry of the pipe (i.e., diameter and thickness) and its distance to the induction heating system is also evaluated. Using large diameters of the tube reduces the difference between the angular temperature profile obtained using induction heating and a simplified wall boundary condition. For small wall thicknesses, the induction heating is capable of penetrating along the whole thickness of the tube, the total heat generated in the volume of the tube being exposed to the counteracting effects of the volumetric generation and the enhancement of the heat dissipation by the molten salt, as both of them increase for small thicknesses. The distance of the inductor to the pipe wall appears to maintain the volumetric characteristics of the heating and only affects the induction heating magnitude and efficiency.
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•Fully coupled model of induction heating of a molten salt pipe is presented.•Induction promotes a volumetric heat generation in the pipe.•No equivalent surface heating can replicate induction heating.•Effect of different pipe geometries on the induction heating was characterized.•Induction reaches the whole pipe thickness for sufficiently thin tubes.
•Semiempirical model for fuel particles motion in fluidized beds is established.•Considering 3 mixing zones: bubble wake solids, bulk solids, and a splash zone.•Viscoplastic stress model to solve the ...force balance for axial fuel motion.•Validation with wide range of lateral dispersion coefficients from industrial units.•Model investigates different parameters influencing lateral dispersion.
A semiempirical model for the mixing of fuel particles in a fluidized bed is presented and validated against experimental data from the literature regarding lateral fuel mixing. The model of fuel particle mixing categorizes the fluidized bed into three mixing zones: a rising bubble wake solid zone, an emulsion zone with sinking bulk solids, and a splash zone located above the dense bed. In the emulsion zone, the axial motion of the fuel particle is described by a force balance, applying a viscoplastic stress model, i.e., with a dominant yield stress and only a minor contribution of the shear stress, using an empirical expression from the literature. In the lateral direction, the model is divided into so-called ‘recirculation cells’, which are crucial for the lateral mixing.
Comparisons of the modeled and measured lateral dispersion coefficients of different fuel types measured in three different large-scale fluidized bed units under both hot and cold conditions (covering a broad range of coefficients: 10−4–10−1 m2/s) reveal satisfactory agreement. The validated model was used to investigate how the lateral mixing of fuel particles depends on the excess gas velocity, the bed height, and the lateral distribution of bubbles over the bed cross-section (which is typically uneven in industrial FB furnaces), as well as the size and density of the fuel particles.
In a gas fluidized bed, bubbles are mainly responsible for the displacement and mixing of the bed particles, with a direct impact on the bed heat and mass transfer. In this work, the motion of solids ...in the wake region of an isolated bubble rising in a vibrated fluidized bed is experimentally studied using combined digital image and bubble averaging techniques. The results show that the bubble wake behavior depends on the vibration phase and the bubble position in the bed. Particles penetrate inside the bubble volume during the deceleration of the bed vessel, provoking their characteristic wavy contour. The volume of particles dragged by the bubble wake is affected by the vibration phase due to the interaction of the bubble with the compression and expansion waves travelling inside the vibrated bed. Independently increasing the vibration amplitude or frequency augments the volume of particles dragged by the bubble wake.
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•Isolated bubble experiments were performed in a vertically vibrated fluidized bed.•DIA, PIV and bubble averaging served to analyze the solids motion around bubbles.•The results provide a characterization of the bubble wake behavior.•The bubble wake solids motion depends on the vibration phase and bubble position.•Vibration augments the volume of solids dragged by the bubble wake.
The present work experimentally studies the influence of vibration and gas velocity on the density-induced segregation of particles in a pseudo-2D vibrated fluidized bed. One half of the particles of ...the bed are ballotini spheres of density 2500kg/m3 and the other half are heavier ceramic particles of density 4100kg/m3 or 6000kg/m3. Digital Image Analysis is used to characterize the rate and extent of particle mixing with time for different gas velocities, vibration amplitudes and frequencies. The results of the experiments indicate that the vibration strength and the gas velocity have an important effect on both the evolution and the final extent of density-induced particle segregation. It was observed that by introducing vertical vibration to a bed that is fluidized close to minimum fluidization conditions the rate of segregation and the final segregation index of a mixture of light and dense particles is enhanced. However, for vibration strengths greater than a critical value around 3–4, the degree of segregation decreases due to a more vigorous three dimensional mixing of particles in the bed.
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•Density segregation is studied experimentally in a vibrated fluidized bed.•Particles of the same size and different density were used as bed material.•A segregation index is proposed to quantify the segregation rate and extent.•Adding vibration close to minimum fluidization conditions enhances segregation.•Vibration strength over a critical value decreases the degree of segregation.
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•Isolated bubbles in a vibrated pseudo-2D bed were experimentally measured using DIA.•Oscillations and phase delays of bubble centroid, diameter and velocity were obtained.•Vibration ...amplitude affects the oscillation amplitude of bubbles.•Vibration frequency influences the phase delay of bubble oscillations.•Bubble velocity decreases with vibration amplitude for a given diameter.
In this work the motion of isolated bubbles in a pseudo-2D fluidized bed subjected to vertical sinusoidal vibration is experimentally studied by means of Digital Image Analysis (DIA). The oscillatory behavior of the bed bulk as well as the bubble position, equivalent diameter and velocity, is studied using an averaging of cycles method that takes into account the intrinsic unsteadiness produced by the bed vibration. The results indicate that the bed is compressed and expanded by the system vibration, the movement of the bed surface being opposed to that of the bed vessel. Besides, the bubble diameter, centroid position and velocity oscillate with similar frequency as the bed vessel vibration. A phase delay was found between these bubble characteristics and the bed vessel displacement. This delay grows with the distance between the bubble centroid and the bed bottom, which suggests that the oscillation of the bubble characteristics is caused by compression–expansion waves traveling upwards through the bed. Both the phase delay and the amplitude of the oscillation of the bubble characteristics are affected differently by the frequency and the amplitude of vibration. The experimental results show that the amplitude of the vibration has an important role on the link between the average bubble diameter and velocity. In particular, increasing the amplitude of vibration produces a decrease of the average rising velocity of a bubble for a given bubble diameter.
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•DIA measurements of a bubbling fluidized bed subjected to vibration were performed.•Bubbles were individually tracked and their oscillations were analyzed.•Amplitude and phase of ...bubbles oscillations depend on the distance to the distributor.•Bubbles present a phase delay between the upper and lower sections of the bed.
The effect of the bed vessel vibration on the oscillatory behavior of the bed bulk and the bubbles is experimentally studied in the present work by means of Digital Image Analysis (DIA) in a pseudo-2D bed. The bed material was three different powders of Geldart A, B and A/B classifications and was operated in bubbling regime for different superficial gas velocities and vibration amplitudes and frequencies. A tracking methodology was developed in order to follow the oscillatory motion of the bed bulk and each individual bubble in the system. This allowed the analysis of the interaction of the dense phase of the bed with the oscillations of the bubble diameter, position and velocity. The results indicate that both the center of mass of the bed and the bubble characteristics follow the oscillation of the bed vessel with a similar frequency but with a phase delay. The amplitude and phase delay of the oscillation of the center of mass of the bed are more sensitive to variations of the vibration frequency than to variations of the vibration amplitude of the bed vessel. Both the amplitude and the frequency of the bed vessel vibration have a stronger impact on the bubble behavior of beds filled with small particles. The existence of a phase delay between the oscillations of bubble characteristics in the lower and upper sections of the bed indicates the existence of compression-expansion waves in the dense phase that modify the bubble behavior along the bed despite bubbles are interacting with each other. The presence of compression-expansion waves may shed light onto the different behaviors encountered for the mean bubble behavior in vibrated fluidized beds.
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•Experiments of a fluidized pseudo-2D bed subject to vibration were performed.•Different particle sizes of the bed operated in bubbling regime were tested.•Mean solids hold-up and ...bubble characteristics were obtained with DIA.•Bubble velocity decreases with vibration amplitude close to the distributor.•Confinement due to vibration promotes bubble coalescence far from the distributor.
The solids hold-up and mean bubble behavior in a vertically-vibrated fluidized bed are experimentally studied in the present work by means of Digital Image Analysis (DIA) for four different powders with Geldart classifications A, B and A/B. The bed has a small thickness (i.e. pseudo-2D bed) and operates in bubbling regime subject to a wide range of gas superficial velocities, vibration frequencies and vibration amplitudes. Mean parameters of the bed and the bubbles, such as solids hold-up, bubble fraction, bubble number density and bubble diameter and velocity, are characterized here by averaging the results over time and space. The results reveal that vibration of the bed promotes a confinement of the bubble path to the central section of the bed. This bubble confinement is more intense for the smallest particles tested and for high vibration strengths and creates two different bubble regimes in the bed. In particular, close to the distributor, the bubble velocity decreases when increasing the vibration amplitude of the bed vessel because bubbles are smaller and less confined, and they behave like isolated bubbles. The behavior of bubbles changes when they are far from the distributor, where the interaction between bubbles becomes greater due to their bigger size and the confinement of bubbles induced by vibration. This confinement promotes coalescence of bubbles. It is shown that consideration of these two different regimes of bubble dynamics allows to shed light on understanding the apparently contradictory results encountered in the literature regarding bubble behavior in bubbling vibrated fluidized beds.
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•Experiments were performed in a pseudo-2D fluidized bed subjected to vibration.•Bubbles were injected in the bed operated at minimum fluidization.•DIA and PIV were used to ...characterize the solids velocity around the bubbles.•The solids motion around a bubble is affected by the bed bulk oscillation.•Despite vibration, the solids velocity follows the potential flow theory.
The motion of solids around isolated bubbles rising in a vertically vibrated pseudo-2D bed is experimentally studied in this work by combining Digital Image Analysis (DIA) and Particle Image Velocimetry (PIV). The bed material is Geldart B spherical particles. Different vibration amplitudes and frequencies are applied to the bed vessel while the bed is fluidized with air at minimum fludization conditions and isolated bubbles are sequentially injected in the bed. An averaging of bubbles method is presented and used to statistically characterize the average motion of solids around the bubbles. The results show that the presence of a bubble in the system perturbs the cyclic compression and expansion behavior of the bed bulk and, in particular, influences the velocity of the expansion wave front traveling upwards the bed. Analogously, the motion of solids around the bubble and, specially, in the bubble wake region, are strongly affected by the cyclic compression and expansion of the bed bulk. However, direct comparisons of the experimental results with the Davidson & Harrison potential flow model reveal that this model is still applicable for the prediction of the solids velocity around the bubble in a vertically vibrated fluidized bed.
This work studies the solids mixing process in fluidized beds by means of numerical simulations using the two-fluid model (TFM) available in the MFIX code. The numerical results are compared with ...experiments conducted in a pseudo-2D fluidized bed. The experiments were performed by placing particles of the same diameter and density but of different colour in two vertical layers. To reproduce numerically the experimental results, three phases are defined: one for the gas phase and two for the solid phases, corresponding to the particles of different colours employed in the experiments, to make them separately traceable. To improve the simulation prediction, a friction model that accounts for the effect of the front and rear walls on the continuum solid phases was introduced in the TFM. Mixing times of the same order of magnitude are obtained from the simulations and the experiments when the mixing process is analysed macroscopically. Furthermore, the simulations are employed to study the solids mixing in the fluidized bed based on a more detailed mixing index. This new mixing index is determined from information of the three phases involved and it is used to predict the mixing behaviours beyond the capabilities of the experimental facility.
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•The lateral mixing of solids is studied in a pseudo-2D bed using TFM simulations.•Numerical results are compared with experiments.•The simulation prediction is improved by considering front and rear wall friction.•Simulation results are further used to analyse mixing at a meso-scale level.
Abstract
Crab cavities are fundamental components of the HL-LHC upgrade project. These Radio Frequency cavities, operated at the appropriate frequency, ‘tilt’ the proton bunches to increase the ...luminosity at the collision points IP1 (ATLAS) and IP5 (CMS). Two different superconducting crab cavities were developed: RF Dipole (RFD) for horizontal deflection and Double Quarter Wave (DQW) for vertical deflection. During operation, the cavity walls are deformed due to the loading conditions. This deformation changes the electro-magnetic field inside the cavity and consequently its RF frequency. In the present study, the numerical evaluation of the Lorentz Force Detuning (LFD) and the Pressure Sensitivity (PS) of the DQW cavity, using COMSOL Multiphysics, is presented. The LFD is the fundamental frequency change of the cavity due to the electro-magnetic forces acting on its walls, while the PS is the frequency shift when the cavity is subjected to pressure fluctuations of the helium bath. Finally, a comparison with the results measured during the cold test of the manufactured cavities, and with the previous simulations results obtained for the RFD cavity is done.
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