Rise Velocity Research Articles

Measuring three-dimensional bubble dynamics for hydrogen production via water electrolysis

The commercialization of mass hydrogen production via water electrolysis is presently limited by low operational current densities. The optimal performance of electrolysis cells is significantly influenced by the substantial formation and residence of bubbles at high current densities. Thus, it is crucial to design electrodes with the ability for rapid bubble discharge to ensure appropriate bubble management. However, the quantitative volumetric measurements required to determine the bubble discharge ability of an electrode are not yet sufficiently accurate. This paper describes a quantitative volumetric method that combines a stereoscopic shadowgraph imaging system with particle tracking velocimetry (PTV) to measure the three-dimensional position, size, and velocity of micrometer-sized bubbles. The proposed method successfully captures hydrogen bubbles larger than 30 μm bubbles in an alkaline water electrolyzer. Considering the different luminance patterns of small bubbles (r ≤ 4 pixels) and large bubbles (r > 4 pixels) in the current imaging system, a bubble-size adaptive detection algorithm is established based on the cascade correlation method to obtain the two-dimensional centroid coordinates and radius of the observed bubbles. The bubble size information is also introduced into a two-view PTV algorithm for retrieving the Lagrangian trajectory of each bubble. Both the bubble detection and PTV algorithms are validated using synthetic datasets. Once the bubble trajectories are resolved successfully, the three-dimensional bubble velocity is obtained, and the actual bubble sizes are further corrected using the depth information. Analysis of the trajectory and velocity components indicates the existence of lateral bubble motion, reflecting interactions among bubbles. The rise velocity is positively correlated with the bubble radius in two regions, respectively, and the deviation from the theoretical value reveals the influence of non-buoyancy factors. The proposed technique provides effective diagnostics of the three-dimensional dynamic characteristics of micrometer-sized bubbles and can be used to evaluate and design bubble management systems for various electrochemical energy conversion devices.

Influence of buoyancy on phase separation during laser melting of Silicon and Iron ore

Phase separation is a well-known effect in liquid-liquid interactions, which can also occur during laser-related processes such as laser melting and laser alloying. However, the mechanism of phase separation between immiscible liquids on a millimeter scale during rapid laser processes has not been fully investigated, in which the extent of buoyancy’s contribution to it has remained unclear. Therefore, this investigation focused on the effect of buoyancy on liquid phase separation during the laser melting of silicon (Si) and iron ore. A simplified 2D numerical model was established to simulate the motion of a single Si liquid droplet in iron ore melt with and without the impact of gravity, respectively. The rise velocity of the droplet was calculated and analyzed under the effect of gravity. In addition, the phenomena of simultaneous laser remelting of Si and iron ore in layers were recorded with a high-speed camera, and the element and phase distributions of the target nugget were analyzed by Scanning Electron Microscopy/Energy Dispersive Spectroscopy (SEM/EDS). By combining the simulation, high-speed imaging, and SEM/EDS analysis, the effect of buoyancy on phase separation has been qualitatively analyzed. This investigation revealed that buoyancy is not the main driving force of liquid-liquid phase separation during rapid laser processing.

Simulation examining the factors influencing capillary wick transport in a refrigerant direct cooling system for power battery packs

The effectiveness of power battery refrigerant direct cooling systems of electric vehicles incorporating capillary wicks is directly determined by these wicks’ transport performance. The Fries–Dreyer equation describes wicking behavior, but there is a significant gap between its predictions and the experimental results as reported in the literature. This work examines the factors influencing transport performance in an unconsolidated capillary wick with spherical particles. A mathematical and physical model is developed, the latter using the COMSOL software platform. Both the developed mathematical form and the numerically simulated results of this model are closer to the experimental results than those obtained using the Fries–Dreyer equation. The simulation results enable optimizing the equilibrium height and capillary time numbers providing a fitted Fries–Dreyer equation that is then used to analyze the influence of saturation, inclination angle, wick particle diameter, and tortuosity on the liquid rise mass and velocity and the equilibrium height, and the effects are in close but not perfect accord with experimental data. To narrow the gap, the Fries–Dreyer equation is further optimized using the numerically simulated results, substantially improving the accord with the experimental results.

Phase field simulation of single bubble behavior under magnetic field

By combining the continuum equation with the momentum equation, phase field and magnetic field, a three-dimensional multi-field coupled model of the single bubble rising dynamics in the gas–liquid two-phase flow is established. The phase field method is used to capture the two-phase interface and simulate the movement of the gas–liquid interface. Compare the model with the numerical simulation under the Level Set method, it turns out that the simulation effect of the model established by the phase field method is better. The effects of different magnetic field intensity on the rise velocity of bubble and bubble deformation under vertical and horizontal magnetic field are analyzed. The results show that the bubble stretches along the magnetic field line under the action of the magnetic field, and the degree of bubble deformation is proportional to the intensity of the magnetic field. The rising speed of the bubble is affected by the magnetic field, which speeds up the overall rising speed of the bubble in the vertical direction and slows down the rising speed of the bubble in the horizontal direction.

The role of the water–air and pulp-froth interfaces on particle detachment: Impact of particle size, type, contact angle and bubble rise velocity

Although the pulp-froth interface is thought to be very important to particle detachment and therefore overall flotation recovery, experimental evidence to back this is contradictory with recent observation indicating that detachment may not be as rigorous as previously thought. We investigate the effect of the interface (air–water and froth-water) on particle detachment as function of particle size, density, hydrophobicity, and bubble sizes. Bubbles were loaded with particles of size classes between 53 µm and 1018 µm and were allowed to collide with the a given interface while videos of the interaction were taken. using a high-speed video camera. The results from the experiments indicate that particles attached to bubbles do not detach when a loaded bubble collides with the interfaces. Further, the particle properties - (size and type of the particles, and contact angle) and bubble had no influence on particle detachment at the interface. However, the particles attached as agglomerates dropped off upon impact and as a result of bubble shape deformations. Further, observations from the water froth interface show that the impact upon collision can significantly shake of particles from within the froth while the particles on the bubble remain attached. Under our experimental conditions, coalescence was also observed not to be as rapid, with loaded bubbles remaining in contact with the water-froth interface for not less than 26 s.

Comparison of bubble parameters in natural and chemical surfactant solutions: a force analysis

The authors have investigated the potential of a plant-based natural surfactant in the modification of various bubble parameters. Bubble dynamics at the orifice were studied in natural surfactant solutions extracted from the plant Sapindus mukorossi at concentrations below and above its critical micellar concentration (CMC). The results were compared to the ones obtained with Sodium Dodecyl Sulfate solutions. The CMC values of Sapindus mukorossi and Sodium Dodecyl Sulfate are 7.5 × 10−3 g/cc and 2.39 × 10−3 g/cc, respectively. A photographic method was employed to observe bubble formation at the orifice. The results show that biosurfactants, like chemical surfactants, have a comparable effect on bubble density, size, and rise velocity. Experimentally determined bubble radius, volume, and radial velocity were used to calculate various forces contributing to the bubble dynamics. The buoyancy, pressure, and surface tension forces were significantly stronger in magnitude in comparison to the gas momentum, viscous drag, and added mass forces. Our findings suggest that the significance of various dynamic forces involved in bubble growth dynamics varies according to the bubble generation frequency regimes. We report for the first time the potential of Sapindus mukorossi in altering bubble properties and surface forces at the orifice and its usage in various bubble-related industrial applications.

Fate of bubble clusters rising in a quiescent liquid

We use experiments to study the evolution of bubble clusters in a swarm of freely rising, deformable bubbles. A new machine learning-aided algorithm allows us to identify and track bubbles in clusters and measure the cluster lifetimes. The results indicate that contamination in the carrier liquid can enhance the formation of bubble clusters and prolong the cluster lifetimes. The mean bubble rise velocities conditioned on the bubble cluster size are also explored, and we find a positive correlation between the cluster size and the rise speed of the bubbles in the cluster, with clustered bubbles rising up to $20\,\%$ faster than unclustered bubbles.

Investigation of Taylor bubble dynamics in annular conduits with counter-current flow

This study numerically investigates counter-current slug flow by considering the motion of a Taylor bubble in annular conduits with downward-flowing liquids using the Volume-of-Fluid method implemented in the commercial computational fluid dynamics software ANSYS Fluent (Release 19.2). The translational velocity of a counter-current ascending or co-current descending Taylor bubble in vertical concentric annuli and the corresponding distribution parameter (C0) are analyzed. The latter is correlated in terms of Eötvös number (Eo) and inverse viscosity number (Nf) within the range of Eo between 40 and 400 and Nf between 40 and 320. The proposed correlation provides an accurate fit to the numerical data with an average error of 2.64%, and is successfully compared with published numerical findings. In general, the smooth and stable shape of the bubble is disrupted as the counter-current flow velocity (Frl) increases above a critical value, leading to the formation of surface waves and the displacement of the bubble tip away from the annular gap center and towards the outer pipe. C0 increases with Eo and Nf, plateauing at high values of Eo. The effects of annulus inclination (θ) and eccentricity (ε) on bubble rise velocity are examined within the common range of θ and ε encountered during the drilling of oil, gas, or geothermal wells, i.e. 0° ≤ θ ≤ 60° and 0 ≤ ε ≤ 0.7, and their impact on the C0. The increasing Frl and θ lead to a streamlined bubble with pointed nose and thus a reduction in the wrap angle (θwrap), ultimately leading to reduced drag compared to the vertical annulus case and a decrease in C0. As the ε increases, which is accompanied by an increase in the degree of bubble eccentricity, the corresponding C0 decreases. For a constant Eo = 100 and Nf = 160 with inclination angle of θ = 40°and eccentricity of ε = 0.5, the C0 < 1 is observed.

Bubble detection in liquid metal by perturbation of eddy currents: Model and experiments

A model has been developed to predict the response of an eddy current flow meter (ECFM) to the passage of a non-conductive inclusion moving in a cylindrical tube filled with a liquid metal. The model can be solved analytically for small inclusion diameters and moderate AC frequencies of the excitation signal. This condition is expressed as vbSω≪1, where vb is the dimensionless inclusion volume and Sω is a function of the ratio between the characteristic length of the system and the penetration depth of the magnetic field. The magnetic induction equation for this problem has also been solved numerically. A very good agreement between the analytical model and numerical solutions has been found for vbSω≪1. Two experimental setups have been designed. First, the ECFM model has been validated by comparing the response due to the passage of traveling beads of known diameters in a low melting point alloy. In a second experiment, the diameters of ascending argon bubbles have been estimated with the ECFM model. The numerical model predicts the gas volume with very good accuracy in the range of bubble diameters studied, between 1.5 and 6 mm, while the analytical model only deviates significantly from the experimental data when vbSω≳0.1. Moreover, we establish that the ECFM can also measure the radial deviation of the bubble trajectory, and the results are consistent with the theoretical limit for isolated bubbles between the regimes of oscillating/zigzag motion of ellipsoidal bubbles and non-oscillating motion of spherical bubbles. Another observation is that the dependence of the ECFM response on the shape of the bubble is negligible; indeed, the ECFM response is well approximated by a linear relation with the bubble volume as is assumed in the analytical model. Finally, an estimation of the terminal rising velocity of bubbles was also carried out.

Study on wettability model of coal particles based on composition

ABSTRACT In order to assess coal floatability, it is necessary to understand how different coal compositions affect particle-wetting behavior. In this study, the influence of different sizes and densities of particles on coal wettability was conducted, respectively. For this purpose, the coal compositions were explored via XRF and the wetting rising velocity experiment of each coal composition was investigated based on the capillary force. The contact angle decreases obviously with the decrease in particle size. The contact angle decreases as the coal particle density increases. The larger the contact angle, the worse the wettability. The coal compositions had a significant effect on the coal-wetting behavior. The content of organic substances decreased with the decrease in powder size. SiO2 had the highest content and the lowest contact angle among the inorganic oxygen-containing. Hydrogen bonds were created between the hydrogen and oxygen atoms on the surface. The stronger the hydrogen bonding force, the more tightly the water molecules adsorbed. Furthermore, the organic content decreased as the coal density increased. The increase in contaminants could be responsible for this phenomenon. The predictive wetting model between the coal compositions and the contact angle was established and its accuracy was evaluated. The predictive model is reliable at larger coal sizes and lower densities due to an average error at 7.2% of 0.35 mm and 10.61% of 1.35 g/cm3. The results provide some valuable insight into the efficient clean utilization of technology and pre-flotation feedback for coal processing.

Direct measurements of gas flux at seep sites using a broadband split-beam echosounder

Measurement of methane gas flux from oceanic seep sites is challenging, given the ephemeral nature and the heterogeneous spatial distribution of seeps. Acoustic systems offer a solution, as they make synoptic measurements of the water column, and the gas bubbles are strong acoustic scatterers. Here, we present a method to directly estimate gas flux using a calibrated broadband split-beam echosounder. The vertical range resolution of the broadband system facilitates discrimination of individual bubbles in the acoustic record. By comparing measurements of bubble target strength to an analytical scattering model, bubble radii can be directly measured from the acoustic data. Concurrently, split-aperture processing allows for the precise tracking of bubbles as they rise from the seafloor for measurement of bubble rise velocity. Together, the observations of bubble radius and rise velocity offer a measure of gas flux, requiring nothing more than a vessel transiting over a seep site. Application of this method to seep data collected on the East Siberian Arctic Shelf shows good agreement between resulting measurements of bubble radii (0.68–8.40 mm) with those made using optical sensors, and bubble rise velocities (4–36 cm/s) are consistent with published measurements and models. Extrapolating from single bubbles measurements, our estimates of regional methane flux (2.9 × 104 kg/year) suggest that carbon emissions in this region may be lower than previously believed.

Motion of Air Bubbles in a Cement Slurry.

The dynamics of air (gas) bubbles in a column of cement slurry is examined numerically. The air injected at the bottom of a laboratory-scale column through a porous distributor plate spatially distributes and migrates as a swarm of bubbles throughout the slurry toward the freeboard. The two-phase system of the cement slurry and the air bubbles is modeled using the conservation equations of mass and linear momentum in the framework of the volume-of-fluid (VOF) approach. The cement slurry is modeled using the Herschel-Bulkley and Bingham fluid models. Results show that the mean Sauter diameter and the mean rise velocity of the bubbles decrease with the gas flow rate. Meanwhile, it is found that the rising of the bubbles is controlled by breakup events, along with relatively weak path instabilities of the bubbles resulting in relatively straight trajectories, independent of the gas flow rate. The extent of the yielded region appears larger for the Herschel-Bulkley model compared to the Bingham fluid model (by approximately 10%).

Bubble behavior in a vacuum fluidized bed

Bubble behavior in a vacuum fluidized bed was investigated in this work. Experimental results showed that bubble diameter and rise velocity increased with declining the pressure, whereas bubble density decreased. The evolution of bubble density with bed height could be divided into three stages on the basis of the corresponding net-coalescence rates. The decrease in bubble density in the bottom region accelerated as the pressure decreased, whereas the increase in bubble density in the top region was gentle. Increasing the vacuum degree enlarged the variation in bubble size, resulting in the decline of operating stability in the fluidized bed. A new correlation that considered the effect of operating pressure on bubble behaviors exhibited accurate prediction in the vacuum fluidized bed. Bubble velocity was proportional to bubble diameter for small bubbles, and bed structure obviously affected the rise velocity of large bubbles. The distribution of the bubble aspect ratio was positively skewed and many bubbles had a tendency to become slender as the operating pressure decreased.

Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm

This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation is located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the piecewise-linear interface calculation (PLIC) scheme of the VOF method is performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface is accounted for using the continuum interfacial force (CSF) model. To solve the Navier–Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software are employed. The 3D PLIC-VOF HiG-Flow algorithm is used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation is evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found in the scientific literature, specifically, the piecewise-constant flux surface calculation, the volume of fluid method implemented in OpenFOAM, and the high-order finite-element software FEEL. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm is found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. The volume fraction conservation absolute errors obtained using our algorithm are 4.48×10−5 and 9.41×10−6 for both shearing and deforming flow tests, respectively, being two orders lower than the results presented in the scientific literature at the same level of mesh refinement. Lastly, the 3D bubble rising problem is simulated for different fluid densities (ρ1/ρ2=10 and ρ1/ρ2=1000) and viscosity ratios (μ1/μ2=10 and μ1/μ2=100). Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and OpenFOAM, DROPS, and NaSt3D software. The 3D PLIC-VOF HiG-Flow algorithm predicted a stable ellipsoidal droplet shape for ρ1/ρ2=10 and μ1/μ2=10, and a stable cap shape for ρ1/ρ2=1000 and μ1/μ2=100. The bubble’s rise velocity and evolution of the bubble’s center of mass are also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with those software. The rise velocity of the droplet for both the ellipsoidal and cap flow regime’s is found, in the initial stages of the simulation, to gradually increase from its initial value of zero to a maximum magnitude; then, the steady-state velocity of the droplet decreases, being more accentuated for the cap regime.

Characteristics of bubble behavior in petal-shaped fuel rod bundle channels under different flow conditions

The petal-shaped fuel element is a novel type of fuel element suitable for small-scale reactors. The motion of bubbles in the rod bundle channel has a significant impact on the surrounding flow and temperature fields, thereby influencing the two-phase flow and heat transfer characteristics. To investigate the dynamics of bubbles in the rod channel of the petal-shaped fuel rod, we simulated the rising motion of bubbles with different inlet flow rates using the volume of fluid method (VOF). We obtained the trajectory, rising speed, and shape changes of the bubbles with varying initial sizes, and analyzed the flow field around the bubbles. Our results indicate that the transverse displacement of bubbles in the radius range of 0.5 mm–1.25 mm increases gradually with their initial size, and the degree of deformation and maximum rising velocity of the bubbles also increase. However, bubbles with a radius of 1.5 mm experience less transverse displacement due to their larger size and contact with multiple fuel rods during the ascent process. Furthermore, the transverse displacement distance of the bubble increases and then decreases with the increase of fluid flow rate in the channel, while the aspect ratio of the bubble remains unaffected by the inlet flow rate. The study of bubble behavior sheds light on the mechanism of bubble motion in the channel of petal-shaped rod bundles, and provides a foundation for the study of two-phase flow and heat transfer in the channel.

Numerical study of bubble rise in a three-dimensional sinusoidal channel

The bubble formation phenomenon and its movement have numerous applications in the shipbuilding, nuclear, mechanical, and ocean industries. Thus, a complete understanding of bubble rise is of immense importance in the fields mentioned above. Although, even after a plethora of research, a significant understanding of bubble wobbling and path instability still needs to be achieved. Furthermore, the complexity increases when a bubble rises in complex channels. Although various two-dimensional studies have attempted to report the bubble wobbling in the complex channels, a three-dimensional study on it still needs to be explored. Thus, in the present study, we attempted to report the bubble rise tendency in a three-dimensional sinusoidal channel. As bubble rise velocity plays a significant role in bubble wobbling, we attempted to study the bubble's path instability and rising velocity at different Reynolds numbers (Re) and Bond numbers (Bo). The maximum bubble rise velocity was observed to increase with Reynolds number (Re) while it decreases with an increase in Bond number (Bo). Furthermore, the wobbling tendency was also less in three-dimensional cases compared to previously reported two-dimensional studies. The bubble wobbling was reported to increase with the Reynolds number with a more periodic nature of the velocity profile. Bubble wobbling increased with an increase in a Bond number less than 9. The multi-phase simulation was performed on the open-source solver Gerris. The present study unveiled various aspects of bubble rise in three-dimensional sinusoidal channels and highlighted the role of rising velocity in the path instability of bubble rise.

Impact of surfactants on the rise of deformable bubbles and interfacial gas–liquid mass transfer

Axisymmetric numerical simulations of the hydrodynamics around rising bubbles are performed in order to investigate the impact of surfactants on the bubble dynamics. Surfactants are assumed to be insoluble. The transport of the adsorbed surfactants is computed along the deforming surface at large surface Péclet number, and Marangoni stresses are taken into account. This simulation model leads to the stagnant-cap regime, with partially immobile interfaces. A parametric study is performed on cases at given Archimedes number, by varying the degree of contamination (Marangoni number) but maintaining a nearly constant Eötvös number. The presence of surfactants affects the rise velocity for oblate bubbles less than for spherical bubbles: the increase of the drag coefficient, due to interface contamination, is mitigated by a lower bubble deformation. When the cap angle $\theta _{cap}$ belongs to the southern hemisphere, the aspect ratio $\chi$ is found to decrease with contamination: the dynamic pressure responsible for the bubble distortion is lowered, related to the decline of kinetic energy. As soon as $\theta _{cap}$ lies in the northern hemisphere, the pressure stress causing distortion becomes independent on $\theta _{cap}: \chi$ no longer evolves with contamination, and already matches the prediction for fully immobile interfaces. Mass transfer of a passive scalar across the contaminated interface is also analysed. Surprisingly, the Sherwood number $Sh$ is found to follow the same law as for spherical shapes (Kentheswaran et al., Intl J. Heat Mass Transfer, vol. 198, 2022, 123325), allowing us to predict the decrease in $Sh$ due to contamination. These results reveal the couplings between interface immobilisation, bubble deformation, rise velocity and interfacial mass transfer.

Droplet attraction and coalescence mechanism on textured oil-impregnated surfaces

Droplets residing on textured oil-impregnated surfaces form a wetting ridge due to the imbalance of interfacial forces at the contact line, leading to a wealth of phenomena not seen on traditional lotus-leaf-inspired non-wetting surfaces. Here, we show that the wetting ridge leads to long-range attraction between millimeter-sized droplets, which coalesce in three distinct stages: droplet attraction, lubricant draining, and droplet merging. Our experiments and model show that the magnitude of the velocity and acceleration at which droplets approach each other horizontally is the same as the vertical oil rise velocity and acceleration in the wetting ridge. Moreover, the droplet coalescence mechanism can be modeled using the classical mass-spring system. The insights gained from this work will inform future fundamental studies on remote droplet interaction on textured oil-impregnated surfaces for optimizing water harvesting and condensation heat transfer.

Optimizing Design and Operational Parameters for Enhanced Mixing and Hydrodynamics in Bubbling Fluidized Bed Gasifiers: An Experimental and CFD-Based Approach

An experimental investigation of hydrodynamics of gas-solid flow is carried out by engaging different designs of air distributor plates. An analysis of three different plates, i.e., perforated, 45° slotted and novel hybrid plate, revealed the difference in pressure drop and minimum fluidization velocities (Umf) for varying input operational variables. Umf is found to be lowest for perforated and highest for 45° slotted plate, whereas pressure drop is found to be highest for 45° slotted plate and lowest for novel hybrid distributor plate. The bubbles rise velocity ratio (Umf,b/Umf,f) is noticed minimum for 45° slotted plate due to relatively larger bubbles originating from the bigger slot openings and maximum for perforated distributor plate owing to smaller bubbles with dominant axial rise. Furthermore, the bed height rise ratio (h/L) is observed as a minimum for perforated distributor and maximum for 45° slotted plate due to larger bubbles through 45° slots rupturing the bed surface, causing more bed expansion. Furthermore, CFD analysis is also carried out to observe the insight flow dynamics using the distributor plates. The simulations use a two-fluid model (TFM) and K-Epsilon turbulence models. CFD model shows promising results in agreement with the experimental results. CFD results revealed that the lower portion enhanced lateral dispersion/mixing of solid particles due to 45° angular openings of an air inlet. In contrast, the perforated plate exhibited a straight upward motion of small air bubbles, causing no radial/lateral mixing. CFD results for the hybrid plate show the mixed axial as well as lateral mixing of solids by revealing velocity distribution; therefore, the novel hybrid plate is found to be an optimum distributor plate due to its lowest pressure drop, adequate Umf, intermediary bed height rise ratio and moderate bubble rise velocity ratio across the bed.

An OpenFOAM solver for computing suspended particles in water currents

Abstract A new OpenFOAM solver has been developed for computing the spatial variation of particle concentrations in flowing water. The new solver was programmed in C ++ using OpenFOAM libraries, and the source code has been made openly available. The current article describes the coding of how the water flow and particle movements are computed. The solver is based on a Eulearian approach, where the particles are computed as concentrations in cells of a grid that resolves the computational domain. The Reynolds-averaged Navier–Stokes equations are solved by simpleFoam, using the k-ε turbulence model. The new solver uses a drift-flux approach to take the fall or rise velocity of the particles into account in a convection-diffusion equation. The model is therefore called sediDriftFoam. The results from the solver were tested on two cases with different types of particles. The first case was a sand trap with sand particles. The geometry was three-dimensional with a recirculation zone. The computed sediment concentrations in three vertical profiles compared well with earlier numerical studies and laboratory measurements. The second case was a straight channel flume with plastic particles that had a positive rise velocity. In this case, the results also compared well with the laboratory measurements.