Dynamics Of Columns Research Articles

Hydrodynamic characterization of bubble column using Dynamical High Order Decomposition approach

Bubble columns play a crucial role in a wide range of industries, including chemical and biochemical processes, petrochemicals, and environmental engineering. Understanding the dynamics of bubble columns is essential for optimizing their performance in various applications. This study proposes a data-driven approach for analyzing the dynamics of a two-dimensional bubble column system. We conducted simulations with varying superficial velocities and generated a comprehensive training dataset encompassing the entire velocity and pressure fields to achieve this. We then compared the performance of two approaches, the Fast Fourier Transformation (FFT) and the High-Order Dynamic Mode Decomposition (HODMD), in representing the system’s dynamics. Our findings demonstrate that the conventional FFT approach fails to adequately capture the complex dynamics of the dispersed multiphase flow system. This limitation arises due to the distribution of frequencies along the domain. Conversely, our work highlights the success of the HODMD method in accurately representing the system’s dynamics using only a few arbitrary sampling points within the domain. The implications of this study are significant, as it sheds light on the potential benefits of employing HODMD for analyzing bubble column dynamics. By utilizing this approach, industrial processes can be optimized more effectively across various applications.

A Lagrangian theory of equatorial upwelling

An explicit expression is derived for the speed of equatorial upwelling by filtering out the inertial oscillations from the wind-forced, Lagrangian, dynamics north and south of the equator. The derivation focuses on the poleward motion of the steady states of the meridional dynamics of water columns of unit zonal length forced by a uniform, westward directed, wind stress. A significant advance is achieved by substituting the pseudo angular momentum for the zonal velocity in all equations. The derived expression for the speed is independent of the Ekman layer's depth and varies linearly with the wind stress. Its only free parameter is the initial meridional extent of the water column that straddles the equator. The theoretical speed matches available observations of the upwelling speed when the column's meridional extent is 350–400 km on each side of the equator.

Numerical simulations of granular dam break: Comparison between discrete element, Navier-Stokes, and thin-layer models.

Granular flows occur in various contexts, including laboratory experiments, industrial processes, and natural geophysical flows. To investigate their dynamics, different kinds of physically based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microscopic scale to individually model each grain, Navier-Stokes models use a mesoscopic scale to consider elementary volumes of grains, and thin-layer models use a macroscopic scale to model the dynamics of elementary columns of fluids. In each case, the derivation of the associated equationsis well-known. However, few studies focus on the extent to which these modeling solutions yield mutually coherent results. In this article, we compare the simulations of a granular dam break on a horizontal or inclined planes for the discrete model convex optimization contact dynamics (COCD), the Navier-Stokes model Basilisk, and the thin-layer depth-averaged model SHALTOP. We show that, although all three models allow reproducing the temporal evolution of the free surface in the horizontal case (except for SHALTOP at the initiation), the modeled flow dynamics are significantly different, and, in particular, during the stopping phase. The stresses measured at the flow's bottom, reflecting the flow dynamics, are in relatively good agreement, but significant variations are obtained with the COCD model due to complex and fast-varying granular lattices. Similar conclusions are drawn using the same rheological parameters to model a granular dam break on an inclined plane. This comparison exercise is essential for assessing the limits and uncertainties of granular flow modeling.

Can a Computer “Learn” Nonlinear Chromatography?: Experimental Validation of Physics-Based Deep Neural Networks for the Simulation of Chromatographic Processes

This article presents the capabilities of machine learning in addressing the challenges related to the accurate description of adsorption equilibria in the design of chromatographic processes. Our previously developed physics-based artificial neural network framework for adsorption and chromatography emulation (PANACHE) approach is extended to simulate the dynamics of chromatographic columns without using adsorption isotherms. The incorporation of underlying conservation laws in the form of a physics-constrained loss function during training enables PANACHE models to infer the complex dynamics of chromatographic columns, even without the knowledge of adsorption isotherms. The isotherm-agnostic abilities of PANACHE models are tested by considering two binary systems with complex adsorption equilibria: 1) mixed Langmuir M1-type binary system and 2) Tröger’s base enantiomers on Chiralpak AD that show inflection in the isotherm. For each case study, unique feed-forward deep neural networks with an input layer, five hidden layers, and an output layer are trained for two solute components using the elution data either from simulations or experiments. The results show that PANACHE models are successful in predicting the dynamics of binary solute mixtures in chromatographic columns even in the absence of adsorption isotherms, with prediction errors in the order of 10–2 in the measure of relative L2-norm, for most of the cases. The ability of PANACHE models to infer the adsorption isotherms is also demonstrated.

Wire density for a wetted-wire column

Arrays of vertical parallel wires (‘wetted wires’) are a promising alternative to industrial columns such as spray, tray, or packed columns. Yet, further research is required to optimize their performance and competitiveness against packed columns. This work investigates the maximum wire density using the minimum pitch (center-to-center wire distance). Results show that the pitch can be smaller than two millimeters, which is significantly less than the minimum pitches recommended in the literature. Results are discussed for liquid flow rates, wire diameters, and counter-current gas velocities. The minimum pitch is often less than the diameter of the drops due to a bead-passing phenomenon. An analytical model illustrates the pressure drop characteristics of wetted-wire columns compared to existing packings. This model shows that wetted-wire columns including those with small pitches have very low pressure drops. However, this model also shows that packing factors do not adequately describe wetted-wire columns. This implies that gas-side fluid dynamics of wetted-wire columns are fundamentally different from the gas-side fluid dynamics of packed columns.

Design of Robust Decentralized Control Systems for Distillation Columns

This paper is devoted to the development of a decentralized control system design method with improved robustness, applicable to distillation columns control problem. The aim is attained by solving the following tasks: selection of representative models of columns; development of an effective transfer function identification algorithm; development of a decentralized controller design algorithm, which takes into account the cross-links impact; verification of the developed method for the selected models of columns. The most important result is the developed design method, which includes two algorithms. The first algorithm can be used to identify simplified models of the effective transfer functions. The second algorithm makes it possible to design a decentralized control system based on the ratio between the diagonals of the original model and effective transfer functions. Modified PI controller is used. The achievement of the distillation column control system robustness to the synchronous technologically conditioned deviation of the model parameters by up to three hundred percent of the nominal value is the paper significant result. The digital implementation of the designed controllers is simple. The analysis of the literature shows that none of the previously proposed methods for designing decentralized automatic control systems solved such a problem. The efficiency of the developed algorithms is illustrated using the known models of dynamics of distillation columns. The analysis of limitations of the method as well as its significant differences to the Biggest Log Tuning and H∞ loop shaping methods is presented.

Collapse dynamics of dry granular columns: From free-fall to quasistatic flow.

Gravity-driven collapses involving large amounts of dense granular material, such as landslides, avalanches, or rock falls, in a geophysical context, represent significant natural hazards. Understanding their complex dynamics is hence a key concern for risk assessment. In the present work, we report experiments on the collapse of quasi-two-dimensional dry granular columns under the effect of gravity, where both the velocity at which the grains are released and the aspect ratio of the column are varied to investigate the dynamics of the falling grains. At high release velocity, classical power laws for the final deposit are recovered, meaning those are representative of a free-fall-like regime. For sufficiently high aspect ratios, the top of the column undergoes an overall free-fall-like motion. In addition, for all experiments, the falling grains also spread horizontally in a free-fall-like motion, and the characteristic time of spreading is related to the horizontal extension reached by the deposit at all altitudes. At low release velocity, a quasistatic state is observed, with scaling laws for the final geometry identical to those of the viscous regime of granular-fluid flow. The velocity at which the grains are released governs the collapse dynamics. Between these two asymptotic regimes, higher release velocity correlates with smaller impact on the collapse dynamics. The criterion V[over ¯]≥0.4sqrt[gH_{0}], where H_{0} is the initial height of the column, is found for the mean release velocity V[over ¯] not to influence the granular collapse.

An experimental study on aquatic collapses of bidisperse granular deposits

A laboratory experiment is conducted to study the mobility and the segregation of aquatic bidisperse granular columns. The effects of the ambient fluid, the particle composition, and the initial geometry on the dynamics of bidisperse granular columns are investigated. It is identified that the ambient fluid plays diverse roles in the phenomenon but is to retard the collapsing process in an overall sense. The instantaneous frontal positions of the granular mass in a bidisperse collapsing case could be shorter or longer than in a monodisperse case under the aquatic condition, but its final run-out is always longer. Compared to dry cases, particle segregations in aquatic cases are found to be more pronounced with columns composed of fine and coarse particles than with columns composed of fine and medium-sized particles. In general, the segregation phenomenon becomes less obvious at relatively large values of the finer-particle fraction and in cases with relatively small particle size difference. It is demonstrated that particle segregation contributes to an increased mobility of the bidisperse granular mass, probably due to the fact that smaller particles fall downward through the gaps between larger particles as the mixture deforms continuously, leading to an increased possibility for large particles to be separated by isolated small particles or an increased possibility for the rolling friction to take place of the sliding friction between large particles.

Discusión sobre las formas lineal y no-lineal del modelo de Thomas para el modelado de curvas de ruptura

The Thomas model is the most common equation to describe the dynamics of fixed-bed adsorption columns. However, its parameters’ validity strongly depends on the region of the breakthrough curve considered for the data fitting. A rigorous analysis based on different error functions was carried out to determine the accuracy of both linear and non-linear forms of the model. The non-linear equation proved to be more robust and less susceptible to experimental error, with less than 0.5% of deviation in qTh calculation. A complete statistical analysis should be carried out to determine the fitting region if linear regression is preferred.

Reversible and concerted atom diffusion on supported gold nanoparticles

Traditionally, direct imaging of atom diffusion is only available by scanning tunneling microscopy and field ion microscopy on geometry-constrained samples: flat surfaces for STM and needle tips for FIM. Here we show time-resolved atomic-scale HRTEM investigations of CeO2-supported Au nanoparticle surfaces to characterize the surface dynamics of atom columns on gold nanoparticles. The observed surface dynamics have been categorized into four types: layer jumping, layer gliding, re-orientation and surface reconstruction. We successfully captured atoms moving in a concerted manner with a time resolution of 0.1 s. A quantitative approach for measuring the dynamics in various gaseous surroundings at elevated temperatures is presented. An approach for measuring quantitative electron beam effects on the surface dynamics is presented by counting atom column occupation as a function of time under a range of dose rates in high vacuum.

Evolutionary dynamics of single-multiple columns in atmospheric helium dielectric barrier discharge

Dielectric barrier discharge is widely used as a low-temperature plasma source in industry. Columnar discharge is an important form of dielectric barrier discharge. However, its discharge theory has not been clear yet. In this paper, the dielectric barrier discharges in helium at atmospheric pressure are carried out between parallel dielectric barrier electrodes to study the evolutionary dynamics of single-multiple columns. By reducing the applied voltages to a value lower than the initial discharge voltage, the pattern of the columnar discharge evolves from a single column into multiple columns. Discharge images from the bottom are taken to observe the evolution of discharge and measure the diameter of discharge column and spacing between columns. The applied voltage, the Lissajous figure, the discharge current, and the discharge transferred charge are measured in order to calculate the Coulomb force and the magnetic field force exerted on the column by the other columns. It is found that in columnar discharge, there is a dynamic evolution process that the single columnar discharge evolves into the two-layered columnar discharge when the applied voltage slightly decreases instantaneously. On the one hand, the column diameter is different in different layer: the column diameter increases from the center to the outer layer. On the other hand, as the applied voltage decreases, the diameter of the center column grows and the spacing between the center column and its adjacent column decreases. The calculations show that the Coulomb force is far greater than the magnetic field force when the evolution is stable, which indicates that, as mentioned in the established knowledge, there is a confinement potential to balance the Coulomb force, thereby keeping the distribution of discharge columns stable. Furthermore, the results also show that the Coulomb force on the discharge columns at different voltage and position is different. The strength of Coulomb force on column is different at different layer: it decreases from the outermost layer to the center column, which is zero on the center column. Based on the balance between the Coulomb force and the confinement potential in columnar discharge, it is suggested that the strength of the latter may also follow the same law. In addition, as the applied voltage decreases, the charges accumulated on the surface of the dielectric and the number of discharge columns both increase, which results in the increase of the maximum of the Coulomb force. The confinement potential may increase as well and follow the same law.

Dynamic simulation of an original Joule cycle liquid pistons hot air Ericsson engine

An Ericsson engine is an external heat supply engine working according to a Joule thermodynamic cycle. It is based on reciprocating piston-cylinder machines. Such engines are especially interesting for low power solar energy conversion, micro-CHP from conventional fossil fuels or from biomass and waste heat recovery. An innovative configuration has been designed where the mechanical pistons are replaced by liquid pistons. The engine is composed of two U-shape tubes partially filled with water, one for the compression spaces and one another for the expansion spaces. A thermodynamic model of the engine is developed. The model takes into account the dynamics of the liquid columns. It is shown that the engine indicated efficiency decreases when the rotation speed increases. The sign of the instantaneous torque on the flywheel changes four times per cycle, calling for a heavy flywheel. When the rotation speed increases above the natural frequency of oscillation of the liquid columns, the influence of the liquid pistons inertia is growing. Its impact is globally opposite to the one of the pressure in the cylinders. So, the effect of the inertia of the liquid columns is to reduce the amplitude of the torque variations.

Impacts of Climate Change on Volcanic Stratospheric Injections: Comparison of 1‐D and 3‐D Plume Model Projections

AbstractExplosive volcanic eruptions are one of the most important driver of climate variability. Yet, we still lack a fundamental understanding of how climate change may affect future eruptions. Here, we use an ensemble of simulations by 1‐D and 3‐D volcanic plume models spanning a large range of eruption source and atmospheric conditions to assess changes in the dynamics of future eruptive columns. Our results shed new light on differences between the predictions of 1‐D and 3‐D plume models. Furthermore, both models suggest that as a result of ongoing climate change, for tropical eruptions, (i) higher eruption intensities will be required for plumes to reach the upper troposphere/lower stratosphere and (ii) the height of plumes currently reaching the upper troposphere/lower stratosphere or above will increase. We discuss the implications of these results for the climatic impacts of future eruptions. Our simulations can directly inform climate model experiments on climate‐volcano feedback.

Numerical simulation of a square bubble column using Detached Eddy Simulation and Euler–Lagrange approach

To accurately simulate industrial sized bubble columns, the accurate prediction of the turbulent structures is important. Currently used RANS and LES models cannot capture the dynamics of the bubble columns or require a high grid resolution, respectively. In this work the Detached Eddy Simulation (DES) was used to combine the advantages of RANS and LES approaches. The DES method was based on Spalart–Allmaras, k−ϵ and k−ω SST turbulence models and was used to simulate gas–liquid flow for a bubble column with a square cross-section. The results are compared with experimental data and Large Eddy Simulation (LES) results, based on the Vreman and Smagorinsky subgrid-scale models. Profiles of turbulence kinetic energy and average axial liquid and gas velocities are compared at three heights of the column: near the sparger, in the middle and at the top of the column. The obtained results are in a very good agreement with the experimental data and LES simulations, proving ability of DES to capture highly dynamic flow motion and accurately predict main liquid characteristics in gas–liquid systems.

Radiation pressure in galactic discs: stability, turbulence, and winds in the single-scattering limit

The radiation force on dust grains may be dynamically important in driving turbulence and outflows in rapidly star-forming galaxies. Recent studies focus on the highly optically-thick limit relevant to the densest ultra-luminous galaxies and super star clusters, where reprocessed infrared photons provide the dominant source of electromagnetic momentum. However, even among starburst galaxies, the great majority instead lie in the so-called "single-scattering" limit, where the system is optically-thick to the incident starlight, but optically-thin to the re-radiated infrared. In this paper we present a stability analysis and multidimensional radiation-hydrodynamic simulations exploring the stability and dynamics of isothermal dusty gas columns in this regime. We describe our algorithm for full angle-dependent radiation transport based on the discontinuous Galerkin finite element method. For a range of near-Eddington fluxes, we show that the medium is unstable, producing convective-like motions in a turbulent atmosphere with a scale height significantly inflated compared to the gas pressure scale height and mass-weighted turbulent energy densities of $\sim 0.01-0.1$ of the midplane radiation energy density, corresponding to mass-weighted velocity dispersions of Mach number $\sim 0.5-2$. Extrapolation of our results to optical depths of $10^3$ implies maximum turbulent Mach numbers of $\sim20$. Comparing our results to galaxy-averaged observations, and subject to the approximations of our calculations, we find that radiation pressure does not contribute significantly to the effective supersonic pressure support in star-forming disks, which in general are substantially sub-Eddington. We further examine the time-averaged vertical density profiles in dynamical equilibrium and comment on implications for radiation-pressure-driven galactic winds.

Numerical simulations of high-energy flows in accreting magnetic white dwarfs

Some polars show quasi-periodic oscillations (QPO) in their optical light curves which have been interpreted as the result of shock oscillations driven by the cooling instability. Although numerical simulations can recover this physics, they wrongly predict QPOs in the X-ray luminosity and have also failed to reproduce the observed frequencies, at least for the limited range of parameters explored so far. Given the uncertainties on the observed polar parameters, it is still unclear whether simulations can reproduce the observations. The aim of this work is to study QPOs covering all relevant polars showing QPOs. We perform numerical simulations including gravity, cyclotron and bremsstrahlung radiative losses, for a wide range of polar parameters, and compare our results with the astronomical data using synthetic X-ray and optical luminosities.We show that shock oscillations are the result of complex shock dynamics triggered by the interplay of two radiative instabilities. The secondary shock forms at the acoustic horizon in the post-shock region in agreement with our estimates from steady-state solutions. We also demonstrate that the secondary shock is essential to sustain the accretion shock oscillations at the average height predicted by our steady-state accretion model. Finally, in spite of the large explored parameter space, matching the observed QPO parameters requires a combination of parameters inconsistent with the observed ones. This difficulty highlights the limits of one-dimensional simulations, suggesting that multi-dimensional effects are needed to understand the non-linear dynamics of accretion columns in polars and the origins of QPOs.

Dynamics and Control of Reactive Distillation Columns with Double Reactive Sections: Feed-Splitting Influences

Reactive distillation columns with double reactive sections (RDCs-DRS) at the top and bottom are especially favorable for the separations of reacting mixtures featuring the most unfavorable ranking of relative volatilities. In this article, their dynamics and control are studied in great detail, with special attention given to the influences of feed splitting on process dynamics and controllability. Because of the totally refluxed and totally reboiled operation mode plus an intermediate-product withdrawal, the RDC-DRS is generally characterized by severe under-dampness between the intermediate-product compositions and the reboiler heat duty (i.e., the regulation path) and by severe asymmetry between the intermediate-product compositions and the heaviest reactant feed flow rate (i.e., the disturbance path), consequently posing a great challenge to tight product quality control. With feed splitting of the lightest and heaviest reactants in the RDC-DRS (RDC-DRSFS), the simultaneous suppression of the under-d...

Three-dimensional modeling of the wave dynamics of tensegrity lattices

This paper develops effective numerical models to study the wave dynamics of highly nonlinear tensegrity metamaterials. Recent studies have highlighted the geometrically nonlinear response of structural lattices based on tensegrity prisms, which may gradually change their elastic response from stiffening to softening through the modification of mechanical, geometrical, and prestress variables. We here study the nonlinear dynamics of columns of tensegrity prisms subject to impulsive compressive loading. An effective nonlinear rigid body dynamics is employed to simulate the dynamic response of such metamaterials. We illustrate how to pass from the matrix to the vector form of the equations of motions, on accounting for a rigid response of the compressive members (bars). Numerical simulations show that the wave dynamics of the examined metamaterials supports compression solitary pulses with profile dependent on the elastic properties of the tensile members (strings), the given impact velocity, and the applied prestress. We conclude that tensegrity columns can be effectively used as tunable acoustic lenses, which are able to generate acoustic solitary waves with adjustable profile in a host medium.

The effect of liquid phase properties on bubble column fluid dynamics: Gas holdup, flow regime transition, bubble size distributions and shapes, interfacial areas and foaming phenomena

The correct design, operation and scale-up of bubble columns rely on the knowledge of the fluid dynamics at the “bubble-scale” and at the “reactor-scale”. This paper contributes to the existing discussion on the multi-scale fluid dynamics of bubble columns, and provides a complete dataset concerning the influence of the liquid phase properties on bubble column fluid dynamics at “bubble-scale” and at the “reactor-scale”. The bubble column is large-diameter and large-scale (5.3m in height, inner diameter of 0.24m), it was operated with superficial gas velocities in the range of 0.004–0.20m/s, and it was tested for different aspect ratios (in the range 5–12.5). Air was used as the dispersed phase and various fluids (tap water, aqueous solutions of NaCl, a water-ethanol mixture and solutions of water-monoethylene glycol of different concentrations) were employed as liquid phases. The gas holdup measurements were used to investigate the global fluid dynamics, the flow regime transition and the foaming phenomena. Subsequently, the image analysis was used to characterize the bubble size distributions and shapes in the homogeneous flow regime. Finally, the gas holdup and image analysis data were used to estimate the interfacial areas. The experimental data were extensively compared with previous studies and correlations and were used to propose novel correlations to estimate the bubble shapes and the interfacial areas, for the different liquid phases tested. It was found that a change in the liquid phase properties affects the bubble interfacial properties at the “bubble-scale”, thus changing the prevailing bubble size distribution because of the reduced/promoted coalescence phenomena. The variation in the prevailing bubble size distribution affects the “reactor-scale” (gas holdup and flow regime transition) and a lift-force-based approach is used to analyze the relationship between the “bubble-scale” and the “reactor-scale”. When the prevailing bubble size distribution shifts towards larger bubbles, because of the promoted coalescence (i.e., high viscous liquid phases), the lift force pushes the larger bubbles towards the center of the bubble column, inducing “coalescence-induced bubbles” and, consequently, destabilizing the homogeneous flow regime and decreasing the gas holdup. Conversely, when the prevailing bubble size distribution shifts towards smaller bubbles, because of the reduced coalescence (i.e., organic and inorganic active compounds, and low viscous liquid phases), the lift force pushes the small bubbles towards the wall, inducing cluster of bubbles and, consequently, stabilizing the homogeneous flow regime and increasing the gas holdup. In addition, foaming phenomena were observed for organic active compounds, in the case of high aspect ratios only: this observation suggests that the validity of the scale-up criteria is not ensured for all binary systems and future studies will be devoted to provide insights in the scale-up criteria.

Modelling of packed bed adsorption columns for the separation of green tea catechins

ABSTRACTGreen tea is a rich source of catechins, which when purified have a high economic value as they can be used as a supplement in several products, to increase their health benefits. Catechins are regarded as desired components with several applications in a variety of areas such as foods, cosmetics and pharmaceuticals. A multicomponent sorption model has been developed for the separation of catechins from liquid tea streams, with macroporous resins in a packed bed column. Two commercially available food grade resins were considered: Amberlite XADHP and Diaion HP20. For the desorption step, two food grade solvents are used: water and ethanol. The adsorption and desorption behaviour is subsequently mathematically described with one-dimensional axial dispersed plug flow model that can accurately simulate the dynamics of the solvent swing sorption columns. The model parameters were regressed from experimental data. Five components are modelled in the competitive sorption: the main four catechins present in green tea and caffeine. The model was used for the process design and optimization for the recovery of catechins from green tea.